From 4c7a57fffcb293a22e0c05094b79f8aec623c855 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 17 Apr 2026 10:52:23 +0200 Subject: [PATCH 01/62] Feature: Snyder Polyhedral Equal Area projections --- src/lib_proj.cmake | 1 + src/pj_list.h | 1 + src/projections/polyhedral.cpp | 90 +++++++++ src/projections/polyhedral/authalic.h | 92 +++++++++ src/projections/polyhedral/nets/tsea/tsea.h | 39 ++++ .../polyhedra/hexakis_tetrahedron.h | 37 ++++ src/projections/polyhedral/snyder.h | 169 ++++++++++++++++ src/projections/polyhedral/sphere.h | 134 +++++++++++++ src/projections/polyhedral/vec3.h | 94 +++++++++ src/projections/polyhedral/vec3_helpers.h | 100 ++++++++++ test/render_net.py | 186 ++++++++++++++++++ test/render_nets.sh | 12 ++ test/unit/CMakeLists.txt | 12 ++ test/unit/test_polyhedral.cpp | 75 +++++++ 14 files changed, 1042 insertions(+) create mode 100644 src/projections/polyhedral.cpp create mode 100644 src/projections/polyhedral/authalic.h create mode 100644 src/projections/polyhedral/nets/tsea/tsea.h create mode 100644 src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h create mode 100644 src/projections/polyhedral/snyder.h create mode 100644 src/projections/polyhedral/sphere.h create mode 100644 src/projections/polyhedral/vec3.h create mode 100644 src/projections/polyhedral/vec3_helpers.h create mode 100644 test/render_net.py create mode 100755 test/render_nets.sh create mode 100644 test/unit/test_polyhedral.cpp diff --git a/src/lib_proj.cmake b/src/lib_proj.cmake index cfde386a61..2088cdd780 100644 --- a/src/lib_proj.cmake +++ b/src/lib_proj.cmake @@ -35,6 +35,7 @@ set(SRC_LIBPROJ_PROJECTIONS projections/bipc.cpp projections/bonne.cpp projections/eqdc.cpp + projections/polyhedral.cpp projections/isea.cpp projections/ccon.cpp projections/imw_p.cpp diff --git a/src/pj_list.h b/src/pj_list.h index b813f9899e..893359b4be 100644 --- a/src/pj_list.h +++ b/src/pj_list.h @@ -169,6 +169,7 @@ PROJ_HEAD(tobmerc, "Tobler-Mercator") PROJ_HEAD(topocentric, "Geocentric/Topocentric conversion") PROJ_HEAD(tpeqd, "Two Point Equidistant") PROJ_HEAD(tpers, "Tilted perspective") +PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") PROJ_HEAD(unitconvert, "Unit conversion") PROJ_HEAD(ups, "Universal Polar Stereographic") PROJ_HEAD(urm5, "Urmaev V") diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp new file mode 100644 index 0000000000..bf634272b1 --- /dev/null +++ b/src/projections/polyhedral.cpp @@ -0,0 +1,90 @@ +/****************************************************************************** + * Project: PROJ + * Purpose: Polyhedral Snyder equal-area map projections. + * Author: Felix Palmer + * + ****************************************************************************** + * Derived from A5 (Apache-2.0). + * https://github.com/felixpalmer/a5 + * + * Copyright (c) A5 contributors + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + ****************************************************************************/ + +#include "polyhedral/sphere.h" +#include "polyhedral/polyhedra/hexakis_tetrahedron.h" +#include "polyhedral/nets/tsea/tsea.h" + +#include "proj.h" +#include "proj_internal.h" + +#include + +using polyhedral::pj_polyhedral_data; + +// Shared forward projection +static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { + PJ_XY xy = {0.0, 0.0}; + auto *Q = static_cast(P->opaque); + + polyhedral::Vec3 v = polyhedral::lonlat_to_cart(Q, lp.lam, lp.phi); + + int tri_idx = polyhedral::find_triangle(Q, v); + if (tri_idx < 0) { + proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN); + return proj_coord_error().xy; + } + + polyhedral::Face2D result = polyhedral::snyder_fwd( + v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); + + xy.x = result.x; + xy.y = result.y; + + return xy; +} + +// Shared inverse projection +static PJ_LP polyhedral_inv(PJ_XY xy, PJ *P) { + PJ_LP lp = {0.0, 0.0}; + auto *Q = static_cast(P->opaque); + + for (int i = 0; i < Q->n_triangles; i++) { + polyhedral::Barycentric bary = + polyhedral::face_to_barycentric({xy.x, xy.y}, Q->face_tris[i]); + if (bary.u >= -1e-10 && bary.v >= -1e-10 && bary.w >= -1e-10) { + polyhedral::Vec3 v = polyhedral::snyder_inv( + {xy.x, xy.y}, Q->face_tris[i], Q->sph_tris[i]); + polyhedral::cart_to_lonlat(Q, v, lp.lam, lp.phi); + return lp; + } + } + + proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN); + return proj_coord_error().lp; +} + +PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") "\n\tSph"; +PJ *PJ_PROJECTION(tsea) { + auto *Q = static_cast(calloc(1, sizeof(pj_polyhedral_data))); + if (nullptr == Q) return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); + P->opaque = Q; + + polyhedral::load_triangles(Q, hexakis_tetrahedron::SPH_TRI, nets::tsea::tsea::FACE_TRI); + polyhedral::set_orient_from_angles(Q, 90.0, 0.0, 0.0); + + P->fwd = polyhedral_fwd; + P->inv = polyhedral_inv; + return P; +} \ No newline at end of file diff --git a/src/projections/polyhedral/authalic.h b/src/projections/polyhedral/authalic.h new file mode 100644 index 0000000000..37ba571e46 --- /dev/null +++ b/src/projections/polyhedral/authalic.h @@ -0,0 +1,92 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Authalic latitude conversion via Clenshaw summation (order 6). + * Author: Felix Palmer + * + ****************************************************************************** + * Coefficients from Karney (2022): https://arxiv.org/pdf/2212.05818 + * + * Clenshaw summation adapted from DGGAL project (authalic.ec). + * + * BSD 3-Clause License + * + * Copyright (c) 2014-2025, Ecere Corporation + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are met: + * + * 1. Redistributions of source code must retain the above copyright notice, + * this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * 3. Neither the name of the copyright holder nor the names of its + * contributors may be used to endorse or promote products derived from + * this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE + * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + ****************************************************************************/ + +#ifndef AUTHALIC_H +#define AUTHALIC_H + +#include + +namespace polyhedral { + +constexpr double GEODETIC_TO_AUTHALIC[6] = { + -2.2392098386786394e-03, + 2.1308606513250217e-06, + -2.5592576864212742e-09, + 3.3701965267802837e-12, + -4.6675453126112487e-15, + 6.6749287038481596e-18, +}; + +constexpr double AUTHALIC_TO_GEODETIC[6] = { + 2.2392089963541657e-03, + 2.8831978048607556e-06, + 5.0862207399726603e-09, + 1.0201812377816100e-11, + 2.1912872306767718e-14, + 4.9284235482523806e-17, +}; + +inline double apply_clenshaw(double phi, const double c[6]) { + double sin_phi = std::sin(phi); + double cos_phi = std::cos(phi); + double x = 2.0 * (cos_phi - sin_phi) * (cos_phi + sin_phi); // cos(2*phi) + + double u0 = x * c[5] + c[4]; + double u1 = x * u0 + c[3]; + u0 = x * u1 - u0 + c[2]; + u1 = x * u0 - u1 + c[1]; + u0 = x * u1 - u0 + c[0]; + + return phi + 2.0 * sin_phi * cos_phi * u0; +} + +inline double geodetic_to_authalic(double phi) { + return apply_clenshaw(phi, GEODETIC_TO_AUTHALIC); +} + +inline double authalic_to_geodetic(double phi) { + return apply_clenshaw(phi, AUTHALIC_TO_GEODETIC); +} + +} // namespace polyhedral + +#endif // AUTHALIC_H diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h new file mode 100644 index 0000000000..f10c698e05 --- /dev/null +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -0,0 +1,39 @@ +// Auto-generated by scripts/generate_tsea_mapping.py — DO NOT EDIT + +#ifndef NETS_TSEA_TSEA_H +#define NETS_TSEA_TSEA_H + +namespace nets { namespace tsea { namespace tsea { + +// Planar triangle vertices (net coordinates) +// [tri][vertex: 0=apex, 1=left, 2=right][x, y] +constexpr double FACE_TRI[24][3][2] = { + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-1.34677368708859979e+00, -1.55512030155621428e+00}, {-2.69354737417719736e+00, -1.55512030155621428e+00}}, + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, { 2.22044604925031308e-16, -1.55512030155621428e+00}, {-1.34677368708859979e+00, -1.55512030155621428e+00}}, + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-6.73386843544298785e-01, -3.88780075389053625e-01}, { 2.22044604925031308e-16, -1.55512030155621428e+00}}, + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-1.34677368708859846e+00, 7.77560150778106918e-01}, {-6.73386843544298785e-01, -3.88780075389053625e-01}}, + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-2.02016053063289824e+00, -3.88780075389055069e-01}, {-1.34677368708859846e+00, 7.77560150778106918e-01}}, + {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-2.69354737417719736e+00, -1.55512030155621428e+00}, {-2.02016053063289824e+00, -3.88780075389055069e-01}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-6.73386843544299007e-01, 1.94390037694526763e+00}, { 7.40148683083437653e-17, 3.11024060311242767e+00}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-1.34677368708859846e+00, 7.77560150778107140e-01}, {-6.73386843544299007e-01, 1.94390037694526763e+00}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-3.70074341541718888e-17, 7.77560150778106696e-01}, {-1.34677368708859846e+00, 7.77560150778107140e-01}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 1.34677368708859824e+00, 7.77560150778106030e-01}, {-3.70074341541718888e-17, 7.77560150778106696e-01}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 6.73386843544299118e-01, 1.94390037694526718e+00}, { 1.34677368708859824e+00, 7.77560150778106030e-01}}, + {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 7.40148683083437653e-17, 3.11024060311242767e+00}, { 6.73386843544299118e-01, 1.94390037694526718e+00}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 2.02016053063289780e+00, -3.88780075389053903e-01}, { 2.69354737417719692e+00, -1.55512030155621428e+00}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 1.34677368708859868e+00, 7.77560150778107140e-01}, { 2.02016053063289780e+00, -3.88780075389053903e-01}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 6.73386843544299118e-01, -3.88780075389053459e-01}, { 1.34677368708859868e+00, 7.77560150778107140e-01}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, {-6.66133814775093924e-16, -1.55512030155621428e+00}, { 6.73386843544299118e-01, -3.88780075389053459e-01}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 1.34677368708859846e+00, -1.55512030155621384e+00}, {-6.66133814775093924e-16, -1.55512030155621428e+00}}, + {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 2.69354737417719692e+00, -1.55512030155621428e+00}, { 1.34677368708859846e+00, -1.55512030155621384e+00}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, {-6.73386843544300118e-01, -3.88780075389052238e-01}, {-1.34677368708859846e+00, 7.77560150778107140e-01}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 3.70074341541745142e-17, -1.55512030155621428e+00}, {-6.73386843544300118e-01, -3.88780075389052238e-01}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 6.73386843544300673e-01, -3.88780075389050961e-01}, { 3.70074341541745142e-17, -1.55512030155621428e+00}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 1.34677368708859868e+00, 7.77560150778107251e-01}, { 6.73386843544300673e-01, -3.88780075389050961e-01}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 1.64683081986065150e-15, 7.77560150778107140e-01}, { 1.34677368708859868e+00, 7.77560150778107251e-01}}, + {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, {-1.34677368708859846e+00, 7.77560150778107140e-01}, { 1.64683081986065150e-15, 7.77560150778107140e-01}} +}; + +} } } // namespace nets::tsea::tsea + +#endif // NETS_TSEA_TSEA_H diff --git a/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h b/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h new file mode 100644 index 0000000000..e6e8d87ac1 --- /dev/null +++ b/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h @@ -0,0 +1,37 @@ +// Auto-generated by scripts/generate_tsea_mapping.py — DO NOT EDIT + +#ifndef POLYHEDRA_HEXAKIS_TETRAHEDRON_H +#define POLYHEDRA_HEXAKIS_TETRAHEDRON_H + +namespace hexakis_tetrahedron { + +constexpr double SPH_TRI[24][3][3] = { + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}}, + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}}, + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, + {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, + {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, + {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, + {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}} +}; + +} // namespace hexakis_tetrahedron + +#endif // POLYHEDRA_HEXAKIS_TETRAHEDRON_H diff --git a/src/projections/polyhedral/snyder.h b/src/projections/polyhedral/snyder.h new file mode 100644 index 0000000000..e853e16a02 --- /dev/null +++ b/src/projections/polyhedral/snyder.h @@ -0,0 +1,169 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Snyder equal-area polyhedral projection — forward and inverse. + * Author: Felix Palmer + * + ****************************************************************************** + * Derived from A5 (Apache-2.0). + * + * https://github.com/felixpalmer/a5 + * + * modules/projections/polyhedral.ts + + * Copyright (c) A5 contributors + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + **************************************************************************** + * Derived from DGGAL (BSD 3-Clause License) + * + * Copyright (c) 2014-2025, Ecere Corporation + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are met: + * + * 1. Redistributions of source code must retain the above copyright notice, this + * list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright notice, + * this list of conditions and the following disclaimer in the documentation + * and/or other materials provided with the distribution. + * + * 3. Neither the name of the copyright holder nor the names of its + * contributors may be used to endorse or promote products derived from + * this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE + * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR + * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER + * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, + * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + **************************************************************************** + * + * Closed from equations adapted from: + * https://brsr.github.io/2021/08/31/snyder-equal-area.html + * + ****************************************************************************/ + +#ifndef SNYDER_H +#define SNYDER_H + +#include "authalic.h" +#include "vec3.h" +#include "vec3_helpers.h" + +namespace polyhedral { + +struct Face2D { + double x, y; +}; + +struct Barycentric { + double u, v, w; +}; + +struct FaceTriangle { + Face2D a, b, c; +}; + +struct SphericalTriangle { + Vec3 a, b, c; +}; + +inline Barycentric face_to_barycentric(Face2D p, FaceTriangle tri) { + double d31[2] = {tri.a.x - tri.c.x, tri.a.y - tri.c.y}; + double d23[2] = {tri.c.x - tri.b.x, tri.c.y - tri.b.y}; + double d3p[2] = {p.x - tri.c.x, p.y - tri.c.y}; + + double det = d23[0] * d31[1] - d23[1] * d31[0]; + double b0 = (d23[0] * d3p[1] - d23[1] * d3p[0]) / det; + double b1 = (d31[0] * d3p[1] - d31[1] * d3p[0]) / det; + double b2 = 1.0 - (b0 + b1); + return {b0, b1, b2}; +} + +inline Face2D barycentric_to_face(Barycentric b, FaceTriangle tri) { + return {b.u * tri.a.x + b.v * tri.b.x + b.w * tri.c.x, + b.u * tri.a.y + b.v * tri.b.y + b.w * tri.c.y}; +} + +inline Face2D snyder_fwd(Vec3 v, SphericalTriangle stri, + FaceTriangle ftri) { + Vec3 a = stri.a, b = stri.b, c = stri.c; + + Vec3 z = vec3_normalize(vec3_subtract(v, a)); + Vec3 p = vec3_normalize(quadruple_product(a, z, b, c)); + + // Ensure p is on the same hemisphere as b and c (the quadruple product + // may return the antipodal intersection depending on vertex winding) + if (vec3_dot(p, b) + vec3_dot(p, c) < 0) { + p = {-p.x, -p.y, -p.z}; + } + + double h = vector_difference(a, v) / vector_difference(a, p); + double area_abc = spherical_triangle_area(a, b, c); + double scaled_area = h / area_abc; + double area_apc = spherical_triangle_area(a, p, c); + double area_abp = spherical_triangle_area(a, b, p); + + Barycentric bary = {1.0 - h, + scaled_area * area_apc, + scaled_area * area_abp}; + return barycentric_to_face(bary, ftri); +} + +inline Vec3 snyder_inv(Face2D face_point, FaceTriangle ftri, + SphericalTriangle stri) { + Vec3 a = stri.a, b = stri.b, c = stri.c; + Barycentric bcoords = face_to_barycentric(face_point, ftri); + + constexpr double threshold = 1.0 - 1e-14; + if (bcoords.u > threshold) + return a; + if (bcoords.v > threshold) + return b; + if (bcoords.w > threshold) + return c; + + Vec3 c1 = vec3_cross(b, c); + double area_abc = spherical_triangle_area(a, b, c); + double h = 1.0 - bcoords.u; + double r = bcoords.w / h; + double alpha = r * area_abc; + double s = std::sin(alpha); + double half_c = std::sin(alpha / 2.0); + double cc = 2.0 * half_c * half_c; // 1 - cos(alpha) + + double c01 = vec3_dot(a, b); + double c12 = vec3_dot(b, c); + double c20 = vec3_dot(c, a); + double s12 = vec3_length(c1); + + double tp = vec3_dot(a, c1); // triple product A·(B×C) + double f = s * tp + cc * (c01 * c12 - c20); + double g = cc * s12 * (1.0 + c01); + double q = (2.0 / std::acos(c12)) * std::atan2(g, f); + Vec3 pp = slerp(b, c, q); + double k = vector_difference(a, pp); + double t = safe_acos(h * k) / safe_acos(k); + return slerp(a, pp, t); +} + +} // namespace polyhedral + +#endif // SNYDER_H diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h new file mode 100644 index 0000000000..ec6f64075a --- /dev/null +++ b/src/projections/polyhedral/sphere.h @@ -0,0 +1,134 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Spherical coordinate helpers for polyhedral projections — + * triangle containment, lon/lat ↔ cartesian with orientation. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRAL_SPHERE_H +#define POLYHEDRAL_SPHERE_H + +#include "authalic.h" +#include "snyder.h" + +#include + +#ifndef M_PI +#define M_PI 3.14159265358979323846 +#endif + +namespace polyhedral { + +constexpr int MAX_TRIANGLES = 120; + +struct pj_polyhedral_data { + int n_triangles; + + SphericalTriangle sph_tris[MAX_TRIANGLES]; + FaceTriangle face_tris[MAX_TRIANGLES]; + + double orient[3][3]; + double orient_inv[3][3]; +}; + +// Load triangle data from generated header arrays. +template +inline void load_triangles(pj_polyhedral_data *Q, + const double (&sph)[N][3][3], + const double (&face)[N][3][2]) { + Q->n_triangles = N; + for (int i = 0; i < N; i++) { + Q->sph_tris[i] = { + {sph[i][0][0], sph[i][0][1], sph[i][0][2]}, + {sph[i][1][0], sph[i][1][1], sph[i][1][2]}, + {sph[i][2][0], sph[i][2][1], sph[i][2][2]}, + }; + Q->face_tris[i] = { + {face[i][0][0], face[i][0][1]}, + {face[i][1][0], face[i][1][1]}, + {face[i][2][0], face[i][2][1]}, + }; + } +} + +// Build rotation matrix from three angles (degrees): +// lat, lon: the geographic point to rotate to the north pole +// az: an azimuthal (z-axis) rotation applied after the above +inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, + double lon_deg, double az_deg) { + const double lat = lat_deg * M_PI / 180.0; + const double lon = lon_deg * M_PI / 180.0; + const double az = az_deg * M_PI / 180.0; + const double alpha = M_PI / 2.0 - lat; + const double ca = std::cos(alpha), sa = std::sin(alpha); + const double cl = std::cos(lon), sl = std::sin(lon); + const double cz = std::cos(az), sz = std::sin(az); + + const double r00 = ca * cl, r01 = ca * sl, r02 = -sa; + const double r10 = -sl, r11 = cl, r12 = 0.0; + const double r20 = sa * cl, r21 = sa * sl, r22 = ca; + + double m[3][3]; + m[0][0] = cz * r00 - sz * r10; + m[0][1] = cz * r01 - sz * r11; + m[0][2] = cz * r02 - sz * r12; + m[1][0] = sz * r00 + cz * r10; + m[1][1] = sz * r01 + cz * r11; + m[1][2] = sz * r02 + cz * r12; + m[2][0] = r20; + m[2][1] = r21; + m[2][2] = r22; + + for (int r = 0; r < 3; r++) + for (int c = 0; c < 3; c++) { + Q->orient[r][c] = m[r][c]; + Q->orient_inv[r][c] = m[c][r]; + } +} + +// Find the triangle containing point v by linear search. +inline int find_triangle(const pj_polyhedral_data *Q, Vec3 v) { + for (int i = 0; i < Q->n_triangles; i++) { + if (vec3_dot(v, Q->sph_tris[i].a) <= 0) + continue; + double t1 = triple_product(v, Q->sph_tris[i].a, Q->sph_tris[i].b); + double t2 = triple_product(v, Q->sph_tris[i].b, Q->sph_tris[i].c); + double t3 = triple_product(v, Q->sph_tris[i].c, Q->sph_tris[i].a); + if ((t1 >= 0 && t2 >= 0 && t3 >= 0) || (t1 <= 0 && t2 <= 0 && t3 <= 0)) + return i; + } + return -1; +} + +// Convert geodetic lon/lat to unit vector, applying orientation rotation. +inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, double lam, double phi) { + double auth_lat = geodetic_to_authalic(phi); + double ca = std::cos(auth_lat), sa = std::sin(auth_lat); + double cl = std::cos(lam), sl = std::sin(lam); + double gx = ca * cl, gy = ca * sl, gz = sa; + return {Q->orient[0][0] * gx + Q->orient[0][1] * gy + Q->orient[0][2] * gz, + Q->orient[1][0] * gx + Q->orient[1][1] * gy + Q->orient[1][2] * gz, + Q->orient[2][0] * gx + Q->orient[2][1] * gy + Q->orient[2][2] * gz}; +} + +// Convert unit vector back to lon/lat, applying inverse orientation. +inline void cart_to_lonlat(const pj_polyhedral_data *Q, Vec3 v, double &lam, double &phi) { + double gx = Q->orient_inv[0][0] * v.x + Q->orient_inv[0][1] * v.y + Q->orient_inv[0][2] * v.z; + double gy = Q->orient_inv[1][0] * v.x + Q->orient_inv[1][1] * v.y + Q->orient_inv[1][2] * v.z; + double gz = Q->orient_inv[2][0] * v.x + Q->orient_inv[2][1] * v.y + Q->orient_inv[2][2] * v.z; + + if (gz > 1.0) gz = 1.0; + if (gz < -1.0) gz = -1.0; + + double auth_lat = std::asin(gz); + phi = authalic_to_geodetic(auth_lat); + lam = std::atan2(gy, gx); + if (lam < -M_PI) lam += 2 * M_PI; + if (lam > M_PI) lam -= 2 * M_PI; +} + +} // namespace polyhedral + +#endif // POLYHEDRAL_SPHERE_H diff --git a/src/projections/polyhedral/vec3.h b/src/projections/polyhedral/vec3.h new file mode 100644 index 0000000000..ce0e1a1400 --- /dev/null +++ b/src/projections/polyhedral/vec3.h @@ -0,0 +1,94 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: 3D vector operations for polyhedral projections. + * Author: Felix Palmer + * + ****************************************************************************** + * Derived from gl-matrix (MIT License). + * + * gl-matrix: Copyright (c) 2015-2021, Brandon Jones, Colin MacKenzie IV. + * https://github.com/toji/gl-matrix + * + * Permission is hereby granted, free of charge, to any person obtaining a + * copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING + * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER + * DEALINGS IN THE SOFTWARE. + ****************************************************************************/ + +#ifndef VEC3_H +#define VEC3_H + +#include +#include + +namespace polyhedral { + +struct Vec3 { + double x, y, z; +}; + +inline double vec3_dot(Vec3 a, Vec3 b) { + return a.x * b.x + a.y * b.y + a.z * b.z; +} + +inline Vec3 vec3_cross(Vec3 a, Vec3 b) { + return {a.y * b.z - a.z * b.y, + a.z * b.x - a.x * b.z, + a.x * b.y - a.y * b.x}; +} + +inline double vec3_length(Vec3 v) { + return std::sqrt(v.x * v.x + v.y * v.y + v.z * v.z); +} + +inline Vec3 vec3_normalize(Vec3 v) { + double len = vec3_length(v); + if (len == 0.0) + return v; + return {v.x / len, v.y / len, v.z / len}; +} + +inline Vec3 vec3_subtract(Vec3 a, Vec3 b) { + return {a.x - b.x, a.y - b.y, a.z - b.z}; +} + +inline Vec3 vec3_add(Vec3 a, Vec3 b) { + return {a.x + b.x, a.y + b.y, a.z + b.z}; +} + +inline Vec3 vec3_scale(Vec3 v, double s) { + return {v.x * s, v.y * s, v.z * s}; +} + +inline Vec3 vec3_lerp(Vec3 a, Vec3 b, double t) { + return {a.x + t * (b.x - a.x), + a.y + t * (b.y - a.y), + a.z + t * (b.z - a.z)}; +} + +inline double vec3_distance(Vec3 a, Vec3 b) { + return vec3_length(vec3_subtract(a, b)); +} + +inline double vec3_angle(Vec3 a, Vec3 b) { + double d = vec3_dot(a, b) / (vec3_length(a) * vec3_length(b)); + return std::acos(std::clamp(d, -1.0, 1.0)); +} + +} // namespace polyhedral + +#endif // VEC3_H diff --git a/src/projections/polyhedral/vec3_helpers.h b/src/projections/polyhedral/vec3_helpers.h new file mode 100644 index 0000000000..5c03bbe11a --- /dev/null +++ b/src/projections/polyhedral/vec3_helpers.h @@ -0,0 +1,100 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Higher-level 3D vector helpers for spherical geometry. + * Author: Felix Palmer + * + ****************************************************************************** + * Derived from A5 (Apache-2.0). + * https://github.com/felixpalmer/a5 + * + * modules/utils/vector.ts + * + * Copyright (c) A5 contributors + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + ****************************************************************************/ + +#ifndef VEC3_HELPERS_H +#define VEC3_HELPERS_H + +#include "vec3.h" + +#include +#include + +namespace polyhedral { + +// Numerically stable angular distance measure. +// Returns a value proportional to sin(angle/2) between a and b. +inline double vector_difference(Vec3 a, Vec3 b) { + Vec3 midpoint_ab = vec3_normalize(vec3_lerp(a, b, 0.5)); + Vec3 cross_result = vec3_cross(a, midpoint_ab); + double d = vec3_length(cross_result); + + if (d < 1e-8) { + // When A and B are very close, sin(x/2) ≈ x/2 + return 0.5 * vec3_length(vec3_subtract(a, b)); + } + return d; +} + +inline double triple_product(Vec3 a, Vec3 b, Vec3 c) { + return vec3_dot(a, vec3_cross(b, c)); +} + +// Great-circle intersection helper. +// Returns dot(b,cross(c,d))*a - dot(a,cross(c,d))*b +inline Vec3 quadruple_product(Vec3 a, Vec3 b, Vec3 c, Vec3 d) { + Vec3 cross_cd = vec3_cross(c, d); + double tp_acd = vec3_dot(a, cross_cd); + double tp_bcd = vec3_dot(b, cross_cd); + return vec3_subtract(vec3_scale(b, tp_acd), vec3_scale(a, tp_bcd)); +} + +inline Vec3 slerp(Vec3 a, Vec3 b, double t) { + double gamma = vec3_angle(a, b); + if (gamma < 1e-12) { + return vec3_lerp(a, b, t); + } + double sin_gamma = std::sin(gamma); + double wa = std::sin((1.0 - t) * gamma) / sin_gamma; + double wb = std::sin(t * gamma) / sin_gamma; + return vec3_add(vec3_scale(a, wa), vec3_scale(b, wb)); +} + +// Spherical triangle area via midpoint triple product method. +// More numerically stable than vertex-based spherical excess. +inline double spherical_triangle_area(Vec3 v1, Vec3 v2, Vec3 v3) { + Vec3 mid_a = vec3_normalize(vec3_lerp(v2, v3, 0.5)); + Vec3 mid_b = vec3_normalize(vec3_lerp(v3, v1, 0.5)); + Vec3 mid_c = vec3_normalize(vec3_lerp(v1, v2, 0.5)); + double s = triple_product(mid_a, mid_b, mid_c); + s = std::clamp(s, -1.0, 1.0); + if (std::fabs(s) < 1e-8) { + return 2.0 * s; + } + return 2.0 * std::asin(s); +} + +// Computes acos(1 - 2*x*x) without precision loss for small x. +inline double safe_acos(double x) { + if (x < 1e-3) { + return 2.0 * x + x * x * x / 3.0; + } + return std::acos(1.0 - 2.0 * x * x); +} + +} // namespace polyhedral + +#endif // VEC3_HELPERS_H diff --git a/test/render_net.py b/test/render_net.py new file mode 100644 index 0000000000..75dbb14a47 --- /dev/null +++ b/test/render_net.py @@ -0,0 +1,186 @@ +#!/usr/bin/env python3 +"""Render a polyhedral net projection to an image. + +Usage: + python3 test/render_net.py --proj="+proj=tsea +R=1" \\ + --title="TSEA" --figsize=16,10 -o tsea_net.png +""" + +import argparse +import ctypes +import json +import math +import os + +import numpy as np + +# ============================================================ +# ctypes setup +# ============================================================ + +_lib = ctypes.CDLL(os.path.join(os.path.dirname(__file__), "..", "build", + "lib", "libproj.dylib")) +_lib.proj_context_create.restype = ctypes.c_void_p +_lib.proj_create.restype = ctypes.c_void_p +_lib.proj_create.argtypes = [ctypes.c_void_p, ctypes.c_char_p] + + +class PJ_UV(ctypes.Structure): + _fields_ = [("u", ctypes.c_double), ("v", ctypes.c_double)] + + +class PJ_COORD(ctypes.Union): + _fields_ = [("lp", PJ_UV), ("xy", PJ_UV), ("v", ctypes.c_double * 4)] + + +_lib.proj_trans.restype = PJ_COORD +_lib.proj_trans.argtypes = [ctypes.c_void_p, ctypes.c_int, PJ_COORD] +PJ_FWD = 1 + +# ============================================================ +# Projection and segment extraction +# ============================================================ + +# Densification step in degrees. With 0.5° steps, within-face +# projected distances are ~0.008 while cross-face jumps are >0.5, +# so a gap threshold of 0.05 cleanly separates them. +DENSIFY_STEP = 0.5 +MAX_GAP = 0.05 + + +def proj_forward_array(pj, lons, lats): + n = len(lons) + xs = np.empty(n) + ys = np.empty(n) + c = PJ_COORD() + for i in range(n): + c.lp.u = math.radians(lons[i]) + c.lp.v = math.radians(lats[i]) + r = _lib.proj_trans(pj, PJ_FWD, c) + xs[i] = r.xy.u + ys[i] = r.xy.v + return xs, ys + + +def densify(lons, lats, max_step=DENSIFY_STEP): + out_lon = [lons[0]] + out_lat = [lats[0]] + for i in range(1, len(lons)): + d = max(abs(lons[i] - lons[i - 1]), abs(lats[i] - lats[i - 1])) + n = max(1, int(math.ceil(d / max_step))) + for j in range(1, n + 1): + t = j / n + out_lon.append(lons[i - 1] + t * (lons[i] - lons[i - 1])) + out_lat.append(lats[i - 1] + t * (lats[i] - lats[i - 1])) + return np.array(out_lon), np.array(out_lat) + + +def extract_segments(xs, ys, max_gap=MAX_GAP): + """Break line into segments, cutting at large gaps (face boundaries).""" + segments = [] + current = [] + max_gap_sq = max_gap * max_gap + for i in range(len(xs)): + if np.isnan(xs[i]) or np.isinf(xs[i]): + if len(current) > 1: + segments.append(np.array(current)) + current = [] + continue + if current and ((xs[i] - current[-1][0]) ** 2 + + (ys[i] - current[-1][1]) ** 2) > max_gap_sq: + if len(current) > 1: + segments.append(np.array(current)) + current = [] + current.append([xs[i], ys[i]]) + if len(current) > 1: + segments.append(np.array(current)) + return segments + + +def process_line(pj, lons, lats): + lons, lats = densify(lons, lats) + xs, ys = proj_forward_array(pj, lons, lats) + return extract_segments(xs, ys) + + +# ============================================================ +# Main +# ============================================================ + +def main(): + parser = argparse.ArgumentParser(description="Render polyhedral net projection") + parser.add_argument("--proj", required=True, + help="Full PROJ string, e.g. '+proj=tsea +R=1'") + parser.add_argument("--title", required=True, help="Plot title") + parser.add_argument("--resolution", type=float, default=1.0, + help="Output resolution multiplier (default: 1)") + parser.add_argument("-o", "--output", required=True, help="Output filename") + args = parser.parse_args() + + figsize = (10 * args.resolution, 10 * args.resolution) + + import matplotlib + matplotlib.use("Agg") + import matplotlib.pyplot as plt + from matplotlib.collections import LineCollection + + ctx = _lib.proj_context_create() + pj = _lib.proj_create(ctx, args.proj.encode()) + assert pj, f"Failed to create projection: {args.proj}" + + fig, ax = plt.subplots(1, 1, figsize=figsize) + + # Graticule + print("Projecting graticule...") + grat_segs = [] + for lat in range(-80, 90, 10): + lo = np.linspace(-180, 180, 720) + la = np.full_like(lo, float(lat)) + grat_segs.extend(process_line(pj, lo, la)) + for lon in range(-180, 180, 10): + la = np.linspace(-89, 89, 360) + lo = np.full_like(la, float(lon)) + grat_segs.extend(process_line(pj, lo, la)) + print(f" {len(grat_segs)} graticule segments") + + if grat_segs: + lc = LineCollection(grat_segs, colors="lightgray", linewidths=0.3) + ax.add_collection(lc) + + # Coastlines + coast_path = os.path.join(os.path.dirname(__file__), "..", "docs", "plot", + "data", "coastline.geojson") + print("Projecting coastlines...") + coast_segs = [] + if os.path.exists(coast_path): + with open(coast_path) as f: + gj = json.load(f) + for feat in gj["features"]: + geom = feat["geometry"] + rings = [] + if geom["type"] == "LineString": + rings.append(geom["coordinates"]) + elif geom["type"] == "MultiLineString": + rings.extend(geom["coordinates"]) + for ring in rings: + coords = np.array(ring) + coast_segs.extend( + process_line(pj, coords[:, 0], coords[:, 1])) + print(f" {len(coast_segs)} coastline segments") + + if coast_segs: + lc = LineCollection(coast_segs, colors="black", linewidths=0.5) + ax.add_collection(lc) + + ax.set_aspect("equal") + ax.autoscale_view() + ax.set_title(args.title, fontsize=14, pad=12) + ax.axis("off") + fig.tight_layout() + + fig.savefig(args.output, dpi=200, bbox_inches="tight") + print(f"Saved {args.output}") + + +if __name__ == "__main__": + main() diff --git a/test/render_nets.sh b/test/render_nets.sh new file mode 100755 index 0000000000..60b1f8c15b --- /dev/null +++ b/test/render_nets.sh @@ -0,0 +1,12 @@ +#!/bin/sh +# Render all polyhedral net projections. +# Usage: sh test/render_nets.sh + +set -e + +SCRIPT_DIR=`dirname "$0"` +RENDER="python3 $SCRIPT_DIR/render_net.py" + +$RENDER --proj="+proj=tsea +R=1" \ + --title="TSEA: Tetrahedral Snyder Equal Area" \ + -o tsea_net.png diff --git a/test/unit/CMakeLists.txt b/test/unit/CMakeLists.txt index 3fc36c9827..2993967720 100644 --- a/test/unit/CMakeLists.txt +++ b/test/unit/CMakeLists.txt @@ -256,6 +256,18 @@ add_test(NAME test_misc COMMAND test_misc) set_property(TEST test_misc PROPERTY ENVIRONMENT ${PROJ_TEST_ENVIRONMENT}) +add_executable(test_polyhedral + main.cpp + test_polyhedral.cpp) +target_link_libraries(test_polyhedral + PRIVATE GTest::gtest + PRIVATE ${PROJ_LIBRARIES}) +target_include_directories(test_polyhedral + PRIVATE ${CMAKE_SOURCE_DIR}/src/projections) +add_test(NAME test_polyhedral COMMAND test_polyhedral) +set_property(TEST test_polyhedral + PROPERTY ENVIRONMENT ${PROJ_TEST_ENVIRONMENT}) + if (Threads_FOUND AND CMAKE_USE_PTHREADS_INIT AND NOT APPLE) add_definitions(-DPROJ_HAS_PTHREADS) add_executable(test_fork diff --git a/test/unit/test_polyhedral.cpp b/test/unit/test_polyhedral.cpp new file mode 100644 index 0000000000..f851e0844a --- /dev/null +++ b/test/unit/test_polyhedral.cpp @@ -0,0 +1,75 @@ +/****************************************************************************** + * Project: PROJ + * Purpose: Tests for the polyhedral equal-area projections. + * Author: Felix Palmer + * + ****************************************************************************/ + +#include "gtest_include.h" + +// PROJ include order is sensitive +// clang-format off +#include "proj.h" +#include "proj_internal.h" +// clang-format on + +#include + +namespace { + +struct RoundtripPoint { + double lat; + double lon; +}; + +static const RoundtripPoint test_points[] = { + { 0.0, 0.0}, + { 45.0, 90.0}, + {-45.0, -90.0}, + { 89.0, 0.0}, + {-89.0, 170.0}, + { 30.0, 120.0}, + {-60.0, -150.0}, + { 15.0, 45.0}, + {-30.0, -60.0}, + { 70.0, -170.0}, +}; + +static const char *proj_strings[] = { + "+proj=tsea +R=1", +}; + +static void roundtrip_test(const char *proj_string, double tolerance) { + PJ *testProj = proj_create(PJ_DEFAULT_CTX, proj_string); + ASSERT_TRUE(testProj != nullptr) << "Failed to create: " << proj_string; + + for (const auto &point : test_points) { + PJ_COORD coord = proj_coord(0, 0, 0, 0); + coord.lp.lam = proj_torad(point.lon); + coord.lp.phi = proj_torad(point.lat); + + PJ_COORD flat = proj_trans(testProj, PJ_FWD, coord); + ASSERT_FALSE(flat.lp.lam == HUGE_VAL) + << "Forward failed for lon=" << point.lon << " lat=" << point.lat; + + PJ_COORD new_coord = proj_trans(testProj, PJ_INV, flat); + ASSERT_FALSE(new_coord.lp.lam == HUGE_VAL) + << "Inverse failed for lon=" << point.lon << " lat=" << point.lat; + + EXPECT_NEAR(coord.lp.lam, new_coord.lp.lam, tolerance) + << "lon roundtrip for lon=" << point.lon << " lat=" << point.lat; + EXPECT_NEAR(coord.lp.phi, new_coord.lp.phi, tolerance) + << "lat roundtrip for lon=" << point.lon << " lat=" << point.lat; + } + + proj_destroy(testProj); +} + +TEST(polyhedral, roundtrip) { + for (const auto *proj_string : proj_strings) { + // 1e-13 radians corresponds to accuracy to ~0.6nm (worst case at equator) + roundtrip_test(proj_string, 1e-13); + } +} + +} // namespace From f382bfd9779eeff1a475d4bc6e3ea26b4ab5212c Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 17 Apr 2026 10:54:33 +0200 Subject: [PATCH 02/62] Documentation --- .../images/polyhedral_dsea_icosahedron.png | Bin 0 -> 383812 bytes .../images/polyhedral_dsea_two_flower.png | Bin 0 -> 558157 bytes .../projections/images/polyhedral_isea.png | Bin 0 -> 475894 bytes .../projections/images/polyhedral_title.png | Bin 0 -> 394236 bytes .../projections/images/polyhedral_tsea.png | Bin 0 -> 636558 bytes docs/source/operations/projections/index.rst | 1 + .../operations/projections/polyhedral.rst | 125 ++++++++++++++++++ 7 files changed, 126 insertions(+) create mode 100644 docs/source/operations/projections/images/polyhedral_dsea_icosahedron.png create mode 100644 docs/source/operations/projections/images/polyhedral_dsea_two_flower.png create mode 100644 docs/source/operations/projections/images/polyhedral_isea.png create mode 100644 docs/source/operations/projections/images/polyhedral_title.png create mode 100644 docs/source/operations/projections/images/polyhedral_tsea.png create mode 100644 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zeC*$`uvch><+{v&rJ-O@C(s7d1bc>HG?ptO#+4M!6k&^l19l485Qq13l@%+JYQ|lh z1G|)VZEugWwmx+k6pv}bFClz>3etc918C*5yS1oGC{>qdY_U1PC*@Pi!@3=OCOh%V z7ay*b+mVwh+piWs?v%2MNXHRdmwbDFfEX8({Pl0YY)P$8WvKCDZ3xa@X=O`(3etjq zM7*dQ+hq%1BMRaBa-XQtNbLk;01Ov-4^l1;rEu{?cfNdPlXrH4QjOF4-CGZc;9_MTRW{T|pUM3@y za@31r!Y!Z{+Bow$9#g?mr|YLE$wZBQz;b=VY6D>$cg;QH_f+NfLYEsx_ow_TT>C+5 z)7nNOVj21SubYZ#O~)xpqoSbRXS}o9UKVY)oqbZ`Ohht*8Y#B*NC?d*L^W_mKRArlzKW-IO!wi$sa}Z}zlwdMhhp zA%%jn2l16Z?H^oo8dF~(`+{1w@DE~&z^g|}Eu+|p`VkfMHUc7G@)?BMy&LmJ>7~R| zO!XKmY%%}doukir?t@`bP#b+N_0ZXi9G3SqcF_sEe#&-NMM!+Vh%BbbuvFF_ z>vXiBv@vA+_7kgi?7HLS+aY+~hy%N7TPBh9Aj}^^t)vLfnZ*#X%e9Y$GcgN?H#+ga zqogNJGK^qv$rhqrL)@M!rrch{LaeGn4pncJS0)4^rtf}xKJ%<)@vuB=CK_e?uPp)= z{jO)vtdeJn#KO8E+lp<{dtC0}(IvX2eai0f)>>{ywxKNk_pgDYo83#!-cr9mCfIHi z2*LmPwN>NcQDp1?