# geopandas.GeoSeries.delaunay_triangles#

GeoSeries.delaunay_triangles(tolerance=0.0, only_edges=False)[source]#

Returns a GeoSeries consisting of objects representing the computed Delaunay triangulation between the vertices of an input geometry.

All geometries within the GeoSeries are considered together within a single Delaunay triangulation. The resulting geometries therefore do not map 1:1 to input geometries. Note that each vertex of a geometry is considered a site for the triangulation, so the triangles will be constructed between the vertices of each geometry.

Parameters:
tolerancefloat, default 0.0

Snap input vertices together if their distance is less than this value.

only_edgesbool (optional, default False)

If set to True, the triangulation will return linestrings instead of polygons.

GeoSeries.voronoi_polygons

Voronoi diagram around vertices

Notes

If you want to generate Delaunay triangles for each geometry separately, use shapely.delaunay_triangles() instead.

Examples

>>> from shapely import LineString, MultiPoint, Point, Polygon
>>> s = geopandas.GeoSeries(
...     [
...         Point(1, 1),
...         Point(2, 2),
...         Point(1, 3),
...         Point(0, 2),
...     ]
... )
>>> s
0    POINT (1 1)
1    POINT (2 2)
2    POINT (1 3)
3    POINT (0 2)
dtype: geometry
>>> s.delaunay_triangles()
0    POLYGON ((0 2, 1 1, 1 3, 0 2))
1    POLYGON ((1 3, 1 1, 2 2, 1 3))
dtype: geometry
>>> s.delaunay_triangles(only_edges=True)
0    LINESTRING (1 3, 2 2)
1    LINESTRING (0 2, 1 3)
2    LINESTRING (0 2, 1 1)
3    LINESTRING (1 1, 2 2)
4    LINESTRING (1 1, 1 3)
dtype: geometry

The method supports any geometry type but keep in mind that the underlying algorithm is based on the vertices of the input geometries only and does not consider edge segments between vertices.

>>> s2 = geopandas.GeoSeries(
...     [
...         Polygon([(0, 0), (1, 1), (0, 1)]),
...         LineString([(1, 0), (2, 1), (1, 2)]),
...         MultiPoint([(2, 3), (2, 0), (3, 1)]),
...     ]
... )
>>> s2
0      POLYGON ((0 0, 1 1, 0 1, 0 0))
1          LINESTRING (1 0, 2 1, 1 2)
2    MULTIPOINT ((2 3), (2 0), (3 1))
dtype: geometry
>>> s2.delaunay_triangles()
0    POLYGON ((0 1, 0 0, 1 0, 0 1))
1    POLYGON ((0 1, 1 0, 1 1, 0 1))
2    POLYGON ((0 1, 1 1, 1 2, 0 1))
3    POLYGON ((1 2, 1 1, 2 1, 1 2))
4    POLYGON ((1 2, 2 1, 2 3, 1 2))
5    POLYGON ((2 3, 2 1, 3 1, 2 3))
6    POLYGON ((3 1, 2 1, 2 0, 3 1))
7    POLYGON ((2 0, 2 1, 1 1, 2 0))
8    POLYGON ((2 0, 1 1, 1 0, 2 0))
dtype: geometry