Constructive operations

pygeos.constructive.boundary(geometry, **kwargs)

Returns the topological boundary of a geometry.

Parameters
geometryGeometry or array_like

This function will return None for geometrycollections.

Examples

>>> boundary(Geometry("POINT (0 0)"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>
>>> boundary(Geometry("LINESTRING(0 0, 1 1, 1 2)"))
<pygeos.Geometry MULTIPOINT (0 0, 1 2)>
>>> boundary(Geometry("LINEARRING (0 0, 1 0, 1 1, 0 1, 0 0)"))
<pygeos.Geometry MULTIPOINT EMPTY>
>>> boundary(Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))"))
<pygeos.Geometry LINESTRING (0 0, 1 0, 1 1, 0 1, 0 0)>
>>> boundary(Geometry("MULTIPOINT (0 0, 1 2)"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>
>>> boundary(Geometry("MULTILINESTRING ((0 0, 1 1), (0 1, 1 0))"))
<pygeos.Geometry MULTIPOINT (0 0, 0 1, 1 0, 1 1)>
>>> boundary(Geometry("GEOMETRYCOLLECTION (POINT (0 0))")) is None
True
pygeos.constructive.buffer(geometry, radius, quadsegs=8, cap_style='round', join_style='round', mitre_limit=5.0, single_sided=False, **kwargs)

Computes the buffer of a geometry for positive and negative buffer radius.

The buffer of a geometry is defined as the Minkowski sum (or difference, for negative width) of the geometry with a circle with radius equal to the absolute value of the buffer radius.

The buffer operation always returns a polygonal result. The negative or zero-distance buffer of lines and points is always empty.

Parameters
geometryGeometry or array_like
widthfloat or array_like

Specifies the circle radius in the Minkowski sum (or difference).

quadsegsint

Specifies the number of linear segments in a quarter circle in the approximation of circular arcs.

cap_style{‘round’, ‘square’, ‘flat’}

Specifies the shape of buffered line endings. ‘round’ results in circular line endings (see quadsegs). Both ‘square’ and ‘flat’ result in rectangular line endings, only ‘flat’ will end at the original vertex, while ‘square’ involves adding the buffer width.

join_style{‘round’, ‘bevel’, ‘mitre’}

Specifies the shape of buffered line midpoints. ‘round’ results in rounded shapes. ‘bevel’ results in a beveled edge that touches the original vertex. ‘mitre’ results in a single vertex that is beveled depending on the mitre_limit parameter.

mitre_limitfloat

Crops of ‘mitre’-style joins if the point is displaced from the buffered vertex by more than this limit.

single_sidedbool

Only buffer at one side of the geometry.

Examples

>>> buffer(Geometry("POINT (10 10)"), 2, quadsegs=1)
<pygeos.Geometry POLYGON ((12 10, 10 8, 8 10, 10 12, 12 10))>
>>> buffer(Geometry("POINT (10 10)"), 2, quadsegs=2)
<pygeos.Geometry POLYGON ((12 10, 11.4 8.59, 10 8, 8.59 8.59, 8 10, 8.59 11....>
>>> buffer(Geometry("POINT (10 10)"), -2, quadsegs=1)
<pygeos.Geometry POLYGON EMPTY>
>>> line = Geometry("LINESTRING (10 10, 20 10)")
>>> buffer(line, 2, cap_style="square")
<pygeos.Geometry POLYGON ((20 12, 22 12, 22 8, 10 8, 8 8, 8 12, 20 12))>
>>> buffer(line, 2, cap_style="flat")
<pygeos.Geometry POLYGON ((20 12, 20 8, 10 8, 10 12, 20 12))>
>>> buffer(line, 2, single_sided=True, cap_style="flat")
<pygeos.Geometry POLYGON ((20 10, 10 10, 10 12, 20 12, 20 10))>
>>> line2 = Geometry("LINESTRING (10 10, 20 10, 20 20)")
>>> buffer(line2, 2, cap_style="flat", join_style="bevel")
<pygeos.Geometry POLYGON ((18 12, 18 20, 22 20, 22 10, 20 8, 10 8, 10 12, 18...>
>>> buffer(line2, 2, cap_style="flat", join_style="mitre")
<pygeos.Geometry POLYGON ((18 12, 18 20, 22 20, 22 8, 10 8, 10 12, 18 12))>
>>> buffer(line2, 2, cap_style="flat", join_style="mitre", mitre_limit=1)
<pygeos.Geometry POLYGON ((18 12, 18 20, 22 20, 21.8 9, 21 8.17, 10 8, 10 12...>
>>> square = Geometry("POLYGON((0 0, 10 0, 10 10, 0 10, 0 0))")
>>> buffer(square, 2, join_style="mitre")
<pygeos.Geometry POLYGON ((-2 -2, -2 12, 12 12, 12 -2, -2 -2))>
>>> buffer(square, -2, join_style="mitre")
<pygeos.Geometry POLYGON ((2 2, 2 8, 8 8, 8 2, 2 2))>
>>> buffer(square, -5, join_style="mitre")
<pygeos.Geometry POLYGON EMPTY>
>>> buffer(line, float("nan")) is None
True
pygeos.constructive.build_area(geometry, **kwargs)

Creates an areal geometry formed by the constituent linework of given geometry.