=hu Date: Tue, 21 Apr 2026 21:57:45 +0200 Subject: [PATCH 03/62] Remove authalic.h, replacing with pj_authalic_xxx --- src/projections/polyhedral.cpp | 33 ++++++++-- src/projections/polyhedral/authalic.h | 92 --------------------------- src/projections/polyhedral/snyder.h | 1 - src/projections/polyhedral/sphere.h | 35 ++++++---- test/render_net.py | 11 +++- test/render_nets.sh | 2 +- test/unit/test_polyhedral.cpp | 1 + 7 files changed, 61 insertions(+), 114 deletions(-) delete mode 100644 src/projections/polyhedral/authalic.h diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index bf634272b1..99bae4ff59 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -38,7 +38,7 @@ static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { PJ_XY xy = {0.0, 0.0}; auto *Q = static_cast(P->opaque); - polyhedral::Vec3 v = polyhedral::lonlat_to_cart(Q, lp.lam, lp.phi); + polyhedral::Vec3 v = polyhedral::lonlat_to_cart(Q, P, lp.lam, lp.phi); int tri_idx = polyhedral::find_triangle(Q, v); if (tri_idx < 0) { @@ -66,7 +66,7 @@ static PJ_LP polyhedral_inv(PJ_XY xy, PJ *P) { if (bary.u >= -1e-10 && bary.v >= -1e-10 && bary.w >= -1e-10) { polyhedral::Vec3 v = polyhedral::snyder_inv( {xy.x, xy.y}, Q->face_tris[i], Q->sph_tris[i]); - polyhedral::cart_to_lonlat(Q, v, lp.lam, lp.phi); + polyhedral::cart_to_lonlat(Q, P, v, lp.lam, lp.phi); return lp; } } @@ -75,16 +75,37 @@ static PJ_LP polyhedral_inv(PJ_XY xy, PJ *P) { return proj_coord_error().lp; } -PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") "\n\tSph"; +static PJ *polyhedral_destructor(PJ *P, int errlev) { + if (nullptr == P) + return nullptr; + if (nullptr == P->opaque) + return pj_default_destructor(P, errlev); + free(static_cast(P->opaque)->apa); + return pj_default_destructor(P, errlev); +} + +static PJ *polyhedral_setup(PJ *P) { + auto *Q = static_cast(P->opaque); + if (P->es != 0.0) { + Q->apa = pj_authalic_lat_compute_coeffs(P->n); + if (nullptr == Q->apa) + return polyhedral_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); + Q->qp = pj_authalic_lat_q(1.0, P); + } + P->fwd = polyhedral_fwd; + P->inv = polyhedral_inv; + return P; +} + +PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") "\n\tSph&Ell"; PJ *PJ_PROJECTION(tsea) { auto *Q = static_cast(calloc(1, sizeof(pj_polyhedral_data))); if (nullptr == Q) return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); P->opaque = Q; + P->destructor = polyhedral_destructor; polyhedral::load_triangles(Q, hexakis_tetrahedron::SPH_TRI, nets::tsea::tsea::FACE_TRI); polyhedral::set_orient_from_angles(Q, 90.0, 0.0, 0.0); - P->fwd = polyhedral_fwd; - P->inv = polyhedral_inv; - return P; + return polyhedral_setup(P); } \ No newline at end of file diff --git a/src/projections/polyhedral/authalic.h b/src/projections/polyhedral/authalic.h deleted file mode 100644 index 37ba571e46..0000000000 --- a/src/projections/polyhedral/authalic.h +++ /dev/null @@ -1,92 +0,0 @@ -/****************************************************************************** - * - * Project: PROJ - * Purpose: Authalic latitude conversion via Clenshaw summation (order 6). - * Author: Felix Palmer - * - ****************************************************************************** - * Coefficients from Karney (2022): https://arxiv.org/pdf/2212.05818 - * - * Clenshaw summation adapted from DGGAL project (authalic.ec). - * - * BSD 3-Clause License - * - * Copyright (c) 2014-2025, Ecere Corporation - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions are met: - * - * 1. Redistributions of source code must retain the above copyright notice, - * this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * 3. Neither the name of the copyright holder nor the names of its - * contributors may be used to endorse or promote products derived from - * this software without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" - * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE - * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR - * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF - * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS - * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN - * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) - * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE - * POSSIBILITY OF SUCH DAMAGE. - ****************************************************************************/ - -#ifndef AUTHALIC_H -#define AUTHALIC_H - -#include - -namespace polyhedral { - -constexpr double GEODETIC_TO_AUTHALIC[6] = { - -2.2392098386786394e-03, - 2.1308606513250217e-06, - -2.5592576864212742e-09, - 3.3701965267802837e-12, - -4.6675453126112487e-15, - 6.6749287038481596e-18, -}; - -constexpr double AUTHALIC_TO_GEODETIC[6] = { - 2.2392089963541657e-03, - 2.8831978048607556e-06, - 5.0862207399726603e-09, - 1.0201812377816100e-11, - 2.1912872306767718e-14, - 4.9284235482523806e-17, -}; - -inline double apply_clenshaw(double phi, const double c[6]) { - double sin_phi = std::sin(phi); - double cos_phi = std::cos(phi); - double x = 2.0 * (cos_phi - sin_phi) * (cos_phi + sin_phi); // cos(2*phi) - - double u0 = x * c[5] + c[4]; - double u1 = x * u0 + c[3]; - u0 = x * u1 - u0 + c[2]; - u1 = x * u0 - u1 + c[1]; - u0 = x * u1 - u0 + c[0]; - - return phi + 2.0 * sin_phi * cos_phi * u0; -} - -inline double geodetic_to_authalic(double phi) { - return apply_clenshaw(phi, GEODETIC_TO_AUTHALIC); -} - -inline double authalic_to_geodetic(double phi) { - return apply_clenshaw(phi, AUTHALIC_TO_GEODETIC); -} - -} // namespace polyhedral - -#endif // AUTHALIC_H diff --git a/src/projections/polyhedral/snyder.h b/src/projections/polyhedral/snyder.h index e853e16a02..bdf5a28d46 100644 --- a/src/projections/polyhedral/snyder.h +++ b/src/projections/polyhedral/snyder.h @@ -63,7 +63,6 @@ #ifndef SNYDER_H #define SNYDER_H -#include "authalic.h" #include "vec3.h" #include "vec3_helpers.h" diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index ec6f64075a..9f7c2e83cc 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -10,9 +10,11 @@ #ifndef POLYHEDRAL_SPHERE_H #define POLYHEDRAL_SPHERE_H -#include "authalic.h" #include "snyder.h" +#include "proj.h" +#include "proj_internal.h" + #include #ifndef M_PI @@ -31,6 +33,11 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; + + // Authalic latitude conversion (ellipsoidal case only; apa is null for + // spheres, where geodetic and authalic latitudes coincide). + double *apa; + double qp; }; // Load triangle data from generated header arrays. @@ -103,8 +110,15 @@ inline int find_triangle(const pj_polyhedral_data *Q, Vec3 v) { } // Convert geodetic lon/lat to unit vector, applying orientation rotation. -inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, double lam, double phi) { - double auth_lat = geodetic_to_authalic(phi); +// In the ellipsoidal case the latitude is first converted to the authalic +// latitude so that equal-area properties are preserved on the sphere. +inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, const PJ *P, + double lam, double phi) { + double auth_lat = phi; + if (P->es != 0.0) { + auth_lat = pj_authalic_lat(phi, std::sin(phi), std::cos(phi), + Q->apa, P, Q->qp); + } double ca = std::cos(auth_lat), sa = std::sin(auth_lat); double cl = std::cos(lam), sl = std::sin(lam); double gx = ca * cl, gy = ca * sl, gz = sa; @@ -114,19 +128,16 @@ inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, double lam, double phi) } // Convert unit vector back to lon/lat, applying inverse orientation. -inline void cart_to_lonlat(const pj_polyhedral_data *Q, Vec3 v, double &lam, double &phi) { +inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, Vec3 v, + double &lam, double &phi) { double gx = Q->orient_inv[0][0] * v.x + Q->orient_inv[0][1] * v.y + Q->orient_inv[0][2] * v.z; double gy = Q->orient_inv[1][0] * v.x + Q->orient_inv[1][1] * v.y + Q->orient_inv[1][2] * v.z; double gz = Q->orient_inv[2][0] * v.x + Q->orient_inv[2][1] * v.y + Q->orient_inv[2][2] * v.z; - if (gz > 1.0) gz = 1.0; - if (gz < -1.0) gz = -1.0; - - double auth_lat = std::asin(gz); - phi = authalic_to_geodetic(auth_lat); - lam = std::atan2(gy, gx); - if (lam < -M_PI) lam += 2 * M_PI; - if (lam > M_PI) lam -= 2 * M_PI; + double auth_lat = aasin(P->ctx, gz); + phi = (P->es != 0.0) ? pj_authalic_lat_inverse(auth_lat, Q->apa, P, Q->qp) + : auth_lat; + lam = adjlon(std::atan2(gy, gx)); } } // namespace polyhedral diff --git a/test/render_net.py b/test/render_net.py index 75dbb14a47..38af4885bd 100644 --- a/test/render_net.py +++ b/test/render_net.py @@ -1,8 +1,15 @@ -#!/usr/bin/env python3 +#!/usr/bin/env -S uv run --script +# /// script +# requires-python = ">=3.9" +# dependencies = [ +# "numpy", +# "matplotlib", +# ] +# /// """Render a polyhedral net projection to an image. Usage: - python3 test/render_net.py --proj="+proj=tsea +R=1" \\ + uv run test/render_net.py --proj="+proj=tsea +R=1" \\ --title="TSEA" --figsize=16,10 -o tsea_net.png """ diff --git a/test/render_nets.sh b/test/render_nets.sh index 60b1f8c15b..0cbeb26449 100755 --- a/test/render_nets.sh +++ b/test/render_nets.sh @@ -5,7 +5,7 @@ set -e SCRIPT_DIR=`dirname "$0"` -RENDER="python3 $SCRIPT_DIR/render_net.py" +RENDER="uv run $SCRIPT_DIR/render_net.py" $RENDER --proj="+proj=tsea +R=1" \ --title="TSEA: Tetrahedral Snyder Equal Area" \ diff --git a/test/unit/test_polyhedral.cpp b/test/unit/test_polyhedral.cpp index f851e0844a..5aaa3c06b8 100644 --- a/test/unit/test_polyhedral.cpp +++ b/test/unit/test_polyhedral.cpp @@ -37,6 +37,7 @@ static const RoundtripPoint test_points[] = { static const char *proj_strings[] = { "+proj=tsea +R=1", + "+proj=tsea +ellps=WGS84", }; static void roundtrip_test(const char *proj_string, double tolerance) { From f461d3e74ce5b484d3d3a70555ad38f0e58c0cb6 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 10:07:34 +0200 Subject: [PATCH 04/62] Don't redefine PI --- src/projections/polyhedral/sphere.h | 12 ++++-------- 1 file changed, 4 insertions(+), 8 deletions(-) diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 9f7c2e83cc..3b79140338 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -17,10 +17,6 @@ #include -#ifndef M_PI -#define M_PI 3.14159265358979323846 -#endif - namespace polyhedral { constexpr int MAX_TRIANGLES = 120; @@ -65,10 +61,10 @@ inline void load_triangles(pj_polyhedral_data *Q, // az: an azimuthal (z-axis) rotation applied after the above inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, double lon_deg, double az_deg) { - const double lat = lat_deg * M_PI / 180.0; - const double lon = lon_deg * M_PI / 180.0; - const double az = az_deg * M_PI / 180.0; - const double alpha = M_PI / 2.0 - lat; + const double lat = lat_deg * DEG_TO_RAD; + const double lon = lon_deg * DEG_TO_RAD; + const double az = az_deg * DEG_TO_RAD; + const double alpha = M_HALFPI - lat; const double ca = std::cos(alpha), sa = std::sin(alpha); const double cl = std::cos(lon), sl = std::sin(lon); const double cz = std::cos(az), sz = std::sin(az); From 85a00f54f51e3fedc91638627ac381a7d6f789ea Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 10:32:31 +0200 Subject: [PATCH 05/62] Remove render scripts --- test/render_net.py | 193 -------------------------------------------- test/render_nets.sh | 12 --- 2 files changed, 205 deletions(-) delete mode 100644 test/render_net.py delete mode 100755 test/render_nets.sh diff --git a/test/render_net.py b/test/render_net.py deleted file mode 100644 index 38af4885bd..0000000000 --- a/test/render_net.py +++ /dev/null @@ -1,193 +0,0 @@ -#!/usr/bin/env -S uv run --script -# /// script -# requires-python = ">=3.9" -# dependencies = [ -# "numpy", -# "matplotlib", -# ] -# /// -"""Render a polyhedral net projection to an image. - -Usage: - uv run test/render_net.py --proj="+proj=tsea +R=1" \\ - --title="TSEA" --figsize=16,10 -o tsea_net.png -""" - -import argparse -import ctypes -import json -import math -import os - -import numpy as np - -# ============================================================ -# ctypes setup -# ============================================================ - -_lib = ctypes.CDLL(os.path.join(os.path.dirname(__file__), "..", "build", - "lib", "libproj.dylib")) -_lib.proj_context_create.restype = ctypes.c_void_p -_lib.proj_create.restype = ctypes.c_void_p -_lib.proj_create.argtypes = [ctypes.c_void_p, ctypes.c_char_p] - - -class PJ_UV(ctypes.Structure): - _fields_ = [("u", ctypes.c_double), ("v", ctypes.c_double)] - - -class PJ_COORD(ctypes.Union): - _fields_ = [("lp", PJ_UV), ("xy", PJ_UV), ("v", ctypes.c_double * 4)] - - -_lib.proj_trans.restype = PJ_COORD -_lib.proj_trans.argtypes = [ctypes.c_void_p, ctypes.c_int, PJ_COORD] -PJ_FWD = 1 - -# ============================================================ -# Projection and segment extraction -# ============================================================ - -# Densification step in degrees. With 0.5° steps, within-face -# projected distances are ~0.008 while cross-face jumps are >0.5, -# so a gap threshold of 0.05 cleanly separates them. -DENSIFY_STEP = 0.5 -MAX_GAP = 0.05 - - -def proj_forward_array(pj, lons, lats): - n = len(lons) - xs = np.empty(n) - ys = np.empty(n) - c = PJ_COORD() - for i in range(n): - c.lp.u = math.radians(lons[i]) - c.lp.v = math.radians(lats[i]) - r = _lib.proj_trans(pj, PJ_FWD, c) - xs[i] = r.xy.u - ys[i] = r.xy.v - return xs, ys - - -def densify(lons, lats, max_step=DENSIFY_STEP): - out_lon = [lons[0]] - out_lat = [lats[0]] - for i in range(1, len(lons)): - d = max(abs(lons[i] - lons[i - 1]), abs(lats[i] - lats[i - 1])) - n = max(1, int(math.ceil(d / max_step))) - for j in range(1, n + 1): - t = j / n - out_lon.append(lons[i - 1] + t * (lons[i] - lons[i - 1])) - out_lat.append(lats[i - 1] + t * (lats[i] - lats[i - 1])) - return np.array(out_lon), np.array(out_lat) - - -def extract_segments(xs, ys, max_gap=MAX_GAP): - """Break line into segments, cutting at large gaps (face boundaries).""" - segments = [] - current = [] - max_gap_sq = max_gap * max_gap - for i in range(len(xs)): - if np.isnan(xs[i]) or np.isinf(xs[i]): - if len(current) > 1: - segments.append(np.array(current)) - current = [] - continue - if current and ((xs[i] - current[-1][0]) ** 2 + - (ys[i] - current[-1][1]) ** 2) > max_gap_sq: - if len(current) > 1: - segments.append(np.array(current)) - current = [] - current.append([xs[i], ys[i]]) - if len(current) > 1: - segments.append(np.array(current)) - return segments - - -def process_line(pj, lons, lats): - lons, lats = densify(lons, lats) - xs, ys = proj_forward_array(pj, lons, lats) - return extract_segments(xs, ys) - - -# ============================================================ -# Main -# ============================================================ - -def main(): - parser = argparse.ArgumentParser(description="Render polyhedral net projection") - parser.add_argument("--proj", required=True, - help="Full PROJ string, e.g. '+proj=tsea +R=1'") - parser.add_argument("--title", required=True, help="Plot title") - parser.add_argument("--resolution", type=float, default=1.0, - help="Output resolution multiplier (default: 1)") - parser.add_argument("-o", "--output", required=True, help="Output filename") - args = parser.parse_args() - - figsize = (10 * args.resolution, 10 * args.resolution) - - import matplotlib - matplotlib.use("Agg") - import matplotlib.pyplot as plt - from matplotlib.collections import LineCollection - - ctx = _lib.proj_context_create() - pj = _lib.proj_create(ctx, args.proj.encode()) - assert pj, f"Failed to create projection: {args.proj}" - - fig, ax = plt.subplots(1, 1, figsize=figsize) - - # Graticule - print("Projecting graticule...") - grat_segs = [] - for lat in range(-80, 90, 10): - lo = np.linspace(-180, 180, 720) - la = np.full_like(lo, float(lat)) - grat_segs.extend(process_line(pj, lo, la)) - for lon in range(-180, 180, 10): - la = np.linspace(-89, 89, 360) - lo = np.full_like(la, float(lon)) - grat_segs.extend(process_line(pj, lo, la)) - print(f" {len(grat_segs)} graticule segments") - - if grat_segs: - lc = LineCollection(grat_segs, colors="lightgray", linewidths=0.3) - ax.add_collection(lc) - - # Coastlines - coast_path = os.path.join(os.path.dirname(__file__), "..", "docs", "plot", - "data", "coastline.geojson") - print("Projecting coastlines...") - coast_segs = [] - if os.path.exists(coast_path): - with open(coast_path) as f: - gj = json.load(f) - for feat in gj["features"]: - geom = feat["geometry"] - rings = [] - if geom["type"] == "LineString": - rings.append(geom["coordinates"]) - elif geom["type"] == "MultiLineString": - rings.extend(geom["coordinates"]) - for ring in rings: - coords = np.array(ring) - coast_segs.extend( - process_line(pj, coords[:, 0], coords[:, 1])) - print(f" {len(coast_segs)} coastline segments") - - if coast_segs: - lc = LineCollection(coast_segs, colors="black", linewidths=0.5) - ax.add_collection(lc) - - ax.set_aspect("equal") - ax.autoscale_view() - ax.set_title(args.title, fontsize=14, pad=12) - ax.axis("off") - fig.tight_layout() - - fig.savefig(args.output, dpi=200, bbox_inches="tight") - print(f"Saved {args.output}") - - -if __name__ == "__main__": - main() diff --git a/test/render_nets.sh b/test/render_nets.sh deleted file mode 100755 index 0cbeb26449..0000000000 --- a/test/render_nets.sh +++ /dev/null @@ -1,12 +0,0 @@ -#!/bin/sh -# Render all polyhedral net projections. -# Usage: sh test/render_nets.sh - -set -e - -SCRIPT_DIR=`dirname "$0"` -RENDER="uv run $SCRIPT_DIR/render_net.py" - -$RENDER --proj="+proj=tsea +R=1" \ - --title="TSEA: Tetrahedral Snyder Equal Area" \ - -o tsea_net.png From 26d7234a86dec2da78f764e83c57ce51c27803a7 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 10:32:43 +0200 Subject: [PATCH 06/62] Linting --- src/projections/polyhedral/snyder.h | 8 ++++---- src/projections/polyhedral/sphere.h | 2 +- src/projections/polyhedral/vec3.h | 20 ++++++++++---------- src/projections/polyhedral/vec3_helpers.h | 12 +++++++----- 4 files changed, 22 insertions(+), 20 deletions(-) diff --git a/src/projections/polyhedral/snyder.h b/src/projections/polyhedral/snyder.h index bdf5a28d46..1003ddf3ba 100644 --- a/src/projections/polyhedral/snyder.h +++ b/src/projections/polyhedral/snyder.h @@ -101,8 +101,8 @@ inline Face2D barycentric_to_face(Barycentric b, FaceTriangle tri) { b.u * tri.a.y + b.v * tri.b.y + b.w * tri.c.y}; } -inline Face2D snyder_fwd(Vec3 v, SphericalTriangle stri, - FaceTriangle ftri) { +inline Face2D snyder_fwd(const Vec3 &v, const SphericalTriangle &stri, + const FaceTriangle &ftri) { Vec3 a = stri.a, b = stri.b, c = stri.c; Vec3 z = vec3_normalize(vec3_subtract(v, a)); @@ -126,8 +126,8 @@ inline Face2D snyder_fwd(Vec3 v, SphericalTriangle stri, return barycentric_to_face(bary, ftri); } -inline Vec3 snyder_inv(Face2D face_point, FaceTriangle ftri, - SphericalTriangle stri) { +inline Vec3 snyder_inv(const Face2D &face_point, const FaceTriangle &ftri, + const SphericalTriangle &stri) { Vec3 a = stri.a, b = stri.b, c = stri.c; Barycentric bcoords = face_to_barycentric(face_point, ftri); diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 3b79140338..3c07553427 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -92,7 +92,7 @@ inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, } // Find the triangle containing point v by linear search. -inline int find_triangle(const pj_polyhedral_data *Q, Vec3 v) { +inline int find_triangle(const pj_polyhedral_data *Q, const Vec3 &v) { for (int i = 0; i < Q->n_triangles; i++) { if (vec3_dot(v, Q->sph_tris[i].a) <= 0) continue; diff --git a/src/projections/polyhedral/vec3.h b/src/projections/polyhedral/vec3.h index ce0e1a1400..2d889d9eba 100644 --- a/src/projections/polyhedral/vec3.h +++ b/src/projections/polyhedral/vec3.h @@ -41,50 +41,50 @@ struct Vec3 { double x, y, z; }; -inline double vec3_dot(Vec3 a, Vec3 b) { +inline double vec3_dot(const Vec3 &a, const Vec3 &b) { return a.x * b.x + a.y * b.y + a.z * b.z; } -inline Vec3 vec3_cross(Vec3 a, Vec3 b) { +inline Vec3 vec3_cross(const Vec3 &a, const Vec3 &b) { return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x}; } -inline double vec3_length(Vec3 v) { +inline double vec3_length(const Vec3 &v) { return std::sqrt(v.x * v.x + v.y * v.y + v.z * v.z); } -inline Vec3 vec3_normalize(Vec3 v) { +inline Vec3 vec3_normalize(const Vec3 &v) { double len = vec3_length(v); if (len == 0.0) return v; return {v.x / len, v.y / len, v.z / len}; } -inline Vec3 vec3_subtract(Vec3 a, Vec3 b) { +inline Vec3 vec3_subtract(const Vec3 &a, const Vec3 &b) { return {a.x - b.x, a.y - b.y, a.z - b.z}; } -inline Vec3 vec3_add(Vec3 a, Vec3 b) { +inline Vec3 vec3_add(const Vec3 &a, const Vec3 &b) { return {a.x + b.x, a.y + b.y, a.z + b.z}; } -inline Vec3 vec3_scale(Vec3 v, double s) { +inline Vec3 vec3_scale(const Vec3 &v, double s) { return {v.x * s, v.y * s, v.z * s}; } -inline Vec3 vec3_lerp(Vec3 a, Vec3 b, double t) { +inline Vec3 vec3_lerp(const Vec3 &a, const Vec3 &b, double t) { return {a.x + t * (b.x - a.x), a.y + t * (b.y - a.y), a.z + t * (b.z - a.z)}; } -inline double vec3_distance(Vec3 a, Vec3 b) { +inline double vec3_distance(const Vec3 &a, const Vec3 &b) { return vec3_length(vec3_subtract(a, b)); } -inline double vec3_angle(Vec3 a, Vec3 b) { +inline double vec3_angle(const Vec3 &a, const Vec3 &b) { double d = vec3_dot(a, b) / (vec3_length(a) * vec3_length(b)); return std::acos(std::clamp(d, -1.0, 1.0)); } diff --git a/src/projections/polyhedral/vec3_helpers.h b/src/projections/polyhedral/vec3_helpers.h index 5c03bbe11a..e04a435e5b 100644 --- a/src/projections/polyhedral/vec3_helpers.h +++ b/src/projections/polyhedral/vec3_helpers.h @@ -37,7 +37,7 @@ namespace polyhedral { // Numerically stable angular distance measure. // Returns a value proportional to sin(angle/2) between a and b. -inline double vector_difference(Vec3 a, Vec3 b) { +inline double vector_difference(const Vec3 &a, const Vec3 &b) { Vec3 midpoint_ab = vec3_normalize(vec3_lerp(a, b, 0.5)); Vec3 cross_result = vec3_cross(a, midpoint_ab); double d = vec3_length(cross_result); @@ -49,20 +49,21 @@ inline double vector_difference(Vec3 a, Vec3 b) { return d; } -inline double triple_product(Vec3 a, Vec3 b, Vec3 c) { +inline double triple_product(const Vec3 &a, const Vec3 &b, const Vec3 &c) { return vec3_dot(a, vec3_cross(b, c)); } // Great-circle intersection helper. // Returns dot(b,cross(c,d))*a - dot(a,cross(c,d))*b -inline Vec3 quadruple_product(Vec3 a, Vec3 b, Vec3 c, Vec3 d) { +inline Vec3 quadruple_product(const Vec3 &a, const Vec3 &b, const Vec3 &c, + const Vec3 &d) { Vec3 cross_cd = vec3_cross(c, d); double tp_acd = vec3_dot(a, cross_cd); double tp_bcd = vec3_dot(b, cross_cd); return vec3_subtract(vec3_scale(b, tp_acd), vec3_scale(a, tp_bcd)); } -inline Vec3 slerp(Vec3 a, Vec3 b, double t) { +inline Vec3 slerp(const Vec3 &a, const Vec3 &b, double t) { double gamma = vec3_angle(a, b); if (gamma < 1e-12) { return vec3_lerp(a, b, t); @@ -75,7 +76,8 @@ inline Vec3 slerp(Vec3 a, Vec3 b, double t) { // Spherical triangle area via midpoint triple product method. // More numerically stable than vertex-based spherical excess. -inline double spherical_triangle_area(Vec3 v1, Vec3 v2, Vec3 v3) { +inline double spherical_triangle_area(const Vec3 &v1, const Vec3 &v2, + const Vec3 &v3) { Vec3 mid_a = vec3_normalize(vec3_lerp(v2, v3, 0.5)); Vec3 mid_b = vec3_normalize(vec3_lerp(v3, v1, 0.5)); Vec3 mid_c = vec3_normalize(vec3_lerp(v1, v2, 0.5)); From 7d09495d6f683f41f2ee819c0f897b9b0523fc1e Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 10:32:48 +0200 Subject: [PATCH 07/62] spelling --- docs/source/spelling_wordlist.txt | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/docs/source/spelling_wordlist.txt b/docs/source/spelling_wordlist.txt index 3cfc298c3d..cd5c1c1393 100644 --- a/docs/source/spelling_wordlist.txt +++ b/docs/source/spelling_wordlist.txt @@ -10,6 +10,7 @@ airocean Airocean aitoff Aitoff +akisation Albers Alegre Aleksejenko @@ -237,6 +238,7 @@ Deakin Deallocate deallocated Deault +Decakis decimalyear decimalyears decimeter @@ -453,6 +455,8 @@ helmert Helmert hemi Hernando +hexakis +Hexakis hgridshift Himmelscharten hoc @@ -768,6 +772,8 @@ poder Poder polewards Polyconic +polyhedra +Polyhedra polynormal pre Pre From 1d851a55505321740b07462fb581e0df35d04e67 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 10:37:49 +0200 Subject: [PATCH 08/62] clang-format --- src/projections/polyhedral.cpp | 17 ++++---- src/projections/polyhedral/snyder.h | 47 ++++++++++++----------- src/projections/polyhedral/sphere.h | 26 +++++++------ src/projections/polyhedral/vec3.h | 6 +-- src/projections/polyhedral/vec3_helpers.h | 2 +- test/unit/test_polyhedral.cpp | 16 +++----- 6 files changed, 56 insertions(+), 58 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 99bae4ff59..4ce49acbcb 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -22,9 +22,9 @@ * limitations under the License. ****************************************************************************/ -#include "polyhedral/sphere.h" -#include "polyhedral/polyhedra/hexakis_tetrahedron.h" #include "polyhedral/nets/tsea/tsea.h" +#include "polyhedral/polyhedra/hexakis_tetrahedron.h" +#include "polyhedral/sphere.h" #include "proj.h" #include "proj_internal.h" @@ -46,8 +46,8 @@ static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { return proj_coord_error().xy; } - polyhedral::Face2D result = polyhedral::snyder_fwd( - v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); + polyhedral::Face2D result = + polyhedral::snyder_fwd(v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); xy.x = result.x; xy.y = result.y; @@ -99,12 +99,15 @@ static PJ *polyhedral_setup(PJ *P) { PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") "\n\tSph&Ell"; PJ *PJ_PROJECTION(tsea) { - auto *Q = static_cast(calloc(1, sizeof(pj_polyhedral_data))); - if (nullptr == Q) return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); + auto *Q = static_cast( + calloc(1, sizeof(pj_polyhedral_data))); + if (nullptr == Q) + return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::load_triangles(Q, hexakis_tetrahedron::SPH_TRI, nets::tsea::tsea::FACE_TRI); + polyhedral::load_triangles(Q, hexakis_tetrahedron::SPH_TRI, + nets::tsea::tsea::FACE_TRI); polyhedral::set_orient_from_angles(Q, 90.0, 0.0, 0.0); return polyhedral_setup(P); diff --git a/src/projections/polyhedral/snyder.h b/src/projections/polyhedral/snyder.h index 1003ddf3ba..4d96a6e6cf 100644 --- a/src/projections/polyhedral/snyder.h +++ b/src/projections/polyhedral/snyder.h @@ -8,7 +8,7 @@ * Derived from A5 (Apache-2.0). * * https://github.com/felixpalmer/a5 - * + * * modules/projections/polyhedral.ts * Copyright (c) A5 contributors @@ -26,33 +26,35 @@ * limitations under the License. **************************************************************************** * Derived from DGGAL (BSD 3-Clause License) - * + * * Copyright (c) 2014-2025, Ecere Corporation - * + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: - * - * 1. Redistributions of source code must retain the above copyright notice, this - * list of conditions and the following disclaimer. - * + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * 2. Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. - * + * * 3. Neither the name of the copyright holder nor the names of its * contributors may be used to endorse or promote products derived from * this software without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" - * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE - * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR - * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER - * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, - * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE - * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS + * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE + * COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, + * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER + * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN + * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. **************************************************************************** * * Closed from equations adapted from: @@ -102,7 +104,7 @@ inline Face2D barycentric_to_face(Barycentric b, FaceTriangle tri) { } inline Face2D snyder_fwd(const Vec3 &v, const SphericalTriangle &stri, - const FaceTriangle &ftri) { + const FaceTriangle &ftri) { Vec3 a = stri.a, b = stri.b, c = stri.c; Vec3 z = vec3_normalize(vec3_subtract(v, a)); @@ -120,14 +122,13 @@ inline Face2D snyder_fwd(const Vec3 &v, const SphericalTriangle &stri, double area_apc = spherical_triangle_area(a, p, c); double area_abp = spherical_triangle_area(a, b, p); - Barycentric bary = {1.0 - h, - scaled_area * area_apc, + Barycentric bary = {1.0 - h, scaled_area * area_apc, scaled_area * area_abp}; return barycentric_to_face(bary, ftri); } inline Vec3 snyder_inv(const Face2D &face_point, const FaceTriangle &ftri, - const SphericalTriangle &stri) { + const SphericalTriangle &stri) { Vec3 a = stri.a, b = stri.b, c = stri.c; Barycentric bcoords = face_to_barycentric(face_point, ftri); diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 3c07553427..0338ca36e0 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -38,8 +38,7 @@ struct pj_polyhedral_data { // Load triangle data from generated header arrays. template -inline void load_triangles(pj_polyhedral_data *Q, - const double (&sph)[N][3][3], +inline void load_triangles(pj_polyhedral_data *Q, const double (&sph)[N][3][3], const double (&face)[N][3][2]) { Q->n_triangles = N; for (int i = 0; i < N; i++) { @@ -70,7 +69,7 @@ inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, const double cz = std::cos(az), sz = std::sin(az); const double r00 = ca * cl, r01 = ca * sl, r02 = -sa; - const double r10 = -sl, r11 = cl, r12 = 0.0; + const double r10 = -sl, r11 = cl, r12 = 0.0; const double r20 = sa * cl, r21 = sa * sl, r22 = ca; double m[3][3]; @@ -108,12 +107,12 @@ inline int find_triangle(const pj_polyhedral_data *Q, const Vec3 &v) { // Convert geodetic lon/lat to unit vector, applying orientation rotation. // In the ellipsoidal case the latitude is first converted to the authalic // latitude so that equal-area properties are preserved on the sphere. -inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, const PJ *P, - double lam, double phi) { +inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, const PJ *P, double lam, + double phi) { double auth_lat = phi; if (P->es != 0.0) { - auth_lat = pj_authalic_lat(phi, std::sin(phi), std::cos(phi), - Q->apa, P, Q->qp); + auth_lat = pj_authalic_lat(phi, std::sin(phi), std::cos(phi), Q->apa, P, + Q->qp); } double ca = std::cos(auth_lat), sa = std::sin(auth_lat); double cl = std::cos(lam), sl = std::sin(lam); @@ -124,11 +123,14 @@ inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, const PJ *P, } // Convert unit vector back to lon/lat, applying inverse orientation. -inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, Vec3 v, - double &lam, double &phi) { - double gx = Q->orient_inv[0][0] * v.x + Q->orient_inv[0][1] * v.y + Q->orient_inv[0][2] * v.z; - double gy = Q->orient_inv[1][0] * v.x + Q->orient_inv[1][1] * v.y + Q->orient_inv[1][2] * v.z; - double gz = Q->orient_inv[2][0] * v.x + Q->orient_inv[2][1] * v.y + Q->orient_inv[2][2] * v.z; +inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, + const Vec3 &v, double &lam, double &phi) { + double gx = Q->orient_inv[0][0] * v.x + Q->orient_inv[0][1] * v.y + + Q->orient_inv[0][2] * v.z; + double gy = Q->orient_inv[1][0] * v.x + Q->orient_inv[1][1] * v.y + + Q->orient_inv[1][2] * v.z; + double gz = Q->orient_inv[2][0] * v.x + Q->orient_inv[2][1] * v.y + + Q->orient_inv[2][2] * v.z; double auth_lat = aasin(P->ctx, gz); phi = (P->es != 0.0) ? pj_authalic_lat_inverse(auth_lat, Q->apa, P, Q->qp) diff --git a/src/projections/polyhedral/vec3.h b/src/projections/polyhedral/vec3.h index 2d889d9eba..d3a7d3b92a 100644 --- a/src/projections/polyhedral/vec3.h +++ b/src/projections/polyhedral/vec3.h @@ -46,8 +46,7 @@ inline double vec3_dot(const Vec3 &a, const Vec3 &b) { } inline Vec3 vec3_cross(const Vec3 &a, const Vec3 &b) { - return {a.y * b.z - a.z * b.y, - a.z * b.x - a.x * b.z, + return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x}; } @@ -75,8 +74,7 @@ inline Vec3 vec3_scale(const Vec3 &v, double s) { } inline Vec3 vec3_lerp(const Vec3 &a, const Vec3 &b, double t) { - return {a.x + t * (b.x - a.x), - a.y + t * (b.y - a.y), + return {a.x + t * (b.x - a.x), a.y + t * (b.y - a.y), a.z + t * (b.z - a.z)}; } diff --git a/src/projections/polyhedral/vec3_helpers.h b/src/projections/polyhedral/vec3_helpers.h index e04a435e5b..de8e6203fb 100644 --- a/src/projections/polyhedral/vec3_helpers.h +++ b/src/projections/polyhedral/vec3_helpers.h @@ -7,7 +7,7 @@ ****************************************************************************** * Derived from A5 (Apache-2.0). * https://github.com/felixpalmer/a5 - * + * * modules/utils/vector.ts * * Copyright (c) A5 contributors diff --git a/test/unit/test_polyhedral.cpp b/test/unit/test_polyhedral.cpp index 5aaa3c06b8..d0bbc9ca2b 100644 --- a/test/unit/test_polyhedral.cpp +++ b/test/unit/test_polyhedral.cpp @@ -23,16 +23,9 @@ struct RoundtripPoint { }; static const RoundtripPoint test_points[] = { - { 0.0, 0.0}, - { 45.0, 90.0}, - {-45.0, -90.0}, - { 89.0, 0.0}, - {-89.0, 170.0}, - { 30.0, 120.0}, - {-60.0, -150.0}, - { 15.0, 45.0}, - {-30.0, -60.0}, - { 70.0, -170.0}, + {0.0, 0.0}, {45.0, 90.0}, {-45.0, -90.0}, {89.0, 0.0}, + {-89.0, 170.0}, {30.0, 120.0}, {-60.0, -150.0}, {15.0, 45.0}, + {-30.0, -60.0}, {70.0, -170.0}, }; static const char *proj_strings[] = { @@ -68,7 +61,8 @@ static void roundtrip_test(const char *proj_string, double tolerance) { TEST(polyhedral, roundtrip) { for (const auto *proj_string : proj_strings) { - // 1e-13 radians corresponds to accuracy to ~0.6nm (worst case at equator) + // 1e-13 radians corresponds to accuracy to ~0.6nm (worst case at + // equator) roundtrip_test(proj_string, 1e-13); } } From 7d9658ea959600959e847d295ee359e2439f89e4 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 14:25:26 +0200 Subject: [PATCH 09/62] try with meta operator --- src/projections/polyhedral.cpp | 16 ++-- src/projections/polyhedral/conway.h | 81 +++++++++++++++++++ .../polyhedra/hexakis_tetrahedron.h | 37 --------- .../polyhedral/polyhedra/tetrahedron.h | 40 +++++++++ 4 files changed, 132 insertions(+), 42 deletions(-) create mode 100644 src/projections/polyhedral/conway.h delete mode 100644 src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h create mode 100644 src/projections/polyhedral/polyhedra/tetrahedron.h diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 4ce49acbcb..573aab109d 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -22,13 +22,15 @@ * limitations under the License. ****************************************************************************/ +#include "polyhedral/conway.h" #include "polyhedral/nets/tsea/tsea.h" -#include "polyhedral/polyhedra/hexakis_tetrahedron.h" +#include "polyhedral/polyhedra/tetrahedron.h" #include "polyhedral/sphere.h" #include "proj.h" #include "proj_internal.h" +#include #include using polyhedral::pj_polyhedral_data; @@ -106,9 +108,13 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::load_triangles(Q, hexakis_tetrahedron::SPH_TRI, - nets::tsea::tsea::FACE_TRI); - polyhedral::set_orient_from_angles(Q, 90.0, 0.0, 0.0); + double spherical_triangles[24][3][3]; + polyhedral::meta_spherical(polyhedra::tetrahedron::V, + polyhedra::tetrahedron::F, spherical_triangles); + polyhedral::load_triangles(Q, spherical_triangles, nets::tsea::tsea::FACE_TRI); + + const double apex_lat_deg = std::asin(1.0 / std::sqrt(3.0)) * RAD_TO_DEG; + polyhedral::set_orient_from_angles(Q, apex_lat_deg, 120.0, 135.0); return polyhedral_setup(P); -} \ No newline at end of file +} diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h new file mode 100644 index 0000000000..22dfd70d6d --- /dev/null +++ b/src/projections/polyhedral/conway.h @@ -0,0 +1,81 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Conway polyhedron operations. + * Currently provides the "meta" (a.k.a. bevel) operation specialised + * to triangular-faced polyhedra projected onto the unit sphere. + * See https://en.wikipedia.org/wiki/Conway_polyhedron_notation + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRAL_CONWAY_H +#define POLYHEDRAL_CONWAY_H + +#include + +namespace polyhedral { + +// Project a 3-vector onto the unit sphere in place. +inline void normalize3(double v[3]) { + const double n = std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); + v[0] /= n; + v[1] /= n; + v[2] /= n; +} + +// Apply the Conway "meta" operation to a polyhedron whose faces are triangles, +// projecting every derived point onto the unit sphere. Each face yields 6 +// right triangles, each spanning (face center, edge midpoint, original vertex). +// +// For a face (a, b, c) we walk the boundary +// +// a → mid(a,b) → b → mid(b,c) → c → mid(c,a) → a +// +// and emit 6 triangles (center, walk[k+1], walk[k]) for k = 0..5. This +// preserves the outward winding of the input face, so spherical containment +// tests on the resulting triangulation behave consistently across faces. +// +// Output buffer is sized 6 * NF triangles. Caller passes V (NV vertices) and +// F (NF triangular faces) as flat arrays; templated on NV/NF so the array +// dimensions stay self-describing at the call site. +template +inline void meta_spherical(const double (&V)[NV][3], const int (&F)[NF][3], + double (&out)[6 * NF][3][3]) { + for (int i = 0; i < NF; i++) { + const int ia = F[i][0], ib = F[i][1], ic = F[i][2]; + const double *Va = V[ia], *Vb = V[ib], *Vc = V[ic]; + + double walk[6][3]; + for (int d = 0; d < 3; d++) { + walk[0][d] = Va[d]; + walk[2][d] = Vb[d]; + walk[4][d] = Vc[d]; + walk[1][d] = 0.5 * (Va[d] + Vb[d]); + walk[3][d] = 0.5 * (Vb[d] + Vc[d]); + walk[5][d] = 0.5 * (Vc[d] + Va[d]); + } + normalize3(walk[1]); + normalize3(walk[3]); + normalize3(walk[5]); + + double center[3] = {(Va[0] + Vb[0] + Vc[0]) / 3.0, + (Va[1] + Vb[1] + Vc[1]) / 3.0, + (Va[2] + Vb[2] + Vc[2]) / 3.0}; + normalize3(center); + + for (int k = 0; k < 6; k++) { + const double *p1 = walk[(k + 1) % 6]; + const double *p2 = walk[k]; + for (int d = 0; d < 3; d++) { + out[6 * i + k][0][d] = center[d]; + out[6 * i + k][1][d] = p1[d]; + out[6 * i + k][2][d] = p2[d]; + } + } + } +} + +} // namespace polyhedral + +#endif // POLYHEDRAL_CONWAY_H diff --git a/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h b/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h deleted file mode 100644 index e6e8d87ac1..0000000000 --- a/src/projections/polyhedral/polyhedra/hexakis_tetrahedron.h +++ /dev/null @@ -1,37 +0,0 @@ -// Auto-generated by scripts/generate_tsea_mapping.py — DO NOT EDIT - -#ifndef POLYHEDRA_HEXAKIS_TETRAHEDRON_H -#define POLYHEDRA_HEXAKIS_TETRAHEDRON_H - -namespace hexakis_tetrahedron { - -constexpr double SPH_TRI[24][3][3] = { - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}}, - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}}, - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, - {{ 4.71404520791031401e-01, -8.16496580927726034e-01, 3.33333333333333759e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 8.16496580927726034e-01, 0.00000000000000000e+00, 5.77350269189625842e-01}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, - {{ 4.71404520791031734e-01, 8.16496580927725923e-01, 3.33333333333333537e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, {-4.08248290463862795e-01, 7.07106781186547573e-01, 5.77350269189625842e-01}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, - {{-9.42809041582063245e-01, 4.44089209850062419e-16, 3.33333333333333537e-01}, { 0.00000000000000000e+00, 0.00000000000000000e+00, 1.00000000000000000e+00}, {-4.08248290463863406e-01, -7.07106781186547240e-01, 5.77350269189625842e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}, { 4.08248290463862851e-01, -7.07106781186547684e-01, -5.77350269189625731e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}, {-4.71404520791032178e-01, -8.16496580927725812e-01, -3.33333333333333148e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}, {-8.16496580927726257e-01, 3.84592537276712714e-16, -5.77350269189625398e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}, {-4.71404520791031512e-01, 8.16496580927726257e-01, -3.33333333333333148e-01}}, - {{-2.22044604925031456e-16, 4.44089209850062912e-16, -1.00000000000000000e+00}, { 9.42809041582063467e-01, 0.00000000000000000e+00, -3.33333333333333148e-01}, { 4.08248290463863184e-01, 7.07106781186547573e-01, -5.77350269189625398e-01}} -}; - -} // namespace hexakis_tetrahedron - -#endif // POLYHEDRA_HEXAKIS_TETRAHEDRON_H diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h new file mode 100644 index 0000000000..2cc04d30f4 --- /dev/null +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -0,0 +1,40 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Regular tetrahedron inscribed in the unit sphere. + * Seed polyhedron for TSEA — the 24 spherical triangles used by + * the projection are obtained at setup time by applying the Conway + * "meta" operation (see conway.h) to the 4 faces below. