diff --git a/README.md b/README.md
index 972614a..f4d166a 100644
--- a/README.md
+++ b/README.md
@@ -81,3 +81,22 @@ int main() {
     mapbox::util::apply_visitor(visitor,geom);
 }
 ```
+
+Geometry types with a custom point type:
+
+```cpp
+#include <mapbox/geometry/geometry.hpp>
+
+// geometry.hpp provides a `geometry_t` template that supports any point type with a
+// `coordinate_type` member.
+struct my_point {
+    using coordinate_type = double;
+    double x;
+    double y;
+    double elevation;
+};
+
+using my_geometry = mapbox::geometry::geometry_t<my_point>;
+using my_line_string = my_geometry::line_string_type;
+using my_polygon = my_geometry::polygon_type;
+// etc.
diff --git a/include/mapbox/geometry/geometry.hpp b/include/mapbox/geometry/geometry.hpp
index cf70d8e..a40e12f 100644
--- a/include/mapbox/geometry/geometry.hpp
+++ b/include/mapbox/geometry/geometry.hpp
@@ -14,38 +14,52 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct geometry_collection;
-
-template <typename T>
-using geometry_base = mapbox::util::variant<point<T>,
-                                            line_string<T>,
-                                            polygon<T>,
-                                            multi_point<T>,
-                                            multi_line_string<T>,
-                                            multi_polygon<T>,
-                                            geometry_collection<T>>;
-
-template <typename T>
-struct geometry : geometry_base<T>
+template <typename Point, template <typename...> class Cont = std::vector>
+struct geometry_collection_t;
+
+template <typename Point>
+using geometry_base_t = mapbox::util::variant<Point,
+                                              line_string_t<Point>,
+                                              polygon_t<Point>,
+                                              multi_point_t<Point>,
+                                              multi_line_string_t<Point>,
+                                              multi_polygon_t<Point>,
+                                              geometry_collection_t<Point>>;
+
+template <typename Point>
+struct geometry_t : geometry_base_t<Point>
 {
-    using coordinate_type = T;
-    using geometry_base<T>::geometry_base;
+    using point_type               = Point;
+    using line_string_type         = line_string_t<Point>;
+    using polygon_type             = polygon_t<Point>;
+    using multi_point_type         = multi_point_t<Point>;
+    using multi_line_string_type   = multi_line_string_t<Point>;
+    using multi_polygon_type       = multi_polygon_t<Point>;
+    using geometry_collection_type = geometry_collection_t<Point>;
+    using coordinate_type = typename point_type::coordinate_type;
+    using geometry_base_t<Point>::geometry_base_t;
 
     /*
      * The default constructor would create a point geometry with default-constructed coordinates;
      * i.e. (0, 0). Since this is not particularly useful, and could hide bugs, it is disabled.
      */
-    geometry() = delete;
+    geometry_t() = delete;
 };
 
-template <typename T, template <typename...> class Cont>
-struct geometry_collection : Cont<geometry<T>>
+template <class T>
+using geometry = geometry_t<point<T>>;
+
+template <typename Point, template <typename...> class Container>
+struct geometry_collection_t : Container<geometry_t<Point>>
 {
-    using coordinate_type = T;
-    using geometry_type = geometry<T>;
-    using container_type = Cont<geometry_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using geometry_type = geometry_t<Point>;
+    using container_type = Container<geometry_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using geometry_collection = geometry_collection_t<point<T>, Container>;
+
 }}
diff --git a/include/mapbox/geometry/line_string.hpp b/include/mapbox/geometry/line_string.hpp
index 03a0954..c13dc0b 100644
--- a/include/mapbox/geometry/line_string.hpp
+++ b/include/mapbox/geometry/line_string.hpp
@@ -7,13 +7,16 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct line_string : Cont<point<T> >
+template <class Point, template <typename...> class Container = std::vector>
+struct line_string_t : Container<Point>
 {
-    using coordinate_type = T;
-    using point_type = point<T>;
-    using container_type = Cont<point_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using container_type = Container<point_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using line_string = line_string_t<point<T>, Container>;
+
 }}
diff --git a/include/mapbox/geometry/multi_line_string.hpp b/include/mapbox/geometry/multi_line_string.hpp
index 4864dd2..e91d90a 100644