Equivalent of the PostGIS ST_BuildArea() function.

Requires at least GEOS 3.8.0.

Parameters
geometryGeometry or array_like

Examples

>>> build_area(Geometry("GEOMETRYCOLLECTION(POLYGON((0 0, 3 0, 3 3, 0 3, 0 0)), POLYGON((1 1, 1 2, 2 2, 1 1)))"))
<pygeos.Geometry POLYGON ((0 0, 0 3, 3 3, 3 0, 0 0), (1 1, 2 2, 1 2, 1 1))>
pygeos.constructive.centroid(geometry, **kwargs)

Computes the geometric center (center-of-mass) of a geometry.

For multipoints this is computed as the mean of the input coordinates. For multilinestrings the centroid is weighted by the length of each line segment. For multipolygons the centroid is weighted by the area of each polygon.

Parameters
geometryGeometry or array_like

Examples

>>> centroid(Geometry("POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0))"))
<pygeos.Geometry POINT (5 5)>
>>> centroid(Geometry("LINESTRING (0 0, 2 2, 10 10)"))
<pygeos.Geometry POINT (5 5)>
>>> centroid(Geometry("MULTIPOINT (0 0, 10 10)"))
<pygeos.Geometry POINT (5 5)>
>>> centroid(Geometry("POLYGON EMPTY"))
<pygeos.Geometry POINT EMPTY>
pygeos.constructive.clip_by_rect(geometry, xmin, ymin, xmax, ymax, **kwargs)

Returns the portion of a geometry within a rectangle.

The geometry is clipped in a fast but possibly dirty way. The output is not guaranteed to be valid. No exceptions will be raised for topological errors.

Note: empty geometries or geometries that do not overlap with the specified bounds will result in GEOMETRYCOLLECTION EMPTY.

Parameters
geometryGeometry or array_like

The geometry to be clipped

xminfloat

Minimum x value of the rectangle

yminfloat

Minimum y value of the rectangle

xmaxfloat

Maximum x value of the rectangle

ymaxfloat

Maximum y value of the rectangle

Examples

>>> line = Geometry("LINESTRING (0 0, 10 10)")
>>> clip_by_rect(line, 0., 0., 1., 1.)
<pygeos.Geometry LINESTRING (0 0, 1 1)>
pygeos.constructive.convex_hull(geometry, **kwargs)

Computes the minimum convex geometry that encloses an input geometry.

Parameters
geometryGeometry or array_like

Examples

>>> convex_hull(Geometry("MULTIPOINT (0 0, 10 0, 10 10)"))
<pygeos.Geometry POLYGON ((0 0, 10 10, 10 0, 0 0))>
>>> convex_hull(Geometry("POLYGON EMPTY"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>
pygeos.constructive.delaunay_triangles(geometry, tolerance=0.0, only_edges=False, **kwargs)

Computes a Delaunay triangulation around the vertices of an input geometry.

The output is a geometrycollection containing polygons (default) or linestrings (see only_edges). Returns an None if an input geometry contains less than 3 vertices.

Parameters
geometryGeometry or array_like
tolerancefloat or array_like

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

only_edgesbool or array_like

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

Examples

>>> points = Geometry("MULTIPOINT (50 30, 60 30, 100 100)")
>>> delaunay_triangles(points)
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((50 30, 60 30, 100 100, 50 30)))>
>>> delaunay_triangles(points, only_edges=True)
<pygeos.Geometry MULTILINESTRING ((50 30, 100 100), (50 30, 60 30), (60 30, ...>
>>> delaunay_triangles(Geometry("MULTIPOINT (50 30, 51 30, 60 30, 100 100)"), tolerance=2)
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((50 30, 60 30, 100 100, 50 30)))>
>>> delaunay_triangles(Geometry("POLYGON ((50 30, 60 30, 100 100, 50 30))"))
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((50 30, 60 30, 100 100, 50 30)))>
>>> delaunay_triangles(Geometry("LINESTRING (50 30, 60 30, 100 100)"))
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((50 30, 60 30, 100 100, 50 30)))>
>>> delaunay_triangles(Geometry("GEOMETRYCOLLECTION EMPTY"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>
pygeos.constructive.envelope(geometry, **kwargs)

Computes the minimum bounding box that encloses an input geometry.

Parameters
geometryGeometry or array_like

Examples

>>> envelope(Geometry("LINESTRING (0 0, 10 10)"))
<pygeos.Geometry POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0))>
>>> envelope(Geometry("MULTIPOINT (0 0, 10 0, 10 10)"))
<pygeos.Geometry POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0))>
>>> envelope(Geometry("POINT (0 0)"))
<pygeos.Geometry POINT (0 0)>
>>> envelope(Geometry("GEOMETRYCOLLECTION EMPTY"))
<pygeos.Geometry POINT EMPTY>
pygeos.constructive.extract_unique_points(geometry, **kwargs)

Returns all distinct vertices of an input geometry as a multipoint.