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRA_TETRAHEDRON_H +#define POLYHEDRA_TETRAHEDRON_H + +namespace polyhedra { +namespace tetrahedron { + +// 4 vertices on the unit sphere, with one apex at the north pole. +// Coordinates: (0, 0, 1) and three points at z = -1/3, evenly spaced in +// longitude, with horizontal radius 2*sqrt(2)/3. +constexpr double V[4][3] = { + { 0.0, 0.0, 1.0 }, // 0 apex + { 0.94280904158206336586779e+00, 0.0, -1.0/3.0 }, // 1 2*sqrt(2)/3 + {-0.47140452079103168293390e+00, 0.81649658092772603273243e+00, -1.0/3.0 }, // 2 + {-0.47140452079103168293390e+00, -0.81649658092772603273243e+00, -1.0/3.0 }, // 3 +}; + +// 4 triangular faces, each listed with outward-pointing winding. +// The order here matches the order TSEA's planar net expects. +constexpr int F[4][3] = { + {0, 3, 1}, + {0, 1, 2}, + {0, 2, 3}, + {1, 3, 2}, +}; + +} // namespace tetrahedron +} // namespace polyhedra + +#endif // POLYHEDRA_TETRAHEDRON_H From b2b88852239eeed868a902467c3dc1bae6d29a8a Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 15:14:22 +0200 Subject: [PATCH 10/62] reduce planar triangles storage via meta --- src/projections/polyhedral.cpp | 11 ++- src/projections/polyhedral/conway.h | 86 ++++++++++--------- src/projections/polyhedral/nets/tsea/tsea.h | 64 ++++++++------ .../polyhedral/polyhedra/tetrahedron.h | 16 ++-- 4 files changed, 98 insertions(+), 79 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 573aab109d..cf0b84c50e 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -109,9 +109,14 @@ PJ *PJ_PROJECTION(tsea) { P->destructor = polyhedral_destructor; double spherical_triangles[24][3][3]; - polyhedral::meta_spherical(polyhedra::tetrahedron::V, - polyhedra::tetrahedron::F, spherical_triangles); - polyhedral::load_triangles(Q, spherical_triangles, nets::tsea::tsea::FACE_TRI); + polyhedral::conway_meta(polyhedra::tetrahedron::V, + polyhedra::tetrahedron::F, spherical_triangles); + + double face_triangles[24][3][2]; + polyhedral::conway_meta(nets::tsea::tsea::V, nets::tsea::tsea::F, + face_triangles); + + polyhedral::load_triangles(Q, spherical_triangles, face_triangles); const double apex_lat_deg = std::asin(1.0 / std::sqrt(3.0)) * RAD_TO_DEG; polyhedral::set_orient_from_angles(Q, apex_lat_deg, 120.0, 135.0); diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h index 22dfd70d6d..83527302eb 100644 --- a/src/projections/polyhedral/conway.h +++ b/src/projections/polyhedral/conway.h @@ -2,8 +2,9 @@ * * Project: PROJ * Purpose: Conway polyhedron operations. - * Currently provides the "meta" (a.k.a. bevel) operation specialised - * to triangular-faced polyhedra projected onto the unit sphere. + * Provides the "meta" (a.k.a. bevel) operation generalised to + * polyhedra with NVF-gon faces, in either 2D (planar net) or + * 3D (vertices projected onto the unit sphere). * See https://en.wikipedia.org/wiki/Conway_polyhedron_notation * Author: Felix Palmer * @@ -24,53 +25,56 @@ inline void normalize3(double v[3]) { v[2] /= n; } -// Apply the Conway "meta" operation to a polyhedron whose faces are triangles, -// projecting every derived point onto the unit sphere. Each face yields 6 -// right triangles, each spanning (face center, edge midpoint, original vertex). +// Apply the Conway "meta" operation to a polyhedron whose faces all have +// NVF vertices. Each face yields 2*NVF triangles fanning out from the face +// centroid. For a face (v_0, ..., v_{NVF-1}) the 2*NVF fan vertices are // -// For a face (a, b, c) we walk the boundary +// v_0, mid(v_0,v_1), v_1, mid(v_1,v_2), ..., v_{NVF-1}, mid(v_{NVF-1},v_0) // -// a → mid(a,b) → b → mid(b,c) → c → mid(c,a) → a +// and the emitted triangles are (centroid, fan[k+1], fan[k]) for k = 0..2*NVF-1. +// This preserves the outward winding of the input face, so containment tests +// on the resulting triangulation behave consistently across faces. // -// and emit 6 triangles (center, walk[k+1], walk[k]) for k = 0..5. This -// preserves the outward winding of the input face, so spherical containment -// tests on the resulting triangulation behave consistently across faces. +// DIM == 3: vertices are projected onto the unit sphere (so callers can +// supply unnormalized symmetric Cartesian coordinates, e.g. McCooey-style). +// DIM == 2: planar input — the centroid is the unweighted average of the +// face vertices and no normalization is applied. // -// Output buffer is sized 6 * NF triangles. Caller passes V (NV vertices) and -// F (NF triangular faces) as flat arrays; templated on NV/NF so the array -// dimensions stay self-describing at the call site. -template -inline void meta_spherical(const double (&V)[NV][3], const int (&F)[NF][3], - double (&out)[6 * NF][3][3]) { +// Output buffer is sized 2 * NVF * NF triangles. Templated on every array +// dimension so they stay self-describing at the call site. +template +inline void conway_meta(const double (&V)[NV][DIM], const int (&F)[NF][NVF], + double (&out)[2 * NVF * NF][3][DIM]) { + constexpr int N = 2 * NVF; for (int i = 0; i < NF; i++) { - const int ia = F[i][0], ib = F[i][1], ic = F[i][2]; - const double *Va = V[ia], *Vb = V[ib], *Vc = V[ic]; - - double walk[6][3]; - for (int d = 0; d < 3; d++) { - walk[0][d] = Va[d]; - walk[2][d] = Vb[d]; - walk[4][d] = Vc[d]; - walk[1][d] = 0.5 * (Va[d] + Vb[d]); - walk[3][d] = 0.5 * (Vb[d] + Vc[d]); - walk[5][d] = 0.5 * (Vc[d] + Va[d]); + double fan[N][DIM]; + double center[DIM] = {}; + for (int k = 0; k < NVF; k++) { + const int ia = F[i][k]; + const int ib = F[i][(k + 1) % NVF]; + for (int d = 0; d < DIM; d++) { + fan[2 * k][d] = V[ia][d]; + fan[2 * k + 1][d] = 0.5 * (V[ia][d] + V[ib][d]); + center[d] += V[ia][d]; + } } - normalize3(walk[1]); - normalize3(walk[3]); - normalize3(walk[5]); - double center[3] = {(Va[0] + Vb[0] + Vc[0]) / 3.0, - (Va[1] + Vb[1] + Vc[1]) / 3.0, - (Va[2] + Vb[2] + Vc[2]) / 3.0}; - normalize3(center); + if constexpr (DIM == 3) { + for (int k = 0; k < N; k++) + normalize3(fan[k]); + normalize3(center); + } else { + for (int d = 0; d < DIM; d++) + center[d] /= NVF; + } - for (int k = 0; k < 6; k++) { - const double *p1 = walk[(k + 1) % 6]; - const double *p2 = walk[k]; - for (int d = 0; d < 3; d++) { - out[6 * i + k][0][d] = center[d]; - out[6 * i + k][1][d] = p1[d]; - out[6 * i + k][2][d] = p2[d]; + for (int k = 0; k < N; k++) { + const double *p1 = fan[(k + 1) % N]; + const double *p2 = fan[k]; + for (int d = 0; d < DIM; d++) { + out[N * i + k][0][d] = center[d]; + out[N * i + k][1][d] = p1[d]; + out[N * i + k][2][d] = p2[d]; } } } diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index f10c698e05..1a0f9b8eb8 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -1,37 +1,45 @@ -// Auto-generated by scripts/generate_tsea_mapping.py — DO NOT EDIT +/****************************************************************************** + * + * Project: PROJ + * Purpose: Planar net for the TSEA projection — a regular tetrahedron + * unfolded into the plane. The 24 face triangles used by the + * projection are obtained at setup time by applying the Conway + * "meta" operation (see conway.h) to the 4 faces below. + * Author: Felix Palmer + * + ****************************************************************************/ #ifndef NETS_TSEA_TSEA_H #define NETS_TSEA_TSEA_H namespace nets { namespace tsea { namespace tsea { -// Planar triangle vertices (net coordinates) -// [tri][vertex: 0=apex, 1=left, 2=right][x, y] -constexpr double FACE_TRI[24][3][2] = { - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-1.34677368708859979e+00, -1.55512030155621428e+00}, {-2.69354737417719736e+00, -1.55512030155621428e+00}}, - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, { 2.22044604925031308e-16, -1.55512030155621428e+00}, {-1.34677368708859979e+00, -1.55512030155621428e+00}}, - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-6.73386843544298785e-01, -3.88780075389053625e-01}, { 2.22044604925031308e-16, -1.55512030155621428e+00}}, - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-1.34677368708859846e+00, 7.77560150778106918e-01}, {-6.73386843544298785e-01, -3.88780075389053625e-01}}, - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-2.02016053063289824e+00, -3.88780075389055069e-01}, {-1.34677368708859846e+00, 7.77560150778106918e-01}}, - {{-1.34677368708859935e+00, -7.77560150778107806e-01}, {-2.69354737417719736e+00, -1.55512030155621428e+00}, {-2.02016053063289824e+00, -3.88780075389055069e-01}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-6.73386843544299007e-01, 1.94390037694526763e+00}, { 7.40148683083437653e-17, 3.11024060311242767e+00}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-1.34677368708859846e+00, 7.77560150778107140e-01}, {-6.73386843544299007e-01, 1.94390037694526763e+00}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, {-3.70074341541718888e-17, 7.77560150778106696e-01}, {-1.34677368708859846e+00, 7.77560150778107140e-01}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 1.34677368708859824e+00, 7.77560150778106030e-01}, {-3.70074341541718888e-17, 7.77560150778106696e-01}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 6.73386843544299118e-01, 1.94390037694526718e+00}, { 1.34677368708859824e+00, 7.77560150778106030e-01}}, - {{ 7.40148683083437653e-17, 1.55512030155621384e+00}, { 7.40148683083437653e-17, 3.11024060311242767e+00}, { 6.73386843544299118e-01, 1.94390037694526718e+00}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 2.02016053063289780e+00, -3.88780075389053903e-01}, { 2.69354737417719692e+00, -1.55512030155621428e+00}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 1.34677368708859868e+00, 7.77560150778107140e-01}, { 2.02016053063289780e+00, -3.88780075389053903e-01}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 6.73386843544299118e-01, -3.88780075389053459e-01}, { 1.34677368708859868e+00, 7.77560150778107140e-01}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, {-6.66133814775093924e-16, -1.55512030155621428e+00}, { 6.73386843544299118e-01, -3.88780075389053459e-01}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 1.34677368708859846e+00, -1.55512030155621384e+00}, {-6.66133814775093924e-16, -1.55512030155621428e+00}}, - {{ 1.34677368708859846e+00, -7.77560150778107140e-01}, { 2.69354737417719692e+00, -1.55512030155621428e+00}, { 1.34677368708859846e+00, -1.55512030155621384e+00}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, {-6.73386843544300118e-01, -3.88780075389052238e-01}, {-1.34677368708859846e+00, 7.77560150778107140e-01}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 3.70074341541745142e-17, -1.55512030155621428e+00}, {-6.73386843544300118e-01, -3.88780075389052238e-01}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 6.73386843544300673e-01, -3.88780075389050961e-01}, { 3.70074341541745142e-17, -1.55512030155621428e+00}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 1.34677368708859868e+00, 7.77560150778107251e-01}, { 6.73386843544300673e-01, -3.88780075389050961e-01}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, { 1.64683081986065150e-15, 7.77560150778107140e-01}, { 1.34677368708859868e+00, 7.77560150778107251e-01}}, - {{ 1.03620815631681540e-15, 1.99840144432528651e-15}, {-1.34677368708859846e+00, 7.77560150778107140e-01}, { 1.64683081986065150e-15, 7.77560150778107140e-01}} +// Half side length S and centroid-to-base distance H of each net face. +// The net is composed of 4 equilateral triangles of side 2S; equal-area +// projection from the unit sphere (area 4π) requires +// 4 * sqrt(3) * S^2 = 4π ⇒ S = sqrt(π / sqrt(3)), H = S / sqrt(3). +constexpr double S = 1.34677368708859935e+00; // sqrt(pi / sqrt(3)) +constexpr double H = 0.77756015077810714e+00; // sqrt(pi / (3 * sqrt(3))) + +// 6 vertices of the unfolded net. The central face has its centroid at the +// origin; the three outer faces unfold across each of its edges. +constexpr double V[6][2] = { + { -S, H}, // 0 + { 0.0, -2*H}, // 1 + { S, H}, // 2 + {-2*S, -2*H}, // 3 + { 0.0, 4*H}, // 4 + { 2*S, -2*H}, // 5 +}; + +// 4 triangular faces. The vertex ordering of each face matches the matching +// face in polyhedra::tetrahedron::F so that conway_meta produces sub-triangles +// in the same order for both the planar and spherical triangulations. +constexpr int F[4][3] = { + {3, 1, 0}, + {4, 0, 2}, + {5, 2, 1}, + {0, 1, 2}, }; } } } // namespace nets::tsea::tsea diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 2cc04d30f4..848ff92771 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -15,14 +15,16 @@ namespace polyhedra { namespace tetrahedron { -// 4 vertices on the unit sphere, with one apex at the north pole. -// Coordinates: (0, 0, 1) and three points at z = -1/3, evenly spaced in -// longitude, with horizontal radius 2*sqrt(2)/3. +// 4 vertices in the symmetric Cartesian form (C0 = sqrt(2)/4). The +// tetrahedron is centered at the origin; vertices lie on a sphere of +// radius sqrt(6)/4 and are normalized to the unit sphere by conway_meta. +constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 + constexpr double V[4][3] = { - { 0.0, 0.0, 1.0 }, // 0 apex - { 0.94280904158206336586779e+00, 0.0, -1.0/3.0 }, // 1 2*sqrt(2)/3 - {-0.47140452079103168293390e+00, 0.81649658092772603273243e+00, -1.0/3.0 }, // 2 - {-0.47140452079103168293390e+00, -0.81649658092772603273243e+00, -1.0/3.0 }, // 3 + { C0, -C0, C0}, // 0 + { C0, C0, -C0}, // 1 + {-C0, C0, C0}, // 2 + {-C0, -C0, -C0}, // 3 }; // 4 triangular faces, each listed with outward-pointing winding. From 58a3a1bb505d63620249948657d9be9b1ee4d58f Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 15:32:20 +0200 Subject: [PATCH 11/62] tidy --- src/projections/polyhedral.cpp | 9 +-- src/projections/polyhedral/conway.h | 71 ++++++++++--------- src/projections/polyhedral/nets/tsea/tsea.h | 39 +++++----- .../polyhedral/polyhedra/tetrahedron.h | 4 +- 4 files changed, 66 insertions(+), 57 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index cf0b84c50e..024ee7b9aa 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -109,12 +109,13 @@ PJ *PJ_PROJECTION(tsea) { P->destructor = polyhedral_destructor; double spherical_triangles[24][3][3]; - polyhedral::conway_meta(polyhedra::tetrahedron::V, - polyhedra::tetrahedron::F, spherical_triangles); + polyhedral::conway_meta(polyhedra::tetrahedron::VERTICES, + polyhedra::tetrahedron::FACES, + spherical_triangles); double face_triangles[24][3][2]; - polyhedral::conway_meta(nets::tsea::tsea::V, nets::tsea::tsea::F, - face_triangles); + polyhedral::conway_meta(nets::tsea::tsea::VERTICES, + nets::tsea::tsea::FACES, face_triangles); polyhedral::load_triangles(Q, spherical_triangles, face_triangles); diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h index 83527302eb..6d1e6dd7ca 100644 --- a/src/projections/polyhedral/conway.h +++ b/src/projections/polyhedral/conway.h @@ -26,55 +26,58 @@ inline void normalize3(double v[3]) { } // Apply the Conway "meta" operation to a polyhedron whose faces all have -// NVF vertices. Each face yields 2*NVF triangles fanning out from the face -// centroid. For a face (v_0, ..., v_{NVF-1}) the 2*NVF fan vertices are +// NumFaceVertices (NFV) vertices. Each face yields 2*NFV triangles fanning +// out from the face centroid. For a face (v_0, ..., v_{NFV-1}) the 2*NFV +// fan vertices are // -// v_0, mid(v_0,v_1), v_1, mid(v_1,v_2), ..., v_{NVF-1}, mid(v_{NVF-1},v_0) +// v_0, mid(v_0,v_1), v_1, mid(v_1,v_2), ..., v_{NFV-1}, mid(v_{NFV-1},v_0) // -// and the emitted triangles are (centroid, fan[k+1], fan[k]) for k = 0..2*NVF-1. -// This preserves the outward winding of the input face, so containment tests -// on the resulting triangulation behave consistently across faces. +// and the emitted triangles are (centroid, fan[k+1], fan[k]) for k in +// [0, 2*NFV). This preserves the outward winding of the input face, so +// containment tests on the resulting triangulation behave consistently. // -// DIM == 3: vertices are projected onto the unit sphere (so callers can +// Dim == 3: vertices are projected onto the unit sphere (so callers can // supply unnormalized symmetric Cartesian coordinates, e.g. McCooey-style). -// DIM == 2: planar input — the centroid is the unweighted average of the +// Dim == 2: planar input — the centroid is the unweighted average of the // face vertices and no normalization is applied. // -// Output buffer is sized 2 * NVF * NF triangles. Templated on every array -// dimension so they stay self-describing at the call site. -template -inline void conway_meta(const double (&V)[NV][DIM], const int (&F)[NF][NVF], - double (&out)[2 * NVF * NF][3][DIM]) { - constexpr int N = 2 * NVF; - for (int i = 0; i < NF; i++) { - double fan[N][DIM]; - double center[DIM] = {}; - for (int k = 0; k < NVF; k++) { - const int ia = F[i][k]; - const int ib = F[i][(k + 1) % NVF]; - for (int d = 0; d < DIM; d++) { - fan[2 * k][d] = V[ia][d]; - fan[2 * k + 1][d] = 0.5 * (V[ia][d] + V[ib][d]); - center[d] += V[ia][d]; +// Output buffer is sized 2 * NFV * NumFaces triangles. Templated on every +// array dimension so they stay self-describing at the call site. +template +inline void conway_meta( + const double (&vertices)[NumVertices][Dim], + const int (&faces)[NumFaces][NumFaceVertices], + double (&out)[2 * NumFaceVertices * NumFaces][3][Dim]) { + constexpr int FanSize = 2 * NumFaceVertices; + for (int i = 0; i < NumFaces; i++) { + double fan[FanSize][Dim]; + double center[Dim] = {}; + for (int k = 0; k < NumFaceVertices; k++) { + const int ia = faces[i][k]; + const int ib = faces[i][(k + 1) % NumFaceVertices]; + for (int d = 0; d < Dim; d++) { + fan[2 * k][d] = vertices[ia][d]; + fan[2 * k + 1][d] = 0.5 * (vertices[ia][d] + vertices[ib][d]); + center[d] += vertices[ia][d]; } } - if constexpr (DIM == 3) { - for (int k = 0; k < N; k++) + if constexpr (Dim == 3) { + for (int k = 0; k < FanSize; k++) normalize3(fan[k]); normalize3(center); } else { - for (int d = 0; d < DIM; d++) - center[d] /= NVF; + for (int d = 0; d < Dim; d++) + center[d] /= NumFaceVertices; } - for (int k = 0; k < N; k++) { - const double *p1 = fan[(k + 1) % N]; + for (int k = 0; k < FanSize; k++) { + const double *p1 = fan[(k + 1) % FanSize]; const double *p2 = fan[k]; - for (int d = 0; d < DIM; d++) { - out[N * i + k][0][d] = center[d]; - out[N * i + k][1][d] = p1[d]; - out[N * i + k][2][d] = p2[d]; + for (int d = 0; d < Dim; d++) { + out[FanSize * i + k][0][d] = center[d]; + out[FanSize * i + k][1][d] = p1[d]; + out[FanSize * i + k][2][d] = p2[d]; } } } diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 1a0f9b8eb8..0c8cc3b58f 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -14,28 +14,33 @@ namespace nets { namespace tsea { namespace tsea { -// Half side length S and centroid-to-base distance H of each net face. -// The net is composed of 4 equilateral triangles of side 2S; equal-area -// projection from the unit sphere (area 4π) requires -// 4 * sqrt(3) * S^2 = 4π ⇒ S = sqrt(π / sqrt(3)), H = S / sqrt(3). -constexpr double S = 1.34677368708859935e+00; // sqrt(pi / sqrt(3)) -constexpr double H = 0.77756015077810714e+00; // sqrt(pi / (3 * sqrt(3))) +// SCALE fixes the absolute size of the net so that total planar area equals +// the unit sphere's surface area (4π) — preserving PROJ's convention that +// equal-area projections with +R=1 emit unit² on the plane per unit² on the +// sphere. With each face an equilateral triangle of side 6W and altitude 6H: +// 4 * (sqrt(3)/4) * (6W)^2 = 4π ⇒ 6W = SCALE = 2 * sqrt(π / sqrt(3)). +// W and H are 1/6 of the side and altitude respectively, chosen so that the +// VERTICES table below is a clean grid of integer multiples. +constexpr double SCALE = 2.69354737417719870e+00; // 2 * sqrt(pi / sqrt(3)) +constexpr double W = SCALE / 6.0; +constexpr double H = 0.86602540378443865e+00 * SCALE / 6.0; // sqrt(3)/12 * SCALE // 6 vertices of the unfolded net. The central face has its centroid at the -// origin; the three outer faces unfold across each of its edges. -constexpr double V[6][2] = { - { -S, H}, // 0 - { 0.0, -2*H}, // 1 - { S, H}, // 2 - {-2*S, -2*H}, // 3 - { 0.0, 4*H}, // 4 - { 2*S, -2*H}, // 5 +// origin; the three outer faces unfold across each of its edges. Each face's +// centroid sits at 2H from each edge and 4H from each opposite vertex. +constexpr double VERTICES[6][2] = { + {-3 * W, 2 * H}, // 0 + { 0.0, -4 * H}, // 1 + { 3 * W, 2 * H}, // 2 + {-6 * W, -4 * H}, // 3 + { 0.0, 8 * H}, // 4 + { 6 * W, -4 * H}, // 5 }; // 4 triangular faces. The vertex ordering of each face matches the matching -// face in polyhedra::tetrahedron::F so that conway_meta produces sub-triangles -// in the same order for both the planar and spherical triangulations. -constexpr int F[4][3] = { +// face in polyhedra::tetrahedron::FACES so that conway_meta produces +// sub-triangles in the same order for both triangulations. +constexpr int FACES[4][3] = { {3, 1, 0}, {4, 0, 2}, {5, 2, 1}, diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 848ff92771..fd5d1039d5 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -20,7 +20,7 @@ namespace tetrahedron { // radius sqrt(6)/4 and are normalized to the unit sphere by conway_meta. constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 -constexpr double V[4][3] = { +constexpr double VERTICES[4][3] = { { C0, -C0, C0}, // 0 { C0, C0, -C0}, // 1 {-C0, C0, C0}, // 2 @@ -29,7 +29,7 @@ constexpr double V[4][3] = { // 4 triangular faces, each listed with outward-pointing winding. // The order here matches the order TSEA's planar net expects. -constexpr int F[4][3] = { +constexpr int FACES[4][3] = { {0, 3, 1}, {0, 1, 2}, {0, 2, 3}, From e7671e608b637734adc508d82356f18c09a1f8ed Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 16:26:20 +0200 Subject: [PATCH 12/62] consistency --- src/projections/polyhedral/nets/tsea/tsea.h | 6 +++--- src/projections/polyhedral/polyhedra/tetrahedron.h | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 0c8cc3b58f..b12011f7a9 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -41,10 +41,10 @@ constexpr double VERTICES[6][2] = { // face in polyhedra::tetrahedron::FACES so that conway_meta produces // sub-triangles in the same order for both triangulations. constexpr int FACES[4][3] = { - {3, 1, 0}, {4, 0, 2}, - {5, 2, 1}, - {0, 1, 2}, + {0, 3, 1}, + {2, 1, 5}, + {1, 2, 0}, }; } } } // namespace nets::tsea::tsea diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index fd5d1039d5..3d9bdb309e 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -30,10 +30,10 @@ constexpr double VERTICES[4][3] = { // 4 triangular faces, each listed with outward-pointing winding. // The order here matches the order TSEA's planar net expects. constexpr int FACES[4][3] = { - {0, 3, 1}, {0, 1, 2}, - {0, 2, 3}, - {1, 3, 2}, + {1, 0, 3}, + {2, 3, 0}, + {3, 2, 1}, }; } // namespace tetrahedron From 0199fd3366c389688caf03952fa07ee03edf7485 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 18:38:18 +0200 Subject: [PATCH 13/62] Tidy net --- src/projections/polyhedral/nets/tsea/tsea.h | 40 ++++++++------------- 1 file changed, 14 insertions(+), 26 deletions(-) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index b12011f7a9..6029563737 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -1,10 +1,8 @@ /****************************************************************************** * * Project: PROJ - * Purpose: Planar net for the TSEA projection — a regular tetrahedron - * unfolded into the plane. The 24 face triangles used by the - * projection are obtained at setup time by applying the Conway - * "meta" operation (see conway.h) to the 4 faces below. + * Purpose: Net for TSEA projection — a regular tetrahedron unfolded + * into the plane. * Author: Felix Palmer * ****************************************************************************/ @@ -14,32 +12,22 @@ namespace nets { namespace tsea { namespace tsea { -// SCALE fixes the absolute size of the net so that total planar area equals -// the unit sphere's surface area (4π) — preserving PROJ's convention that -// equal-area projections with +R=1 emit unit² on the plane per unit² on the -// sphere. With each face an equilateral triangle of side 6W and altitude 6H: -// 4 * (sqrt(3)/4) * (6W)^2 = 4π ⇒ 6W = SCALE = 2 * sqrt(π / sqrt(3)). -// W and H are 1/6 of the side and altitude respectively, chosen so that the -// VERTICES table below is a clean grid of integer multiples. -constexpr double SCALE = 2.69354737417719870e+00; // 2 * sqrt(pi / sqrt(3)) -constexpr double W = SCALE / 6.0; -constexpr double H = 0.86602540378443865e+00 * SCALE / 6.0; // sqrt(3)/12 * SCALE +// SCALE factor to normalize net area to unit sphere surface area (4π). +constexpr double SCALE = 0.448924562362866; // sqrt(π / sqrt(3)) / 3 +constexpr double W = SCALE; +constexpr double H = 0.86602540378443865e+00 * W; // cos(30) -// 6 vertices of the unfolded net. The central face has its centroid at the -// origin; the three outer faces unfold across each of its edges. Each face's -// centroid sits at 2H from each edge and 4H from each opposite vertex. +// 6 vertices of the unfolded net, centered on origin. constexpr double VERTICES[6][2] = { - {-3 * W, 2 * H}, // 0 - { 0.0, -4 * H}, // 1 - { 3 * W, 2 * H}, // 2 - {-6 * W, -4 * H}, // 3 - { 0.0, 8 * H}, // 4 - { 6 * W, -4 * H}, // 5 + {-3 * W, 2 * H}, + { 0.0, -4 * H}, + { 3 * W, 2 * H}, + {-6 * W, -4 * H}, + { 0.0, 8 * H}, + { 6 * W, -4 * H}, }; -// 4 triangular faces. The vertex ordering of each face matches the matching -// face in polyhedra::tetrahedron::FACES so that conway_meta produces -// sub-triangles in the same order for both triangulations. +// 4 triangular faces, referencing above vertices constexpr int FACES[4][3] = { {4, 0, 2}, {0, 3, 1}, From 714e12534bc2d02bb64ec9fdd4d903e16a8ae9e2 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 19:10:48 +0200 Subject: [PATCH 14/62] Tidy --- .../polyhedral/polyhedra/tetrahedron.h | 18 +++++------------- 1 file changed, 5 insertions(+), 13 deletions(-) diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 3d9bdb309e..712e586060 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -2,9 +2,6 @@ * * Project: PROJ * Purpose: Regular tetrahedron inscribed in the unit sphere. - * Seed polyhedron for TSEA — the 24 spherical triangles used by - * the projection are obtained at setup time by applying the Conway - * "meta" operation (see conway.h) to the 4 faces below. * Author: Felix Palmer * ****************************************************************************/ @@ -15,20 +12,15 @@ namespace polyhedra { namespace tetrahedron { -// 4 vertices in the symmetric Cartesian form (C0 = sqrt(2)/4). The -// tetrahedron is centered at the origin; vertices lie on a sphere of -// radius sqrt(6)/4 and are normalized to the unit sphere by conway_meta. +// Following definition from https://dmccooey.com/polyhedra/Tetrahedron.txt constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 constexpr double VERTICES[4][3] = { - { C0, -C0, C0}, // 0 - { C0, C0, -C0}, // 1 - {-C0, C0, C0}, // 2 - {-C0, -C0, -C0}, // 3 + { C0, -C0, C0}, + { C0, C0, -C0}, + {-C0, C0, C0}, + {-C0, -C0, -C0}, }; - -// 4 triangular faces, each listed with outward-pointing winding. -// The order here matches the order TSEA's planar net expects. constexpr int FACES[4][3] = { {0, 1, 2}, {1, 0, 3}, From ecb8f24c67d174534a862710da16eb34b8a97d9b Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 19:20:57 +0200 Subject: [PATCH 15/62] Run linter --- src/projections/polyhedral.cpp | 7 +++---- src/projections/polyhedral/conway.h | 7 +++---- src/projections/polyhedral/nets/tsea/tsea.h | 16 ++++++++-------- .../polyhedral/polyhedra/tetrahedron.h | 6 +++--- 4 files changed, 17 insertions(+), 19 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 024ee7b9aa..5eeca11925 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -110,12 +110,11 @@ PJ *PJ_PROJECTION(tsea) { double spherical_triangles[24][3][3]; polyhedral::conway_meta(polyhedra::tetrahedron::VERTICES, - polyhedra::tetrahedron::FACES, - spherical_triangles); + polyhedra::tetrahedron::FACES, spherical_triangles); double face_triangles[24][3][2]; - polyhedral::conway_meta(nets::tsea::tsea::VERTICES, - nets::tsea::tsea::FACES, face_triangles); + polyhedral::conway_meta(nets::tsea::tsea::VERTICES, nets::tsea::tsea::FACES, + face_triangles); polyhedral::load_triangles(Q, spherical_triangles, face_triangles); diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h index 6d1e6dd7ca..9c8a77449b 100644 --- a/src/projections/polyhedral/conway.h +++ b/src/projections/polyhedral/conway.h @@ -44,10 +44,9 @@ inline void normalize3(double v[3]) { // Output buffer is sized 2 * NFV * NumFaces triangles. Templated on every // array dimension so they stay self-describing at the call site. template -inline void conway_meta( - const double (&vertices)[NumVertices][Dim], - const int (&faces)[NumFaces][NumFaceVertices], - double (&out)[2 * NumFaceVertices * NumFaces][3][Dim]) { +inline void conway_meta(const double (&vertices)[NumVertices][Dim], + const int (&faces)[NumFaces][NumFaceVertices], + double (&out)[2 * NumFaceVertices * NumFaces][3][Dim]) { constexpr int FanSize = 2 * NumFaceVertices; for (int i = 0; i < NumFaces; i++) { double fan[FanSize][Dim]; diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 6029563737..fbf7f982f1 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -10,7 +10,9 @@ #ifndef NETS_TSEA_TSEA_H #define NETS_TSEA_TSEA_H -namespace nets { namespace tsea { namespace tsea { +namespace nets { +namespace tsea { +namespace tsea { // SCALE factor to normalize net area to unit sphere surface area (4π). constexpr double SCALE = 0.448924562362866; // sqrt(π / sqrt(3)) / 3 @@ -19,12 +21,8 @@ constexpr double H = 0.86602540378443865e+00 * W; // cos(30) // 6 vertices of the unfolded net, centered on origin. constexpr double VERTICES[6][2] = { - {-3 * W, 2 * H}, - { 0.0, -4 * H}, - { 3 * W, 2 * H}, - {-6 * W, -4 * H}, - { 0.0, 8 * H}, - { 6 * W, -4 * H}, + {-3 * W, 2 * H}, {0.0, -4 * H}, {3 * W, 2 * H}, + {-6 * W, -4 * H}, {0.0, 8 * H}, {6 * W, -4 * H}, }; // 4 triangular faces, referencing above vertices @@ -35,6 +33,8 @@ constexpr int FACES[4][3] = { {1, 2, 0}, }; -} } } // namespace nets::tsea::tsea +} // namespace tsea +} // namespace tsea +} // namespace nets #endif // NETS_TSEA_TSEA_H diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 712e586060..6b3a8ae04b 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -16,9 +16,9 @@ namespace tetrahedron { constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 constexpr double VERTICES[4][3] = { - { C0, -C0, C0}, - { C0, C0, -C0}, - {-C0, C0, C0}, + {C0, -C0, C0}, + {C0, C0, -C0}, + {-C0, C0, C0}, {-C0, -C0, -C0}, }; constexpr int FACES[4][3] = { From 19165c1fededfee75858ef104ee04a4cd3a24d49 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 21:16:32 +0200 Subject: [PATCH 16/62] Tidy up conway code --- src/projections/polyhedral.cpp | 15 ++-- src/projections/polyhedral/conway.h | 78 ++++++------------- src/projections/polyhedral/nets/tsea/tsea.h | 12 +-- .../polyhedral/polyhedra/tetrahedron.h | 4 +- src/projections/polyhedral/sphere.h | 18 ++--- 5 files changed, 48 insertions(+), 79 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 5eeca11925..41e64df7d5 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -108,13 +108,14 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - double spherical_triangles[24][3][3]; - polyhedral::conway_meta(polyhedra::tetrahedron::VERTICES, - polyhedra::tetrahedron::FACES, spherical_triangles); - - double face_triangles[24][3][2]; - polyhedral::conway_meta(nets::tsea::tsea::VERTICES, nets::tsea::tsea::FACES, - face_triangles); + polyhedral::Vec3 spherical_triangles[24][3]; + polyhedral::conway_meta( + polyhedra::tetrahedron::VERTICES, polyhedra::tetrahedron::FACES, + spherical_triangles); + + polyhedral::Vec3 face_triangles[24][3]; + polyhedral::conway_meta( + nets::tsea::tsea::VERTICES, nets::tsea::tsea::FACES, face_triangles); polyhedral::load_triangles(Q, spherical_triangles, face_triangles); diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h index 9c8a77449b..21df8e1dae 100644 --- a/src/projections/polyhedral/conway.h +++ b/src/projections/polyhedral/conway.h @@ -1,11 +1,7 @@ /****************************************************************************** * * Project: PROJ - * Purpose: Conway polyhedron operations. - * Provides the "meta" (a.k.a. bevel) operation generalised to - * polyhedra with NVF-gon faces, in either 2D (planar net) or - * 3D (vertices projected onto the unit sphere). - * See https://en.wikipedia.org/wiki/Conway_polyhedron_notation + * Purpose: Conway meta polyhedron operation * Author: Felix Palmer * ****************************************************************************/ @@ -13,71 +9,43 @@ #ifndef POLYHEDRAL_CONWAY_H #define POLYHEDRAL_CONWAY_H -#include +#include "vec3.h" namespace polyhedral { -// Project a 3-vector onto the unit sphere in place. -inline void normalize3(double v[3]) { - const double n = std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); - v[0] /= n; - v[1] /= n; - v[2] /= n; -} +// ConwayMode: +// - Sphere: project centroid + fan vertices onto unit sphere (for polyhedra) +// - Plane: scale centroid to the arithmetic mean (for nets) +enum class ConwayMode { Sphere, Plane }; -// Apply the Conway "meta" operation to a polyhedron whose faces all have -// NumFaceVertices (NFV) vertices. Each face yields 2*NFV triangles fanning -// out from the face centroid. For a face (v_0, ..., v_{NFV-1}) the 2*NFV -// fan vertices are -// -// v_0, mid(v_0,v_1), v_1, mid(v_1,v_2), ..., v_{NFV-1}, mid(v_{NFV-1},v_0) -// -// and the emitted triangles are (centroid, fan[k+1], fan[k]) for k in -// [0, 2*NFV). This preserves the outward winding of the input face, so -// containment tests on the resulting triangulation behave consistently. -// -// Dim == 3: vertices are projected onto the unit sphere (so callers can -// supply unnormalized symmetric Cartesian coordinates, e.g. McCooey-style). -// Dim == 2: planar input — the centroid is the unweighted average of the -// face vertices and no normalization is applied. -// -// Output buffer is sized 2 * NFV * NumFaces triangles. Templated on every -// array dimension so they stay self-describing at the call site. -template -inline void conway_meta(const double (&vertices)[NumVertices][Dim], +template +inline void conway_meta(const Vec3 (&vertices)[NumVertices], const int (&faces)[NumFaces][NumFaceVertices], - double (&out)[2 * NumFaceVertices * NumFaces][3][Dim]) { + Vec3 (&out)[2 * NumFaceVertices * NumFaces][3]) { constexpr int FanSize = 2 * NumFaceVertices; for (int i = 0; i < NumFaces; i++) { - double fan[FanSize][Dim]; - double center[Dim] = {}; + Vec3 fan[FanSize]; + Vec3 center{0.0, 0.0, 0.0}; for (int k = 0; k < NumFaceVertices; k++) { - const int ia = faces[i][k]; - const int ib = faces[i][(k + 1) % NumFaceVertices]; - for (int d = 0; d < Dim; d++) { - fan[2 * k][d] = vertices[ia][d]; - fan[2 * k + 1][d] = 0.5 * (vertices[ia][d] + vertices[ib][d]); - center[d] += vertices[ia][d]; - } + const Vec3 va = vertices[faces[i][k]]; + const Vec3 vb = vertices[faces[i][(k + 1) % NumFaceVertices]]; + fan[2 * k] = va; + fan[2 * k + 1] = vec3_lerp(va, vb, 0.5); + center = vec3_add(center, va); } - if constexpr (Dim == 3) { + if constexpr (Mode == ConwayMode::Sphere) { for (int k = 0; k < FanSize; k++) - normalize3(fan[k]); - normalize3(center); + fan[k] = vec3_normalize(fan[k]); + center = vec3_normalize(center); } else { - for (int d = 0; d < Dim; d++) - center[d] /= NumFaceVertices; + center = vec3_scale(center, 1.0 / NumFaceVertices); } for (int k = 0; k < FanSize; k++) { - const double *p1 = fan[(k + 1) % FanSize]; - const double *p2 = fan[k]; - for (int d = 0; d < Dim; d++) { - out[FanSize * i + k][0][d] = center[d]; - out[FanSize * i + k][1][d] = p1[d]; - out[FanSize * i + k][2][d] = p2[d]; - } + out[FanSize * i + k][0] = center; + out[FanSize * i + k][1] = fan[(k + 1) % FanSize]; + out[FanSize * i + k][2] = fan[k]; } } } diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index fbf7f982f1..2565a89818 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -10,19 +10,21 @@ #ifndef NETS_TSEA_TSEA_H #define NETS_TSEA_TSEA_H +#include "../../vec3.h" + namespace nets { namespace tsea { namespace tsea { -// SCALE factor to normalize net area to unit sphere surface area (4π). +// SCALE factor to normalize net area to unit sphere surface area (4π) constexpr double SCALE = 0.448924562362866; // sqrt(π / sqrt(3)) / 3 constexpr double W = SCALE; constexpr double H = 0.86602540378443865e+00 * W; // cos(30) -// 6 vertices of the unfolded net, centered on origin. -constexpr double VERTICES[6][2] = { - {-3 * W, 2 * H}, {0.0, -4 * H}, {3 * W, 2 * H}, - {-6 * W, -4 * H}, {0.0, 8 * H}, {6 * W, -4 * H}, +// 6 vertices of the unfolded net, centered on origin +constexpr polyhedral::Vec3 VERTICES[6] = { + {-3 * W, 2 * H, 0.0}, {0.0, -4 * H, 0.0}, {3 * W, 2 * H, 0.0}, + {-6 * W, -4 * H, 0.0}, {0.0, 8 * H, 0.0}, {6 * W, -4 * H, 0.0}, }; // 4 triangular faces, referencing above vertices diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 6b3a8ae04b..90bf53c924 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -9,13 +9,15 @@ #ifndef POLYHEDRA_TETRAHEDRON_H #define POLYHEDRA_TETRAHEDRON_H +#include "../vec3.h" + namespace polyhedra { namespace tetrahedron { // Following definition from https://dmccooey.com/polyhedra/Tetrahedron.txt constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 -constexpr double VERTICES[4][3] = { +constexpr polyhedral::Vec3 VERTICES[4] = { {C0, -C0, C0}, {C0, C0, -C0}, {-C0, C0, C0}, diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 0338ca36e0..170336e2f8 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -36,21 +36,17 @@ struct pj_polyhedral_data { double qp; }; -// Load triangle data from generated header arrays. +// Load triangle data from conway_meta output template -inline void load_triangles(pj_polyhedral_data *Q, const double (&sph)[N][3][3], - const double (&face)[N][3][2]) { +inline void load_triangles(pj_polyhedral_data *Q, const Vec3 (&sph)[N][3], + const Vec3 (&face)[N][3]) { Q->n_triangles = N; for (int i = 0; i < N; i++) { - Q->sph_tris[i] = { - {sph[i][0][0], sph[i][0][1], sph[i][0][2]}, - {sph[i][1][0], sph[i][1][1], sph[i][1][2]}, - {sph[i][2][0], sph[i][2][1], sph[i][2][2]}, - }; + Q->sph_tris[i] = {sph[i][0], sph[i][1], sph[i][2]}; Q->face_tris[i] = { - {face[i][0][0], face[i][0][1]}, - {face[i][1][0], face[i][1][1]}, - {face[i][2][0], face[i][2][1]}, + {face[i][0].x, face[i][0].y}, + {face[i][1].x, face[i][1].y}, + {face[i][2].x, face[i][2].y}, }; } } From b6a1fff09d7f8c7939c4fd88de265f2749a3546c Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 21:35:19 +0200 Subject: [PATCH 17/62] Tidy --- src/projections/polyhedral.cpp | 12 +------- src/projections/polyhedral/conway.h | 8 +++++ src/projections/polyhedral/nets/tsea/tsea.h | 29 +++++++++--------- .../polyhedral/polyhedra/tetrahedron.h | 30 ++++++++++--------- src/projections/polyhedral/sphere.h | 17 ++++++++--- 5 files changed, 52 insertions(+), 44 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 41e64df7d5..2ff3c86273 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -108,17 +108,7 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::Vec3 spherical_triangles[24][3]; - polyhedral::conway_meta( - polyhedra::tetrahedron::VERTICES, polyhedra::tetrahedron::FACES, - spherical_triangles); - - polyhedral::Vec3 face_triangles[24][3]; - polyhedral::conway_meta( - nets::tsea::tsea::VERTICES, nets::tsea::tsea::FACES, face_triangles); - - polyhedral::load_triangles(Q, spherical_triangles, face_triangles); - + polyhedral::load_meshes(Q, polyhedra::tetrahedron, nets::tsea::tsea); const double apex_lat_deg = std::asin(1.0 / std::sqrt(3.0)) * RAD_TO_DEG; polyhedral::set_orient_from_angles(Q, apex_lat_deg, 120.0, 135.0); diff --git a/src/projections/polyhedral/conway.h b/src/projections/polyhedral/conway.h index 21df8e1dae..7b941e4537 100644 --- a/src/projections/polyhedral/conway.h +++ b/src/projections/polyhedral/conway.h @@ -13,6 +13,14 @@ namespace polyhedral { +// Mesh struct, both for representing polyhedra & flat nets +template struct Mesh { + // List of vertices as 3D vectors + Vec3 vertices[NumVertices]; + // Faces, indexing above vertices + int faces[NumFaces][NumFaceVertices]; +}; + // ConwayMode: // - Sphere: project centroid + fan vertices onto unit sphere (for polyhedra) // - Plane: scale centroid to the arithmetic mean (for nets) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 2565a89818..6c91841345 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -10,32 +10,31 @@ #ifndef NETS_TSEA_TSEA_H #define NETS_TSEA_TSEA_H -#include "../../vec3.h" +#include "../../conway.h" namespace nets { namespace tsea { -namespace tsea { // SCALE factor to normalize net area to unit sphere surface area (4π) constexpr double SCALE = 0.448924562362866; // sqrt(π / sqrt(3)) / 3 constexpr double W = SCALE; constexpr double H = 0.86602540378443865e+00 * W; // cos(30) -// 6 vertices of the unfolded net, centered on origin -constexpr polyhedral::Vec3 VERTICES[6] = { - {-3 * W, 2 * H, 0.0}, {0.0, -4 * H, 0.0}, {3 * W, 2 * H, 0.0}, - {-6 * W, -4 * H, 0.0}, {0.0, 8 * H, 0.0}, {6 * W, -4 * H, 0.0}, -}; - -// 4 triangular faces, referencing above vertices -constexpr int FACES[4][3] = { - {4, 0, 2}, - {0, 3, 1}, - {2, 1, 5}, - {1, 2, 0}, +constexpr polyhedral::Mesh<6, 4, 3> tsea = { + // Vertices + { + {-3 * W, 2 * H, 0.0}, {0.0, -4 * H, 0.0}, {3 * W, 2 * H, 0.0}, + {-6 * W, -4 * H, 0.0}, {0.0, 8 * H, 0.0}, {6 * W, -4 * H, 0.0}, + }, + // Faces + { + {4, 0, 2}, + {0, 3, 1}, + {2, 1, 5}, + {1, 2, 0}, + }, }; -} // namespace tsea } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 90bf53c924..b16628e219 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -9,28 +9,30 @@ #ifndef POLYHEDRA_TETRAHEDRON_H #define POLYHEDRA_TETRAHEDRON_H -#include "../vec3.h" +#include "../conway.h" namespace polyhedra { -namespace tetrahedron { // Following definition from https://dmccooey.com/polyhedra/Tetrahedron.txt constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 -constexpr polyhedral::Vec3 VERTICES[4] = { - {C0, -C0, C0}, - {C0, C0, -C0}, - {-C0, C0, C0}, - {-C0, -C0, -C0}, -}; -constexpr int FACES[4][3] = { - {0, 1, 2}, - {1, 0, 3}, - {2, 3, 0}, - {3, 2, 1}, +constexpr polyhedral::Mesh<4, 4, 3> tetrahedron = { + // Vertices + { + {C0, -C0, C0}, + {C0, C0, -C0}, + {-C0, C0, C0}, + {-C0, -C0, -C0}, + }, + // Faces + { + {0, 1, 2}, + {1, 0, 3}, + {2, 3, 0}, + {3, 2, 1}, + }, }; -} // namespace tetrahedron } // namespace polyhedra #endif // POLYHEDRA_TETRAHEDRON_H diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 170336e2f8..0c7bd72be8 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -10,6 +10,7 @@ #ifndef POLYHEDRAL_SPHERE_H #define POLYHEDRAL_SPHERE_H +#include "conway.h" #include "snyder.h" #include "proj.h" @@ -36,10 +37,18 @@ struct pj_polyhedral_data { double qp; }; -// Load triangle data from conway_meta output -template -inline void load_triangles(pj_polyhedral_data *Q, const Vec3 (&sph)[N][3], - const Vec3 (&face)[N][3]) { +// Build triangle data from a polyhedron + matching net. +// The `meta` Conway operation is used to cut up the faces +template +inline void load_meshes(pj_polyhedral_data *Q, + const Mesh &polyhedron, + const Mesh &net) { + constexpr int N = 2 * NFV * NF; + Vec3 sph[N][3]; + Vec3 face[N][3]; + conway_meta(polyhedron.vertices, polyhedron.faces, sph); + conway_meta(net.vertices, net.faces, face); + Q->n_triangles = N; for (int i = 0; i < N; i++) { Q->sph_tris[i] = {sph[i][0], sph[i][1], sph[i][2]}; From 05ebb5878a3d95d4f4e899981b6d00a6efcfa0bb Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 4 May 2026 21:36:14 +0200 Subject: [PATCH 18/62] format --- src/projections/polyhedral/nets/tsea/tsea.h | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 6c91841345..7776c743bc 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -23,8 +23,12 @@ constexpr double H = 0.86602540378443865e+00 * W; // cos(30) constexpr polyhedral::Mesh<6, 4, 3> tsea = { // Vertices { - {-3 * W, 2 * H, 0.0}, {0.0, -4 * H, 0.0}, {3 * W, 2 * H, 0.0}, - {-6 * W, -4 * H, 0.0}, {0.0, 8 * H, 0.0}, {6 * W, -4 * H, 0.0}, + {-3 * W, 2 * H, 0.0}, + {0.0, -4 * H, 0.0}, + {3 * W, 2 * H, 0.0}, + {-6 * W, -4 * H, 0.0}, + {0.0, 8 * H, 0.0}, + {6 * W, -4 * H, 0.0}, }, // Faces { From 73997b88ed9f15b0def13af7927d8d320c4f7b13 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Thu, 7 May 2026 08:35:33 +0200 Subject: [PATCH 19/62] Add proj options. Implement DSEA, ISEA & net unfolding --- ..._flower.png => polyhedral_dsea_flower.png} | Bin .../operations/projections/polyhedral.rst | 64 ++++++- src/pj_list.h | 2 + src/projections/polyhedral.cpp | 104 +++++++++-- src/projections/polyhedral/nets/dsea/dsea.h | 33 ++++ src/projections/polyhedral/nets/isea/isea.h | 40 ++++ src/projections/polyhedral/nets/tsea/tsea.h | 31 +-- .../polyhedral/polyhedra/dodecahedron.h | 86 +++++++++ .../polyhedral/polyhedra/icosahedron.h | 86 +++++++++ .../polyhedral/polyhedra/tetrahedron.h | 30 ++- .../polyhedral/polyhedra/validation.h | 68 +++++++ src/projections/polyhedral/sphere.h | 61 ++++++ src/projections/polyhedral/unfold.h | 176 ++++++++++++++++++ src/projections/polyhedral/vec3.h | 18 +- test/gie/builtins.gie | 168 +++++++++++++++++ test/unit/test_polyhedral.cpp | 79 +++++++- 16 files changed, 978 insertions(+), 68 deletions(-) rename docs/source/operations/projections/images/{polyhedral_dsea_two_flower.png => polyhedral_dsea_flower.png} (100%) create mode 100644 src/projections/polyhedral/nets/dsea/dsea.h create mode 100644 src/projections/polyhedral/nets/isea/isea.h create mode 100644 src/projections/polyhedral/polyhedra/dodecahedron.h create mode 100644 src/projections/polyhedral/polyhedra/icosahedron.h create mode 100644 src/projections/polyhedral/polyhedra/validation.h create mode 100644 src/projections/polyhedral/unfold.h diff --git a/docs/source/operations/projections/images/polyhedral_dsea_two_flower.png b/docs/source/operations/projections/images/polyhedral_dsea_flower.png similarity index 100% rename from docs/source/operations/projections/images/polyhedral_dsea_two_flower.png rename to docs/source/operations/projections/images/polyhedral_dsea_flower.png diff --git a/docs/source/operations/projections/polyhedral.rst b/docs/source/operations/projections/polyhedral.rst index 8faa72e0d9..8f6fe1ac5c 100644 --- a/docs/source/operations/projections/polyhedral.rst +++ b/docs/source/operations/projections/polyhedral.rst @@ -94,6 +94,57 @@ When choosing projection, a set of nets is made available to the user by name. The nets are tied to the projection, as the order of the triangles are important. The net parameter can be omitted to use the default net. +Parameters +******************************************************************************** + +.. note:: + All parameters are optional. Each polyhedral projection ships with a + default orientation that places its vertices in symmetric, well-known + positions; the parameters below override that default. + +.. option:: +orient_lat= + + Geodetic latitude of the polyhedron's first vertex, in degrees. + + *Default depends on the projection.