--- a/include/mapbox/geometry/multi_line_string.hpp
+++ b/include/mapbox/geometry/multi_line_string.hpp
@@ -7,13 +7,17 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct multi_line_string : Cont<line_string<T>>
+template <typename Point, template <typename...> class Container = std::vector>
+struct multi_line_string_t : Container<line_string_t<Point>>
 {
-    using coordinate_type = T;
-    using line_string_type = line_string<T>;
-    using container_type = Cont<line_string_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using line_string_type = line_string_t<point_type>;
+    using container_type = Container<line_string_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using multi_line_string = multi_line_string_t<point<T>, Container>;
+
 }}
diff --git a/include/mapbox/geometry/multi_point.hpp b/include/mapbox/geometry/multi_point.hpp
index eb81cd4..24060c6 100644
--- a/include/mapbox/geometry/multi_point.hpp
+++ b/include/mapbox/geometry/multi_point.hpp
@@ -7,13 +7,16 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct multi_point : Cont<point<T>>
+template <class Point, template <typename...> class Container = std::vector>
+struct multi_point_t : Container<Point>
 {
-    using coordinate_type = T;
-    using point_type = point<T>;
-    using container_type = Cont<point_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using container_type = Container<point_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using multi_point = multi_point_t<point<T>, Container>;
+
 }}
diff --git a/include/mapbox/geometry/multi_polygon.hpp b/include/mapbox/geometry/multi_polygon.hpp
index d5da1cb..1f92665 100644
--- a/include/mapbox/geometry/multi_polygon.hpp
+++ b/include/mapbox/geometry/multi_polygon.hpp
@@ -7,13 +7,17 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct multi_polygon : Cont<polygon<T>>
+template <typename Point, template <typename...> class Container = std::vector>
+struct multi_polygon_t : Container<polygon_t<Point>>
 {
-    using coordinate_type = T;
-    using polygon_type = polygon<T>;
-    using container_type = Cont<polygon_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using polygon_type = polygon_t<Point>;
+    using container_type = Container<polygon_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using multi_polygon = multi_polygon_t<point<T>, Container>;
+
 }}
diff --git a/include/mapbox/geometry/polygon.hpp b/include/mapbox/geometry/polygon.hpp
index fab9f4d..510e2b5 100644
--- a/include/mapbox/geometry/polygon.hpp
+++ b/include/mapbox/geometry/polygon.hpp
@@ -8,22 +8,26 @@
 
 namespace mapbox { namespace geometry {
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct linear_ring : Cont<point<T>>
+template <typename Point, template <typename...> class Container = std::vector>
+struct linear_ring_t : Container<Point>
 {
-    using coordinate_type = T;
-    using point_type = point<T>;
-    using container_type = Cont<point_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using container_type = Container<point_type>;
     using container_type::container_type;
 };
 
-template <typename T, template <typename...> class Cont = std::vector>
-struct polygon : Cont<linear_ring<T>>
+template <typename Point, template <typename...> class Container = std::vector>
+struct polygon_t : Container<linear_ring_t<Point>>
 {
-    using coordinate_type = T;
-    using linear_ring_type = linear_ring<T>;
-    using container_type = Cont<linear_ring_type>;
+    using point_type = Point;
+    using coordinate_type = typename point_type::coordinate_type;
+    using linear_ring_type = linear_ring_t<Point>;
+    using container_type = Container<linear_ring_type>;
     using container_type::container_type;
 };
 
+template <class T, template <typename...> class Container = std::vector>
+using polygon = polygon_t<point<T>, Container>;
+
 }}
diff --git a/tests/test.cpp b/tests/test.cpp
index 2dba1c5..75f54cc 100644
--- a/tests/test.cpp
+++ b/tests/test.cpp
@@ -193,6 +193,21 @@ static void testEnvelope() {
     assert(envelope(geometry_collection<int>({point<int>(0, 0)})) == box<int>({0, 0}, {0, 0}));
 }
 
+static void testCustomPointType() {
+    struct point_3d {
+       using coordinate_type = double;
+       double x;
+       double y;
+       double z;
+    };
+
+    using custom_geometry = geometry_t<point_3d>;
+    using custom_polygon = custom_geometry::polygon_type;
+
+    custom_geometry g { custom_polygon({{{0, 1, 2}, {3, 4, 5}}}) };
+    assert(g.get<custom_polygon>()[0][0].x == 0);
+}
+
 int main() {
     testPoint();
     testMultiPoint();
@@ -207,5 +222,6 @@ int main() {
 
     testForEachPoint();
     testEnvelope();
+    testCustomPointType();
     return 0;
 }