mortie

Mortie is a library for applying morton indexing to healpix grids. Morton numbering (also called z-ordering) facilitates several geospatial operators such as buffering and neighborhood look-ups, and can generally be thought of as a type of geohashing.

This particular implementation focuses on hierarchical healpix maps, and is mostly inspired from this paper.

Performance

Mortie uses Rust-accelerated morton indexing functions for high performance. The Rust implementation provides dramatic speedups:

Dataset Size	Rust	Python (reference)	Speedup
1,000 values	1.93 ms	4.14 ms	2.1x
100,000 values	1.85 ms	410.59 ms	222x
1.2M coordinates	102.51 ms	5.1 sec	50x

Pre-built wheels are available for Linux, macOS, and Windows. The Rust extension is required and is included in all pip-installed wheels.

Installation

pip install mortie

For development builds with Rust, see BUILDING.md.

Spatial Buffer

Mortie provides a morton_buffer function for expanding a set of morton cells by a configurable border ring. This is useful for... well, buffering.

import numpy as np
import mortie

# Convert coordinates to morton cells at order 6
cells = np.unique(mortie.geo2mort(lats, lons, order=6))

# Expand by 1-cell ring (8-connected neighbors)
border = mortie.morton_buffer(cells, k=1)
expanded = np.union1d(cells, border)

All input indices must be at the same order. The function returns only the new border cells, not the input cells themselves.

Polygon Coverage

morton_coverage computes the set of morton indices that completely cover a polygon defined by lat/lon vertices. The algorithm builds a contiguous boundary via great-circle interpolation, classifies inner/outer buffer cells using connected components + point-in-polygon testing, then recursively fills the interior.

import mortie

# Define polygon vertices (lat, lon in degrees)
lats = [40.0, 40.0, 50.0, 50.0]
lons = [-125.0, -115.0, -115.0, -125.0]

# Get all morton cells covering the polygon at order 6
cells = mortie.morton_coverage(lats, lons, order=6)

The function handles concave polygons, antimeridian-crossing polygons, and polar regions. Polygon 'donut' holes are not yet supported.

Dependencies

numpy. All HEALPix operations use the Rust-native healpix crate bundled in the compiled extension — no external HEALPix library is needed.

Funding

Initial funding of this work was supported by the ICESat-2 project science office, at the Laboratory for Cryospheric Sciences (NASA Goddard, Section 615).

References

[1] Youngren, Robert W., and Mikel D. Petty. "A multi-resolution HEALPix data structure for spherically mapped point data." Heliyon 3.6 (2017): e00332. doi: 10.1016/j.heliyon.2017.e00332