* + +.. option:: +orient_lon= + + Longitude of the polyhedron's first vertex, in degrees. + + *Default depends on the projection.* + +.. option:: +azi= + + Azimuth from the first vertex to the second, in degrees. Together with + ``+orient_lat`` and ``+orient_lon`` this fully constrains the 3D pose of + the polyhedron on the sphere. + + *Default depends on the projection.* + +.. option:: +net= + + Selects the planar unfolding (net). Only applies to ``+proj=dsea``. + Accepted values: ``dsea`` (default), ``a5``, ``crescent``, ``flower``. + +.. include:: ../options/lat_0.rst + +For polyhedral projections, ``+lat_0`` / ``+lon_0`` specify the geographic +point that should land at the projected origin ``(0, 0)``. They translate +the projected output without rotating the polyhedron — the triangle edges +stay where ``+orient_*`` placed them. ``+x_0`` / ``+y_0`` are applied on top +of this translation. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + Examples: .. figure:: ./images/polyhedral_tsea.png @@ -110,16 +161,9 @@ Examples: proj-string: ``+proj=isea2`` -.. figure:: ./images/polyhedral_dsea_two_flower.png - :width: 500 px - :align: center - :alt: DSEA Two Flower - - proj-string: ``+proj=dsea +net=two_flower`` - -.. figure:: ./images/polyhedral_dsea_icosahedron.png +.. figure:: ./images/polyhedral_dsea_flower.png :width: 500 px :align: center - :alt: DSEA Icosahedron + :alt: DSEA Flower - proj-string: ``+proj=dsea +net=icosahedron`` + proj-string: ``+proj=dsea +net=flower`` diff --git a/src/pj_list.h b/src/pj_list.h index 893359b4be..2f247f3b72 100644 --- a/src/pj_list.h +++ b/src/pj_list.h @@ -37,6 +37,7 @@ PROJ_HEAD(crast, "Craster Parabolic (Putnins P4)") PROJ_HEAD(defmodel, "Deformation model") PROJ_HEAD(deformation, "Kinematic grid shift") PROJ_HEAD(denoy, "Denoyer Semi-Elliptical") +PROJ_HEAD(dsea, "Dodecahedral Snyder Equal Area") PROJ_HEAD(airocean, "Airocean Fuller") PROJ_HEAD(eck1, "Eckert I") PROJ_HEAD(eck2, "Eckert II") @@ -78,6 +79,7 @@ PROJ_HEAD(imoll, "Interrupted Mollweide") PROJ_HEAD(imoll_o, "Interrupted Mollweide Oceanic View") PROJ_HEAD(imw_p, "International Map of the World Polyconic") PROJ_HEAD(isea, "Icosahedral Snyder Equal Area") +PROJ_HEAD(isea2, "Icosahedral Snyder Equal Area (generalized)") PROJ_HEAD(kav5, "Kavrayskiy V") PROJ_HEAD(kav7, "Kavrayskiy VII") PROJ_HEAD(krovak, "Krovak") diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 2ff3c86273..1390c2a639 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -23,15 +23,21 @@ ****************************************************************************/ #include "polyhedral/conway.h" +#include "polyhedral/nets/dsea/dsea.h" +#include "polyhedral/nets/isea/isea.h" #include "polyhedral/nets/tsea/tsea.h" +#include "polyhedral/polyhedra/dodecahedron.h" +#include "polyhedral/polyhedra/icosahedron.h" #include "polyhedral/polyhedra/tetrahedron.h" #include "polyhedral/sphere.h" +#include "polyhedral/unfold.h" #include "proj.h" #include "proj_internal.h" #include #include +#include using polyhedral::pj_polyhedral_data; @@ -51,8 +57,8 @@ static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { polyhedral::Face2D result = polyhedral::snyder_fwd(v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); - xy.x = result.x; - xy.y = result.y; + xy.x = result.x - Q->x_offset; + xy.y = result.y - Q->y_offset; return xy; } @@ -62,12 +68,15 @@ static PJ_LP polyhedral_inv(PJ_XY xy, PJ *P) { PJ_LP lp = {0.0, 0.0}; auto *Q = static_cast(P->opaque); + const double x = xy.x + Q->x_offset; + const double y = xy.y + Q->y_offset; + for (int i = 0; i < Q->n_triangles; i++) { polyhedral::Barycentric bary = - polyhedral::face_to_barycentric({xy.x, xy.y}, Q->face_tris[i]); + polyhedral::face_to_barycentric({x, y}, Q->face_tris[i]); if (bary.u >= -1e-10 && bary.v >= -1e-10 && bary.w >= -1e-10) { - polyhedral::Vec3 v = polyhedral::snyder_inv( - {xy.x, xy.y}, Q->face_tris[i], Q->sph_tris[i]); + polyhedral::Vec3 v = + polyhedral::snyder_inv({x, y}, Q->face_tris[i], Q->sph_tris[i]); polyhedral::cart_to_lonlat(Q, P, v, lp.lam, lp.phi); return lp; } @@ -86,7 +95,7 @@ static PJ *polyhedral_destructor(PJ *P, int errlev) { return pj_default_destructor(P, errlev); } -static PJ *polyhedral_setup(PJ *P) { +static PJ *polyhedral_setup(PJ *P, const polyhedral::PolyhedralDefaults &d) { auto *Q = static_cast(P->opaque); if (P->es != 0.0) { Q->apa = pj_authalic_lat_compute_coeffs(P->n); @@ -94,12 +103,15 @@ static PJ *polyhedral_setup(PJ *P) { return polyhedral_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); Q->qp = pj_authalic_lat_q(1.0, P); } + if (!polyhedral::apply_polyhedral_params(Q, P, d)) + return polyhedral_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); P->fwd = polyhedral_fwd; P->inv = polyhedral_inv; return P; } -PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") "\n\tSph&Ell"; +PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") +"\n\tSph&Ell\n\torient_lat= orient_lon= azi= lat_0= lon_0="; PJ *PJ_PROJECTION(tsea) { auto *Q = static_cast( calloc(1, sizeof(pj_polyhedral_data))); @@ -108,9 +120,79 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::load_meshes(Q, polyhedra::tetrahedron, nets::tsea::tsea); - const double apex_lat_deg = std::asin(1.0 / std::sqrt(3.0)) * RAD_TO_DEG; - polyhedral::set_orient_from_angles(Q, apex_lat_deg, 120.0, 135.0); + const auto net = polyhedral::unfold_net(polyhedra::tetrahedron, nets::tsea::tsea); + polyhedral::load_meshes(Q, polyhedra::tetrahedron, net); + const polyhedral::PolyhedralDefaults d = {90.0, 0.0, 0.0}; + return polyhedral_setup(P, d); +} + +PROJ_HEAD(dsea, "Dodecahedral Snyder Equal Area") +"\n\tSph&Ell\n\tnet= orient_lat= orient_lon= azi= lat_0= lon_0="; +PJ *PJ_PROJECTION(dsea) { + auto *Q = static_cast( + calloc(1, sizeof(pj_polyhedral_data))); + if (nullptr == Q) + return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); + P->opaque = Q; + P->destructor = polyhedral_destructor; + + // +net= selects the unfolding tree. The `a5` net additionally shifts + // orient_lon by -93° to match the LONGITUDE_OFFSET=93° rotation used by + // the A5 reference codebase; F0's centroid still sits at the geographic + // pole, so orient_lat and azi are unchanged. + const char *net_name = pj_param(P->ctx, P->params, "snet").s; + const int(*parents)[12] = &nets::dsea::dsea; + double default_orient_lon = -36.0; + double default_azi = 240.0; + if (net_name != nullptr) { + if (strcmp(net_name, "dsea") == 0) { + parents = &nets::dsea::dsea; + } else if (strcmp(net_name, "a5") == 0) { + parents = &nets::dsea::a5; + default_orient_lon = -36.0 - 93.0; + } else if (strcmp(net_name, "crescent") == 0) { + parents = &nets::dsea::crescent; + } else if (strcmp(net_name, "flower") == 0) { + parents = &nets::dsea::flower; + } else { + proj_log_error(P, _("invalid +net (expected dsea, a5, crescent, " + "or flower)")); + return polyhedral_destructor( + P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); + } + } + + const auto net = polyhedral::unfold_net(polyhedra::dodecahedron, *parents); + polyhedral::load_meshes(Q, polyhedra::dodecahedron, net); + // The dodecahedron data has V0 on +z and V1 on the +x meridian, so + // orient_lat / orient_lon directly specify V0's geographic position + // and +azi is the bearing from V0 toward V1. The defaults below + // (orient_lat ≈ atan((3+√5)/4), orient_lon = -36°, azi varying per net) + // rotate the polyhedron so F0's centroid sits at the geographic north + // pole, with the V0-V1 edge midpoint on the prime meridian. + using polyhedra::dodecahedron_constants::A; + const double default_orient_lat = + std::atan((1 + 2 * A) / 2.0) * 180.0 / M_PI; + const polyhedral::PolyhedralDefaults d = {default_orient_lat, + default_orient_lon, default_azi}; + return polyhedral_setup(P, d); +} + +PROJ_HEAD(isea2, "Icosahedral Snyder Equal Area (generalized)") +"\n\tSph&Ell\n\torient_lat= orient_lon= azi= lat_0= lon_0="; +PJ *PJ_PROJECTION(isea2) { + auto *Q = static_cast( + calloc(1, sizeof(pj_polyhedral_data))); + if (nullptr == Q) + return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/); + P->opaque = Q; + P->destructor = polyhedral_destructor; - return polyhedral_setup(P); + const auto net = + polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); + polyhedral::load_meshes(Q, polyhedra::icosahedron, net); + // Standard Snyder ISEA orientation: V0 (the icosahedron's north-pole + // seed vertex) sits at lat ≈ 58.28°N, lon = 11.25°E. + const polyhedral::PolyhedralDefaults d = {58.282525588539, 11.25, 0.0}; + return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h new file mode 100644 index 0000000000..033e80e7e1 --- /dev/null +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -0,0 +1,33 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Net layouts for the DSEA projection. Each constant is a parents + * tree over the 12 faces of the dodecahedron: parents[i] is face + * i's parent in the unfolding tree, or -1 if i is the root. Every + * parent–child pair must share an edge on the dodecahedron. + * + * The dodecahedron face order in `polyhedra::dodecahedron` is + * chosen so the canonical DSEA net is a simple chain — F0 is the + * cap around V0, F1..F10 zig-zag around the middle band, F11 is + * the cap around V17 — so dsea[i] = i - 1. The other layouts + * (a5, crescent, flower) are valid parents trees over the + * same face indices. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef NETS_DSEA_DSEA_H +#define NETS_DSEA_DSEA_H + +namespace nets { +namespace dsea { + +constexpr int dsea[12] = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; +constexpr int a5[12] = {-1, 0, 1, 4, 2, 3, 8, 5, 7, 10, 11, 6}; +constexpr int crescent[12] = {-1, 3, 4, 0, 3, 3, 4, 5, 6, 1, 2, 4}; +constexpr int flower[12] = {-1, 0, 11, 0, 11, 0, 11, 0, 11, 0, 9, 10}; + +} // namespace dsea +} // namespace nets + +#endif // NETS_DSEA_DSEA_H diff --git a/src/projections/polyhedral/nets/isea/isea.h b/src/projections/polyhedral/nets/isea/isea.h new file mode 100644 index 0000000000..5e60ab92c0 --- /dev/null +++ b/src/projections/polyhedral/nets/isea/isea.h @@ -0,0 +1,40 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Net layout for the ISEA projection — the regular icosahedron + * unfolded into the canonical Snyder 4×5 strip. + * + * The icosahedron face order in `polyhedra::icosahedron` is + * grouped into 4 rows of 5: + * F0..F4 north cap (around V0) + * F5..F9 upper band (down-pointing on the sphere) + * F10..F14 lower band (up-pointing on the sphere) + * F15..F19 south cap (around V11) + * + * The unfold tree zig-zags through the upper and lower bands, + * + * F0 → F5 → F10 → F6 → F11 → F7 → F12 → F8 → F13 → F9 → F14 + * + * and hangs each remaining north-cap face off its upper-band + * neighbour and each south-cap face off its lower-band neighbour. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef NETS_ISEA_ISEA_H +#define NETS_ISEA_ISEA_H + +namespace nets { +namespace isea { + +constexpr int isea[20] = { + -1, 6, 7, 8, 9, // F0 root; F1..F4 north cap, hung off upper band + 0, 10, 11, 12, 13, // F5 child of F0; F6..F9 chained via lower band + 5, 6, 7, 8, 9, // F10 child of F5; F11..F14 chained via upper band + 10, 11, 12, 13, 14, // F15..F19 south cap, hung off lower band +}; + +} // namespace isea +} // namespace nets + +#endif // NETS_ISEA_ISEA_H diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 7776c743bc..eded20fbc2 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -1,8 +1,9 @@ /****************************************************************************** * * Project: PROJ - * Purpose: Net for TSEA projection — a regular tetrahedron unfolded - * into the plane. + * Purpose: Net layout for the TSEA projection — the regular tetrahedron + * unfolded into a "star" net (root face surrounded by its three + * neighbours). * Author: Felix Palmer * ****************************************************************************/ @@ -10,34 +11,10 @@ #ifndef NETS_TSEA_TSEA_H #define NETS_TSEA_TSEA_H -#include "../../conway.h" - namespace nets { namespace tsea { -// SCALE factor to normalize net area to unit sphere surface area (4π) -constexpr double SCALE = 0.448924562362866; // sqrt(π / sqrt(3)) / 3 -constexpr double W = SCALE; -constexpr double H = 0.86602540378443865e+00 * W; // cos(30) - -constexpr polyhedral::Mesh<6, 4, 3> tsea = { - // Vertices - { - {-3 * W, 2 * H, 0.0}, - {0.0, -4 * H, 0.0}, - {3 * W, 2 * H, 0.0}, - {-6 * W, -4 * H, 0.0}, - {0.0, 8 * H, 0.0}, - {6 * W, -4 * H, 0.0}, - }, - // Faces - { - {4, 0, 2}, - {0, 3, 1}, - {2, 1, 5}, - {1, 2, 0}, - }, -}; +constexpr int tsea[4] = {-1, 0, 0, 0}; } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/dodecahedron.h b/src/projections/polyhedral/polyhedra/dodecahedron.h new file mode 100644 index 0000000000..6ab04b843d --- /dev/null +++ b/src/projections/polyhedral/polyhedra/dodecahedron.h @@ -0,0 +1,86 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Regular dodecahedron — 20 vertices, 12 pentagonal faces, + * inscribed in the unit sphere with V0 at (0, 0, 1) and V1 along + * the +x meridian. The 20 vertices form six layers along z: + * + * z = 1 V0 (1 vertex) + * z = √5/3 = (4A−1)/3 V1, V4, V5 (layer 1, 3 vertices) + * z = 1/3 6 vertices (layer 2) + * z = −1/3 6 vertices (layer 3) + * z = −√5/3 3 vertices (layer 4) + * z = −1 V17 (1 vertex) + * + * where A = (1+√5)/4 = cos(36°) and B = √3/3 = 1/√3 are the only + * algebraic constants needed (every other coordinate is a rational + * combination of A, B and 1/3). + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRA_DODECAHEDRON_H +#define POLYHEDRA_DODECAHEDRON_H + +#include "../conway.h" +#include "validation.h" + +namespace polyhedra { +namespace dodecahedron_constants { + +constexpr double A = 0.809016994374947424102293417183; // (1+√5)/4 = cos(36°) +constexpr double B = 0.577350269189625764509148780502; // √3/3 = 1/√3 + +constexpr polyhedral::Mesh<20, 12, 5> mesh = { + // Vertices (unit sphere; V0 at +z, V1 in +x meridian) + { + {0.0, 0.0, 1.0}, + {2.0 / 3.0, 0.0, (4 * A - 1) / 3.0}, + {(4 * A - 1) / 3.0, B, 1.0 / 3.0}, + {(2 - 2 * A) / 3.0, 2 * A * B, 1.0 / 3.0}, + {-1.0 / 3.0, B, (4 * A - 1) / 3.0}, + {-1.0 / 3.0, -B, (4 * A - 1) / 3.0}, + {(4 * A - 1) / 3.0, -B, 1.0 / 3.0}, + {(1 + 2 * A) / 3.0, (2 * A - 1) * B, -1.0 / 3.0}, + {(2 * A - 2) / 3.0, 2 * A * B, -1.0 / 3.0}, + {-(1 + 2 * A) / 3.0, (2 * A - 1) * B, 1.0 / 3.0}, + {(2 - 2 * A) / 3.0, -2 * A * B, 1.0 / 3.0}, + {(1 + 2 * A) / 3.0, -(2 * A - 1) * B, -1.0 / 3.0}, + {1.0 / 3.0, B, -(4 * A - 1) / 3.0}, + {-(4 * A - 1) / 3.0, B, -1.0 / 3.0}, + {-(1 + 2 * A) / 3.0, -(2 * A - 1) * B, 1.0 / 3.0}, + {(2 * A - 2) / 3.0, -2 * A * B, -1.0 / 3.0}, + {1.0 / 3.0, -B, -(4 * A - 1) / 3.0}, + {0.0, 0.0, -1.0}, + {-2.0 / 3.0, 0.0, -(4 * A - 1) / 3.0}, + {-(4 * A - 1) / 3.0, -B, -1.0 / 3.0}, + }, + // Faces (CCW from outside). Ordered to match the canonical DSEA net + // unfolding: F0 is the first 5 vertices, F1..F10 zig-zag around the + // middle band so the default parents tree is a simple chain + // {-1, 0, 1, …, 9}, and F11 is the last 5 vertices. + { + {0, 1, 2, 3, 4}, + {0, 5, 10, 6, 1}, + {6, 10, 15, 16, 11}, + {1, 6, 11, 7, 2}, + {7, 11, 16, 17, 12}, + {2, 7, 12, 8, 3}, + {8, 12, 17, 18, 13}, + {3, 8, 13, 9, 4}, + {9, 13, 18, 19, 14}, + {0, 4, 9, 14, 5}, + {5, 14, 19, 15, 10}, + {15, 19, 18, 17, 16}, + }, +}; + +[[maybe_unused]] constexpr validate_polyhedron _validate{}; + +} // namespace dodecahedron_constants + +constexpr auto &dodecahedron = dodecahedron_constants::mesh; + +} // namespace polyhedra + +#endif // POLYHEDRA_DODECAHEDRON_H diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h new file mode 100644 index 0000000000..265c39dcf4 --- /dev/null +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -0,0 +1,86 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Regular icosahedron inscribed in the unit sphere, oriented with + * V0 at the north pole. The remaining 11 vertices form two rings + * of 5 (at z = ±1/√5) staggered by 36° in longitude, plus V11 at + * the south pole. Faces are listed in 4 groups of 5 — north cap, + * upper band (down-pointing on the sphere), lower band (up-pointing + * on the sphere), south cap — chosen to match the canonical ISEA + * net unfolding. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRA_ICOSAHEDRON_H +#define POLYHEDRA_ICOSAHEDRON_H + +#include "../conway.h" +#include "validation.h" + +namespace polyhedra { +namespace icosahedron_constants { + +constexpr double A = 0.894427190999915878564; // 2/√5 (ring xy radius) +constexpr double B = 0.447213595499957939282; // 1/√5 (ring |z|) + +// cos/sin of multiples of 72° and 36° (used for the two rings). +constexpr double C72 = 0.309016994374947424102; // cos 72° +constexpr double S72 = 0.951056516295153572116; // sin 72° +constexpr double C36 = 0.809016994374947424102; // cos 36° +constexpr double S36 = 0.587785252292473129169; // sin 36° + +constexpr polyhedral::Mesh<12, 20, 3> mesh = { + // Vertices (unit sphere; V0 at +z, V1 in +x meridian) + { + {0.0, 0.0, 1.0}, + {-A, 0.0, B}, + {-A * C72, -A * S72, B}, + {A * C36, -A * S36, B}, + {A * C36, A * S36, B}, + {-A * C72, A * S72, B}, + {-A * C36, -A * S36, -B}, + {A * C72, -A * S72, -B}, + {A, 0.0, -B}, + {A * C72, A * S72, -B}, + {-A * C36, A * S36, -B}, + {0.0, 0.0, -1.0}, + }, + // Faces (CCW from outside). Ordered north to south, in groups of 5 + // F0..F4 north cap (around V0) + // F5..F9 upper band (down-pointing) + // F10..F14 lower band (up-pointing) + // F15..F19 south cap (around V11) + { + {1, 2, 0}, // Permutation to correctly orient net along x-axis + {0, 2, 3}, + {0, 3, 4}, + {0, 4, 5}, + {0, 5, 1}, + {1, 6, 2}, + {2, 7, 3}, + {3, 8, 4}, + {4, 9, 5}, + {5, 10, 1}, + {6, 7, 2}, + {7, 8, 3}, + {8, 9, 4}, + {9, 10, 5}, + {10, 6, 1}, + {11, 7, 6}, + {11, 8, 7}, + {11, 9, 8}, + {11, 10, 9}, + {11, 6, 10}, + }, +}; + +[[maybe_unused]] constexpr validate_polyhedron _validate{}; + +} // namespace icosahedron_constants + +constexpr auto &icosahedron = icosahedron_constants::mesh; + +} // namespace polyhedra + +#endif // POLYHEDRA_ICOSAHEDRON_H diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index b16628e219..dc1a9c8b58 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -1,7 +1,11 @@ /****************************************************************************** * * Project: PROJ - * Purpose: Regular tetrahedron inscribed in the unit sphere. + * Purpose: Regular tetrahedron inscribed in the unit sphere, oriented with + * one vertex at the north pole. The remaining three vertices sit + * at latitude -arcsin(1/3) ≈ -19.47°, separated by 120° in + * longitude (0°, +120°, -120°). Face 0 is the bottom triangle + * opposite the apex — the natural root for a "star" net. * Author: Felix Palmer * ****************************************************************************/ @@ -10,29 +14,37 @@ #define POLYHEDRA_TETRAHEDRON_H #include "../conway.h" +#include "validation.h" namespace polyhedra { +namespace tetrahedron_constants { -// Following definition from https://dmccooey.com/polyhedra/Tetrahedron.txt -constexpr double C0 = 0.35355339059327376220042e+00; // sqrt(2) / 4 +constexpr double A = 0.9428090415820635; // sqrt(8/9) +constexpr double B = 0.8164965809277260; // sqrt(2/3) -constexpr polyhedral::Mesh<4, 4, 3> tetrahedron = { +constexpr polyhedral::Mesh<4, 4, 3> mesh = { // Vertices { - {C0, -C0, C0}, - {C0, C0, -C0}, - {-C0, C0, C0}, - {-C0, -C0, -C0}, + {0.0, 0.0, 1.0}, + {A, 0.0, -1.0 / 3.0}, + {-0.5 * A, B, -1.0 / 3.0}, + {-0.5 * A, -B, -1.0 / 3.0}, }, // Faces { + {3, 2, 1}, {0, 1, 2}, {1, 0, 3}, {2, 3, 0}, - {3, 2, 1}, }, }; +[[maybe_unused]] constexpr validate_polyhedron _validate{}; + +} // namespace tetrahedron_constants + +constexpr auto &tetrahedron = tetrahedron_constants::mesh; + } // namespace polyhedra #endif // POLYHEDRA_TETRAHEDRON_H diff --git a/src/projections/polyhedral/polyhedra/validation.h b/src/projections/polyhedral/polyhedra/validation.h new file mode 100644 index 0000000000..6536985be6 --- /dev/null +++ b/src/projections/polyhedral/polyhedra/validation.h @@ -0,0 +1,68 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Compile-time validation helper for polyhedron seed meshes. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRA_VALIDATION_H +#define POLYHEDRA_VALIDATION_H + +#include "../conway.h" + +namespace polyhedra { + +template +constexpr bool all_vertices_on_unit_sphere( + const polyhedral::Mesh &m) { + constexpr double tol = 1e-12; + for (int i = 0; i < NV; i++) { + const auto &v = m.vertices[i]; + const double err = v.x * v.x + v.y * v.y + v.z * v.z - 1.0; + if (err < -tol || err > tol) + return false; + } + return true; +} + +template +constexpr bool face_indices_well_formed( + const polyhedral::Mesh &m) { + for (int f = 0; f < NF; f++) { + for (int k = 0; k < NFV; k++) { + if (m.faces[f][k] < 0 || m.faces[f][k] >= NV) + return false; + for (int j = k + 1; j < NFV; j++) { + if (m.faces[f][k] == m.faces[f][j]) + return false; + } + } + } + return true; +} + +// Two topological conditions: +// V - E + F = 2 for any closed convex polyhedron, +// E = NF * NFV / 2 (each edge shared by exactly two NFV-gon faces). +template +constexpr bool euler_holds(const polyhedral::Mesh &) { + return (NF * NFV) % 2 == 0 && NV - (NF * NFV) / 2 + NF == 2; +} + +template struct validate_polyhedron { + static_assert(M.vertices[0].x == 0.0 && M.vertices[0].y == 0.0 && + M.vertices[0].z == 1.0, + "V0 must be at (0, 0, 1)"); + static_assert(all_vertices_on_unit_sphere(M), + "all vertices must lie on the unit sphere"); + static_assert(face_indices_well_formed(M), + "face vertex indices must be in [0, NV) " + "and unique within each face"); + static_assert(euler_holds(M), + "polyhedron must satisfy Euler's formula V - E + F = 2"); +}; + +} // namespace polyhedra + +#endif // POLYHEDRA_VALIDATION_H diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 0c7bd72be8..57382498ea 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -31,12 +31,26 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; + // Translation in projected space so that the geographic point + // (P->phi0, P->lam0) lands at (0, 0). +x_0/+y_0 stack on top via PROJ + // core. Both zero unless +lat_0 / +lon_0 was supplied. + double x_offset; + double y_offset; + // Authalic latitude conversion (ellipsoidal case only; apa is null for // spheres, where geodetic and authalic latitudes coincide). double *apa; double qp; }; +// Per-projection orientation defaults applied when the user does not specify +// +orient_lat / +orient_lon / +azi. +struct PolyhedralDefaults { + double orient_lat_deg; + double orient_lon_deg; + double azi_deg; +}; + // Build triangle data from a polyhedron + matching net. // The `meta` Conway operation is used to cut up the faces template @@ -143,6 +157,53 @@ inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, lam = adjlon(std::atan2(gy, gx)); } +// Read +orient_lat / +orient_lon / +azi (with the supplied defaults) and +// build the orientation matrix. +lat_0 / +lon_0 are loaded into +// P->phi0 / P->lam0 by PROJ core (init.cpp); if they are non-zero, run the +// forward projection on that point once and store the result as the +// projected-space offset so (lat_0, lon_0) maps to (0, 0). +// +// Authalic-latitude state (Q->apa, Q->qp) must already be initialized +// because the offset computation uses lonlat_to_cart on the ellipsoid. +// +// Returns false (with proj_log_error already called) if (lat_0, lon_0) does +// not lie within the polyhedron's coverage and so cannot be used as the +// projected origin. +inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, + const PolyhedralDefaults &d) { + double orient_lat = d.orient_lat_deg; + double orient_lon = d.orient_lon_deg; + double azi = d.azi_deg; + if (pj_param(P->ctx, P->params, "torient_lat").i) + orient_lat = pj_param(P->ctx, P->params, "dorient_lat").f; + if (pj_param(P->ctx, P->params, "torient_lon").i) + orient_lon = pj_param(P->ctx, P->params, "dorient_lon").f; + if (pj_param(P->ctx, P->params, "tazi").i) + azi = pj_param(P->ctx, P->params, "dazi").f; + + set_orient_from_angles(Q, orient_lat, orient_lon, azi); + + Q->x_offset = 0.0; + Q->y_offset = 0.0; + if (P->phi0 == 0.0 && P->lam0 == 0.0) + return true; + + // PROJ core (src/fwd.cpp) subtracts P->lam0 from the input longitude + // before calling polyhedral_fwd, so we mirror that here by passing lam=0. + // The offset is therefore the projection of (phi0, lam=0). + Vec3 v = lonlat_to_cart(Q, P, 0.0, P->phi0); + int tri_idx = find_triangle(Q, v); + if (tri_idx < 0) { + proj_log_error(P, _("+lat_0 / +lon_0 lies outside the polyhedron's " + "coverage; cannot be used as projected origin")); + return false; + } + Face2D r = snyder_fwd(v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); + Q->x_offset = r.x; + Q->y_offset = r.y; + return true; +} + } // namespace polyhedral #endif // POLYHEDRAL_SPHERE_H diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h new file mode 100644 index 0000000000..39dd0721b4 --- /dev/null +++ b/src/projections/polyhedral/unfold.h @@ -0,0 +1,176 @@ +/****************************************************************************** + * + * Project: PROJ + * Purpose: Unfold a 3D polyhedron Mesh into a planar net Mesh by laying each + * face flat in its own local 2D frame and chaining 2D rigid + * transforms over a parents-tree of faces. + * Author: Felix Palmer + * + ****************************************************************************/ + +#ifndef POLYHEDRAL_UNFOLD_H +#define POLYHEDRAL_UNFOLD_H + +#include "conway.h" +#include "vec3.h" + +#include "proj_internal.h" + +#include + +namespace polyhedral { + +// Number of net vertices produced by unfolding NF faces with NFV vertices each +template constexpr int unfolded_vertex_count() { + return NFV + (NFV - 2) * (NF - 1); +} + +template +inline Vec3 face_normal(const Vec3 (&vertices)[NV_p], const int (&face)[NFV]) { + const Vec3 v0 = vertices[face[0]]; + return vec3_normalize(vec3_cross(vec3_subtract(vertices[face[1]], v0), + vec3_subtract(vertices[face[2]], v0))); +} + +// Rigid transform mapping the polyhedron face f onto the 2D plane (z=0) such +// that the face's directed edge from slot idx_a to slot idx_b is aligned +// with the 2D edge net_vertex_a → net_vertex_b. +template +inline Mat4 mat4_rigidTransform(const Mesh &polyhedron, int f, + int idx_a, int idx_b, const Vec3 &net_vertex_a, + const Vec3 &net_vertex_b) { + const Vec3 poly_vertex_a = polyhedron.vertices[polyhedron.faces[f][idx_a]]; + const Vec3 poly_vertex_b = polyhedron.vertices[polyhedron.faces[f][idx_b]]; + + // Face local unit vectors + const Vec3 normal = face_normal(polyhedron.vertices, polyhedron.faces[f]); + const Vec3 u = vec3_normalize(vec3_subtract(poly_vertex_b, poly_vertex_a)); + const Vec3 v = vec3_cross(normal, u); + + // Transform the face-local frame (u, v) into the net plane. + const Vec3 edge_direction = + vec3_normalize(vec3_subtract(net_vertex_b, net_vertex_a)); + const Vec3 r0 = vec3_subtract(vec3_scale(u, edge_direction.x), + vec3_scale(v, edge_direction.y)); + const Vec3 r1 = vec3_add(vec3_scale(u, edge_direction.y), + vec3_scale(v, edge_direction.x)); + const double t0 = net_vertex_a.x - vec3_dot(r0, poly_vertex_a); + const double t1 = net_vertex_a.y - vec3_dot(r1, poly_vertex_a); + return {{{r0.x, r0.y, r0.z, t0}, + {r1.x, r1.y, r1.z, t1}, + {0.0, 0.0, 0.0, 0.0}, + {0.0, 0.0, 0.0, 1.0}}}; +} + +template +inline double polygon_area_2d(const Vec3 *verts, const int (&face)[NFV]) { + double a = 0.0; + for (int k = 0; k < NFV; k++) + a += vec3_cross(verts[face[k]], verts[face[(k + 1) % NFV]]).z; + return std::fabs(a) * 0.5; +} + +// Unfold a polyhedron Mesh into a planar net Mesh. +// +// `parents[i]` is the index of face i's parent in the unfolding tree, or -1 +// if i is the root. Exactly one entry must be -1. +// +// The polyhedron faces must have consistent CCW winding from the outside. +// Each child face is hinged about its shared edge with its parent; the +// algorithm relies on shared edges being traversed in opposite directions +// in the two adjacent faces (which is the case for any closed polyhedron +// with consistent outward winding). +// +// The resulting net is auto-scaled so its total area equals 4π (i.e. the +// area of the unit sphere) and translated so the root face's centroid lies +// at the origin, with the first edge along the x-axis. +template +inline Mesh(), NF, NFV> +unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { + constexpr int NV_n = unfolded_vertex_count(); + Mesh net{}; + int n_verts = 0; + + // Find and place root face + int root = 0; + while (parents[root] != -1) + root++; + const Mat4 root_face_to_plane = mat4_rigidTransform( + polyhedron, root, 0, 1, {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}); + for (int k = 0; k < NFV; k++) { + Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; + net.vertices[n_verts] = vec3_applyMat4(root_face_to_plane, face_vertex); + net.faces[root][k] = n_verts++; + } + + // Initialize queue with direct children of parent face + int queue[NF]; + int q_head = 0, q_tail = 0; + for (int i = 0; i < NF; i++) + if (parents[i] == root) + queue[q_tail++] = i; + + // Hinge each child onto its parent at the shared edge. + while (q_head < q_tail) { + const int c = queue[q_head++]; + const int p = parents[c]; + + // Find shared edge + int ia_c = -1, ib_c = -1, ia_p = -1, ib_p = -1; + for (int kc = 0; kc < NFV; kc++) + for (int kp = 0; kp < NFV; kp++) + if (polyhedron.faces[c][kc] == polyhedron.faces[p][kp]) { + if (ia_c == -1) { + ia_c = kc; + ia_p = kp; + } else if (ib_c == -1) { + ib_c = kc; + ib_p = kp; + } + } + + // Place face onto net using shared edge for orientation + const int na = net.faces[p][ia_p]; + const int nb = net.faces[p][ib_p]; + const Mat4 face_to_plane = mat4_rigidTransform( + polyhedron, c, ia_c, ib_c, net.vertices[na], net.vertices[nb]); + for (int k = 0; k < NFV; k++) { + if (k == ia_c) { + net.faces[c][k] = na; + } else if (k == ib_c) { + net.faces[c][k] = nb; + } else { + Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[c][k]]; + net.vertices[n_verts] = + vec3_applyMat4(face_to_plane, face_vertex); + net.faces[c][k] = n_verts++; + } + } + + // Append children of this face to queue + for (int i = 0; i < NF; i++) + if (parents[i] == c) + queue[q_tail++] = i; + } + + // Rescale so the net's total area equals the unit sphere's (4π). + double total_area = 0.0; + for (int f = 0; f < NF; f++) + total_area += polygon_area_2d(net.vertices, net.faces[f]); + const double scale = std::sqrt(4.0 * M_PI / total_area); + + // Translate so the root face's centroid is at origin, then scale. + Vec3 centroid{0.0, 0.0, 0.0}; + for (int k = 0; k < NFV; k++) + centroid = vec3_add(centroid, net.vertices[net.faces[root][k]]); + centroid = vec3_scale(centroid, 1.0 / NFV); + for (int i = 0; i < NV_n; i++) + net.vertices[i] = + vec3_scale(vec3_subtract(net.vertices[i], centroid), scale); + + return net; +} + +} // namespace polyhedral + +#endif // POLYHEDRAL_UNFOLD_H diff --git a/src/projections/polyhedral/vec3.h b/src/projections/polyhedral/vec3.h index d3a7d3b92a..eb11b8edf2 100644 --- a/src/projections/polyhedral/vec3.h +++ b/src/projections/polyhedral/vec3.h @@ -78,15 +78,25 @@ inline Vec3 vec3_lerp(const Vec3 &a, const Vec3 &b, double t) { a.z + t * (b.z - a.z)}; } -inline double vec3_distance(const Vec3 &a, const Vec3 &b) { - return vec3_length(vec3_subtract(a, b)); -} - inline double vec3_angle(const Vec3 &a, const Vec3 &b) { double d = vec3_dot(a, b) / (vec3_length(a) * vec3_length(b)); return std::acos(std::clamp(d, -1.0, 1.0)); } +struct Mat4 { + double m[4][4]; +}; + +// Apply an affine 4x4 to a 3D point (treated as (v.x, v.y, v.z, 1)). Assumes +// the bottom row is [0, 0, 0, 1] (true affine, no perspective divide). +inline Vec3 vec3_applyMat4(const Mat4 &m, const Vec3 &v) { + return { + m.m[0][0] * v.x + m.m[0][1] * v.y + m.m[0][2] * v.z + m.m[0][3], + m.m[1][0] * v.x + m.m[1][1] * v.y + m.m[1][2] * v.z + m.m[1][3], + m.m[2][0] * v.x + m.m[2][1] * v.y + m.m[2][2] * v.z + m.m[2][3], + }; +} + } // namespace polyhedral #endif // VEC3_H diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 886bd0ebb8..ee7e194064 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3227,6 +3227,174 @@ accept 0 45 expect 0 4726854.770339427515864 roundtrip 1 +=============================================================================== +# Tetrahedral Snyder Equal Area +# Sph&Ell +=============================================================================== + +------------------------------------------------------------------------------- +operation +proj=tsea +R=6371007.18091875 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 0 0 +expect 3235993.22451040 9907682.60840717 +roundtrip 1 + +accept 45 0 +expect 5752617.07966014 5734785.00018046 +roundtrip 1 + +accept 2 49 +expect 10611559.5707055 9798969.47180896 +roundtrip 1 + +accept -110 54 +expect -13838645.5935957 5122850.34539395 +roundtrip 1 + +------------------------------------------------------------------------------- +# +orient_lat / +orient_lon / +azi rotate the polyhedron on the sphere. +# Here the first vertex (apex) lands at the equator on the prime meridian. +operation +proj=tsea +R=6371007.18091875 +orient_lat=0 +orient_lon=0 +azi=0 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 0 0 +expect 17160609.6630278 9907682.60840717 +roundtrip 1 + +accept 45 0 +expect 12233639.0746285 4919488.85110285 +roundtrip 1 + +accept 2 49 +expect 110325.228702713 -13001663.8698201 +roundtrip 1 + +------------------------------------------------------------------------------- +# +lat_0 / +lon_0 pan the projected output: (lat_0, lon_0) lands at (0, 0). +operation +proj=tsea +R=6371007.18091875 +lat_0=49 +lon_0=2 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 2 49 +expect 0 0 +roundtrip 1 + +accept 0 0 +expect -13897150.2959435 -156173.591497305 +roundtrip 1 + +------------------------------------------------------------------------------- +# +x_0 / +y_0 stack on top of the +lat_0 / +lon_0 pan. +operation +proj=tsea +R=6371007.18091875 +lat_0=49 +lon_0=2 +x_0=500000 +y_0=1000000 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 2 49 +expect 500000 1000000 +roundtrip 1 + +accept 0 0 +expect -13397150.2959435 843826.408502695 +roundtrip 1 + +=============================================================================== +# Dodecahedral Snyder Equal Area +# Sph&Ell +=============================================================================== + +------------------------------------------------------------------------------- +operation +proj=dsea +R=6371007.18091875 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 0 0 +expect 0 -9872947.35628115 +roundtrip 1 + +accept 45 0 +expect 5018607.99435854 -9485537.57508639 +roundtrip 1 + +accept 2 49 +expect 151412.117573414 -4403884.01108735 +roundtrip 1 + +accept -110 54 +expect -3813952.97764993 1378763.12588854 +roundtrip 1 + +------------------------------------------------------------------------------- +# +lat_0 / +lon_0 pan the projected output: (lat_0, lon_0) lands at (0, 0). +operation +proj=dsea +R=6371007.18091875 +lat_0=49 +lon_0=2 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 2 49 +expect 0 0 +roundtrip 1 + +accept 0 0 +expect -220718.052648629 -5430960.59821442 +roundtrip 1 + +------------------------------------------------------------------------------- +# +net=a5 selects an alternate unfolding tree (and applies an A5 longitude +# offset of -93°). +operation +proj=dsea +R=6371007.18091875 +net=a5 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 0 0 +expect 10826790.5654831 -11235323.5817327 +roundtrip 1 + +accept 45 0 +expect 16370612.0092947 -12695836.0892119 +roundtrip 1 + +=============================================================================== +# Icosahedral Snyder Equal Area (generalized) +# Sph&Ell +=============================================================================== + +------------------------------------------------------------------------------- +operation +proj=isea2 +R=6371007.18091875 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 0 0 +expect 14017461.8221269 -2215425.18118909 +roundtrip 1 + +accept 45 0 +expect 19387947.6094421 -2331936.04658942 +roundtrip 1 + +accept 2 49 +expect 14706662.9573990 3257666.05633906 +roundtrip 1 + +accept -110 54 +expect 27514.3911635408 -2200204.09400224 +roundtrip 1 + +------------------------------------------------------------------------------- +# +lat_0 / +lon_0 pan the projected output: (lat_0, lon_0) lands at (0, 0). +operation +proj=isea2 +R=6371007.18091875 +lat_0=49 +lon_0=2 +------------------------------------------------------------------------------- +tolerance 0.2 mm + +accept 2 49 +expect 0 0 +roundtrip 1 + +accept 0 0 +expect 5474227.04847173 -5379819.15463861 +roundtrip 1 + =============================================================================== # Kavrayskiy V # PCyl., Sph. diff --git a/test/unit/test_polyhedral.cpp b/test/unit/test_polyhedral.cpp index d0bbc9ca2b..2b55985433 100644 --- a/test/unit/test_polyhedral.cpp +++ b/test/unit/test_polyhedral.cpp @@ -14,6 +14,7 @@ // clang-format on #include +#include namespace { @@ -28,9 +29,29 @@ static const RoundtripPoint test_points[] = { {-30.0, -60.0}, {70.0, -170.0}, }; -static const char *proj_strings[] = { - "+proj=tsea +R=1", - "+proj=tsea +ellps=WGS84", +struct ProjConfig { + const char *str; + double tol; +}; + +// 1e-13 rad is ~0.6 nm at the equator on Earth — the precision the original +// (no-offset) implementation hits. Configs that compose extra rotations and +// projected-space offsets give up a few bits to cancellation near triangle +// edges; 1e-11 rad is still ~60 μm, well below any practical tolerance. +static const ProjConfig proj_strings[] = { + {"+proj=tsea +R=1", 1e-13}, + {"+proj=tsea +ellps=WGS84", 1e-13}, + {"+proj=tsea +R=1 +orient_lat=90 +orient_lon=0 +azi=0", 1e-13}, + {"+proj=tsea +R=1 +lat_0=10 +lon_0=20", 1e-11}, + {"+proj=tsea +R=1 +orient_lat=45 +orient_lon=30 +azi=60 +lat_0=15 " + "+lon_0=-25 +x_0=1000 +y_0=-2000", + 1e-11}, + {"+proj=dsea +R=1", 1e-13}, + {"+proj=dsea +ellps=WGS84", 1e-13}, + {"+proj=dsea +R=1 +lat_0=10 +lon_0=20", 1e-11}, + {"+proj=isea2 +R=1", 1e-13}, + {"+proj=isea2 +ellps=WGS84", 1e-13}, + {"+proj=isea2 +R=1 +lat_0=10 +lon_0=20", 1e-11}, }; static void roundtrip_test(const char *proj_string, double tolerance) { @@ -60,11 +81,55 @@ static void roundtrip_test(const char *proj_string, double tolerance) { } TEST(polyhedral, roundtrip) { - for (const auto *proj_string : proj_strings) { - // 1e-13 radians corresponds to accuracy to ~0.6nm (worst case at - // equator) - roundtrip_test(proj_string, 1e-13); + for (const auto &cfg : proj_strings) { + roundtrip_test(cfg.str, cfg.tol); } } +// +lat_0 / +lon_0 must place the supplied geographic point at the projected +// origin (0, 0). +x_0 / +y_0 then stack on top via PROJ core. +TEST(polyhedral, lat0_lon0_at_origin) { + PJ *p = proj_create(PJ_DEFAULT_CTX, "+proj=tsea +R=1 +lat_0=10 +lon_0=20"); + ASSERT_TRUE(p != nullptr); + + PJ_COORD c = proj_coord(0, 0, 0, 0); + c.lp.lam = proj_torad(20.0); + c.lp.phi = proj_torad(10.0); + PJ_COORD f = proj_trans(p, PJ_FWD, c); + EXPECT_NEAR(f.xy.x, 0.0, 1e-13); + EXPECT_NEAR(f.xy.y, 0.0, 1e-13); + + proj_destroy(p); +} + +TEST(polyhedral, dsea_invalid_net_rejected) { + PJ *p = proj_create(PJ_DEFAULT_CTX, "+proj=dsea +R=1 +net=does_not_exist"); + EXPECT_TRUE(p == nullptr); + proj_destroy(p); +} + +TEST(polyhedral, dsea_known_nets_accepted) { + for (const char *net : {"dsea", "a5", "crescent", "flower"}) { + std::string s = std::string("+proj=dsea +R=1 +net=") + net; + PJ *p = proj_create(PJ_DEFAULT_CTX, s.c_str()); + ASSERT_TRUE(p != nullptr) << "Failed to create: " << s; + proj_destroy(p); + } +} + +TEST(polyhedral, x0_y0_stacks_on_lat0_lon0) { + PJ *p = proj_create(PJ_DEFAULT_CTX, + "+proj=tsea +R=1 +lat_0=10 +lon_0=20 +x_0=7 +y_0=-3"); + ASSERT_TRUE(p != nullptr); + + PJ_COORD c = proj_coord(0, 0, 0, 0); + c.lp.lam = proj_torad(20.0); + c.lp.phi = proj_torad(10.0); + PJ_COORD f = proj_trans(p, PJ_FWD, c); + EXPECT_NEAR(f.xy.x, 7.0, 1e-13); + EXPECT_NEAR(f.xy.y, -3.0, 1e-13); + + proj_destroy(p); +} + } // namespace From 4dcb330589d1556049c30a089a777c30f82713f3 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Thu, 7 May 2026 09:08:58 +0200 Subject: [PATCH 20/62] Code review --- .../operations/projections/polyhedral.rst | 20 ++++---- src/projections/polyhedral.cpp | 19 ++----- .../polyhedral/polyhedra/icosahedron.h | 2 +- src/projections/polyhedral/snyder.h | 6 +-- src/projections/polyhedral/sphere.h | 50 ++++++++----------- src/projections/polyhedral/unfold.h | 10 ++-- src/projections/polyhedral/vec3.h | 2 +- 7 files changed, 43 insertions(+), 66 deletions(-) diff --git a/docs/source/operations/projections/polyhedral.rst b/docs/source/operations/projections/polyhedral.rst index 8f6fe1ac5c..81bd68784e 100644 --- a/docs/source/operations/projections/polyhedral.rst +++ b/docs/source/operations/projections/polyhedral.rst @@ -43,10 +43,10 @@ An example is taking a tetrahedron, and cutting each of its 4 triangular faces into 6 right triangles. The result is a hexakis tetrahedron, with 24 faces. By defining polyhedra in this manner we can describe both the geometry of the -solid, as well as making clear which of the vertices should be treated as the -apex. For example, if we take the regular icosahedral and dodecahedron, and -apply the akisation described above to both we get the same 120 vertices, but -we can distinguish between the shapes: +solid and which of the vertices should be treated as the apex. For example, +if we take the regular icosahedron and dodecahedron, and apply the akisation +described above to both, we get the same 120 vertices, but we can distinguish +between the shapes: - Hexakis icosahedron (20 triangular faces, cut into 6) - Decakis dodecahedron (12 triangular faces, cut into 10) @@ -59,15 +59,15 @@ Net mapping ******************************************************************************** Internally, the projection outputs triangles in barycentric coordinates, which -are then be transformed into triangles on a 2D plane. Here is ``tsea``, -projecting the 24 faces of the hexakis tetrahedron into triangular net. +are then transformed into triangles on a 2D plane. Here is ``tsea``, +projecting the 24 faces of the hexakis tetrahedron into a triangular net. While it feels natural to project onto the net of the unfolded polyhedron, e.g. - **Hexakis Icosahedron** onto **Icosahedron Net** - **Decakis Dodecahedron** onto **Dodecahedron Net** -we can equally we unfold onto any net that has the same symmetry group (in other +we can equally unfold onto any net that has the same symmetry group (in other words, shares the same set of triangles). So it is completely valid to unfold: - **Hexakis Icosahedron** onto **Dodecahedron Net** @@ -88,10 +88,8 @@ Equal Area**. - ``dsea`` **Dodecahedral Snyder Equal Area**: Decakis Dodecahedron (120 triangles) - ``isea2`` **Icosahedral Snyder Equal Area**: Hexakis Icosahedron (120 triangles) -(Note ``isea2`` can be renamed to ``isea`` if it replaces the existing implementation) - -When choosing projection, a set of nets is made available to the user by name. -The nets are tied to the projection, as the order of the triangles are important. +When choosing a projection, a set of nets is available to the user by name. +The nets are tied to the projection, as the ordering of the triangles matters. The net parameter can be omitted to use the default net. Parameters diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 1390c2a639..61045f0896 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -41,7 +41,6 @@ using polyhedral::pj_polyhedral_data; -// Shared forward projection static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { PJ_XY xy = {0.0, 0.0}; auto *Q = static_cast(P->opaque); @@ -63,7 +62,6 @@ static PJ_XY polyhedral_fwd(PJ_LP lp, PJ *P) { return xy; } -// Shared inverse projection static PJ_LP polyhedral_inv(PJ_XY xy, PJ *P) { PJ_LP lp = {0.0, 0.0}; auto *Q = static_cast(P->opaque); @@ -136,10 +134,8 @@ PJ *PJ_PROJECTION(dsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - // +net= selects the unfolding tree. The `a5` net additionally shifts - // orient_lon by -93° to match the LONGITUDE_OFFSET=93° rotation used by - // the A5 reference codebase; F0's centroid still sits at the geographic - // pole, so orient_lat and azi are unchanged. + // +net= selects the unfolding tree. The `a5` net shifts orient_lon by + // -93° to match the LONGITUDE_OFFSET used by the A5 reference codebase. const char *net_name = pj_param(P->ctx, P->params, "snet").s; const int(*parents)[12] = &nets::dsea::dsea; double default_orient_lon = -36.0; @@ -164,12 +160,8 @@ PJ *PJ_PROJECTION(dsea) { const auto net = polyhedral::unfold_net(polyhedra::dodecahedron, *parents); polyhedral::load_meshes(Q, polyhedra::dodecahedron, net); - // The dodecahedron data has V0 on +z and V1 on the +x meridian, so - // orient_lat / orient_lon directly specify V0's geographic position - // and +azi is the bearing from V0 toward V1. The defaults below - // (orient_lat ≈ atan((3+√5)/4), orient_lon = -36°, azi varying per net) - // rotate the polyhedron so F0's centroid sits at the geographic north - // pole, with the V0-V1 edge midpoint on the prime meridian. + // Defaults rotate the polyhedron so F0's centroid sits at the geographic + // north pole. orient_lat = atan((1+2A)/2) places V0 on the F0 axis. using polyhedra::dodecahedron_constants::A; const double default_orient_lat = std::atan((1 + 2 * A) / 2.0) * 180.0 / M_PI; @@ -191,8 +183,7 @@ PJ *PJ_PROJECTION(isea2) { const auto net = polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); polyhedral::load_meshes(Q, polyhedra::icosahedron, net); - // Standard Snyder ISEA orientation: V0 (the icosahedron's north-pole - // seed vertex) sits at lat ≈ 58.28°N, lon = 11.25°E. + // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N, lon = 11.25°E. const polyhedral::PolyhedralDefaults d = {58.282525588539, 11.25, 0.0}; return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h index 265c39dcf4..c5caae40b4 100644 --- a/src/projections/polyhedral/polyhedra/icosahedron.h +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -52,7 +52,7 @@ constexpr polyhedral::Mesh<12, 20, 3> mesh = { // F10..F14 lower band (up-pointing) // F15..F19 south cap (around V11) { - {1, 2, 0}, // Permutation to correctly orient net along x-axis + {1, 2, 0}, // permuted so the net's first edge lies along +x {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, diff --git a/src/projections/polyhedral/snyder.h b/src/projections/polyhedral/snyder.h index 4d96a6e6cf..76869be5c9 100644 --- a/src/projections/polyhedral/snyder.h +++ b/src/projections/polyhedral/snyder.h @@ -6,11 +6,9 @@ * ****************************************************************************** * Derived from A5 (Apache-2.0). - * * https://github.com/felixpalmer/a5 + * (modules/projections/polyhedral.ts) * - * modules/projections/polyhedral.ts - * Copyright (c) A5 contributors * * Licensed under the Apache License, Version 2.0 (the "License"); @@ -57,7 +55,7 @@ * POSSIBILITY OF SUCH DAMAGE. **************************************************************************** * - * Closed from equations adapted from: + * Closed-form equations adapted from: * https://brsr.github.io/2021/08/31/snyder-equal-area.html * ****************************************************************************/ diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 57382498ea..466ec9da67 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -31,28 +31,26 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; - // Translation in projected space so that the geographic point - // (P->phi0, P->lam0) lands at (0, 0). +x_0/+y_0 stack on top via PROJ - // core. Both zero unless +lat_0 / +lon_0 was supplied. + // Translation so that (P->phi0, P->lam0) lands at (0, 0). Zero unless + // +lat_0 / +lon_0 was supplied; +x_0/+y_0 stack on top via PROJ core. double x_offset; double y_offset; - // Authalic latitude conversion (ellipsoidal case only; apa is null for - // spheres, where geodetic and authalic latitudes coincide). + // Authalic latitude state (ellipsoidal case only; apa is null on spheres). double *apa; double qp; }; -// Per-projection orientation defaults applied when the user does not specify -// +orient_lat / +orient_lon / +azi. +// Orientation defaults used when the user does not supply +orient_lat / +// +orient_lon / +azi. struct PolyhedralDefaults { double orient_lat_deg; double orient_lon_deg; double azi_deg; }; -// Build triangle data from a polyhedron + matching net. -// The `meta` Conway operation is used to cut up the faces +// Build triangle data from a polyhedron + matching net by applying the Conway +// `meta` operation to both. template inline void load_meshes(pj_polyhedral_data *Q, const Mesh &polyhedron, @@ -74,9 +72,9 @@ inline void load_meshes(pj_polyhedral_data *Q, } } -// Build rotation matrix from three angles (degrees): -// lat, lon: the geographic point to rotate to the north pole -// az: an azimuthal (z-axis) rotation applied after the above +// Build rotation matrix that takes the geographic point (lat, lon) to the +// north pole, followed by an azimuthal rotation about the z-axis. All angles +// are in degrees. inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, double lon_deg, double az_deg) { const double lat = lat_deg * DEG_TO_RAD; @@ -123,9 +121,9 @@ inline int find_triangle(const pj_polyhedral_data *Q, const Vec3 &v) { return -1; } -// Convert geodetic lon/lat to unit vector, applying orientation rotation. -// In the ellipsoidal case the latitude is first converted to the authalic -// latitude so that equal-area properties are preserved on the sphere. +// Convert geodetic lon/lat to a unit vector and apply the orientation +// rotation. On an ellipsoid, latitude is first mapped to the authalic +// latitude so that equal-area is preserved on the sphere. inline Vec3 lonlat_to_cart(const pj_polyhedral_data *Q, const PJ *P, double lam, double phi) { double auth_lat = phi; @@ -157,18 +155,11 @@ inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, lam = adjlon(std::atan2(gy, gx)); } -// Read +orient_lat / +orient_lon / +azi (with the supplied defaults) and -// build the orientation matrix. +lat_0 / +lon_0 are loaded into -// P->phi0 / P->lam0 by PROJ core (init.cpp); if they are non-zero, run the -// forward projection on that point once and store the result as the -// projected-space offset so (lat_0, lon_0) maps to (0, 0). -// -// Authalic-latitude state (Q->apa, Q->qp) must already be initialized -// because the offset computation uses lonlat_to_cart on the ellipsoid. -// -// Returns false (with proj_log_error already called) if (lat_0, lon_0) does -// not lie within the polyhedron's coverage and so cannot be used as the -// projected origin. +// Read +orient_lat / +orient_lon / +azi (falling back to the supplied +// defaults) and build the orientation matrix. If +lat_0 / +lon_0 is set, +// project that point once and cache the result as a projected-space offset +// so (lat_0, lon_0) maps to (0, 0). Authalic-latitude state must already be +// initialized. Returns false if (lat_0, lon_0) lies outside the polyhedron. inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, const PolyhedralDefaults &d) { double orient_lat = d.orient_lat_deg; @@ -188,9 +179,8 @@ inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, if (P->phi0 == 0.0 && P->lam0 == 0.0) return true; - // PROJ core (src/fwd.cpp) subtracts P->lam0 from the input longitude - // before calling polyhedral_fwd, so we mirror that here by passing lam=0. - // The offset is therefore the projection of (phi0, lam=0). + // PROJ core subtracts P->lam0 before calling polyhedral_fwd, so the + // offset is the projection of (phi0, lam=0). Vec3 v = lonlat_to_cart(Q, P, 0.0, P->phi0); int tri_idx = find_triangle(Q, v); if (tri_idx < 0) { diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 39dd0721b4..65c1b82640 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -36,7 +36,7 @@ inline Vec3 face_normal(const Vec3 (&vertices)[NV_p], const int (&face)[NFV]) { // that the face's directed edge from slot idx_a to slot idx_b is aligned // with the 2D edge net_vertex_a → net_vertex_b. template -inline Mat4 mat4_rigidTransform(const Mesh &polyhedron, int f, +inline Mat4 mat4_rigid_transform(const Mesh &polyhedron, int f, int idx_a, int idx_b, const Vec3 &net_vertex_a, const Vec3 &net_vertex_b) { const Vec3 poly_vertex_a = polyhedron.vertices[polyhedron.faces[f][idx_a]]; @@ -95,11 +95,11 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { int root = 0; while (parents[root] != -1) root++; - const Mat4 root_face_to_plane = mat4_rigidTransform( + const Mat4 root_face_to_plane = mat4_rigid_transform( polyhedron, root, 0, 1, {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}); for (int k = 0; k < NFV; k++) { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; - net.vertices[n_verts] = vec3_applyMat4(root_face_to_plane, face_vertex); + net.vertices[n_verts] = vec3_apply_mat4(root_face_to_plane, face_vertex); net.faces[root][k] = n_verts++; } @@ -132,7 +132,7 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { // Place face onto net using shared edge for orientation const int na = net.faces[p][ia_p]; const int nb = net.faces[p][ib_p]; - const Mat4 face_to_plane = mat4_rigidTransform( + const Mat4 face_to_plane = mat4_rigid_transform( polyhedron, c, ia_c, ib_c, net.vertices[na], net.vertices[nb]); for (int k = 0; k < NFV; k++) { if (k == ia_c) { @@ -142,7 +142,7 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { } else { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[c][k]]; net.vertices[n_verts] = - vec3_applyMat4(face_to_plane, face_vertex); + vec3_apply_mat4(face_to_plane, face_vertex); net.faces[c][k] = n_verts++; } } diff --git a/src/projections/polyhedral/vec3.h b/src/projections/polyhedral/vec3.h index eb11b8edf2..a14858b10e 100644 --- a/src/projections/polyhedral/vec3.h +++ b/src/projections/polyhedral/vec3.h @@ -89,7 +89,7 @@ struct Mat4 { // Apply an affine 4x4 to a 3D point (treated as (v.x, v.y, v.z, 1)). Assumes // the bottom row is [0, 0, 0, 1] (true affine, no perspective divide). -inline Vec3 vec3_applyMat4(const Mat4 &m, const Vec3 &v) { +inline Vec3 vec3_apply_mat4(const Mat4 &m, const Vec3 &v) { return { m.m[0][0] * v.x + m.m[0][1] * v.y + m.m[0][2] * v.z + m.m[0][3], m.m[1][0] * v.x + m.m[1][1] * v.y + m.m[1][2] * v.z + m.m[1][3], From ad34fb75527727feb1f404248a4d48ee7be1eddf Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 8 May 2026 14:39:52 +0200 Subject: [PATCH 21/62] Tidy --- src/projections/polyhedral.cpp | 7 +-- src/projections/polyhedral/nets/isea/isea.h | 6 +-- .../polyhedral/polyhedra/dodecahedron.h | 8 ++-- .../polyhedral/polyhedra/icosahedron.h | 47 +++++++------------ .../polyhedral/polyhedra/validation.h | 8 ++-- src/projections/polyhedral/unfold.h | 7 +-- 6 files changed, 35 insertions(+), 48 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 61045f0896..bff9522d01 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -118,7 +118,8 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - const auto net = polyhedral::unfold_net(polyhedra::tetrahedron, nets::tsea::tsea); + const auto net = + polyhedral::unfold_net(polyhedra::tetrahedron, nets::tsea::tsea); polyhedral::load_meshes(Q, polyhedra::tetrahedron, net); const polyhedral::PolyhedralDefaults d = {90.0, 0.0, 0.0}; return polyhedral_setup(P, d); @@ -153,8 +154,8 @@ PJ *PJ_PROJECTION(dsea) { } else { proj_log_error(P, _("invalid +net (expected dsea, a5, crescent, " "or flower)")); - return polyhedral_destructor( - P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); + return polyhedral_destructor(P, + PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); } } diff --git a/src/projections/polyhedral/nets/isea/isea.h b/src/projections/polyhedral/nets/isea/isea.h index 5e60ab92c0..8301a4e508 100644 --- a/src/projections/polyhedral/nets/isea/isea.h +++ b/src/projections/polyhedral/nets/isea/isea.h @@ -28,9 +28,9 @@ namespace nets { namespace isea { constexpr int isea[20] = { - -1, 6, 7, 8, 9, // F0 root; F1..F4 north cap, hung off upper band - 0, 10, 11, 12, 13, // F5 child of F0; F6..F9 chained via lower band - 5, 6, 7, 8, 9, // F10 child of F5; F11..F14 chained via upper band + -1, 6, 7, 8, 9, // F0 root; F1..F4 north cap, hung off upper band + 0, 10, 11, 12, 13, // F5 child of F0; F6..F9 chained via lower band + 5, 6, 7, 8, 9, // F10 child of F5; F11..F14 chained via upper band 10, 11, 12, 13, 14, // F15..F19 south cap, hung off lower band }; diff --git a/src/projections/polyhedral/polyhedra/dodecahedron.h b/src/projections/polyhedral/polyhedra/dodecahedron.h index 6ab04b843d..0f3a6c687f 100644 --- a/src/projections/polyhedral/polyhedra/dodecahedron.h +++ b/src/projections/polyhedral/polyhedra/dodecahedron.h @@ -37,19 +37,19 @@ constexpr polyhedral::Mesh<20, 12, 5> mesh = { {0.0, 0.0, 1.0}, {2.0 / 3.0, 0.0, (4 * A - 1) / 3.0}, {(4 * A - 1) / 3.0, B, 1.0 / 3.0}, - {(2 - 2 * A) / 3.0, 2 * A * B, 1.0 / 3.0}, + {(2 - 2 * A) / 3.0, 2 * A *B, 1.0 / 3.0}, {-1.0 / 3.0, B, (4 * A - 1) / 3.0}, {-1.0 / 3.0, -B, (4 * A - 1) / 3.0}, {(4 * A - 1) / 3.0, -B, 1.0 / 3.0}, {(1 + 2 * A) / 3.0, (2 * A - 1) * B, -1.0 / 3.0}, - {(2 * A - 2) / 3.0, 2 * A * B, -1.0 / 3.0}, + {(2 * A - 2) / 3.0, 2 * A *B, -1.0 / 3.0}, {-(1 + 2 * A) / 3.0, (2 * A - 1) * B, 1.0 / 3.0}, - {(2 - 2 * A) / 3.0, -2 * A * B, 1.0 / 3.0}, + {(2 - 2 * A) / 3.0, -2 * A *B, 1.0 / 3.0}, {(1 + 2 * A) / 3.0, -(2 * A - 1) * B, -1.0 / 3.0}, {1.0 / 3.0, B, -(4 * A - 1) / 3.0}, {-(4 * A - 1) / 3.0, B, -1.0 / 3.0}, {-(1 + 2 * A) / 3.0, -(2 * A - 1) * B, 1.0 / 3.0}, - {(2 * A - 2) / 3.0, -2 * A * B, -1.0 / 3.0}, + {(2 * A - 2) / 3.0, -2 * A *B, -1.0 / 3.0}, {1.0 / 3.0, -B, -(4 * A - 1) / 3.0}, {0.0, 0.0, -1.0}, {-2.0 / 3.0, 0.0, -(4 * A - 1) / 3.0}, diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h index c5caae40b4..97a1ceefa6 100644 --- a/src/projections/polyhedral/polyhedra/icosahedron.h +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -25,25 +25,25 @@ constexpr double A = 0.894427190999915878564; // 2/√5 (ring xy radius) constexpr double B = 0.447213595499957939282; // 1/√5 (ring |z|) // cos/sin of multiples of 72° and 36° (used for the two rings). -constexpr double C72 = 0.309016994374947424102; // cos 72° -constexpr double S72 = 0.951056516295153572116; // sin 72° -constexpr double C36 = 0.809016994374947424102; // cos 36° -constexpr double S36 = 0.587785252292473129169; // sin 36° +constexpr double C72 = 0.309016994374947424102; // cos 72° +constexpr double S72 = 0.951056516295153572116; // sin 72° +constexpr double C36 = 0.809016994374947424102; // cos 36° +constexpr double S36 = 0.587785252292473129169; // sin 36° constexpr polyhedral::Mesh<12, 20, 3> mesh = { // Vertices (unit sphere; V0 at +z, V1 in +x meridian) { {0.0, 0.0, 1.0}, {-A, 0.0, B}, - {-A * C72, -A * S72, B}, - {A * C36, -A * S36, B}, - {A * C36, A * S36, B}, - {-A * C72, A * S72, B}, - {-A * C36, -A * S36, -B}, - {A * C72, -A * S72, -B}, + {-A * C72, -A *S72, B}, + {A * C36, -A *S36, B}, + {A * C36, A *S36, B}, + {-A * C72, A *S72, B}, + {-A * C36, -A *S36, -B}, + {A * C72, -A *S72, -B}, {A, 0.0, -B}, - {A * C72, A * S72, -B}, - {-A * C36, A * S36, -B}, + {A * C72, A *S72, -B}, + {-A * C36, A *S36, -B}, {0.0, 0.0, -1.0}, }, // Faces (CCW from outside). Ordered north to south, in groups of 5 @@ -53,25 +53,10 @@ constexpr polyhedral::Mesh<12, 20, 3> mesh = { // F15..F19 south cap (around V11) { {1, 2, 0}, // permuted so the net's first edge lies along +x - {0, 2, 3}, - {0, 3, 4}, - {0, 4, 5}, - {0, 5, 1}, - {1, 6, 2}, - {2, 7, 3}, - {3, 8, 4}, - {4, 9, 5}, - {5, 10, 1}, - {6, 7, 2}, - {7, 8, 3}, - {8, 9, 4}, - {9, 10, 5}, - {10, 6, 1}, - {11, 7, 6}, - {11, 8, 7}, - {11, 9, 8}, - {11, 10, 9}, - {11, 6, 10}, + {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, {1, 6, 2}, + {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, {6, 7, 2}, + {7, 8, 3}, {8, 9, 4}, {9, 10, 5}, {10, 6, 1}, {11, 7, 6}, + {11, 8, 7}, {11, 9, 8}, {11, 10, 9}, {11, 6, 10}, }, }; diff --git a/src/projections/polyhedral/polyhedra/validation.h b/src/projections/polyhedral/polyhedra/validation.h index 6536985be6..9cd5d48f4a 100644 --- a/src/projections/polyhedral/polyhedra/validation.h +++ b/src/projections/polyhedral/polyhedra/validation.h @@ -14,8 +14,8 @@ namespace polyhedra { template -constexpr bool all_vertices_on_unit_sphere( - const polyhedral::Mesh &m) { +constexpr bool +all_vertices_on_unit_sphere(const polyhedral::Mesh &m) { constexpr double tol = 1e-12; for (int i = 0; i < NV; i++) { const auto &v = m.vertices[i]; @@ -27,8 +27,8 @@ constexpr bool all_vertices_on_unit_sphere( } template -constexpr bool face_indices_well_formed( - const polyhedral::Mesh &m) { +constexpr bool +face_indices_well_formed(const polyhedral::Mesh &m) { for (int f = 0; f < NF; f++) { for (int k = 0; k < NFV; k++) { if (m.faces[f][k] < 0 || m.faces[f][k] >= NV) diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 65c1b82640..d50af1f296 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -37,8 +37,8 @@ inline Vec3 face_normal(const Vec3 (&vertices)[NV_p], const int (&face)[NFV]) { // with the 2D edge net_vertex_a → net_vertex_b. template inline Mat4 mat4_rigid_transform(const Mesh &polyhedron, int f, - int idx_a, int idx_b, const Vec3 &net_vertex_a, - const Vec3 &net_vertex_b) { + int idx_a, int idx_b, const Vec3 &net_vertex_a, + const Vec3 &net_vertex_b) { const Vec3 poly_vertex_a = polyhedron.vertices[polyhedron.faces[f][idx_a]]; const Vec3 poly_vertex_b = polyhedron.vertices[polyhedron.faces[f][idx_b]]; @@ -99,7 +99,8 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { polyhedron, root, 0, 1, {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}); for (int k = 0; k < NFV; k++) { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; - net.vertices[n_verts] = vec3_apply_mat4(root_face_to_plane, face_vertex); + net.vertices[n_verts] = + vec3_apply_mat4(root_face_to_plane, face_vertex); net.faces[root][k] = n_verts++; } From 61ee123c62af2c22ed16ff8188b6cdf85c52801f Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 8 May 2026 15:09:09 +0200 Subject: [PATCH 22/62] ISEA back-compatibilty --- src/projections/polyhedral.cpp | 17 ++++- src/projections/polyhedral/sphere.h | 105 ++++++++++++++++++++++------ test/gie/builtins.gie | 22 +++--- 3 files changed, 112 insertions(+), 32 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index bff9522d01..86a68437a8 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -184,7 +184,20 @@ PJ *PJ_PROJECTION(isea2) { const auto net = polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); polyhedral::load_meshes(Q, polyhedra::icosahedron, net); - // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N, lon = 11.25°E. - const polyhedral::PolyhedralDefaults d = {58.282525588539, 11.25, 0.0}; + // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N. Legacy +proj=isea + // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid; preserve + // that split when the user explicitly drops to a sphere via +ellps=sphere + // or +f=0. + // + // For drop-in compatibility with legacy +proj=isea, the default projected + // origin is the bbox center (mid-width, mid-height) of icosahedron face F7 + // — the central upper-band face — rather than its centroid. This matches + // legacy ISEA's 4×5 strip-layout geometric center, which sits inside F7 + // but not at any face's centroid. Other polyhedra default to the centroid + // of face 0 (root of the unfold). + const double orient_lon = (P->es == 0.0) ? 11.25 : 11.20; + polyhedral::PolyhedralDefaults d = {58.282525588539, orient_lon, 0.0}; + d.default_face_index = 7; + d.default_origin = polyhedral::DefaultOrigin::FaceBboxCenter; return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 466ec9da67..7b057efef1 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -17,6 +17,7 @@ #include "proj_internal.h" #include +#include namespace polyhedral { @@ -24,6 +25,8 @@ constexpr int MAX_TRIANGLES = 120; struct pj_polyhedral_data { int n_triangles; + int face_vertex_count; // NFV: 3 for triangular faces, 5 for pentagonal + int num_faces; SphericalTriangle sph_tris[MAX_TRIANGLES]; FaceTriangle face_tris[MAX_TRIANGLES]; @@ -31,8 +34,9 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; - // Translation so that (P->phi0, P->lam0) lands at (0, 0). Zero unless - // +lat_0 / +lon_0 was supplied; +x_0/+y_0 stack on top via PROJ core. + // Translation in projected space so the geographic anchor named by + // +lat_0 / +lon_0 (or its dynamic default) lands at (0, 0). + // +x_0/+y_0 stack on top via PROJ core. double x_offset; double y_offset; @@ -41,12 +45,20 @@ struct pj_polyhedral_data { double qp; }; -// Orientation defaults used when the user does not supply +orient_lat / -// +orient_lon / +azi. +// Projected origin location on chosen reference face when the user does not +// supply +lat_0 / +lon_0. +enum class DefaultOrigin { + FaceCentroid, // arithmetic mean of the face's outer vertices in the net + FaceBboxCenter, // axis-aligned bbox center of the face's outer vertices +}; + +// Defaults supplied per-projection; user params override these where present. struct PolyhedralDefaults { double orient_lat_deg; double orient_lon_deg; double azi_deg; + int default_face_index = 0; + DefaultOrigin default_origin = DefaultOrigin::FaceCentroid; }; // Build triangle data from a polyhedron + matching net by applying the Conway @@ -62,6 +74,8 @@ inline void load_meshes(pj_polyhedral_data *Q, conway_meta(net.vertices, net.faces, face); Q->n_triangles = N; + Q->face_vertex_count = NFV; + Q->num_faces = NF; for (int i = 0; i < N; i++) { Q->sph_tris[i] = {sph[i][0], sph[i][1], sph[i][2]}; Q->face_tris[i] = { @@ -72,6 +86,35 @@ inline void load_meshes(pj_polyhedral_data *Q, } } +// Reference point on face_idx in the unfolded planar net (centroid or bbox +// center) +inline Face2D face_reference_point(const pj_polyhedral_data *Q, int face_idx, + DefaultOrigin kind) { + const int nfv = Q->face_vertex_count; + const int fan_size = 2 * nfv; + double sum_x = 0.0, sum_y = 0.0; + double min_x = std::numeric_limits::infinity(); + double max_x = -std::numeric_limits::infinity(); + double min_y = std::numeric_limits::infinity(); + double max_y = -std::numeric_limits::infinity(); + for (int k = 0; k < nfv; k++) { + const Face2D &v = Q->face_tris[fan_size * face_idx + 2 * k].c; + sum_x += v.x; + sum_y += v.y; + if (v.x < min_x) + min_x = v.x; + if (v.x > max_x) + max_x = v.x; + if (v.y < min_y) + min_y = v.y; + if (v.y > max_y) + max_y = v.y; + } + if (kind == DefaultOrigin::FaceBboxCenter) + return {0.5 * (min_x + max_x), 0.5 * (min_y + max_y)}; + return {sum_x / nfv, sum_y / nfv}; +} + // Build rotation matrix that takes the geographic point (lat, lon) to the // north pole, followed by an azimuthal rotation about the z-axis. All angles // are in degrees. @@ -155,11 +198,9 @@ inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, lam = adjlon(std::atan2(gy, gx)); } -// Read +orient_lat / +orient_lon / +azi (falling back to the supplied -// defaults) and build the orientation matrix. If +lat_0 / +lon_0 is set, -// project that point once and cache the result as a projected-space offset -// so (lat_0, lon_0) maps to (0, 0). Authalic-latitude state must already be -// initialized. Returns false if (lat_0, lon_0) lies outside the polyhedron. +// Read +orient_lat / +orient_lon / +azi / +lat_0 / +lon_0 (falling back to +// derived defaults) and build the orientation matrix plus the projected-space +// offset so the chosen geographic anchor lands at (0, 0). inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, const PolyhedralDefaults &d) { double orient_lat = d.orient_lat_deg; @@ -174,23 +215,43 @@ inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, set_orient_from_angles(Q, orient_lat, orient_lon, azi); + // Bypass PROJ core's automatic +lon_0 subtraction. +lat_0/+lon_0 names a + // geographic point that must be applied through orient, not a plain + // longitude shift on the input. + P->lam0 = 0.0; + P->phi0 = 0.0; Q->x_offset = 0.0; Q->y_offset = 0.0; - if (P->phi0 == 0.0 && P->lam0 == 0.0) - return true; - // PROJ core subtracts P->lam0 before calling polyhedral_fwd, so the - // offset is the projection of (phi0, lam=0). - Vec3 v = lonlat_to_cart(Q, P, 0.0, P->phi0); - int tri_idx = find_triangle(Q, v); - if (tri_idx < 0) { - proj_log_error(P, _("+lat_0 / +lon_0 lies outside the polyhedron's " - "coverage; cannot be used as projected origin")); - return false; + const bool user_lat_0 = pj_param(P->ctx, P->params, "tlat_0").i != 0; + const bool user_lon_0 = pj_param(P->ctx, P->params, "tlon_0").i != 0; + + if (user_lat_0 || user_lon_0) { + // User-supplied geographic anchor: project it through the full orient. + const double lat_0 = + user_lat_0 ? pj_param(P->ctx, P->params, "rlat_0").f : 0.0; + const double lon_0 = + user_lon_0 ? pj_param(P->ctx, P->params, "rlon_0").f : 0.0; + Vec3 v = lonlat_to_cart(Q, P, lon_0, lat_0); + int tri_idx = find_triangle(Q, v); + if (tri_idx < 0) { + proj_log_error(P, + _("+lat_0 / +lon_0 lies outside the polyhedron's " + "coverage; cannot be used as projected origin")); + return false; + } + Face2D r = snyder_fwd(v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); + Q->x_offset = r.x; + Q->y_offset = r.y; + return true; } - Face2D r = snyder_fwd(v, Q->sph_tris[tri_idx], Q->face_tris[tri_idx]); - Q->x_offset = r.x; - Q->y_offset = r.y; + + // Default anchor: a planar reference point on the chosen face. This is + // already in projected coords (the unfolded net), so use it directly. + const Face2D ref = + face_reference_point(Q, d.default_face_index, d.default_origin); + Q->x_offset = ref.x; + Q->y_offset = ref.y; return true; } diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index ee7e194064..d858b86242 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3283,7 +3283,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect -13897150.2959435 -156173.591497305 +expect -7375566.34619513 108713.136598217 roundtrip 1 ------------------------------------------------------------------------------- @@ -3297,7 +3297,7 @@ expect 500000 1000000 roundtrip 1 accept 0 0 -expect -13397150.2959435 843826.408502695 +expect -6875566.34619513 1108713.13659822 roundtrip 1 =============================================================================== @@ -3337,7 +3337,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect -220718.052648629 -5430960.59821442 +expect -151412.117573417 -5469063.34519380 roundtrip 1 ------------------------------------------------------------------------------- @@ -3360,25 +3360,31 @@ roundtrip 1 # Sph&Ell =============================================================================== +------------------------------------------------------------------------------- +# At default settings on a sphere, +proj=isea2 reproduces +proj=isea: the +# projected origin is the geographic point that legacy ISEA places at (0, 0) — +# the bbox center of icosahedron face F7 (the central upper-band face), which +# corresponds to (lon=11.25°E, lat≈-30.0945°S) under the default orientation. +# On an ellipsoid, +orient_lon defaults to 11.20° instead of 11.25°. ------------------------------------------------------------------------------- operation +proj=isea2 +R=6371007.18091875 ------------------------------------------------------------------------------- tolerance 0.2 mm accept 0 0 -expect 14017461.8221269 -2215425.18118909 +expect -1331454.07462099 3323137.77178363 roundtrip 1 accept 45 0 -expect 19387947.6094421 -2331936.04658942 +expect 4039031.71269420 3206626.90638330 roundtrip 1 accept 2 49 -expect 14706662.9573990 3257666.05633906 +expect -642252.939348975 8796229.00931178 roundtrip 1 accept -110 54 -expect 27514.3911635408 -2200204.09400224 +expect -15321401.5055844 3338358.85897048 roundtrip 1 ------------------------------------------------------------------------------- @@ -3392,7 +3398,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect 5474227.04847173 -5379819.15463861 +expect -689201.135272012 -5473091.23752815 roundtrip 1 =============================================================================== From 69dadc81fd2546b61b1154168d59cceac8c865e2 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 8 May 2026 15:19:58 +0200 Subject: [PATCH 23/62] Tidy --- src/projections/polyhedral.cpp | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 86a68437a8..08e04a8605 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -184,19 +184,19 @@ PJ *PJ_PROJECTION(isea2) { const auto net = polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); polyhedral::load_meshes(Q, polyhedra::icosahedron, net); + // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N. Legacy +proj=isea - // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid; preserve - // that split when the user explicitly drops to a sphere via +ellps=sphere - // or +f=0. - // + // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid. + const bool sphere = (P->es == 0.0); + const double orient_lon = sphere ? 11.25 : 11.20; + polyhedral::PolyhedralDefaults d = {58.282525588539, orient_lon, 0.0}; + // For drop-in compatibility with legacy +proj=isea, the default projected // origin is the bbox center (mid-width, mid-height) of icosahedron face F7 // — the central upper-band face — rather than its centroid. This matches // legacy ISEA's 4×5 strip-layout geometric center, which sits inside F7 // but not at any face's centroid. Other polyhedra default to the centroid // of face 0 (root of the unfold). - const double orient_lon = (P->es == 0.0) ? 11.25 : 11.20; - polyhedral::PolyhedralDefaults d = {58.282525588539, orient_lon, 0.0}; d.default_face_index = 7; d.default_origin = polyhedral::DefaultOrigin::FaceBboxCenter; return polyhedral_setup(P, d); From 7cc1cee7569ed7a034399d2f7887dfdb01fe6163 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 8 May 2026 15:46:32 +0200 Subject: [PATCH 24/62] orient option for ISEA --- src/projections/polyhedral.cpp | 26 +++++++++++++++++++++++--- 1 file changed, 23 insertions(+), 3 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 08e04a8605..b57e284999 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -172,7 +172,7 @@ PJ *PJ_PROJECTION(dsea) { } PROJ_HEAD(isea2, "Icosahedral Snyder Equal Area (generalized)") -"\n\tSph&Ell\n\torient_lat= orient_lon= azi= lat_0= lon_0="; +"\n\tSph&Ell\n\torient= orient_lat= orient_lon= azi= lat_0= lon_0="; PJ *PJ_PROJECTION(isea2) { auto *Q = static_cast( calloc(1, sizeof(pj_polyhedral_data))); @@ -188,8 +188,28 @@ PJ *PJ_PROJECTION(isea2) { // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N. Legacy +proj=isea // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid. const bool sphere = (P->es == 0.0); - const double orient_lon = sphere ? 11.25 : 11.20; - polyhedral::PolyhedralDefaults d = {58.282525588539, orient_lon, 0.0}; + double orient_lat = 58.282525588539; + double orient_lon = sphere ? 11.25 : 11.20; + double azi = 0.0; + + // +orient= shorthand for two named orientations from legacy +proj=isea. + // Individual +orient_lat / +orient_lon / +azi still override. + const char *orient_name = pj_param(P->ctx, P->params, "sorient").s; + if (orient_name != nullptr) { + if (strcmp(orient_name, "isea") == 0) { + // Defaults above already match. + } else if (strcmp(orient_name, "pole") == 0) { + orient_lat = 90.0; + orient_lon = 0.0; + azi = 0.0; + } else { + proj_log_error(P, _("invalid +orient (expected isea or pole)")); + return polyhedral_destructor(P, + PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); + } + } + + polyhedral::PolyhedralDefaults d = {orient_lat, orient_lon, azi}; // For drop-in compatibility with legacy +proj=isea, the default projected // origin is the bbox center (mid-width, mid-height) of icosahedron face F7 From 0309c49a98152bb48798489f51c59ad2a901dc26 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Fri, 8 May 2026 17:01:27 +0200 Subject: [PATCH 25/62] Authalic conversion of orient_lat --- src/projections/polyhedral.cpp | 5 ++++- src/projections/polyhedral/sphere.h | 27 ++++++++++++++++++++++----- 2 files changed, 26 insertions(+), 6 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index b57e284999..7aebe7e425 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -185,7 +185,10 @@ PJ *PJ_PROJECTION(isea2) { polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); polyhedral::load_meshes(Q, polyhedra::icosahedron, net); - // Standard Snyder ISEA orientation: V0 at lat ≈ 58.28°N. Legacy +proj=isea + // Standard Snyder ISEA orientation: V0 at authalic latitude arctan(φ) ≈ + // 58.28°N (φ = golden ratio). On WGS84 this corresponds to ~58.40° + // geodetic — PolyhedralDefaults stores the authalic value; user + // +orient_lat is geodetic and converted internally. Legacy +proj=isea // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid. const bool sphere = (P->es == 0.0); double orient_lat = 58.282525588539; diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 7b057efef1..9b5d36067f 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -53,6 +53,11 @@ enum class DefaultOrigin { }; // Defaults supplied per-projection; user params override these where present. +// +// orient_lat_deg is in *authalic* latitude — this is the frame the rotation +// operates in (the unit sphere is the authalic sphere for equal-area +// projections). User-supplied +orient_lat is geodetic and gets converted to +// authalic before use. On a sphere the two are identical. struct PolyhedralDefaults { double orient_lat_deg; double orient_lon_deg; @@ -115,9 +120,10 @@ inline Face2D face_reference_point(const pj_polyhedral_data *Q, int face_idx, return {sum_x / nfv, sum_y / nfv}; } -// Build rotation matrix that takes the geographic point (lat, lon) to the -// north pole, followed by an azimuthal rotation about the z-axis. All angles -// are in degrees. +// Build rotation matrix that takes the (lat, lon) point on the authalic unit +// sphere to the north pole, followed by an azimuthal rotation about the +// z-axis. All angles are in degrees; lat is authalic latitude (callers must +// convert from geodetic if needed). inline void set_orient_from_angles(pj_polyhedral_data *Q, double lat_deg, double lon_deg, double az_deg) { const double lat = lat_deg * DEG_TO_RAD; @@ -203,11 +209,22 @@ inline void cart_to_lonlat(const pj_polyhedral_data *Q, const PJ *P, // offset so the chosen geographic anchor lands at (0, 0). inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, const PolyhedralDefaults &d) { + // Default is authalic; user input is geodetic and converted below. double orient_lat = d.orient_lat_deg; double orient_lon = d.orient_lon_deg; double azi = d.azi_deg; - if (pj_param(P->ctx, P->params, "torient_lat").i) - orient_lat = pj_param(P->ctx, P->params, "dorient_lat").f; + if (pj_param(P->ctx, P->params, "torient_lat").i) { + const double user_lat_deg = + pj_param(P->ctx, P->params, "dorient_lat").f; + if (P->es != 0.0) { + const double phi = user_lat_deg * DEG_TO_RAD; + const double auth = pj_authalic_lat( + phi, std::sin(phi), std::cos(phi), Q->apa, P, Q->qp); + orient_lat = auth / DEG_TO_RAD; + } else { + orient_lat = user_lat_deg; + } + } if (pj_param(P->ctx, P->params, "torient_lon").i) orient_lon = pj_param(P->ctx, P->params, "dorient_lon").f; if (pj_param(P->ctx, P->params, "tazi").i) From 4a2942ea7c713abeca10e77024317dcc45aac361 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 17:48:36 +0200 Subject: [PATCH 26/62] General rigid_transform --- src/projections/polyhedral.cpp | 23 +++---- src/projections/polyhedral/nets/isea/isea.h | 23 ++++--- .../polyhedral/polyhedra/icosahedron.h | 9 ++- src/projections/polyhedral/sphere.h | 20 +++--- src/projections/polyhedral/unfold.h | 62 ++++++++++++------- test/gie/builtins.gie | 32 +++++----- 6 files changed, 96 insertions(+), 73 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 7aebe7e425..ef4cf91fff 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -30,7 +30,6 @@ #include "polyhedral/polyhedra/icosahedron.h" #include "polyhedral/polyhedra/tetrahedron.h" #include "polyhedral/sphere.h" -#include "polyhedral/unfold.h" #include "proj.h" #include "proj_internal.h" @@ -118,9 +117,7 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - const auto net = - polyhedral::unfold_net(polyhedra::tetrahedron, nets::tsea::tsea); - polyhedral::load_meshes(Q, polyhedra::tetrahedron, net); + polyhedral::load_meshes(Q, polyhedra::tetrahedron, nets::tsea::tsea); const polyhedral::PolyhedralDefaults d = {90.0, 0.0, 0.0}; return polyhedral_setup(P, d); } @@ -159,8 +156,7 @@ PJ *PJ_PROJECTION(dsea) { } } - const auto net = polyhedral::unfold_net(polyhedra::dodecahedron, *parents); - polyhedral::load_meshes(Q, polyhedra::dodecahedron, net); + polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents); // Defaults rotate the polyhedron so F0's centroid sits at the geographic // north pole. orient_lat = atan((1+2A)/2) places V0 on the F0 axis. using polyhedra::dodecahedron_constants::A; @@ -181,9 +177,7 @@ PJ *PJ_PROJECTION(isea2) { P->opaque = Q; P->destructor = polyhedral_destructor; - const auto net = - polyhedral::unfold_net(polyhedra::icosahedron, nets::isea::isea); - polyhedral::load_meshes(Q, polyhedra::icosahedron, net); + polyhedral::load_meshes(Q, polyhedra::icosahedron, nets::isea::isea); // Standard Snyder ISEA orientation: V0 at authalic latitude arctan(φ) ≈ // 58.28°N (φ = golden ratio). On WGS84 this corresponds to ~58.40° @@ -215,12 +209,11 @@ PJ *PJ_PROJECTION(isea2) { polyhedral::PolyhedralDefaults d = {orient_lat, orient_lon, azi}; // For drop-in compatibility with legacy +proj=isea, the default projected - // origin is the bbox center (mid-width, mid-height) of icosahedron face F7 - // — the central upper-band face — rather than its centroid. This matches - // legacy ISEA's 4×5 strip-layout geometric center, which sits inside F7 - // but not at any face's centroid. Other polyhedra default to the centroid - // of face 0 (root of the unfold). - d.default_face_index = 7; + // origin is the bbox center (mid-width, mid-height) of the unfold's root + // face — the "South Africa" upper-band face F7 — rather than its + // centroid. This matches legacy ISEA's 4×5 strip-layout geometric centre, + // which sits inside F7 but not at its centroid. Other polyhedra default + // to the centroid of the root face. d.default_origin = polyhedral::DefaultOrigin::FaceBboxCenter; return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/nets/isea/isea.h b/src/projections/polyhedral/nets/isea/isea.h index 8301a4e508..5ccf3f9c1a 100644 --- a/src/projections/polyhedral/nets/isea/isea.h +++ b/src/projections/polyhedral/nets/isea/isea.h @@ -11,12 +11,20 @@ * F10..F14 lower band (up-pointing on the sphere) * F15..F19 south cap (around V11) * - * The unfold tree zig-zags through the upper and lower bands, + * F7 is the centred upper-band face — the "South Africa" face in + * Snyder's Figure 12 (face 8 in his 1-indexed numbering, our F7 + * in 0-indexed) — and is chosen as the root of the unfolding tree + * so that the default projected origin is its centroid / bbox + * centre, matching the geometric centre of the legacy ISEA strip. * - * F0 → F5 → F10 → F6 → F11 → F7 → F12 → F8 → F13 → F9 → F14 + * The unfold tree zig-zags from the root F7 outward across the + * upper and lower bands, * - * and hangs each remaining north-cap face off its upper-band - * neighbour and each south-cap face off its lower-band neighbour. + * F0 ← F5 ← F10 ← F6 ← F11 ← F7 → F12 → F8 → F13 → F9 → F14 + * + * with each remaining north-cap face hung off its upper-band + * neighbour and each south-cap face hung off its lower-band + * neighbour. * Author: Felix Palmer * ****************************************************************************/ @@ -28,9 +36,10 @@ namespace nets { namespace isea { constexpr int isea[20] = { - -1, 6, 7, 8, 9, // F0 root; F1..F4 north cap, hung off upper band - 0, 10, 11, 12, 13, // F5 child of F0; F6..F9 chained via lower band - 5, 6, 7, 8, 9, // F10 child of F5; F11..F14 chained via upper band + 5, 6, 7, 8, 9, // F0..F4 north cap, hung off upper band + 10, 11, -1, 12, 13, // F5, F6 climb back to F0; F7 is root; F8, F9 chain on + 6, 7, 7, 8, 9, // F10..F14 lower band — left of F7 climbs back, right + // chains forward 10, 11, 12, 13, 14, // F15..F19 south cap, hung off lower band }; diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h index 97a1ceefa6..83c6573b0c 100644 --- a/src/projections/polyhedral/polyhedra/icosahedron.h +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -52,11 +52,10 @@ constexpr polyhedral::Mesh<12, 20, 3> mesh = { // F10..F14 lower band (up-pointing) // F15..F19 south cap (around V11) { - {1, 2, 0}, // permuted so the net's first edge lies along +x - {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, {1, 6, 2}, - {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, {6, 7, 2}, - {7, 8, 3}, {8, 9, 4}, {9, 10, 5}, {10, 6, 1}, {11, 7, 6}, - {11, 8, 7}, {11, 9, 8}, {11, 10, 9}, {11, 6, 10}, + {0, 1, 2}, {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, + {1, 6, 2}, {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, + {6, 7, 2}, {7, 8, 3}, {8, 9, 4}, {9, 10, 5}, {10, 6, 1}, + {11, 7, 6}, {11, 8, 7}, {11, 9, 8}, {11, 10, 9}, {11, 6, 10}, }, }; diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 9b5d36067f..ad0efe0ca4 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -12,6 +12,7 @@ #include "conway.h" #include "snyder.h" +#include "unfold.h" #include "proj.h" #include "proj_internal.h" @@ -34,6 +35,8 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; + int root_face_index; // unfold-tree root; default reference face for lat_0/lon_0 + // Translation in projected space so the geographic anchor named by // +lat_0 / +lon_0 (or its dynamic default) lands at (0, 0). // +x_0/+y_0 stack on top via PROJ core. @@ -62,16 +65,15 @@ struct PolyhedralDefaults { double orient_lat_deg; double orient_lon_deg; double azi_deg; - int default_face_index = 0; DefaultOrigin default_origin = DefaultOrigin::FaceCentroid; }; -// Build triangle data from a polyhedron + matching net by applying the Conway -// `meta` operation to both. -template +// Build triangle data from a polyhedron and the unfold-tree `parents` array. +template inline void load_meshes(pj_polyhedral_data *Q, const Mesh &polyhedron, - const Mesh &net) { + const int (&parents)[NF]) { + const auto net = unfold_net(polyhedron, parents); constexpr int N = 2 * NFV * NF; Vec3 sph[N][3]; Vec3 face[N][3]; @@ -81,6 +83,9 @@ inline void load_meshes(pj_polyhedral_data *Q, Q->n_triangles = N; Q->face_vertex_count = NFV; Q->num_faces = NF; + Q->root_face_index = 0; + while (Q->root_face_index < NF && parents[Q->root_face_index] != -1) + Q->root_face_index++; for (int i = 0; i < N; i++) { Q->sph_tris[i] = {sph[i][0], sph[i][1], sph[i][2]}; Q->face_tris[i] = { @@ -263,10 +268,9 @@ inline bool apply_polyhedral_params(pj_polyhedral_data *Q, PJ *P, return true; } - // Default anchor: a planar reference point on the chosen face. This is - // already in projected coords (the unfolded net), so use it directly. + // Default anchor: a planar reference point on the unfold's root face. const Face2D ref = - face_reference_point(Q, d.default_face_index, d.default_origin); + face_reference_point(Q, Q->root_face_index, d.default_origin); Q->x_offset = ref.x; Q->y_offset = ref.y; return true; diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index d50af1f296..8923cf0e02 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -32,30 +32,23 @@ inline Vec3 face_normal(const Vec3 (&vertices)[NV_p], const int (&face)[NFV]) { vec3_subtract(vertices[face[2]], v0))); } -// Rigid transform mapping the polyhedron face f onto the 2D plane (z=0) such -// that the face's directed edge from slot idx_a to slot idx_b is aligned -// with the 2D edge net_vertex_a → net_vertex_b. -template -inline Mat4 mat4_rigid_transform(const Mesh &polyhedron, int f, - int idx_a, int idx_b, const Vec3 &net_vertex_a, - const Vec3 &net_vertex_b) { - const Vec3 poly_vertex_a = polyhedron.vertices[polyhedron.faces[f][idx_a]]; - const Vec3 poly_vertex_b = polyhedron.vertices[polyhedron.faces[f][idx_b]]; - - // Face local unit vectors - const Vec3 normal = face_normal(polyhedron.vertices, polyhedron.faces[f]); - const Vec3 u = vec3_normalize(vec3_subtract(poly_vertex_b, poly_vertex_a)); +// Rigid transform from a polyhedron face's plane to the 2D plane (z=0), +// sending poly_a → net_a and orienting poly_a→poly_b along net_a→net_b. +// poly_a and poly_b must lie on the face plane; only the direction of +// net_b − net_a is used (the 2D distance is derived from the 3D one). +inline Mat4 mat4_rigid_transform(const Vec3 &normal, const Vec3 &poly_a, + const Vec3 &net_a, const Vec3 &poly_b, + const Vec3 &net_b) { + const Vec3 u = vec3_normalize(vec3_subtract(poly_b, poly_a)); const Vec3 v = vec3_cross(normal, u); - - // Transform the face-local frame (u, v) into the net plane. const Vec3 edge_direction = - vec3_normalize(vec3_subtract(net_vertex_b, net_vertex_a)); + vec3_normalize(vec3_subtract(net_b, net_a)); const Vec3 r0 = vec3_subtract(vec3_scale(u, edge_direction.x), vec3_scale(v, edge_direction.y)); const Vec3 r1 = vec3_add(vec3_scale(u, edge_direction.y), vec3_scale(v, edge_direction.x)); - const double t0 = net_vertex_a.x - vec3_dot(r0, poly_vertex_a); - const double t1 = net_vertex_a.y - vec3_dot(r1, poly_vertex_a); + const double t0 = net_a.x - vec3_dot(r0, poly_a); + const double t1 = net_a.y - vec3_dot(r1, poly_a); return {{{r0.x, r0.y, r0.z, t0}, {r1.x, r1.y, r1.z, t1}, {0.0, 0.0, 0.0, 0.0}, @@ -83,7 +76,9 @@ inline double polygon_area_2d(const Vec3 *verts, const int (&face)[NFV]) { // // The resulting net is auto-scaled so its total area equals 4π (i.e. the // area of the unit sphere) and translated so the root face's centroid lies -// at the origin, with the first edge along the x-axis. +// at the origin. The root face is laid out "north-up": geographic north +// (+z), projected onto its face plane, points along +y; for a root face +// centred on the rotation axis the slot[0] vertex is placed up instead. template inline Mesh(), NF, NFV> unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { @@ -95,8 +90,27 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { int root = 0; while (parents[root] != -1) root++; - const Mat4 root_face_to_plane = mat4_rigid_transform( - polyhedron, root, 0, 1, {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}); + + // Place the root face "north-up": find the in-plane direction that + // matches geographic north (+z projected onto the face), then orient so + // that direction lands on +y. Polar fallback (face on the rotation + // axis): aim from the centroid out toward slot[0] instead. + const Vec3 normal = + face_normal(polyhedron.vertices, polyhedron.faces[root]); + Vec3 c_3d{0.0, 0.0, 0.0}; + for (int k = 0; k < NFV; k++) + c_3d = vec3_add(c_3d, polyhedron.vertices[polyhedron.faces[root][k]]); + c_3d = vec3_scale(c_3d, 1.0 / NFV); + + const Vec3 z{0.0, 0.0, 1.0}; + Vec3 up_3d = vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); + if (vec3_length(up_3d) < 1e-12) + up_3d = vec3_subtract( + polyhedron.vertices[polyhedron.faces[root][0]], c_3d); + + const Mat4 root_face_to_plane = + mat4_rigid_transform(normal, c_3d, {0.0, 0.0, 0.0}, + vec3_add(c_3d, up_3d), {0.0, 1.0, 0.0}); for (int k = 0; k < NFV; k++) { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; net.vertices[n_verts] = @@ -133,8 +147,12 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { // Place face onto net using shared edge for orientation const int na = net.faces[p][ia_p]; const int nb = net.faces[p][ib_p]; + const Vec3 normal_c = + face_normal(polyhedron.vertices, polyhedron.faces[c]); const Mat4 face_to_plane = mat4_rigid_transform( - polyhedron, c, ia_c, ib_c, net.vertices[na], net.vertices[nb]); + normal_c, + polyhedron.vertices[polyhedron.faces[c][ia_c]], net.vertices[na], + polyhedron.vertices[polyhedron.faces[c][ib_c]], net.vertices[nb]); for (int k = 0; k < NFV; k++) { if (k == ia_c) { net.faces[c][k] = na; diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index d858b86242..19ced2319f 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3238,19 +3238,19 @@ operation +proj=tsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect 3235993.22451040 9907682.60840717 +expect 6962308.21925868 -7756293.64310391 roundtrip 1 accept 45 0 -expect 5752617.07966014 5734785.00018046 +expect 2090160.95556815 -7849305.02932016 roundtrip 1 accept 2 49 -expect 10611559.5707055 9798969.47180896 +expect 3180376.70814197 -14089364.89790736 roundtrip 1 accept -110 54 -expect -13838645.5935957 5122850.34539395 +expect 11355841.33569490 9423193.46532648 roundtrip 1 ------------------------------------------------------------------------------- @@ -3261,15 +3261,15 @@ operation +proj=tsea +R=6371007.18091875 +orient_lat=0 +orient_lon=0 +azi=0 tolerance 0.2 mm accept 0 0 -expect 17160609.6630278 9907682.60840717 +expect 0 -19815365.21681434 roundtrip 1 accept 45 0 -expect 12233639.0746285 4919488.85110285 +expect -1856417.21862487 -13054386.64490965 roundtrip 1 accept 2 49 -expect 110325.228702713 -13001663.8698201 +expect -11314933.81708183 6405287.48417516 roundtrip 1 ------------------------------------------------------------------------------- @@ -3283,7 +3283,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect -7375566.34619513 108713.136598217 +expect 3781931.51111671 6333071.25480345 roundtrip 1 ------------------------------------------------------------------------------- @@ -3297,7 +3297,7 @@ expect 500000 1000000 roundtrip 1 accept 0 0 -expect -6875566.34619513 1108713.13659822 +expect 4281931.51111671 7333071.25480345 roundtrip 1 =============================================================================== @@ -3311,19 +3311,19 @@ operation +proj=dsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect 0 -9872947.35628115 +expect -5803172.85268202 7987382.19580066 roundtrip 1 accept 45 0 -expect 5018607.99435854 -9485537.57508639 +expect -9635598.25224392 4724097.33290596 roundtrip 1 accept 2 49 -expect 151412.117573414 -4403884.01108735 +expect -2711033.05079495 3473819.19649775 roundtrip 1 accept -110 54 -expect -3813952.97764993 1378763.12588854 +expect 3895969.40646768 1126342.51313823 roundtrip 1 ------------------------------------------------------------------------------- @@ -3337,7 +3337,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect -151412.117573417 -5469063.34519380 +expect -3092139.80188706 4513562.99930291 roundtrip 1 ------------------------------------------------------------------------------- @@ -3348,11 +3348,11 @@ operation +proj=dsea +R=6371007.18091875 +net=a5 tolerance 0.2 mm accept 0 0 -expect 10826790.5654831 -11235323.5817327 +expect -15363015.06809053 2725739.89087309 roundtrip 1 accept 45 0 -expect 16370612.0092947 -12695836.0892119 +expect -20706528.54259930 648742.84390572 roundtrip 1 =============================================================================== From 66f5a7ddea1a718985d786f2302a98cab6cf9e0f Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 17:48:58 +0200 Subject: [PATCH 27/62] General rigid transform --- src/projections/polyhedral/nets/isea/isea.h | 4 ++-- .../polyhedral/polyhedra/icosahedron.h | 8 ++++---- src/projections/polyhedral/sphere.h | 3 ++- src/projections/polyhedral/unfold.h | 18 ++++++++---------- 4 files changed, 16 insertions(+), 17 deletions(-) diff --git a/src/projections/polyhedral/nets/isea/isea.h b/src/projections/polyhedral/nets/isea/isea.h index 5ccf3f9c1a..01c915fd23 100644 --- a/src/projections/polyhedral/nets/isea/isea.h +++ b/src/projections/polyhedral/nets/isea/isea.h @@ -36,9 +36,9 @@ namespace nets { namespace isea { constexpr int isea[20] = { - 5, 6, 7, 8, 9, // F0..F4 north cap, hung off upper band + 5, 6, 7, 8, 9, // F0..F4 north cap, hung off upper band 10, 11, -1, 12, 13, // F5, F6 climb back to F0; F7 is root; F8, F9 chain on - 6, 7, 7, 8, 9, // F10..F14 lower band — left of F7 climbs back, right + 6, 7, 7, 8, 9, // F10..F14 lower band — left of F7 climbs back, right // chains forward 10, 11, 12, 13, 14, // F15..F19 south cap, hung off lower band }; diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h index 83c6573b0c..8577cec141 100644 --- a/src/projections/polyhedral/polyhedra/icosahedron.h +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -52,10 +52,10 @@ constexpr polyhedral::Mesh<12, 20, 3> mesh = { // F10..F14 lower band (up-pointing) // F15..F19 south cap (around V11) { - {0, 1, 2}, {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, - {1, 6, 2}, {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, - {6, 7, 2}, {7, 8, 3}, {8, 9, 4}, {9, 10, 5}, {10, 6, 1}, - {11, 7, 6}, {11, 8, 7}, {11, 9, 8}, {11, 10, 9}, {11, 6, 10}, + {0, 1, 2}, {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, + {1, 6, 2}, {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, + {6, 7, 2}, {7, 8, 3}, {8, 9, 4}, {9, 10, 5}, {10, 6, 1}, + {11, 7, 6}, {11, 8, 7}, {11, 9, 8}, {11, 10, 9}, {11, 6, 10}, }, }; diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index ad0efe0ca4..a0bfdfe5c0 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -35,7 +35,8 @@ struct pj_polyhedral_data { double orient[3][3]; double orient_inv[3][3]; - int root_face_index; // unfold-tree root; default reference face for lat_0/lon_0 + int root_face_index; // unfold-tree root; default reference face for + // lat_0/lon_0 // Translation in projected space so the geographic anchor named by // +lat_0 / +lon_0 (or its dynamic default) lands at (0, 0). diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 8923cf0e02..07ea15a810 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -41,8 +41,7 @@ inline Mat4 mat4_rigid_transform(const Vec3 &normal, const Vec3 &poly_a, const Vec3 &net_b) { const Vec3 u = vec3_normalize(vec3_subtract(poly_b, poly_a)); const Vec3 v = vec3_cross(normal, u); - const Vec3 edge_direction = - vec3_normalize(vec3_subtract(net_b, net_a)); + const Vec3 edge_direction = vec3_normalize(vec3_subtract(net_b, net_a)); const Vec3 r0 = vec3_subtract(vec3_scale(u, edge_direction.x), vec3_scale(v, edge_direction.y)); const Vec3 r1 = vec3_add(vec3_scale(u, edge_direction.y), @@ -105,12 +104,11 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { const Vec3 z{0.0, 0.0, 1.0}; Vec3 up_3d = vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); if (vec3_length(up_3d) < 1e-12) - up_3d = vec3_subtract( - polyhedron.vertices[polyhedron.faces[root][0]], c_3d); + up_3d = + vec3_subtract(polyhedron.vertices[polyhedron.faces[root][0]], c_3d); - const Mat4 root_face_to_plane = - mat4_rigid_transform(normal, c_3d, {0.0, 0.0, 0.0}, - vec3_add(c_3d, up_3d), {0.0, 1.0, 0.0}); + const Mat4 root_face_to_plane = mat4_rigid_transform( + normal, c_3d, {0.0, 0.0, 0.0}, vec3_add(c_3d, up_3d), {0.0, 1.0, 0.0}); for (int k = 0; k < NFV; k++) { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; net.vertices[n_verts] = @@ -150,9 +148,9 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { const Vec3 normal_c = face_normal(polyhedron.vertices, polyhedron.faces[c]); const Mat4 face_to_plane = mat4_rigid_transform( - normal_c, - polyhedron.vertices[polyhedron.faces[c][ia_c]], net.vertices[na], - polyhedron.vertices[polyhedron.faces[c][ib_c]], net.vertices[nb]); + normal_c, polyhedron.vertices[polyhedron.faces[c][ia_c]], + net.vertices[na], polyhedron.vertices[polyhedron.faces[c][ib_c]], + net.vertices[nb]); for (int k = 0; k < NFV; k++) { if (k == ia_c) { net.faces[c][k] = na; From cf2ecdf7312aaf8e111994c6a9db0c52ccb325a9 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 18:16:56 +0200 Subject: [PATCH 28/62] face_centroid --- src/projections/polyhedral/unfold.h | 23 +++++++++++++---------- 1 file changed, 13 insertions(+), 10 deletions(-) diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 07ea15a810..46ad5f82c2 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -25,13 +25,21 @@ template constexpr int unfolded_vertex_count() { return NFV + (NFV - 2) * (NF - 1); } -template -inline Vec3 face_normal(const Vec3 (&vertices)[NV_p], const int (&face)[NFV]) { +template +inline Vec3 face_normal(const Vec3 (&vertices)[NV], const int (&face)[NFV]) { const Vec3 v0 = vertices[face[0]]; return vec3_normalize(vec3_cross(vec3_subtract(vertices[face[1]], v0), vec3_subtract(vertices[face[2]], v0))); } +template +inline Vec3 face_centroid(const Vec3 (&vertices)[NV], const int (&face)[NFV]) { + Vec3 c{0.0, 0.0, 0.0}; + for (int k = 0; k < NFV; k++) + c = vec3_add(c, vertices[face[k]]); + return vec3_scale(c, 1.0 / NFV); +} + // Rigid transform from a polyhedron face's plane to the 2D plane (z=0), // sending poly_a → net_a and orienting poly_a→poly_b along net_a→net_b. // poly_a and poly_b must lie on the face plane; only the direction of @@ -96,10 +104,8 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { // axis): aim from the centroid out toward slot[0] instead. const Vec3 normal = face_normal(polyhedron.vertices, polyhedron.faces[root]); - Vec3 c_3d{0.0, 0.0, 0.0}; - for (int k = 0; k < NFV; k++) - c_3d = vec3_add(c_3d, polyhedron.vertices[polyhedron.faces[root][k]]); - c_3d = vec3_scale(c_3d, 1.0 / NFV); + const Vec3 c_3d = + face_centroid(polyhedron.vertices, polyhedron.faces[root]); const Vec3 z{0.0, 0.0, 1.0}; Vec3 up_3d = vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); @@ -177,10 +183,7 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { const double scale = std::sqrt(4.0 * M_PI / total_area); // Translate so the root face's centroid is at origin, then scale. - Vec3 centroid{0.0, 0.0, 0.0}; - for (int k = 0; k < NFV; k++) - centroid = vec3_add(centroid, net.vertices[net.faces[root][k]]); - centroid = vec3_scale(centroid, 1.0 / NFV); + const Vec3 centroid = face_centroid(net.vertices, net.faces[root]); for (int i = 0; i < NV_n; i++) net.vertices[i] = vec3_scale(vec3_subtract(net.vertices[i], centroid), scale); From 75081d92cc0e5d686ff4d911bc7c386082b90835 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 20:30:52 +0200 Subject: [PATCH 29/62] Tidy vec names --- src/projections/polyhedral/unfold.h | 45 +++++++++++++++++------------ 1 file changed, 26 insertions(+), 19 deletions(-) diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 46ad5f82c2..0a6dcbcb3b 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -25,13 +25,9 @@ template constexpr int unfolded_vertex_count() { return NFV + (NFV - 2) * (NF - 1); } -template -inline Vec3 face_normal(const Vec3 (&vertices)[NV], const int (&face)[NFV]) { - const Vec3 v0 = vertices[face[0]]; - return vec3_normalize(vec3_cross(vec3_subtract(vertices[face[1]], v0), - vec3_subtract(vertices[face[2]], v0))); -} - +// For a regular face inscribed on the unit sphere centred at the origin, the +// face's outward unit normal is just the centroid direction, so we don't +// need a separate face_normal helper. template inline Vec3 face_centroid(const Vec3 (&vertices)[NV], const int (&face)[NFV]) { Vec3 c{0.0, 0.0, 0.0}; @@ -70,6 +66,9 @@ inline double polygon_area_2d(const Vec3 *verts, const int (&face)[NFV]) { return std::fabs(a) * 0.5; } +// Unit vector in Z +inline constexpr Vec3 z{0.0, 0.0, 1.0}; + // Unfold a polyhedron Mesh into a planar net Mesh. // // `parents[i]` is the index of face i's parent in the unfolding tree, or -1 @@ -102,19 +101,27 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { // matches geographic north (+z projected onto the face), then orient so // that direction lands on +y. Polar fallback (face on the rotation // axis): aim from the centroid out toward slot[0] instead. - const Vec3 normal = - face_normal(polyhedron.vertices, polyhedron.faces[root]); - const Vec3 c_3d = - face_centroid(polyhedron.vertices, polyhedron.faces[root]); - const Vec3 z{0.0, 0.0, 1.0}; - Vec3 up_3d = vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); - if (vec3_length(up_3d) < 1e-12) - up_3d = - vec3_subtract(polyhedron.vertices[polyhedron.faces[root][0]], c_3d); + // Destination in 2d net (origin and unit step in +y) + const Vec3 origin_net = {0.0, 0.0, 0.0}; + const Vec3 offset_net = {0.0, 1.0, 0.0}; + + const Vec3 origin_poly = + face_centroid(polyhedron.vertices, polyhedron.faces[root]); + const Vec3 normal = vec3_normalize(origin_poly); + + // Vector in north direction constrained in the face plane + const Vec3 step_poly = + vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); + Vec3 offset_poly; + if (vec3_length(step_poly) < 1e-12) + // Fallback to 1st vertex at pole + offset_poly = polyhedron.vertices[polyhedron.faces[root][0]]; + else + offset_poly = vec3_add(origin_poly, step_poly); const Mat4 root_face_to_plane = mat4_rigid_transform( - normal, c_3d, {0.0, 0.0, 0.0}, vec3_add(c_3d, up_3d), {0.0, 1.0, 0.0}); + normal, origin_poly, origin_net, offset_poly, offset_net); for (int k = 0; k < NFV; k++) { Vec3 face_vertex = polyhedron.vertices[polyhedron.faces[root][k]]; net.vertices[n_verts] = @@ -151,8 +158,8 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { // Place face onto net using shared edge for orientation const int na = net.faces[p][ia_p]; const int nb = net.faces[p][ib_p]; - const Vec3 normal_c = - face_normal(polyhedron.vertices, polyhedron.faces[c]); + const Vec3 normal_c = vec3_normalize( + face_centroid(polyhedron.vertices, polyhedron.faces[c])); const Mat4 face_to_plane = mat4_rigid_transform( normal_c, polyhedron.vertices[polyhedron.faces[c][ia_c]], net.vertices[na], polyhedron.vertices[polyhedron.faces[c][ib_c]], From 0f2658879425bb6e91d2ac65aca26b09d233972a Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 22:48:18 +0200 Subject: [PATCH 30/62] Improve nets --- src/projections/polyhedral.cpp | 14 ++++++++- src/projections/polyhedral/nets/dsea/dsea.h | 32 ++++++++++++++------- src/projections/polyhedral/sphere.h | 9 ++++-- src/projections/polyhedral/unfold.h | 17 ++++++----- test/gie/builtins.gie | 14 ++++----- 5 files changed, 59 insertions(+), 27 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index ef4cf91fff..0280443986 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -156,12 +156,24 @@ PJ *PJ_PROJECTION(dsea) { } } - polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents); // Defaults rotate the polyhedron so F0's centroid sits at the geographic // north pole. orient_lat = atan((1+2A)/2) places V0 on the F0 axis. using polyhedra::dodecahedron_constants::A; const double default_orient_lat = std::atan((1 + 2 * A) / 2.0) * 180.0 / M_PI; + + // The unfold's "north-up" rotation needs to use geographic north, not + // polyhedron +z (V0) — under these defaults they differ by ~37°. The + // third column of the orient matrix is geographic +z expressed in + // polyhedron coordinates: (-cos(azi)cos(lat), -sin(azi)cos(lat), sin(lat)). + const double lat_rad = default_orient_lat * DEG_TO_RAD; + const double azi_rad = default_azi * DEG_TO_RAD; + const polyhedral::Vec3 up_dir = { + -std::cos(azi_rad) * std::cos(lat_rad), + -std::sin(azi_rad) * std::cos(lat_rad), + std::sin(lat_rad)}; + polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents, up_dir); + const polyhedral::PolyhedralDefaults d = {default_orient_lat, default_orient_lon, default_azi}; return polyhedral_setup(P, d); diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h index 033e80e7e1..de506372a2 100644 --- a/src/projections/polyhedral/nets/dsea/dsea.h +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -6,12 +6,11 @@ * i's parent in the unfolding tree, or -1 if i is the root. Every * parent–child pair must share an edge on the dodecahedron. * - * The dodecahedron face order in `polyhedra::dodecahedron` is - * chosen so the canonical DSEA net is a simple chain — F0 is the - * cap around V0, F1..F10 zig-zag around the middle band, F11 is - * the cap around V17 — so dsea[i] = i - 1. The other layouts - * (a5, crescent, flower) are valid parents trees over the - * same face indices. + * All four layouts are rooted at F2 — the equatorial face whose + * centroid lands over Southern Africa under the default DSEA + * orient. F0 (the polar face around V0) and F11 (around V17) are + * hung off F1 and F8 respectively, the upper- and lower-band faces + * that cover Europe and the South Pacific. * Author: Felix Palmer * ****************************************************************************/ @@ -22,10 +21,23 @@ namespace nets { namespace dsea { -constexpr int dsea[12] = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; -constexpr int a5[12] = {-1, 0, 1, 4, 2, 3, 8, 5, 7, 10, 11, 6}; -constexpr int crescent[12] = {-1, 3, 4, 0, 3, 3, 4, 5, 6, 1, 2, 4}; -constexpr int flower[12] = {-1, 0, 11, 0, 11, 0, 11, 0, 11, 0, 9, 10}; +// Snyder's two-rows-of-5 layout (Figure 6): F2 (Africa) is the central face +// of the lower row, with the row extending left and right via zig-zag +// connections through the upper row — directly hinging adjacent lower-row +// faces would curl the band into a crescent, so each next-lower-row face is +// reached through its upper-row neighbour instead. +// Right: F2 → F3 → F4 → F5 → F6 (L → U → L → U → L) +// Left: F2 → F1 → F10 → F9 → F8 → F7 (L → U → L → U → L → U) +// The two polar caps hang symmetrically above and below the central column: +// F0 (north pole) off F1 (Europe), F11 (south pole) off F2 (Africa). +constexpr int dsea[12] = {1, 2, -1, 2, 3, 4, 5, 8, 9, 10, 1, 2}; + +// The other layouts are the originals re-rooted at F2 (parent pointers +// reversed along the F2 → F0 path in the original tree); their visual +// "shape" is otherwise unchanged. +constexpr int a5[12] = {1, 2, -1, 4, 2, 3, 8, 5, 7, 10, 11, 6}; +constexpr int crescent[12] = {3, 3, -1, 4, 2, 3, 4, 5, 6, 1, 2, 4}; +constexpr int flower[12] = {9, 0, -1, 0, 11, 0, 11, 0, 11, 10, 11, 2}; } // namespace dsea } // namespace nets diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index a0bfdfe5c0..6d06f3abb9 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -70,11 +70,16 @@ struct PolyhedralDefaults { }; // Build triangle data from a polyhedron and the unfold-tree `parents` array. +// `up_dir` is the direction (in polyhedron coordinates) that should appear +// "up" on the root face of the unfolded net — usually the geographic +z +// direction expressed in polyhedron coords (the third column of the orient +// matrix); defaults to polyhedron +z. template inline void load_meshes(pj_polyhedral_data *Q, const Mesh &polyhedron, - const int (&parents)[NF]) { - const auto net = unfold_net(polyhedron, parents); + const int (&parents)[NF], + const Vec3 &up_dir = z) { + const auto net = unfold_net(polyhedron, parents, up_dir); constexpr int N = 2 * NFV * NF; Vec3 sph[N][3]; Vec3 face[N][3]; diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 0a6dcbcb3b..7468bac582 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -87,7 +87,8 @@ inline constexpr Vec3 z{0.0, 0.0, 1.0}; // centred on the rotation axis the slot[0] vertex is placed up instead. template inline Mesh(), NF, NFV> -unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { +unfold_net(const Mesh &polyhedron, const int (&parents)[NF], + const Vec3 &up_dir = z) { constexpr int NV_n = unfolded_vertex_count(); Mesh net{}; int n_verts = 0; @@ -97,9 +98,11 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { while (parents[root] != -1) root++; - // Place the root face "north-up": find the in-plane direction that - // matches geographic north (+z projected onto the face), then orient so - // that direction lands on +y. Polar fallback (face on the rotation + // Place the root face "up-direction-up": project up_dir onto the root + // face's plane, then orient so that direction lands on +y. up_dir is + // typically geographic north expressed in polyhedron coordinates (the + // third column of the orient matrix), so the root face comes out with + // true geographic north up. Polar fallback (face on the rotation // axis): aim from the centroid out toward slot[0] instead. // Destination in 2d net (origin and unit step in +y) @@ -110,9 +113,9 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF]) { face_centroid(polyhedron.vertices, polyhedron.faces[root]); const Vec3 normal = vec3_normalize(origin_poly); - // Vector in north direction constrained in the face plane - const Vec3 step_poly = - vec3_subtract(z, vec3_scale(normal, vec3_dot(z, normal))); + // Vector in up_dir direction constrained to the face plane + const Vec3 step_poly = vec3_subtract( + up_dir, vec3_scale(normal, vec3_dot(up_dir, normal))); Vec3 offset_poly; if (vec3_length(step_poly) < 1e-12) // Fallback to 1st vertex at pole diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 19ced2319f..455adf7d74 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3311,19 +3311,19 @@ operation +proj=dsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect -5803172.85268202 7987382.19580066 +expect -4021198.96415185 2503030.49539516 roundtrip 1 accept 45 0 -expect -9635598.25224392 4724097.33290596 +expect 997409.03020670 2890440.27658991 roundtrip 1 accept 2 49 -expect -2711033.05079495 3473819.19649775 +expect -3869786.84657843 7972093.84058896 roundtrip 1 accept -110 54 -expect 3895969.40646768 1126342.51313823 +expect -7835151.94180176 13754740.97756485 roundtrip 1 ------------------------------------------------------------------------------- @@ -3337,7 +3337,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect -3092139.80188706 4513562.99930291 +expect -151412.11757342 -5469063.34519379 roundtrip 1 ------------------------------------------------------------------------------- @@ -3348,11 +3348,11 @@ operation +proj=dsea +R=6371007.18091875 +net=a5 tolerance 0.2 mm accept 0 0 -expect -15363015.06809053 2725739.89087309 +expect 6805591.60133129 1140654.26994360 roundtrip 1 accept 45 0 -expect -20706528.54259930 648742.84390572 +expect 12349413.04514284 -319858.23753558 roundtrip 1 =============================================================================== From f0ddf00e7584b55f96f7f58ac40241d740350f7e Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 22:48:24 +0200 Subject: [PATCH 31/62] Improve nets --- src/projections/polyhedral.cpp | 7 +++---- src/projections/polyhedral/sphere.h | 3 +-- src/projections/polyhedral/unfold.h | 4 ++-- 3 files changed, 6 insertions(+), 8 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index 0280443986..f1ebcff38e 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -168,10 +168,9 @@ PJ *PJ_PROJECTION(dsea) { // polyhedron coordinates: (-cos(azi)cos(lat), -sin(azi)cos(lat), sin(lat)). const double lat_rad = default_orient_lat * DEG_TO_RAD; const double azi_rad = default_azi * DEG_TO_RAD; - const polyhedral::Vec3 up_dir = { - -std::cos(azi_rad) * std::cos(lat_rad), - -std::sin(azi_rad) * std::cos(lat_rad), - std::sin(lat_rad)}; + const polyhedral::Vec3 up_dir = {-std::cos(azi_rad) * std::cos(lat_rad), + -std::sin(azi_rad) * std::cos(lat_rad), + std::sin(lat_rad)}; polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents, up_dir); const polyhedral::PolyhedralDefaults d = {default_orient_lat, diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 6d06f3abb9..720a4deae0 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -77,8 +77,7 @@ struct PolyhedralDefaults { template inline void load_meshes(pj_polyhedral_data *Q, const Mesh &polyhedron, - const int (&parents)[NF], - const Vec3 &up_dir = z) { + const int (&parents)[NF], const Vec3 &up_dir = z) { const auto net = unfold_net(polyhedron, parents, up_dir); constexpr int N = 2 * NFV * NF; Vec3 sph[N][3]; diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index 7468bac582..a2962c3425 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -114,8 +114,8 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF], const Vec3 normal = vec3_normalize(origin_poly); // Vector in up_dir direction constrained to the face plane - const Vec3 step_poly = vec3_subtract( - up_dir, vec3_scale(normal, vec3_dot(up_dir, normal))); + const Vec3 step_poly = + vec3_subtract(up_dir, vec3_scale(normal, vec3_dot(up_dir, normal))); Vec3 offset_poly; if (vec3_length(step_poly) < 1e-12) // Fallback to 1st vertex at pole From 5073f55e933876b8fb76d46118110fd5e8af1440 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 23:18:29 +0200 Subject: [PATCH 32/62] Rotate nets --- src/projections/polyhedral/nets/dsea/dsea.h | 24 +++++++++++++++------ test/gie/builtins.gie | 4 ++-- 2 files changed, 20 insertions(+), 8 deletions(-) diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h index de506372a2..e38fb17b86 100644 --- a/src/projections/polyhedral/nets/dsea/dsea.h +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -32,12 +32,24 @@ namespace dsea { // F0 (north pole) off F1 (Europe), F11 (south pole) off F2 (Africa). constexpr int dsea[12] = {1, 2, -1, 2, 3, 4, 5, 8, 9, 10, 1, 2}; -// The other layouts are the originals re-rooted at F2 (parent pointers -// reversed along the F2 → F0 path in the original tree); their visual -// "shape" is otherwise unchanged. -constexpr int a5[12] = {1, 2, -1, 4, 2, 3, 8, 5, 7, 10, 11, 6}; -constexpr int crescent[12] = {3, 3, -1, 4, 2, 3, 4, 5, 6, 1, 2, 4}; -constexpr int flower[12] = {9, 0, -1, 0, 11, 0, 11, 0, 11, 10, 11, 2}; +// A5 net (re-rooted at F3 — the Middle East face — to match the A5 +// reference codebase's coordinate origin). The visual shape is the same as +// the published A5 layout; only the parent pointers along the F3 → F0 path +// of the original tree are reversed. +constexpr int a5[12] = {1, 2, 4, 5, 3, -1, 8, 5, 7, 10, 11, 6}; + +// Crescent: central spine F0 → F1 → F2 → F11 (north pole → UK/Europe → +// Africa → south pole). Two symmetric "crescent" arcs extend out from F1 +// and F2: one through the upper row (F1 → F3 → F5 → F7 → F9) and one +// through the lower row (F2 → F4 → F6 → F8 → F10). +constexpr int crescent[12] = {1, -1, 1, 1, 2, 3, 4, 9, 10, 1, 2, 2}; + +// Flower: F2 (Africa) at the centre. Both polar caps hang via Africa — +// F11 (south pole) directly off F2, F0 (north pole) via F1 (Europe). F0's +// four other petals (F3, F5, F7, F9) hang off F0; F11's four other petals +// (F4, F6, F8, F10) hang off F11. This avoids routing the polar caps +// through the Americas (as the original flower did). +constexpr int flower[12] = {1, -1, 1, 0, 11, 0, 11, 0, 11, 0, 11, 2}; } // namespace dsea } // namespace nets diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 455adf7d74..7f53bd7a30 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3348,11 +3348,11 @@ operation +proj=dsea +R=6371007.18091875 +net=a5 tolerance 0.2 mm accept 0 0 -expect 6805591.60133129 1140654.26994360 +expect 2350141.86904343 -2725739.89087309 roundtrip 1 accept 45 0 -expect 12349413.04514284 -319858.23753558 +expect 7693655.34355220 -648742.84390572 roundtrip 1 =============================================================================== From 76dcbe8e1c552a55e7ed590a295fa54b76f6104e Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Sun, 10 May 2026 23:57:24 +0200 Subject: [PATCH 33/62] Rearrange dodecahedron faces --- src/projections/polyhedral/nets/dsea/dsea.h | 60 ++++++++++--------- .../polyhedral/polyhedra/dodecahedron.h | 22 ++++--- test/gie/builtins.gie | 4 +- 3 files changed, 46 insertions(+), 40 deletions(-) diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h index e38fb17b86..f23935c0a1 100644 --- a/src/projections/polyhedral/nets/dsea/dsea.h +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -6,11 +6,14 @@ * i's parent in the unfolding tree, or -1 if i is the root. Every * parent–child pair must share an edge on the dodecahedron. * - * All four layouts are rooted at F2 — the equatorial face whose - * centroid lands over Southern Africa under the default DSEA - * orient. F0 (the polar face around V0) and F11 (around V17) are - * hung off F1 and F8 respectively, the upper- and lower-band faces - * that cover Europe and the South Pacific. + * The dodecahedron face order is top-to-bottom, then left-to-right + * within each band: + * F0 north polar cap + * F1..F5 upper band N.Pacific, N.America, Europe, + * India, Asia + * F6..F10 lower band S.Pacific, S.Atlantic, S.Africa, + * Indian, S.Pacific E + * F11 south polar cap * Author: Felix Palmer * ****************************************************************************/ @@ -21,35 +24,34 @@ namespace nets { namespace dsea { -// Snyder's two-rows-of-5 layout (Figure 6): F2 (Africa) is the central face +// Snyder's two-rows-of-5 layout (Figure 6): F8 (Africa) is the central face // of the lower row, with the row extending left and right via zig-zag // connections through the upper row — directly hinging adjacent lower-row // faces would curl the band into a crescent, so each next-lower-row face is // reached through its upper-row neighbour instead. -// Right: F2 → F3 → F4 → F5 → F6 (L → U → L → U → L) -// Left: F2 → F1 → F10 → F9 → F8 → F7 (L → U → L → U → L → U) +// Right: F8 → F4 → F9 → F5 → F10 (L → U → L → U → L) +// Left: F8 → F3 → F7 → F2 → F6 → F1 (L → U → L → U → L → U) // The two polar caps hang symmetrically above and below the central column: -// F0 (north pole) off F1 (Europe), F11 (south pole) off F2 (Africa). -constexpr int dsea[12] = {1, 2, -1, 2, 3, 4, 5, 8, 9, 10, 1, 2}; - -// A5 net (re-rooted at F3 — the Middle East face — to match the A5 -// reference codebase's coordinate origin). The visual shape is the same as -// the published A5 layout; only the parent pointers along the F3 → F0 path -// of the original tree are reversed. -constexpr int a5[12] = {1, 2, 4, 5, 3, -1, 8, 5, 7, 10, 11, 6}; - -// Crescent: central spine F0 → F1 → F2 → F11 (north pole → UK/Europe → -// Africa → south pole). Two symmetric "crescent" arcs extend out from F1 -// and F2: one through the upper row (F1 → F3 → F5 → F7 → F9) and one -// through the lower row (F2 → F4 → F6 → F8 → F10). -constexpr int crescent[12] = {1, -1, 1, 1, 2, 3, 4, 9, 10, 1, 2, 2}; - -// Flower: F2 (Africa) at the centre. Both polar caps hang via Africa — -// F11 (south pole) directly off F2, F0 (north pole) via F1 (Europe). F0's -// four other petals (F3, F5, F7, F9) hang off F0; F11's four other petals -// (F4, F6, F8, F10) hang off F11. This avoids routing the polar caps -// through the Americas (as the original flower did). -constexpr int flower[12] = {1, -1, 1, 0, 11, 0, 11, 0, 11, 0, 11, 2}; +// F0 (north pole) off F3 (Europe), F11 (south pole) off F8 (Africa). +constexpr int dsea[12] = {3, 6, 7, 8, 8, 9, 2, 3, -1, 4, 5, 8}; + +// A5 net (re-rooted to match the A5 reference codebase's coordinate origin). +// The visual shape is the same as the published A5 layout; only the parent +// pointers along the path to the new root are reversed. +constexpr int a5[12] = {3, 5, 7, 8, 5, -1, 1, 11, 9, 4, 6, 10}; + +// Crescent: central spine F0 → F3 → F8 → F11 (north pole → UK/Europe → +// Africa → south pole). Two symmetric "crescent" arcs extend out from F3 +// and F8: one through the upper row (F3 → F4 → F5 → F1 → F2) and one +// through the lower row (F8 → F9 → F10 → F6 → F7). +constexpr int crescent[12] = {3, 2, 3, -1, 3, 4, 7, 8, 3, 8, 9, 8}; + +// Flower: F3 (Europe) at the centre, with F0 (north pole) as one petal and +// F8 (Africa) as the link down to the south pole. F0's four other petals +// (F1, F2, F4, F5) hang off F0; F11's four other petals (F6, F7, F9, F10) +// hang off F11. This routes the polar caps through Africa rather than +// through the Americas. +constexpr int flower[12] = {3, 0, 0, -1, 0, 0, 11, 11, 3, 11, 11, 8}; } // namespace dsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/dodecahedron.h b/src/projections/polyhedral/polyhedra/dodecahedron.h index 0f3a6c687f..82b93f3021 100644 --- a/src/projections/polyhedral/polyhedra/dodecahedron.h +++ b/src/projections/polyhedral/polyhedra/dodecahedron.h @@ -55,22 +55,26 @@ constexpr polyhedral::Mesh<20, 12, 5> mesh = { {-2.0 / 3.0, 0.0, -(4 * A - 1) / 3.0}, {-(4 * A - 1) / 3.0, -B, -1.0 / 3.0}, }, - // Faces (CCW from outside). Ordered to match the canonical DSEA net - // unfolding: F0 is the first 5 vertices, F1..F10 zig-zag around the - // middle band so the default parents tree is a simple chain - // {-1, 0, 1, …, 9}, and F11 is the last 5 vertices. + // Faces (CCW from outside). Ordered top-to-bottom, then left-to-right + // within each band, so the unfolded DSEA net comes out as: + // F0 (north polar cap, around V0) + // F1 F2 F3 F4 F5 (upper band: N.Pacific, N.America, + // Europe, India, Asia) + // F6 F7 F8 F9 F10 (lower band: S.Pacific, S.Atlantic, + // S.Africa, Indian, S.Pacific E) + // F11 (south polar cap, around V17) { {0, 1, 2, 3, 4}, + {3, 8, 13, 9, 4}, + {0, 4, 9, 14, 5}, {0, 5, 10, 6, 1}, - {6, 10, 15, 16, 11}, {1, 6, 11, 7, 2}, - {7, 11, 16, 17, 12}, {2, 7, 12, 8, 3}, - {8, 12, 17, 18, 13}, - {3, 8, 13, 9, 4}, {9, 13, 18, 19, 14}, - {0, 4, 9, 14, 5}, {5, 14, 19, 15, 10}, + {6, 10, 15, 16, 11}, + {7, 11, 16, 17, 12}, + {8, 12, 17, 18, 13}, {15, 19, 18, 17, 16}, }, }; diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 7f53bd7a30..bff3b666db 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3348,11 +3348,11 @@ operation +proj=dsea +R=6371007.18091875 +net=a5 tolerance 0.2 mm accept 0 0 -expect 2350141.86904343 -2725739.89087309 +expect -6207281.59771581 -1472479.22190498 roundtrip 1 accept 45 0 -expect 7693655.34355220 -648742.84390572 +expect -663460.15390426 -2932991.72938417 roundtrip 1 =============================================================================== From 2c18a51b1cede4662a285e61ff94045c27fdfe11 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 00:29:18 +0200 Subject: [PATCH 34/62] Rearrange tetrahedron --- src/projections/polyhedral/nets/tsea/tsea.h | 7 ++++--- src/projections/polyhedral/polyhedra/tetrahedron.h | 14 ++++++++------ 2 files changed, 12 insertions(+), 9 deletions(-) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index eded20fbc2..0a07548838 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -2,8 +2,9 @@ * * Project: PROJ * Purpose: Net layout for the TSEA projection — the regular tetrahedron - * unfolded into a "star" net (root face surrounded by its three - * neighbours). + * unfolded into a "star" net with the south-cap face (F3) at the + * centre and its three V0-touching neighbours (F0, F1, F2) as + * petals. * Author: Felix Palmer * ****************************************************************************/ @@ -14,7 +15,7 @@ namespace nets { namespace tsea { -constexpr int tsea[4] = {-1, 0, 0, 0}; +constexpr int tsea[4] = {3, 3, 3, -1}; } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index dc1a9c8b58..6422441d49 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -4,8 +4,9 @@ * Purpose: Regular tetrahedron inscribed in the unit sphere, oriented with * one vertex at the north pole. The remaining three vertices sit * at latitude -arcsin(1/3) ≈ -19.47°, separated by 120° in - * longitude (0°, +120°, -120°). Face 0 is the bottom triangle - * opposite the apex — the natural root for a "star" net. + * longitude (0°, +120°, -120°). Faces are listed top-to-bottom: + * F0..F2 are the three faces sharing V0 (CCW around V0, with V0 + * in slot 0), and F3 is the south-cap face opposite V0. * Author: Felix Palmer * ****************************************************************************/ @@ -30,12 +31,13 @@ constexpr polyhedral::Mesh<4, 4, 3> mesh = { {-0.5 * A, B, -1.0 / 3.0}, {-0.5 * A, -B, -1.0 / 3.0}, }, - // Faces + // Faces (CCW from outside). F0..F2 share V0, in CCW order around it; + // F3 is the south-cap face opposite V0. { - {3, 2, 1}, {0, 1, 2}, - {1, 0, 3}, - {2, 3, 0}, + {0, 2, 3}, + {0, 3, 1}, + {3, 2, 1}, }, }; From 98128f23629ec262af6437be6cd82b441849b2da Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 00:52:37 +0200 Subject: [PATCH 35/62] Snyder compatible tetrahedron --- src/projections/polyhedral.cpp | 18 ++++++++-- src/projections/polyhedral/nets/dsea/dsea.h | 2 +- src/projections/polyhedral/nets/tsea/tsea.h | 18 +++++++--- .../polyhedral/polyhedra/tetrahedron.h | 34 +++++++++++-------- test/gie/builtins.gie | 18 +++++----- 5 files changed, 59 insertions(+), 31 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index f1ebcff38e..c6266e5a16 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -108,7 +108,7 @@ static PJ *polyhedral_setup(PJ *P, const polyhedral::PolyhedralDefaults &d) { } PROJ_HEAD(tsea, "Tetrahedral Snyder Equal Area") -"\n\tSph&Ell\n\torient_lat= orient_lon= azi= lat_0= lon_0="; +"\n\tSph&Ell\n\tnet= orient_lat= orient_lon= azi= lat_0= lon_0="; PJ *PJ_PROJECTION(tsea) { auto *Q = static_cast( calloc(1, sizeof(pj_polyhedral_data))); @@ -117,7 +117,21 @@ PJ *PJ_PROJECTION(tsea) { P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::load_meshes(Q, polyhedra::tetrahedron, nets::tsea::tsea); + const char *net_name = pj_param(P->ctx, P->params, "snet").s; + const int(*parents)[4] = &nets::tsea::tsea; + if (net_name != nullptr) { + if (strcmp(net_name, "tsea") == 0) { + parents = &nets::tsea::tsea; + } else if (strcmp(net_name, "star") == 0) { + parents = &nets::tsea::star; + } else { + proj_log_error(P, _("invalid +net (expected tsea or star)")); + return polyhedral_destructor(P, + PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE); + } + } + + polyhedral::load_meshes(Q, polyhedra::tetrahedron, *parents); const polyhedral::PolyhedralDefaults d = {90.0, 0.0, 0.0}; return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h index f23935c0a1..f724170d2f 100644 --- a/src/projections/polyhedral/nets/dsea/dsea.h +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -33,7 +33,7 @@ namespace dsea { // Left: F8 → F3 → F7 → F2 → F6 → F1 (L → U → L → U → L → U) // The two polar caps hang symmetrically above and below the central column: // F0 (north pole) off F3 (Europe), F11 (south pole) off F8 (Africa). -constexpr int dsea[12] = {3, 6, 7, 8, 8, 9, 2, 3, -1, 4, 5, 8}; +constexpr int dsea[12] = {3, 6, 7, -1, 8, 9, 2, 3, 3, 4, 5, 8}; // A5 net (re-rooted to match the A5 reference codebase's coordinate origin). // The visual shape is the same as the published A5 layout; only the parent diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index 0a07548838..b883348f2b 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -1,10 +1,17 @@ /****************************************************************************** * * Project: PROJ - * Purpose: Net layout for the TSEA projection — the regular tetrahedron - * unfolded into a "star" net with the south-cap face (F3) at the - * centre and its three V0-touching neighbours (F0, F1, F2) as - * petals. + * Purpose: Net layouts for the TSEA projection — the regular tetrahedron + * unfolded into a 2D net. + * + * The default `tsea` net matches Snyder's Figure 8: a horizontal + * strip with North America (F0) at the root, then Europe/Africa + * (F1), the south-cap face (F3), and Asia/Australia (F2) chained + * via the shared edges V0-V3, V2-V3, V1-V2. + * + * The `star` net is the alternative classic layout — the south + * face (F3) at the centre with its three V0-touching neighbours + * (F0, F1, F2) hung off each of its edges. * Author: Felix Palmer * ****************************************************************************/ @@ -15,7 +22,8 @@ namespace nets { namespace tsea { -constexpr int tsea[4] = {3, 3, 3, -1}; +constexpr int tsea[4] = {-1, 0, 3, 1}; +constexpr int star[4] = {3, 3, 3, -1}; } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 6422441d49..e921337cb5 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -2,11 +2,17 @@ * * Project: PROJ * Purpose: Regular tetrahedron inscribed in the unit sphere, oriented with - * one vertex at the north pole. The remaining three vertices sit + * V0 at the north pole and V1 on the −x meridian (the same + * convention used by the icosahedron). The remaining vertices sit * at latitude -arcsin(1/3) ≈ -19.47°, separated by 120° in - * longitude (0°, +120°, -120°). Faces are listed top-to-bottom: - * F0..F2 are the three faces sharing V0 (CCW around V0, with V0 - * in slot 0), and F3 is the south-cap face opposite V0. + * longitude (V1 at 180°, V3 at -60°, V2 at +60°). Faces are + * listed top-to-bottom and west-to-east: + * F0 = V0 + V1 + V3 covers North America (and the Pacific) + * F1 = V0 + V3 + V2 covers Europe + Africa (and Atlantic) + * F2 = V0 + V2 + V1 covers Asia + Australia (and W Pacific) + * F3 = V1 + V2 + V3 south-cap face opposite V0 + * The F0–F1 edge V0-V3 lies on the lon=-60° meridian, splitting + * South America between the two faces (matching Snyder Figure 8). * Author: Felix Palmer * ****************************************************************************/ @@ -24,20 +30,20 @@ constexpr double A = 0.9428090415820635; // sqrt(8/9) constexpr double B = 0.8164965809277260; // sqrt(2/3) constexpr polyhedral::Mesh<4, 4, 3> mesh = { - // Vertices + // Vertices (unit sphere; V0 at +z, V1 on -x meridian) { {0.0, 0.0, 1.0}, - {A, 0.0, -1.0 / 3.0}, - {-0.5 * A, B, -1.0 / 3.0}, - {-0.5 * A, -B, -1.0 / 3.0}, + {-A, 0.0, -1.0 / 3.0}, + {0.5 * A, B, -1.0 / 3.0}, + {0.5 * A, -B, -1.0 / 3.0}, }, - // Faces (CCW from outside). F0..F2 share V0, in CCW order around it; - // F3 is the south-cap face opposite V0. + // Faces (CCW from outside). F0..F2 share V0, in CCW order around it + // starting from V1; F3 is the south-cap face opposite V0. { - {0, 1, 2}, - {0, 2, 3}, - {0, 3, 1}, - {3, 2, 1}, + {0, 1, 3}, + {0, 3, 2}, + {0, 2, 1}, + {1, 2, 3}, }, }; diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index bff3b666db..50a7742ed3 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3238,19 +3238,19 @@ operation +proj=tsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect 6962308.21925868 -7756293.64310391 +expect 10158446.94933977 4042700.52765733 roundtrip 1 accept 45 0 -expect 2090160.95556815 -7849305.02932016 +expect 13553290.92002686 8724734.47739539 roundtrip 1 accept 2 49 -expect 3180376.70814197 -14089364.89790736 +expect 4943856.69830819 7182742.29453684 roundtrip 1 accept -110 54 -expect 11355841.33569490 9423193.46532648 +expect 509257.68466195 4682660.28886354 roundtrip 1 ------------------------------------------------------------------------------- @@ -3261,15 +3261,15 @@ operation +proj=tsea +R=6371007.18091875 +orient_lat=0 +orient_lon=0 +azi=0 tolerance 0.2 mm accept 0 0 -expect 0 -19815365.21681434 +expect 0 9907682.60840717 roundtrip 1 accept 45 0 -expect -1856417.21862487 -13054386.64490965 +expect 27537831.51903139 8134897.79380681 roundtrip 1 accept 2 49 -expect -11314933.81708183 6405287.48417516 +expect 30357067.42218800 3260942.81128538 roundtrip 1 ------------------------------------------------------------------------------- @@ -3283,7 +3283,7 @@ expect 0 0 roundtrip 1 accept 0 0 -expect 3781931.51111671 6333071.25480345 +expect 5214590.25103157 -3140041.76687951 roundtrip 1 ------------------------------------------------------------------------------- @@ -3297,7 +3297,7 @@ expect 500000 1000000 roundtrip 1 accept 0 0 -expect 4281931.51111671 7333071.25480345 +expect 5714590.25103157 -2140041.76687951 roundtrip 1 =============================================================================== From 08d5e37109cd84e3dde86c9c04bdac770fad2e77 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 00:53:14 +0200 Subject: [PATCH 36/62] test update --- test/gie/builtins.gie | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 50a7742ed3..547c225a56 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3311,19 +3311,19 @@ operation +proj=dsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect -4021198.96415185 2503030.49539516 +expect 0 -3031675.05748085 roundtrip 1 accept 45 0 -expect 997409.03020670 2890440.27658991 +expect 5018607.99435854 -2644265.27628609 roundtrip 1 accept 2 49 -expect -3869786.84657843 7972093.84058896 +expect 151412.11757341 2437388.28771295 roundtrip 1 accept -110 54 -expect -7835151.94180176 13754740.97756485 +expect -3813952.97764993 8220035.42468884 roundtrip 1 ------------------------------------------------------------------------------- From 6fe2b0eff8c67f3d05816e12df8beb43eb8a7f85 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 01:06:57 +0200 Subject: [PATCH 37/62] Automatically reorient z axis --- src/projections/polyhedral.cpp | 23 +++++------------------ src/projections/polyhedral/sphere.h | 20 ++++++++++++++------ 2 files changed, 19 insertions(+), 24 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index c6266e5a16..a44b80c664 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -131,8 +131,8 @@ PJ *PJ_PROJECTION(tsea) { } } - polyhedral::load_meshes(Q, polyhedra::tetrahedron, *parents); const polyhedral::PolyhedralDefaults d = {90.0, 0.0, 0.0}; + polyhedral::load_meshes(Q, polyhedra::tetrahedron, *parents, d); return polyhedral_setup(P, d); } @@ -175,20 +175,9 @@ PJ *PJ_PROJECTION(dsea) { using polyhedra::dodecahedron_constants::A; const double default_orient_lat = std::atan((1 + 2 * A) / 2.0) * 180.0 / M_PI; - - // The unfold's "north-up" rotation needs to use geographic north, not - // polyhedron +z (V0) — under these defaults they differ by ~37°. The - // third column of the orient matrix is geographic +z expressed in - // polyhedron coordinates: (-cos(azi)cos(lat), -sin(azi)cos(lat), sin(lat)). - const double lat_rad = default_orient_lat * DEG_TO_RAD; - const double azi_rad = default_azi * DEG_TO_RAD; - const polyhedral::Vec3 up_dir = {-std::cos(azi_rad) * std::cos(lat_rad), - -std::sin(azi_rad) * std::cos(lat_rad), - std::sin(lat_rad)}; - polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents, up_dir); - const polyhedral::PolyhedralDefaults d = {default_orient_lat, default_orient_lon, default_azi}; + polyhedral::load_meshes(Q, polyhedra::dodecahedron, *parents, d); return polyhedral_setup(P, d); } @@ -202,8 +191,6 @@ PJ *PJ_PROJECTION(isea2) { P->opaque = Q; P->destructor = polyhedral_destructor; - polyhedral::load_meshes(Q, polyhedra::icosahedron, nets::isea::isea); - // Standard Snyder ISEA orientation: V0 at authalic latitude arctan(φ) ≈ // 58.28°N (φ = golden ratio). On WGS84 this corresponds to ~58.40° // geodetic — PolyhedralDefaults stores the authalic value; user @@ -231,14 +218,14 @@ PJ *PJ_PROJECTION(isea2) { } } - polyhedral::PolyhedralDefaults d = {orient_lat, orient_lon, azi}; - // For drop-in compatibility with legacy +proj=isea, the default projected // origin is the bbox center (mid-width, mid-height) of the unfold's root // face — the "South Africa" upper-band face F7 — rather than its // centroid. This matches legacy ISEA's 4×5 strip-layout geometric centre, // which sits inside F7 but not at its centroid. Other polyhedra default // to the centroid of the root face. - d.default_origin = polyhedral::DefaultOrigin::FaceBboxCenter; + const polyhedral::PolyhedralDefaults d = { + orient_lat, orient_lon, azi, polyhedral::DefaultOrigin::FaceBboxCenter}; + polyhedral::load_meshes(Q, polyhedra::icosahedron, nets::isea::isea, d); return polyhedral_setup(P, d); } diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 720a4deae0..06dfc62b04 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -69,16 +69,24 @@ struct PolyhedralDefaults { DefaultOrigin default_origin = DefaultOrigin::FaceCentroid; }; +// Geographic +z (the orient frame's "up") expressed in polyhedron +// coordinates — the third column of the orient rotation matrix. The unfold +// uses this so the root face comes out with true geographic north up. +inline Vec3 orient_up_in_poly(const PolyhedralDefaults &d) { + const double lat = d.orient_lat_deg * DEG_TO_RAD; + const double az = d.azi_deg * DEG_TO_RAD; + return {-std::cos(az) * std::cos(lat), -std::sin(az) * std::cos(lat), + std::sin(lat)}; +} + // Build triangle data from a polyhedron and the unfold-tree `parents` array. -// `up_dir` is the direction (in polyhedron coordinates) that should appear -// "up" on the root face of the unfolded net — usually the geographic +z -// direction expressed in polyhedron coords (the third column of the orient -// matrix); defaults to polyhedron +z. +// The unfold orients the root face so that geographic north (derived from +// the orient defaults) lands on +y in the net. template inline void load_meshes(pj_polyhedral_data *Q, const Mesh &polyhedron, - const int (&parents)[NF], const Vec3 &up_dir = z) { - const auto net = unfold_net(polyhedron, parents, up_dir); + const int (&parents)[NF], const PolyhedralDefaults &d) { + const auto net = unfold_net(polyhedron, parents, orient_up_in_poly(d)); constexpr int N = 2 * NFV * NF; Vec3 sph[N][3]; Vec3 face[N][3]; From 41ee13bf5a4708bd8df616faa57ccac06dc8854c Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 16:12:28 +0200 Subject: [PATCH 38/62] Switch to 1-indexing --- src/projections/polyhedral/nets/dsea/dsea.h | 52 +++++++++++---------- src/projections/polyhedral/nets/isea/isea.h | 37 ++++++++------- src/projections/polyhedral/nets/tsea/tsea.h | 15 +++--- src/projections/polyhedral/sphere.h | 2 +- src/projections/polyhedral/unfold.h | 22 +++++---- 5 files changed, 70 insertions(+), 58 deletions(-) diff --git a/src/projections/polyhedral/nets/dsea/dsea.h b/src/projections/polyhedral/nets/dsea/dsea.h index f724170d2f..94e088ed3d 100644 --- a/src/projections/polyhedral/nets/dsea/dsea.h +++ b/src/projections/polyhedral/nets/dsea/dsea.h @@ -2,18 +2,20 @@ * * Project: PROJ * Purpose: Net layouts for the DSEA projection. Each constant is a parents - * tree over the 12 faces of the dodecahedron: parents[i] is face - * i's parent in the unfolding tree, or -1 if i is the root. Every - * parent–child pair must share an edge on the dodecahedron. + * tree over the 12 faces of the dodecahedron: parents[i] stores + * the 1-based ID of face F(i+1)'s parent in the unfolding tree, + * or 0 if F(i+1) is the root. Face IDs are 1-based to match the + * Snyder paper; 0 means "no parent". Every parent–child pair + * must share an edge on the dodecahedron. * * The dodecahedron face order is top-to-bottom, then left-to-right * within each band: - * F0 north polar cap - * F1..F5 upper band N.Pacific, N.America, Europe, + * F1 north polar cap + * F2..F6 upper band N.Pacific, N.America, Europe, * India, Asia - * F6..F10 lower band S.Pacific, S.Atlantic, S.Africa, + * F7..F11 lower band S.Pacific, S.Atlantic, S.Africa, * Indian, S.Pacific E - * F11 south polar cap + * F12 south polar cap * Author: Felix Palmer * ****************************************************************************/ @@ -24,34 +26,34 @@ namespace nets { namespace dsea { -// Snyder's two-rows-of-5 layout (Figure 6): F8 (Africa) is the central face +// Snyder's two-rows-of-5 layout (Figure 6): F9 (Africa) is the central face // of the lower row, with the row extending left and right via zig-zag // connections through the upper row — directly hinging adjacent lower-row // faces would curl the band into a crescent, so each next-lower-row face is // reached through its upper-row neighbour instead. -// Right: F8 → F4 → F9 → F5 → F10 (L → U → L → U → L) -// Left: F8 → F3 → F7 → F2 → F6 → F1 (L → U → L → U → L → U) +// Right: F9 → F5 → F10 → F6 → F11 (L → U → L → U → L) +// Left: F9 → F4 → F8 → F3 → F7 → F2 (L → U → L → U → L → U) // The two polar caps hang symmetrically above and below the central column: -// F0 (north pole) off F3 (Europe), F11 (south pole) off F8 (Africa). -constexpr int dsea[12] = {3, 6, 7, -1, 8, 9, 2, 3, 3, 4, 5, 8}; +// F1 (north pole) off F4 (Europe), F12 (south pole) off F9 (Africa). +constexpr int dsea[12] = {4, 7, 8, 0, 9, 10, 3, 4, 4, 5, 6, 9}; // A5 net (re-rooted to match the A5 reference codebase's coordinate origin). // The visual shape is the same as the published A5 layout; only the parent // pointers along the path to the new root are reversed. -constexpr int a5[12] = {3, 5, 7, 8, 5, -1, 1, 11, 9, 4, 6, 10}; - -// Crescent: central spine F0 → F3 → F8 → F11 (north pole → UK/Europe → -// Africa → south pole). Two symmetric "crescent" arcs extend out from F3 -// and F8: one through the upper row (F3 → F4 → F5 → F1 → F2) and one -// through the lower row (F8 → F9 → F10 → F6 → F7). -constexpr int crescent[12] = {3, 2, 3, -1, 3, 4, 7, 8, 3, 8, 9, 8}; - -// Flower: F3 (Europe) at the centre, with F0 (north pole) as one petal and -// F8 (Africa) as the link down to the south pole. F0's four other petals -// (F1, F2, F4, F5) hang off F0; F11's four other petals (F6, F7, F9, F10) -// hang off F11. This routes the polar caps through Africa rather than +constexpr int a5[12] = {4, 6, 8, 9, 6, 0, 2, 12, 10, 5, 7, 11}; + +// Crescent: central spine F1 → F4 → F9 → F12 (north pole → UK/Europe → +// Africa → south pole). Two symmetric "crescent" arcs extend out from F4 +// and F9: one through the upper row (F4 → F5 → F6 → F2 → F3) and one +// through the lower row (F9 → F10 → F11 → F7 → F8). +constexpr int crescent[12] = {4, 3, 4, 0, 4, 5, 8, 9, 4, 9, 10, 9}; + +// Flower: F4 (Europe) at the centre, with F1 (north pole) as one petal and +// F9 (Africa) as the link down to the south pole. F1's four other petals +// (F2, F3, F5, F6) hang off F1; F12's four other petals (F7, F8, F10, F11) +// hang off F12. This routes the polar caps through Africa rather than // through the Americas. -constexpr int flower[12] = {3, 0, 0, -1, 0, 0, 11, 11, 3, 11, 11, 8}; +constexpr int flower[12] = {4, 1, 1, 0, 1, 1, 12, 12, 4, 12, 12, 9}; } // namespace dsea } // namespace nets diff --git a/src/projections/polyhedral/nets/isea/isea.h b/src/projections/polyhedral/nets/isea/isea.h index 01c915fd23..9b2a7aa16e 100644 --- a/src/projections/polyhedral/nets/isea/isea.h +++ b/src/projections/polyhedral/nets/isea/isea.h @@ -4,23 +4,26 @@ * Purpose: Net layout for the ISEA projection — the regular icosahedron * unfolded into the canonical Snyder 4×5 strip. * + * Face IDs are 1-based (matching Snyder); 0 means "no parent" + * (the unfold root). + * * The icosahedron face order in `polyhedra::icosahedron` is * grouped into 4 rows of 5: - * F0..F4 north cap (around V0) - * F5..F9 upper band (down-pointing on the sphere) - * F10..F14 lower band (up-pointing on the sphere) - * F15..F19 south cap (around V11) - * - * F7 is the centred upper-band face — the "South Africa" face in - * Snyder's Figure 12 (face 8 in his 1-indexed numbering, our F7 - * in 0-indexed) — and is chosen as the root of the unfolding tree - * so that the default projected origin is its centroid / bbox - * centre, matching the geometric centre of the legacy ISEA strip. - * - * The unfold tree zig-zags from the root F7 outward across the + * F1..F5 north cap (around V0) + * F6..F10 upper band (down-pointing on the sphere) + * F11..F15 lower band (up-pointing on the sphere) + * F16..F20 south cap (around V11) + * + * F8 is the centred upper-band face — the "South Africa" face in + * Snyder's Figure 12 — and is chosen as the root of the unfolding + * tree so that the default projected origin is its centroid / + * bbox centre, matching the geometric centre of the legacy ISEA + * strip. + * + * The unfold tree zig-zags from the root F8 outward across the * upper and lower bands, * - * F0 ← F5 ← F10 ← F6 ← F11 ← F7 → F12 → F8 → F13 → F9 → F14 + * F1 ← F6 ← F11 ← F7 ← F12 ← F8 → F13 → F9 → F14 → F10 → F15 * * with each remaining north-cap face hung off its upper-band * neighbour and each south-cap face hung off its lower-band @@ -36,11 +39,11 @@ namespace nets { namespace isea { constexpr int isea[20] = { - 5, 6, 7, 8, 9, // F0..F4 north cap, hung off upper band - 10, 11, -1, 12, 13, // F5, F6 climb back to F0; F7 is root; F8, F9 chain on - 6, 7, 7, 8, 9, // F10..F14 lower band — left of F7 climbs back, right + 6, 7, 8, 9, 10, // F1..F5 north cap, hung off upper band + 11, 12, 0, 13, 14, // F6, F7 climb back to F1; F8 is root; F9, F10 chain on + 7, 8, 8, 9, 10, // F11..F15 lower band — left of F8 climbs back, right // chains forward - 10, 11, 12, 13, 14, // F15..F19 south cap, hung off lower band + 11, 12, 13, 14, 15, // F16..F20 south cap, hung off lower band }; } // namespace isea diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index b883348f2b..ddcbb55f62 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -4,14 +4,17 @@ * Purpose: Net layouts for the TSEA projection — the regular tetrahedron * unfolded into a 2D net. * + * Face IDs are 1-based (matching Snyder); 0 means "no parent" + * (the unfold root). + * * The default `tsea` net matches Snyder's Figure 8: a horizontal - * strip with North America (F0) at the root, then Europe/Africa - * (F1), the south-cap face (F3), and Asia/Australia (F2) chained + * strip with North America (F1) at the root, then Europe/Africa + * (F2), the south-cap face (F4), and Asia/Australia (F3) chained * via the shared edges V0-V3, V2-V3, V1-V2. * * The `star` net is the alternative classic layout — the south - * face (F3) at the centre with its three V0-touching neighbours - * (F0, F1, F2) hung off each of its edges. + * face (F4) at the centre with its three V0-touching neighbours + * (F1, F2, F3) hung off each of its edges. * Author: Felix Palmer * ****************************************************************************/ @@ -22,8 +25,8 @@ namespace nets { namespace tsea { -constexpr int tsea[4] = {-1, 0, 3, 1}; -constexpr int star[4] = {3, 3, 3, -1}; +constexpr int tsea[4] = {0, 1, 4, 2}; +constexpr int star[4] = {4, 4, 4, 0}; } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/sphere.h b/src/projections/polyhedral/sphere.h index 06dfc62b04..4fa311dbd0 100644 --- a/src/projections/polyhedral/sphere.h +++ b/src/projections/polyhedral/sphere.h @@ -97,7 +97,7 @@ inline void load_meshes(pj_polyhedral_data *Q, Q->face_vertex_count = NFV; Q->num_faces = NF; Q->root_face_index = 0; - while (Q->root_face_index < NF && parents[Q->root_face_index] != -1) + while (Q->root_face_index < NF && parents[Q->root_face_index] != 0) Q->root_face_index++; for (int i = 0; i < N; i++) { Q->sph_tris[i] = {sph[i][0], sph[i][1], sph[i][2]}; diff --git a/src/projections/polyhedral/unfold.h b/src/projections/polyhedral/unfold.h index a2962c3425..2af1c30cf8 100644 --- a/src/projections/polyhedral/unfold.h +++ b/src/projections/polyhedral/unfold.h @@ -71,8 +71,11 @@ inline constexpr Vec3 z{0.0, 0.0, 1.0}; // Unfold a polyhedron Mesh into a planar net Mesh. // -// `parents[i]` is the index of face i's parent in the unfolding tree, or -1 -// if i is the root. Exactly one entry must be -1. +// Faces are referenced by 1-based IDs F1..F_NF (matching Snyder's paper +// numbering). `parents[i]` holds the parent of face F(i+1) in the unfolding +// tree as a 1-based face ID, or 0 if F(i+1) is the root. Exactly one entry +// must be 0. The C array indexing stays 0-based; only the values it stores +// are 1-based. // // The polyhedron faces must have consistent CCW winding from the outside. // Each child face is hinged about its shared edge with its parent; the @@ -93,9 +96,9 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF], Mesh net{}; int n_verts = 0; - // Find and place root face + // Find and place root face (the entry whose 1-based parent ID is 0). int root = 0; - while (parents[root] != -1) + while (parents[root] != 0) root++; // Place the root face "up-direction-up": project up_dir onto the root @@ -132,17 +135,18 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF], net.faces[root][k] = n_verts++; } - // Initialize queue with direct children of parent face + // Initialize queue with direct children of parent face. `root` is a + // 0-based array index; `parents[i]` is a 1-based face ID. int queue[NF]; int q_head = 0, q_tail = 0; for (int i = 0; i < NF; i++) - if (parents[i] == root) + if (parents[i] == root + 1) queue[q_tail++] = i; // Hinge each child onto its parent at the shared edge. while (q_head < q_tail) { const int c = queue[q_head++]; - const int p = parents[c]; + const int p = parents[c] - 1; // Find shared edge int ia_c = -1, ib_c = -1, ia_p = -1, ib_p = -1; @@ -180,9 +184,9 @@ unfold_net(const Mesh &polyhedron, const int (&parents)[NF], } } - // Append children of this face to queue + // Append children of this face to queue (parents[i] is 1-based). for (int i = 0; i < NF; i++) - if (parents[i] == c) + if (parents[i] == c + 1) queue[q_tail++] = i; } From 15eacb03ed6ffe0e5aa5a89e4db442fcbb599acd Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Mon, 11 May 2026 17:25:13 +0200 Subject: [PATCH 39/62] Recenter tsea --- src/projections/polyhedral/nets/tsea/tsea.h | 19 +++++++----- .../polyhedral/polyhedra/tetrahedron.h | 30 ++++++++++--------- 2 files changed, 27 insertions(+), 22 deletions(-) diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index ddcbb55f62..cb3ea4ff6f 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -7,14 +7,17 @@ * Face IDs are 1-based (matching Snyder); 0 means "no parent" * (the unfold root). * - * The default `tsea` net matches Snyder's Figure 8: a horizontal - * strip with North America (F1) at the root, then Europe/Africa - * (F2), the south-cap face (F4), and Asia/Australia (F3) chained - * via the shared edges V0-V3, V2-V3, V1-V2. + * The default `tsea` net is Snyder's Figure 8 horizontal strip + * F1 — F2 — F4 — F3 (North America — Europe/Africa — south cap — + * Asia/Australia), but rerooted at F4 so the projected (0, 0) + * lands on the south-cap face (Antarctica) — more central than + * Snyder's original F1 (West-coast-of-Mexico) origin. The strip + * shape and shared edges are identical to Snyder's figure; only + * the choice of root face moves. * - * The `star` net is the alternative classic layout — the south - * face (F4) at the centre with its three V0-touching neighbours - * (F1, F2, F3) hung off each of its edges. + * The `star` net is the alternative layout — F4 (south cap) at + * the centre with its three V0-touching neighbours (F1, F2, F3) + * hung off each of its edges in a three-way fan. * Author: Felix Palmer * ****************************************************************************/ @@ -25,7 +28,7 @@ namespace nets { namespace tsea { -constexpr int tsea[4] = {0, 1, 4, 2}; +constexpr int tsea[4] = {2, 4, 4, 0}; constexpr int star[4] = {4, 4, 4, 0}; } // namespace tsea diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index e921337cb5..6d5ea0c01b 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -2,17 +2,19 @@ * * Project: PROJ * Purpose: Regular tetrahedron inscribed in the unit sphere, oriented with - * V0 at the north pole and V1 on the −x meridian (the same - * convention used by the icosahedron). The remaining vertices sit - * at latitude -arcsin(1/3) ≈ -19.47°, separated by 120° in - * longitude (V1 at 180°, V3 at -60°, V2 at +60°). Faces are - * listed top-to-bottom and west-to-east: - * F0 = V0 + V1 + V3 covers North America (and the Pacific) - * F1 = V0 + V3 + V2 covers Europe + Africa (and Atlantic) - * F2 = V0 + V2 + V1 covers Asia + Australia (and W Pacific) + * V0 at the north pole. The remaining vertices sit at latitude + * -arcsin(1/3) ≈ -19.47°, separated by 120° in longitude + * (V1 at +60°, V2 at -60°, V3 at 180°). Faces are listed + * top-to-bottom and west-to-east: + * F0 = V0 + V3 + V2 covers North America (and the Pacific) + * F1 = V0 + V2 + V1 covers Europe + Africa (and Atlantic) + * F2 = V0 + V1 + V3 covers Asia + Australia (and W Pacific) * F3 = V1 + V2 + V3 south-cap face opposite V0 - * The F0–F1 edge V0-V3 lies on the lon=-60° meridian, splitting + * The F0–F1 edge V0-V2 lies on the lon=-60° meridian, splitting * South America between the two faces (matching Snyder Figure 8). + * F3's vertices are listed V1, V2, V3 so the unfold's polar-face + * fallback (which places face[0] along +y) puts V1 — the +60° + * meridian — "up" in the Antarctica-centred tsea net. * Author: Felix Palmer * ****************************************************************************/ @@ -30,19 +32,19 @@ constexpr double A = 0.9428090415820635; // sqrt(8/9) constexpr double B = 0.8164965809277260; // sqrt(2/3) constexpr polyhedral::Mesh<4, 4, 3> mesh = { - // Vertices (unit sphere; V0 at +z, V1 on -x meridian) + // Vertices (unit sphere; V0 at +z, V1 at lon=+60°) { {0.0, 0.0, 1.0}, - {-A, 0.0, -1.0 / 3.0}, {0.5 * A, B, -1.0 / 3.0}, {0.5 * A, -B, -1.0 / 3.0}, + {-A, 0.0, -1.0 / 3.0}, }, - // Faces (CCW from outside). F0..F2 share V0, in CCW order around it - // starting from V1; F3 is the south-cap face opposite V0. + // Faces (CCW from outside). F0..F2 share V0; F3 is the south-cap face + // opposite V0, listed in V1, V2, V3 order so the unfold places V1 up. { - {0, 1, 3}, {0, 3, 2}, {0, 2, 1}, + {0, 1, 3}, {1, 2, 3}, }, }; From 06f22e3209dbc3f185067e94ab07de2266b1616d Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Tue, 12 May 2026 10:20:21 +0200 Subject: [PATCH 40/62] Update comments for 1-indexing --- src/projections/polyhedral.cpp | 8 ++++---- src/projections/polyhedral/nets/tsea/tsea.h | 17 +++++++--------- .../polyhedral/polyhedra/dodecahedron.h | 8 ++++---- .../polyhedral/polyhedra/icosahedron.h | 8 ++++---- .../polyhedral/polyhedra/tetrahedron.h | 20 ++++++++++--------- test/gie/builtins.gie | 14 ++++++------- 6 files changed, 37 insertions(+), 38 deletions(-) diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index a44b80c664..c9db799be2 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -170,8 +170,8 @@ PJ *PJ_PROJECTION(dsea) { } } - // Defaults rotate the polyhedron so F0's centroid sits at the geographic - // north pole. orient_lat = atan((1+2A)/2) places V0 on the F0 axis. + // Defaults rotate the polyhedron so F1's centroid sits at the geographic + // north pole. orient_lat = atan((1+2A)/2) places V0 on the F1 axis. using polyhedra::dodecahedron_constants::A; const double default_orient_lat = std::atan((1 + 2 * A) / 2.0) * 180.0 / M_PI; @@ -220,9 +220,9 @@ PJ *PJ_PROJECTION(isea2) { // For drop-in compatibility with legacy +proj=isea, the default projected // origin is the bbox center (mid-width, mid-height) of the unfold's root - // face — the "South Africa" upper-band face F7 — rather than its + // face — the "South Africa" upper-band face F8 — rather than its // centroid. This matches legacy ISEA's 4×5 strip-layout geometric centre, - // which sits inside F7 but not at its centroid. Other polyhedra default + // which sits inside F8 but not at its centroid. Other polyhedra default // to the centroid of the root face. const polyhedral::PolyhedralDefaults d = { orient_lat, orient_lon, azi, polyhedral::DefaultOrigin::FaceBboxCenter}; diff --git a/src/projections/polyhedral/nets/tsea/tsea.h b/src/projections/polyhedral/nets/tsea/tsea.h index cb3ea4ff6f..b8c5f0761a 100644 --- a/src/projections/polyhedral/nets/tsea/tsea.h +++ b/src/projections/polyhedral/nets/tsea/tsea.h @@ -8,15 +8,12 @@ * (the unfold root). * * The default `tsea` net is Snyder's Figure 8 horizontal strip - * F1 — F2 — F4 — F3 (North America — Europe/Africa — south cap — - * Asia/Australia), but rerooted at F4 so the projected (0, 0) - * lands on the south-cap face (Antarctica) — more central than - * Snyder's original F1 (West-coast-of-Mexico) origin. The strip - * shape and shared edges are identical to Snyder's figure; only - * the choice of root face moves. + * F1 — F2 — F3 — F4 (North America — Europe/Africa — south cap — + * Asia/Australia), rerooted at F3 so the projected (0, 0) lands + * on the south-cap face (Antarctica). * - * The `star` net is the alternative layout — F4 (south cap) at - * the centre with its three V0-touching neighbours (F1, F2, F3) + * The `star` net is the alternative layout — F3 (south cap) at + * the centre with its three V0-touching neighbours (F1, F2, F4) * hung off each of its edges in a three-way fan. * Author: Felix Palmer * @@ -28,8 +25,8 @@ namespace nets { namespace tsea { -constexpr int tsea[4] = {2, 4, 4, 0}; -constexpr int star[4] = {4, 4, 4, 0}; +constexpr int tsea[4] = {2, 3, 0, 3}; +constexpr int star[4] = {3, 3, 0, 3}; } // namespace tsea } // namespace nets diff --git a/src/projections/polyhedral/polyhedra/dodecahedron.h b/src/projections/polyhedral/polyhedra/dodecahedron.h index 82b93f3021..8ccd4e93fb 100644 --- a/src/projections/polyhedral/polyhedra/dodecahedron.h +++ b/src/projections/polyhedral/polyhedra/dodecahedron.h @@ -57,12 +57,12 @@ constexpr polyhedral::Mesh<20, 12, 5> mesh = { }, // Faces (CCW from outside). Ordered top-to-bottom, then left-to-right // within each band, so the unfolded DSEA net comes out as: - // F0 (north polar cap, around V0) - // F1 F2 F3 F4 F5 (upper band: N.Pacific, N.America, + // F1 (north polar cap, around V0) + // F2 F3 F4 F5 F6 (upper band: N.Pacific, N.America, // Europe, India, Asia) - // F6 F7 F8 F9 F10 (lower band: S.Pacific, S.Atlantic, + // F7 F8 F9 F10 F11 (lower band: S.Pacific, S.Atlantic, // S.Africa, Indian, S.Pacific E) - // F11 (south polar cap, around V17) + // F12 (south polar cap, around V17) { {0, 1, 2, 3, 4}, {3, 8, 13, 9, 4}, diff --git a/src/projections/polyhedral/polyhedra/icosahedron.h b/src/projections/polyhedral/polyhedra/icosahedron.h index 8577cec141..0e687ab4e3 100644 --- a/src/projections/polyhedral/polyhedra/icosahedron.h +++ b/src/projections/polyhedral/polyhedra/icosahedron.h @@ -47,10 +47,10 @@ constexpr polyhedral::Mesh<12, 20, 3> mesh = { {0.0, 0.0, -1.0}, }, // Faces (CCW from outside). Ordered north to south, in groups of 5 - // F0..F4 north cap (around V0) - // F5..F9 upper band (down-pointing) - // F10..F14 lower band (up-pointing) - // F15..F19 south cap (around V11) + // F1..F5 north cap (around V0) + // F6..F10 upper band (down-pointing) + // F11..F15 lower band (up-pointing) + // F16..F20 south cap (around V11) { {0, 1, 2}, {0, 2, 3}, {0, 3, 4}, {0, 4, 5}, {0, 5, 1}, {1, 6, 2}, {2, 7, 3}, {3, 8, 4}, {4, 9, 5}, {5, 10, 1}, diff --git a/src/projections/polyhedral/polyhedra/tetrahedron.h b/src/projections/polyhedral/polyhedra/tetrahedron.h index 6d5ea0c01b..442a27e036 100644 --- a/src/projections/polyhedral/polyhedra/tetrahedron.h +++ b/src/projections/polyhedral/polyhedra/tetrahedron.h @@ -4,13 +4,15 @@ * Purpose: Regular tetrahedron inscribed in the unit sphere, oriented with * V0 at the north pole. The remaining vertices sit at latitude * -arcsin(1/3) ≈ -19.47°, separated by 120° in longitude - * (V1 at +60°, V2 at -60°, V3 at 180°). Faces are listed - * top-to-bottom and west-to-east: - * F0 = V0 + V3 + V2 covers North America (and the Pacific) - * F1 = V0 + V2 + V1 covers Europe + Africa (and Atlantic) - * F2 = V0 + V1 + V3 covers Asia + Australia (and W Pacific) + * (V1 at +60°, V2 at -60°, V3 at 180°). The three V0-touching + * faces are listed west-to-east, with the south-cap face slotted + * in between (so the default unfold strip F1 — F2 — F3 — F4 reads + * North America — Europe/Africa — south cap — Asia/Australia): + * F1 = V0 + V3 + V2 covers North America (and the Pacific) + * F2 = V0 + V2 + V1 covers Europe + Africa (and Atlantic) * F3 = V1 + V2 + V3 south-cap face opposite V0 - * The F0–F1 edge V0-V2 lies on the lon=-60° meridian, splitting + * F4 = V0 + V1 + V3 covers Asia + Australia (and W Pacific) + * The F1–F2 edge V0-V2 lies on the lon=-60° meridian, splitting * South America between the two faces (matching Snyder Figure 8). * F3's vertices are listed V1, V2, V3 so the unfold's polar-face * fallback (which places face[0] along +y) puts V1 — the +60° @@ -39,13 +41,13 @@ constexpr polyhedral::Mesh<4, 4, 3> mesh = { {0.5 * A, -B, -1.0 / 3.0}, {-A, 0.0, -1.0 / 3.0}, }, - // Faces (CCW from outside). F0..F2 share V0; F3 is the south-cap face - // opposite V0, listed in V1, V2, V3 order so the unfold places V1 up. + // Faces (CCW from outside). F1, F2, F4 share V0; F3 is the south-cap + // face opposite V0, listed in V1, V2, V3 order so the unfold places V1 up. { {0, 3, 2}, {0, 2, 1}, - {0, 1, 3}, {1, 2, 3}, + {0, 1, 3}, }, }; diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index 547c225a56..bc8ceec6e8 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3238,19 +3238,19 @@ operation +proj=tsea +R=6371007.18091875 tolerance 0.2 mm accept 0 0 -expect 10158446.94933977 4042700.52765733 +expect -7002162.71368800 4042700.52765732 roundtrip 1 accept 45 0 -expect 13553290.92002686 8724734.47739539 +expect -3607318.74300090 8724734.47739539 roundtrip 1 accept 2 49 -expect 4943856.69830819 7182742.29453684 +expect -12216752.96471957 7182742.29453684 roundtrip 1 accept -110 54 -expect 509257.68466195 4682660.28886354 +expect -16651351.97836581 4682660.28886354 roundtrip 1 ------------------------------------------------------------------------------- @@ -3261,15 +3261,15 @@ operation +proj=tsea +R=6371007.18091875 +orient_lat=0 +orient_lon=0 +azi=0 tolerance 0.2 mm accept 0 0 -expect 0 9907682.60840717 +expect -17160609.66302776 9907682.60840717 roundtrip 1 accept 45 0 -expect 27537831.51903139 8134897.79380681 +expect 10377221.85600363 8134897.79380681 roundtrip 1 accept 2 49 -expect 30357067.42218800 3260942.81128538 +expect 13196457.75916024 3260942.81128537 roundtrip 1 ------------------------------------------------------------------------------- From 28400ceb86788ce71fdc860028e07f417f259841 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Tue, 12 May 2026 12:40:51 +0200 Subject: [PATCH 41/62] Utility for dumping nets --- test/unit/CMakeLists.txt | 11 +++++++ test/unit/print_polyhedral_layout.cpp | 47 +++++++++++++++++++++++++++ 2 files changed, 58 insertions(+) create mode 100644 test/unit/print_polyhedral_layout.cpp diff --git a/test/unit/CMakeLists.txt b/test/unit/CMakeLists.txt index 2993967720..4c633bbe53 100644 --- a/test/unit/CMakeLists.txt +++ b/test/unit/CMakeLists.txt @@ -268,6 +268,17 @@ add_test(NAME test_polyhedral COMMAND test_polyhedral) set_property(TEST test_polyhedral PROPERTY ENVIRONMENT ${PROJ_TEST_ENVIRONMENT}) +# Utility (not a test) used by test/render_layout.py to dump the unfolded +# face polygons of a polyhedral projection. Reaches into internal headers, +# so it lives here next to test_polyhedral rather than being exposed via +# the public libproj API. +add_executable(print_polyhedral_layout + print_polyhedral_layout.cpp) +target_link_libraries(print_polyhedral_layout + PRIVATE ${PROJ_LIBRARIES}) +target_include_directories(print_polyhedral_layout + PRIVATE ${CMAKE_SOURCE_DIR}/src/projections) + if (Threads_FOUND AND CMAKE_USE_PTHREADS_INIT AND NOT APPLE) add_definitions(-DPROJ_HAS_PTHREADS) add_executable(test_fork diff --git a/test/unit/print_polyhedral_layout.cpp b/test/unit/print_polyhedral_layout.cpp new file mode 100644 index 0000000000..8c961ad73f --- /dev/null +++ b/test/unit/print_polyhedral_layout.cpp @@ -0,0 +1,47 @@ +// Small utility used by test/render_layout.py to dump the unfolded face +// polygons of a polyhedral projection in plain text. Lives under test/ +// so it can include the internal polyhedral headers without exposing any +// new symbols from libproj. +// +// Usage: print_polyhedral_layout "+proj=tsea +R=1" +// Output: first line " ", followed by one +// line per face with `nfv` space-separated "x y" pairs (net coordinates, +// no lat_0/lon_0/x_0/y_0 offset applied). + +#include "polyhedral/sphere.h" +#include "proj.h" +#include "proj_internal.h" + +#include +#include + +int main(int argc, char **argv) { + if (argc != 2) { + std::fprintf(stderr, "usage: %s \"+proj=... +R=1\"\n", argv[0]); + return 1; + } + PJ_CONTEXT *ctx = proj_context_create(); + PJ *pj = proj_create(ctx, argv[1]); + if (!pj) { + std::fprintf(stderr, "failed to create projection: %s\n", argv[1]); + return 1; + } + auto *Q = static_cast(pj->opaque); + if (!Q || Q->face_vertex_count <= 0) { + std::fprintf(stderr, "not a polyhedral projection: %s\n", argv[1]); + return 1; + } + const int nf = Q->num_faces; + const int nfv = Q->face_vertex_count; + const int fan_size = 2 * nfv; + std::printf("%d %d\n", nf, nfv); + for (int f = 0; f < nf; f++) { + for (int k = 0; k < nfv; k++) { + const auto &v = Q->face_tris[fan_size * f + 2 * k].c; + std::printf("%.17g %.17g%s", v.x, v.y, k + 1 == nfv ? "\n" : " "); + } + } + proj_destroy(pj); + proj_context_destroy(ctx); + return 0; +} From c452348f22b93c4ee03bfda5e062ef6d4fbd8cb3 Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Tue, 12 May 2026 23:12:56 +0200 Subject: [PATCH 42/62] Review polyhedral.rst --- .../operations/projections/polyhedral.rst | 125 ++++++++---------- 1 file changed, 56 insertions(+), 69 deletions(-) diff --git a/docs/source/operations/projections/polyhedral.rst b/docs/source/operations/projections/polyhedral.rst index 81bd68784e..6f066908d2 100644 --- a/docs/source/operations/projections/polyhedral.rst +++ b/docs/source/operations/projections/polyhedral.rst @@ -9,88 +9,75 @@ Polyhedral Snyder Equal Area :align: center :alt: Polyhedral projection (DSEA A5) -The polyhedral Snyder equal-area projection maps the sphere onto the faces of a -polyhedron using the method described in :cite:`Snyder1992`. The projection is -area-preserving and supports both forward and inverse transforms. +The polyhedral Snyder equal-area projection maps the sphere onto the faces of +a polyhedron using the method described in :cite:`Snyder1992`. The projection +is area-preserving and supports both forward and inverse transforms on either +a sphere or an ellipsoid (input geodetic latitudes are converted to authalic +latitudes internally so the equal-area property is preserved). -The implementation is general: any polyhedron whose faces can be decomposed into -right triangles can be used. Each right triangle is independently projected -using Snyder's equal-area mapping between a spherical right triangle and a planar -triangle, then placed according to a *net* — a 2D unfolding of the polyhedron. +The implementation is generic: each polyhedral face is subdivided into right +sub-triangles, Snyder's equal-area mapping is applied independently on each +sub-triangle, and the planar results are laid out according to a *net* — a +2D unfolding of the polyhedron. -Triangles -******************************************************************************** - -At its core, the projection defines a generic method of transforming a spherical -right triangle ABC to a planar triangle XYZ, in an area-preserving manner. +Three projection aliases are registered: -Both spherical and planar triangles ABC have one special vertex, that we call -the apex. By convention we choose this to come first, so for the spherical -triangle it will be vertex A, while for the planar triangle vertex X. +- ``tsea`` :ref:`tsea` +- ``dsea`` :ref:`dsea` +- ``isea`` :ref:`isea` -The planar triangles can be chosen to have any shape (as long as they are all the -same). When unfolded into a net, the edges must map in the same way as the edges -of the spherical triangles, but the choice of which edges to keep is free. - -Polyhedra definitions +Triangles ******************************************************************************** -A straightforward way to obtain spherical right triangles is to take a spherical -polyhedron and apply the akisation operation, forming triangles by connecting: -face center (apex), face vertex and edge midpoint. +At its core, the projection is an area-preserving mapping from a spherical +right triangle ABC to a planar right triangle XYZ. Both triangles have one +distinguished vertex — the *apex* — which is listed first in either triple: +A on the sphere, X in the plane. The apex is shared by the sub-triangles +that fan out from a single face centre, so the sub-triangles meeting at the +apex tile a complete polyhedral face. -An example is taking a tetrahedron, and cutting each of its 4 triangular faces -into 6 right triangles. The result is a hexakis tetrahedron, with 24 faces. +The planar triangles can be chosen with any consistent shape, as long as the +edges around the shared apex match the way the corresponding edges meet on +the sphere. The freedom in choosing this planar shape — together with the +freedom in choosing how to glue the faces together — is what defines a +*net*. -By defining polyhedra in this manner we can describe both the geometry of the -solid and which of the vertices should be treated as the apex. For example, -if we take the regular icosahedron and dodecahedron, and apply the akisation -described above to both, we get the same 120 vertices, but we can distinguish -between the shapes: - -- Hexakis icosahedron (20 triangular faces, cut into 6) -- Decakis dodecahedron (12 triangular faces, cut into 10) - -It is important to note that the choice of polyhedron defines the projection -used, because it uniquely specifies the collection of triangles *and* the -apex vertices. - -Net mapping +Polyhedra and nets ******************************************************************************** -Internally, the projection outputs triangles in barycentric coordinates, which -are then transformed into triangles on a 2D plane. Here is ``tsea``, -projecting the 24 faces of the hexakis tetrahedron into a triangular net. - -While it feels natural to project onto the net of the unfolded polyhedron, e.g. - -- **Hexakis Icosahedron** onto **Icosahedron Net** -- **Decakis Dodecahedron** onto **Dodecahedron Net** +Each polyhedral projection is built from two compact definitions: -we can equally unfold onto any net that has the same symmetry group (in other -words, shares the same set of triangles). So it is completely valid to unfold: - -- **Hexakis Icosahedron** onto **Dodecahedron Net** -- **Decakis Dodecahedron** onto **Icosahedron Net** +- A *polyhedron*: a list of 3D vertices on the unit sphere plus a list of + face vertex indices (CCW from outside). By convention the first vertex is + always `{0, 0, 1}` +- A *net*: a parent tree over the faces. The indexing is 1-based, with `0` + reserved as the marker for the root face (that which has no parent). + For example, `{2, 3, 0, 3}` means: + - the 1st face has the **2nd face** as its parent + - the 2nd face has the **3rd face** as its parent + - the 3rd face has the **no face** as its parent (root) + - the 4th face has the **3rd face** as its parent +.. figure:: ./images/polyhedral_tsea_layout.png + :width: 500 px + :align: center + :alt: TSEA layout Projection specifications ******************************************************************************** -Most users will simply want to use a projection of their choosing and not worry -about the details of polyhedrons. +Because the planar layout is decoupled from the spherical triangulation, the +same polyhedron can be unfolded into several different nets, which can be +selected by name using the `+net` parameter, e.g. `+proj=tsea +net=star` -For this, several aliases are chosen for the projection string name, matching -the convention set by the ISEA projection, short for **Icosahedral Snyder -Equal Area**. -- ``tsea`` **Tetrahedral Snyder Equal Area**: Hexakis Tetrahedron (24 triangles) -- ``dsea`` **Dodecahedral Snyder Equal Area**: Decakis Dodecahedron (120 triangles) -- ``isea2`` **Icosahedral Snyder Equal Area**: Hexakis Icosahedron (120 triangles) - -When choosing a projection, a set of nets is available to the user by name. -The nets are tied to the projection, as the ordering of the triangles matters. -The net parameter can be omitted to use the default net. +The defaults for ``+orient_lat`` / ``+orient_lon`` / ``+azi`` rotate each +polyhedron into a sensible default pose (e.g. centred on Europe / Africa for +``dsea``; matching Snyder's published Figure 12 for ``isea2``). When +``+lat_0`` / ``+lon_0`` are not supplied, the projected origin (0, 0) lands +on the centroid of the unfold's root face — except for ``isea2``, which +defaults to the bounding-box centre of the root face to match the legacy +``+proj=isea`` layout exactly. Parameters ******************************************************************************** @@ -100,6 +87,11 @@ Parameters default orientation that places its vertices in symmetric, well-known positions; the parameters below override that default. +.. option:: +net= + + Selects the planar unfolding (net). The accepted values depend on the + projection: + .. option:: +orient_lat= Geodetic latitude of the polyhedron's first vertex, in degrees. @@ -120,11 +112,6 @@ Parameters *Default depends on the projection.* -.. option:: +net= - - Selects the planar unfolding (net). Only applies to ``+proj=dsea``. - Accepted values: ``dsea`` (default), ``a5``, ``crescent``, ``flower``. - .. include:: ../options/lat_0.rst For polyhedral projections, ``+lat_0`` / ``+lon_0`` specify the geographic From 7d660768317a3e46dee3c68b9fc40e5f7cd00bbc Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Tue, 12 May 2026 23:31:02 +0200 Subject: [PATCH 43/62] options --- docs/source/operations/options/azi.rst | 5 +++ .../operations/options/lat_0_polyhedral.rst | 18 ++++++++++ .../operations/options/lon_0_polyhedral.rst | 18 ++++++++++ docs/source/operations/options/orient_lat.rst | 5 +++ docs/source/operations/options/orient_lon.rst | 5 +++ .../images/polyhedral_tsea_layout.png | Bin 0 -> 65224 bytes .../operations/projections/polyhedral.rst | 33 ++++-------------- 7 files changed, 58 insertions(+), 26 deletions(-) create mode 100644 docs/source/operations/options/azi.rst create mode 100644 docs/source/operations/options/lat_0_polyhedral.rst create mode 100644 docs/source/operations/options/lon_0_polyhedral.rst create mode 100644 docs/source/operations/options/orient_lat.rst create mode 100644 docs/source/operations/options/orient_lon.rst create mode 100644 docs/source/operations/projections/images/polyhedral_tsea_layout.png diff --git a/docs/source/operations/options/azi.rst b/docs/source/operations/options/azi.rst new file mode 100644 index 0000000000..0c39f2b789 --- /dev/null +++ b/docs/source/operations/options/azi.rst @@ -0,0 +1,5 @@ +.. option:: +azi= + + Azimuth from the polyhedron's first vertex to its second, in degrees. + Together with ``+orient_lat`` and ``+orient_lon`` this fully constrains + the 3D pose of the polyhedron on the sphere. diff --git a/docs/source/operations/options/lat_0_polyhedral.rst b/docs/source/operations/options/lat_0_polyhedral.rst new file mode 100644 index 0000000000..40e1cfa0e9 --- /dev/null +++ b/docs/source/operations/options/lat_0_polyhedral.rst @@ -0,0 +1,18 @@ +.. option:: +lat_0= + + Geodetic latitude of the geographic point that should land at the + projected origin ``(0, 0)``. Used together with ``+lon_0``; the pair + translates the projected output without rotating the polyhedron. + ``+x_0`` / ``+y_0`` are applied on top of this translation. + + When unset, the projected origin falls on the unfold's root face + instead (its centroid in general, or its bounding-box centre for + ``+proj=isea``) rather than at a fixed lat / lon. + + .. note:: + The default convention is to interpret this value as decimal degrees. To + specify radians instead, follow the value with the "r" character. + + Example: `+lat_0=1.570796r` + + See :ref:`Projection Units ` for more information. diff --git a/docs/source/operations/options/lon_0_polyhedral.rst b/docs/source/operations/options/lon_0_polyhedral.rst new file mode 100644 index 0000000000..f7fa94c6da --- /dev/null +++ b/docs/source/operations/options/lon_0_polyhedral.rst @@ -0,0 +1,18 @@ +.. option:: +lon_0= + + Geodetic longitude of the geographic point that should land at the + projected origin ``(0, 0)``. Used together with ``+lat_0``; the pair + translates the projected output without rotating the polyhedron. + ``+x_0`` / ``+y_0`` are applied on top of this translation. + + When unset, the projected origin falls on the unfold's root face + instead (its centroid in general, or its bounding-box centre for + ``+proj=isea``) rather than at a fixed lat / lon. + + .. note:: + The default convention is to interpret this value as decimal degrees. To + specify radians instead, follow the value with the "r" character. + + Example: `+lon_0=1.570796r` + + See :ref:`Projection Units ` for more information. diff --git a/docs/source/operations/options/orient_lat.rst b/docs/source/operations/options/orient_lat.rst new file mode 100644 index 0000000000..7bc9606a92 --- /dev/null +++ b/docs/source/operations/options/orient_lat.rst @@ -0,0 +1,5 @@ +.. option:: +orient_lat= + + Geodetic latitude of the polyhedron's first vertex, in degrees. Together + with ``+orient_lon`` and ``+azi`` this fully constrains the 3D pose of + the polyhedron on the sphere. diff --git a/docs/source/operations/options/orient_lon.rst b/docs/source/operations/options/orient_lon.rst new file mode 100644 index 0000000000..b6b365105d --- /dev/null +++ b/docs/source/operations/options/orient_lon.rst @@ -0,0 +1,5 @@ +.. option:: +orient_lon= + + Longitude of the polyhedron's first vertex, in degrees. Together with + ``+orient_lat`` and ``+azi`` this fully constrains the 3D pose of the + polyhedron on the sphere. diff --git a/docs/source/operations/projections/images/polyhedral_tsea_layout.png b/docs/source/operations/projections/images/polyhedral_tsea_layout.png new file mode 100644 index 0000000000000000000000000000000000000000..23fda4cb294d7a2e4f8b0d09c0d934efe8dd4403 GIT binary patch literal 65224 zcmeFZd03BY_dfi=CZa-_8k8-Su@FW1GAD>@p${iiH>v21?{Nd!~dmp}ZQ^Rk_ z#+c>%os2urUjM+lCRyrN_VtGkAFgfR#A3Y_{wLD))4aWWV|%;lKy$(Ari*%-QwodM zxU;l<=eu{Q1R~PuAMNXh&bT}bF41LaTO2xcD6jVJzI=WyMV-#i+qZ4Y<8-%dv`RES z#A11??l3YENzNS^&>GHipN_@pYWG0>RP$e(VFIBg9OKpC2-&pLgs$mVSHG;8{NtPZ{r6ro!d%sq_WcI2Mch{l_aN^OGNc&y;0%7x15X zsIz310XHk4IC#-^)lHi=xwPMT6rAqdS>M!KW5Ty{=T5b{xGm?epULtV?3)JyQo=TlM) zoU_6(bVvbTFL2qV!_6pehq&lpESA*kfyV14rIz_~r{QS-LdD<(Y`{ zw9)=jui*CCnT}s))_aW(w|?IH@Nk%8$glPq>6Td&@ZHnDXZ?8HRh8noCh(&Vo?mDn zT4&}j5-fc8`gL)E)gke$=&iyYKi_;+x%uFMta`-SpGJjdygd0~J!mtn?{ 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planar unfolding (net). The accepted values depend on the - projection: + Selects the planar unfolding (net). -.. option:: +orient_lat= + The accepted values and defaults depend on the projection - Geodetic latitude of the polyhedron's first vertex, in degrees. +.. include:: ../options/orient_lat.rst - *Default depends on the projection.* +.. include:: ../options/orient_lon.rst -.. option:: +orient_lon= +.. include:: ../options/azi.rst - Longitude of the polyhedron's first vertex, in degrees. +.. include:: ../options/lat_0_polyhedral.rst - *Default depends on the projection.* - -.. option:: +azi= - - Azimuth from the first vertex to the second, in degrees. Together with - ``+orient_lat`` and ``+orient_lon`` this fully constrains the 3D pose of - the polyhedron on the sphere. - - *Default depends on the projection.* - -.. include:: ../options/lat_0.rst - -For polyhedral projections, ``+lat_0`` / ``+lon_0`` specify the geographic -point that should land at the projected origin ``(0, 0)``. They translate -the projected output without rotating the polyhedron — the triangle edges -stay where ``+orient_*`` placed them. ``+x_0`` / ``+y_0`` are applied on top -of this translation. - -.. include:: ../options/lon_0.rst +.. include:: ../options/lon_0_polyhedral.rst .. include:: ../options/x_0.rst From 67e20eab2214bf33c2f589cc552d323c5be5f50f Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Tue, 12 May 2026 23:49:10 +0200 Subject: [PATCH 44/62] rename old isea to isea_legacy --- .../operations/projections/all_images.rst | 4 ++-- docs/source/operations/projections/index.rst | 2 +- .../projections/{isea.rst => isea_legacy.rst} | 4 ++-- .../operations/projections/polyhedral.rst | 10 +++++----- src/pj_list.h | 2 +- src/projections/isea.cpp | 10 +++++----- src/projections/polyhedral.cpp | 10 +++++----- test/gie/builtins.gie | 18 +++++++++--------- test/unit/test_polyhedral.cpp | 6 +++--- 9 files changed, 33 insertions(+), 33 deletions(-) rename docs/source/operations/projections/{isea.rst => isea_legacy.rst} (98%) diff --git a/docs/source/operations/projections/all_images.rst b/docs/source/operations/projections/all_images.rst index d7a5eaa03b..88de05e120 100644 --- a/docs/source/operations/projections/all_images.rst +++ b/docs/source/operations/projections/all_images.rst @@ -644,12 +644,12 @@ List of all projection images ******************************************************************************** -:ref:`isea` +:ref:`isea_legacy` .. figure:: ./images/isea.png :width: 500 px :align: center - :alt: isea + :alt: isea_legacy ******************************************************************************** diff --git a/docs/source/operations/projections/index.rst b/docs/source/operations/projections/index.rst index 3afa0ba6b9..c063b394b0 100644 --- a/docs/source/operations/projections/index.rst +++ b/docs/source/operations/projections/index.rst @@ -70,7 +70,7 @@ Projections map the spherical 3D space to a flat 2D space. imoll imoll_o imw_p - isea + isea_legacy polyhedral kav5 kav7 diff --git a/docs/source/operations/projections/isea.rst b/docs/source/operations/projections/isea_legacy.rst similarity index 98% rename from docs/source/operations/projections/isea.rst rename to docs/source/operations/projections/isea_legacy.rst index 686fe8fe73..3e6b887596 100644 --- a/docs/source/operations/projections/isea.rst +++ b/docs/source/operations/projections/isea_legacy.rst @@ -1,7 +1,7 @@ -.. _isea: +.. _isea_legacy: ******************************************************************************** -Icosahedral Snyder Equal Area +Icosahedral Snyder Equal Area (legacy) ******************************************************************************** Snyder's Icosahedral Equal Area map projection on an icosahedron polyhedral globe diff --git a/docs/source/operations/projections/polyhedral.rst b/docs/source/operations/projections/polyhedral.rst index a33222ba5d..591e531eea 100644 --- a/docs/source/operations/projections/polyhedral.rst +++ b/docs/source/operations/projections/polyhedral.rst @@ -73,11 +73,11 @@ selected by name using the `+net` parameter, e.g. `+proj=tsea +net=star` The defaults for ``+orient_lat`` / ``+orient_lon`` / ``+azi`` rotate each polyhedron into a sensible default pose (e.g. centred on Europe / Africa for -``dsea``; matching Snyder's published Figure 12 for ``isea2``). When +``dsea``; matching Snyder's published Figure 12 for ``isea``). When ``+lat_0`` / ``+lon_0`` are not supplied, the projected origin (0, 0) lands -on the centroid of the unfold's root face — except for ``isea2``, which -defaults to the bounding-box centre of the root face to match the legacy -``+proj=isea`` layout exactly. +on the centroid of the unfold's root face — except for ``isea``, which +uses the bounding-box centre of the root face instead so the unfolded net +sits centred in the output. Parameters ******************************************************************************** @@ -125,7 +125,7 @@ Examples: :align: center :alt: ISEA - proj-string: ``+proj=isea2`` + proj-string: ``+proj=isea`` .. figure:: ./images/polyhedral_dsea_flower.png :width: 500 px diff --git a/src/pj_list.h b/src/pj_list.h index 2f247f3b72..1f21726ae1 100644 --- a/src/pj_list.h +++ b/src/pj_list.h @@ -79,7 +79,7 @@ PROJ_HEAD(imoll, "Interrupted Mollweide") PROJ_HEAD(imoll_o, "Interrupted Mollweide Oceanic View") PROJ_HEAD(imw_p, "International Map of the World Polyconic") PROJ_HEAD(isea, "Icosahedral Snyder Equal Area") -PROJ_HEAD(isea2, "Icosahedral Snyder Equal Area (generalized)") +PROJ_HEAD(isea_legacy, "Icosahedral Snyder Equal Area (legacy)") PROJ_HEAD(kav5, "Kavrayskiy V") PROJ_HEAD(kav7, "Kavrayskiy VII") PROJ_HEAD(krovak, "Krovak") diff --git a/src/projections/isea.cpp b/src/projections/isea.cpp index 144bedd53c..e560aa26c8 100644 --- a/src/projections/isea.cpp +++ b/src/projections/isea.cpp @@ -959,7 +959,7 @@ static struct isea_pt isea_forward(struct pj_isea_data *g, * Proj 4 integration code follows */ -PROJ_HEAD(isea, "Icosahedral Snyder Equal Area") "\n\tSph"; +PROJ_HEAD(isea_legacy, "Icosahedral Snyder Equal Area (legacy)") "\n\tSph"; static PJ_XY isea_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */ PJ_XY xy = {0.0, 0.0}; @@ -987,7 +987,7 @@ static PJ_XY isea_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */ static PJ_LP isea_s_inverse(PJ_XY xy, PJ *P); -PJ *PJ_PROJECTION(isea) { +PJ *PJ_PROJECTION(isea_legacy) { char *opt; struct pj_isea_data *Q = static_cast( calloc(1, sizeof(struct pj_isea_data))); @@ -1302,7 +1302,7 @@ class ISEAPlanarProjection { } }; -// Orientation symmetric to equator (+proj=isea) +// Orientation symmetric to equator (+proj=isea_legacy) /* Sets the orientation of the icosahedron such that the north and the south * poles are mapped to the edge midpoints of the icosahedron. The equator is * thus mapped symmetrically. @@ -1311,7 +1311,7 @@ static ISEAPlanarProjection standardISEA( /* DEG_TO_RAD * (90 - 58.282525589) = 31.7174744114613 */ {(E_RAD + F_RAD) / 2, DEG_TO_RAD * -11.25}); -// Polar orientation (+proj=isea +orient=pole) +// Polar orientation (+proj=isea_legacy +orient=pole) /* * One corner of the icosahedron is, by default, facing to the north pole, and * one to the south pole. The provided orientation is relative to the default @@ -1375,7 +1375,7 @@ static PJ_LP isea_s_inverse(PJ_XY xy, PJ *P) { ISEAPlanarProjection *p = Q->p; if (p) { - // Default origin of +proj=isea is different (OGC:1534 is + // Default origin of +proj=isea_legacy is different (OGC:1534 is // +x_0=19186144.870934911 +y_0=-3323137.7717836285) PJ_XY input{xy.x * P->a + Q->xo, xy.y * P->a + Q->yo}; GeoPoint result; diff --git a/src/projections/polyhedral.cpp b/src/projections/polyhedral.cpp index c9db799be2..bebf630764 100644 --- a/src/projections/polyhedral.cpp +++ b/src/projections/polyhedral.cpp @@ -181,9 +181,9 @@ PJ *PJ_PROJECTION(dsea) { return polyhedral_setup(P, d); } -PROJ_HEAD(isea2, "Icosahedral Snyder Equal Area (generalized)") +PROJ_HEAD(isea, "Icosahedral Snyder Equal Area") "\n\tSph&Ell\n\torient= orient_lat= orient_lon= azi= lat_0= lon_0="; -PJ *PJ_PROJECTION(isea2) { +PJ *PJ_PROJECTION(isea) { auto *Q = static_cast( calloc(1, sizeof(pj_polyhedral_data))); if (nullptr == Q) @@ -194,14 +194,14 @@ PJ *PJ_PROJECTION(isea2) { // Standard Snyder ISEA orientation: V0 at authalic latitude arctan(φ) ≈ // 58.28°N (φ = golden ratio). On WGS84 this corresponds to ~58.40° // geodetic — PolyhedralDefaults stores the authalic value; user - // +orient_lat is geodetic and converted internally. Legacy +proj=isea + // +orient_lat is geodetic and converted internally. +proj=isea_legacy // uses orient_lon = 11.25° on a sphere and 11.20° on an ellipsoid. const bool sphere = (P->es == 0.0); double orient_lat = 58.282525588539; double orient_lon = sphere ? 11.25 : 11.20; double azi = 0.0; - // +orient= shorthand for two named orientations from legacy +proj=isea. + // +orient= shorthand for two named orientations from +proj=isea_legacy. // Individual +orient_lat / +orient_lon / +azi still override. const char *orient_name = pj_param(P->ctx, P->params, "sorient").s; if (orient_name != nullptr) { @@ -218,7 +218,7 @@ PJ *PJ_PROJECTION(isea2) { } } - // For drop-in compatibility with legacy +proj=isea, the default projected + // For drop-in compatibility with +proj=isea_legacy, the default projected // origin is the bbox center (mid-width, mid-height) of the unfold's root // face — the "South Africa" upper-band face F8 — rather than its // centroid. This matches legacy ISEA's 4×5 strip-layout geometric centre, diff --git a/test/gie/builtins.gie b/test/gie/builtins.gie index bc8ceec6e8..e6a8733b5c 100644 --- a/test/gie/builtins.gie +++ b/test/gie/builtins.gie @@ -3130,7 +3130,7 @@ expect 0.000898315284 0.000000000000 =============================================================================== ------------------------------------------------------------------------------- -operation +proj=isea +a=6400000 +operation +proj=isea_legacy +a=6400000 ------------------------------------------------------------------------------- tolerance 0.2 mm accept 2 1 @@ -3149,12 +3149,12 @@ accept -2 -1 expect -1575486.353772019501776 3234352.695310209877789 roundtrip 1 -operation +proj=isea +mode=hex +resolution=31 +operation +proj=isea_legacy +mode=hex +resolution=31 accept 0 0 expect failure ------------------------------------------------------------------------------- -operation +proj=isea +R=6371007.18091875 +operation +proj=isea_legacy +R=6371007.18091875 ------------------------------------------------------------------------------- tolerance 0.2 mm @@ -3191,7 +3191,7 @@ expect -837334.699958428042009 8323409.759132191538811 roundtrip 1 ------------------------------------------------------------------------------- -operation +proj=isea +R=6371007.18091875 +orient=pole +operation +proj=isea_legacy +R=6371007.18091875 +orient=pole ------------------------------------------------------------------------------- tolerance 0.2 mm @@ -3356,18 +3356,18 @@ expect -663460.15390426 -2932991.72938417 roundtrip 1 =============================================================================== -# Icosahedral Snyder Equal Area (generalized) +# Icosahedral Snyder Equal Area # Sph&Ell =============================================================================== ------------------------------------------------------------------------------- -# At default settings on a sphere, +proj=isea2 reproduces +proj=isea: the +# At default settings on a sphere, +proj=isea reproduces +proj=isea_legacy: the # projected origin is the geographic point that legacy ISEA places at (0, 0) — -# the bbox center of icosahedron face F7 (the central upper-band face), which +# the bbox center of icosahedron face F8 (the central upper-band face), which # corresponds to (lon=11.25°E, lat≈-30.0945°S) under the default orientation. # On an ellipsoid, +orient_lon defaults to 11.20° instead of 11.25°. ------------------------------------------------------------------------------- -operation +proj=isea2 +R=6371007.18091875 +operation +proj=isea +R=6371007.18091875 ------------------------------------------------------------------------------- tolerance 0.2 mm @@ -3389,7 +3389,7 @@ roundtrip 1 ------------------------------------------------------------------------------- # +lat_0 / +lon_0 pan the projected output: (lat_0, lon_0) lands at (0, 0). -operation +proj=isea2 +R=6371007.18091875 +lat_0=49 +lon_0=2 +operation +proj=isea +R=6371007.18091875 +lat_0=49 +lon_0=2 ------------------------------------------------------------------------------- tolerance 0.2 mm diff --git a/test/unit/test_polyhedral.cpp b/test/unit/test_polyhedral.cpp index 2b55985433..bdbef2afaa 100644 --- a/test/unit/test_polyhedral.cpp +++ b/test/unit/test_polyhedral.cpp @@ -49,9 +49,9 @@ static const ProjConfig proj_strings[] = { {"+proj=dsea +R=1", 1e-13}, {"+proj=dsea +ellps=WGS84", 1e-13}, {"+proj=dsea +R=1 +lat_0=10 +lon_0=20", 1e-11}, - {"+proj=isea2 +R=1", 1e-13}, - {"+proj=isea2 +ellps=WGS84", 1e-13}, - {"+proj=isea2 +R=1 +lat_0=10 +lon_0=20", 1e-11}, + {"+proj=isea +R=1", 1e-13}, + {"+proj=isea +ellps=WGS84", 1e-13}, + {"+proj=isea +R=1 +lat_0=10 +lon_0=20", 1e-11}, }; static void roundtrip_test(const char *proj_string, double tolerance) { From 00af60cb8de459102a1b26e42c8867e7e473636a Mon Sep 17 00:00:00 2001 From: Felix Palmer Date: Wed, 13 May 2026 00:14:34 +0200 Subject: [PATCH 45/62] Doc pages for all projections --- docs/source/operations/projections/dsea.rst | 125 ++++++++++++++++++ .../projections/images/dsea_a5_net.png | Bin 0 -> 394364 bytes .../projections/images/dsea_crescent_net.png | Bin 0 -> 644682 bytes .../projections/images/dsea_flower_net.png | Bin 0 -> 553368 bytes .../projections/images/dsea_net.png | Bin 0 -> 387232 bytes .../projections/images/isea_net.png | Bin 0 -> 476205 bytes .../projections/images/isea_pole_net.png | Bin 0 -> 386176 bytes .../projections/images/tsea_net.png | Bin 0 -> 461672 bytes .../projections/images/tsea_star_net.png | Bin 0 -> 629342 bytes docs/source/operations/projections/index.rst | 3 + docs/source/operations/projections/isea.rst | 108 +++++++++++++++ .../operations/projections/polyhedral.rst | 29 +--- docs/source/operations/projections/tsea.rst | 104 +++++++++++++++ 13 files changed, 343 insertions(+), 26 deletions(-) create mode 100644 docs/source/operations/projections/dsea.rst create mode 100644 docs/source/operations/projections/images/dsea_a5_net.png create mode 100644 docs/source/operations/projections/images/dsea_crescent_net.png create mode 100644 docs/source/operations/projections/images/dsea_flower_net.png create mode 100644 docs/source/operations/projections/images/dsea_net.png create mode 100644 docs/source/operations/projections/images/isea_net.png create mode 100644 docs/source/operations/projections/images/isea_pole_net.png create mode 100644 docs/source/operations/projections/images/tsea_net.png create mode 100644 docs/source/operations/projections/images/tsea_star_net.png create mode 100644 docs/source/operations/projections/isea.rst create mode 100644 docs/source/operations/projections/tsea.rst diff --git a/docs/source/operations/projections/dsea.rst b/docs/source/operations/projections/dsea.rst new file mode 100644 index 0000000000..76aa10c018 --- /dev/null +++ b/docs/source/operations/projections/dsea.rst @@ -0,0 +1,125 @@ +.. _dsea: + +******************************************************************************** +Dodecahedral Snyder Equal Area +******************************************************************************** + +Snyder's equal-area mapping :cite:`Snyder1992` applied to the twelve pentagonal +faces of a regular dodecahedron and unfolded into a planar net. + +The dodecahedron is subdivided into 12 × 10 = 120 right sub-triangles, +and each sub-triangle is mapped independently using the area-preserving +Snyder construction. + +See :ref:`polyhedral` for the shared theory. + ++---------------------+----------------------------------------------------------+ +| **Classification** | Polyhedral, equal area | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, spherical and ellipsoidal | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global | ++---------------------+----------------------------------------------------------+ +| **Alias** | dsea | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + + +.. figure:: ./images/dsea_net.png + :width: 500 px + :align: center + :alt: Dodecahedral Snyder Equal Area + + proj-string: ``+proj=dsea`` + + +Nets +################################################################################ + +dsea (default) +-------------------------------------------------------------------------------- + +Snyder's layout (Figure 6) + +.. figure:: ./images/dsea_net.png + :width: 500 px + :align: center + :alt: DSEA default net + + proj-string: ``+proj=dsea`` + +a5 +-------------------------------------------------------------------------------- + +Layout used by the `A5 index `_. First 8 faces contain the +majority of the populated land mass. + +.. figure:: ./images/dsea_a5_net.png + :width: 500 px + :align: center + :alt: DSEA A5 net + + proj-string: ``+proj=dsea +net=a5`` + +crescent +-------------------------------------------------------------------------------- + +.. figure:: ./images/dsea_crescent_net.png + :width: 500 px + :align: center + :alt: DSEA crescent net + + proj-string: ``+proj=dsea +net=crescent`` + +flower +-------------------------------------------------------------------------------- + +.. figure:: ./images/dsea_flower_net.png + :width: 500 px + :align: center + :alt: DSEA flower net + + proj-string: ``+proj=dsea +net=flower`` + + +Parameters +################################################################################ + +.. note:: + All parameters are optional. + +.. option:: +net= + + Selects the planar unfolding. Accepted values: ``dsea``, ``a5``, + ``crescent``, ``flower``. + + *Defaults to* ``dsea``. + +.. include:: ../options/orient_lat.rst + +*Defaults to* ``atan((1 + 2·cos(36°))/2) ≈ 52.6226°``. + +.. include:: ../options/orient_lon.rst + +*Defaults to −36.0 (or −129.0 when* ``+net=a5`` *).* + +.. include:: ../options/azi.rst + +*Defaults to 240.0.* + +.. include:: ../options/lat_0_polyhedral.rst + +.. include:: ../options/lon_0_polyhedral.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/images/dsea_a5_net.png b/docs/source/operations/projections/images/dsea_a5_net.png new file mode 100644 index 0000000000000000000000000000000000000000..2d4d45d71a17fec8cc777685d6da7283fdc9ff9c GIT binary patch literal 394364 zcmeFZcUaH=|34buvKnSeDTGkcAnnYCRETydrD*T15QQj-NDEQ4llCs{g|wHpwo1K9 z>)akW=X>RM&iUi~d9Lf{y867|e7s+;=XgBs_uINZ?w^yFqFuXfEfp0Nt&H@k3sh9A 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