Note that only 2 dimensions of the vertices are considered when testing for equality.

Parameters
geometryGeometry or array_like

Examples

>>> extract_unique_points(Geometry("POINT (0 0)"))
<pygeos.Geometry MULTIPOINT (0 0)>
>>> extract_unique_points(Geometry("LINESTRING(0 0, 1 1, 1 1)"))
<pygeos.Geometry MULTIPOINT (0 0, 1 1)>
>>> extract_unique_points(Geometry("POLYGON((0 0, 1 0, 1 1, 0 0))"))
<pygeos.Geometry MULTIPOINT (0 0, 1 0, 1 1)>
>>> extract_unique_points(Geometry("MULTIPOINT (0 0, 1 1, 0 0)"))
<pygeos.Geometry MULTIPOINT (0 0, 1 1)>
>>> extract_unique_points(Geometry("LINESTRING EMPTY"))
<pygeos.Geometry MULTIPOINT EMPTY>
pygeos.constructive.make_valid(geometry, **kwargs)

Repairs invalid geometries.

Requires at least GEOS 3.8.0.

Parameters
geometryGeometry or array_like

Examples

>>> make_valid(Geometry("POLYGON((0 0, 1 1, 1 2, 1 1, 0 0))"))
<pygeos.Geometry MULTILINESTRING ((0 0, 1 1), (1 1, 1 2))>
pygeos.constructive.normalize(geometry, **kwargs)

Converts Geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Parameters
geometryGeometry or array_like

Examples

>>> p = Geometry("MULTILINESTRING((0 0, 1 1),(2 2, 3 3))")
>>> normalize(p)
<pygeos.Geometry MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
pygeos.constructive.offset_curve(geometry, distance, quadsegs=8, join_style='round', mitre_limit=5.0, **kwargs)

Returns a (Multi)LineString at a distance from the object on its right or its left side.

For positive distance the offset will be at the left side of the input line and retain the same direction. For a negative distance it will be at the right side and in the opposite direction.

Parameters
geometryGeometry or array_like
distancefloat or array_like

Specifies the offset distance from the input geometry. Negative for right side offset, positive for left side offset.

quadsegsint

Specifies the number of linear segments in a quarter circle in the approximation of circular arcs.

join_style{‘round’, ‘bevel’, ‘mitre’}

Specifies the shape of outside corners. ‘round’ results in rounded shapes. ‘bevel’ results in a beveled edge that touches the original vertex. ‘mitre’ results in a single vertex that is beveled depending on the mitre_limit parameter.

mitre_limitfloat

Crops of ‘mitre’-style joins if the point is displaced from the buffered vertex by more than this limit.

Examples

>>> line = Geometry("LINESTRING (0 0, 0 2)")
>>> offset_curve(line, 2)
<pygeos.Geometry LINESTRING (-2 0, -2 2)>
>>> offset_curve(line, -2)
<pygeos.Geometry LINESTRING (2 2, 2 0)>
pygeos.constructive.point_on_surface(geometry, **kwargs)

Returns a point that intersects an input geometry.

Parameters
geometryGeometry or array_like

Examples

>>> point_on_surface(Geometry("POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0))"))
<pygeos.Geometry POINT (5 5)>
>>> point_on_surface(Geometry("LINESTRING (0 0, 2 2, 10 10)"))
<pygeos.Geometry POINT (2 2)>
>>> point_on_surface(Geometry("MULTIPOINT (0 0, 10 10)"))
<pygeos.Geometry POINT (0 0)>
>>> point_on_surface(Geometry("POLYGON EMPTY"))
<pygeos.Geometry POINT EMPTY>
pygeos.constructive.polygonize(geometries, **kwargs)

Creates polygons formed from the linework of a set of Geometries.

Polygonizes an array of Geometries that contain linework which represents the edges of a planar graph. Any type of Geometry may be provided as input; only the constituent lines and rings will be used to create the output polygons.

Lines or rings that when combined do not completely close a polygon will result in an empty GeometryCollection. Duplicate segments are ignored.

This function returns the polygons within a GeometryCollection. Individual Polygons can be obtained using get_geometry to get a single polygon or get_parts to get an array of polygons. MultiPolygons can be constructed from the output using pygeos.multipolygons(pygeos.get_parts(pygeos.polygonize(geometries))).

Parameters
geometriesarray_like

An array of geometries.

axisint

Axis along which the geometries are polygonized. The default is to perform a reduction over the last dimension of the input array. A 1D array results in a scalar geometry.

Returns
GeometryCollection or array of GeometryCollections

See also

get_parts, get_geometry

Examples

>>> lines = [
...     Geometry("LINESTRING (0 0, 1 1)"),
...     Geometry("LINESTRING (0 0, 0 1)"),
...     Geometry("LINESTRING (0 1, 1 1)"),
... ]
>>> polygonize(lines)
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((1 1, 0 0, 0 1, 1 1)))>
pygeos.constructive.reverse(geometry, **kwargs)

Returns a copy of a Geometry with the order of coordinates reversed.

If a Geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged. None is returned where Geometry is None.

Parameters
geometryGeometry or array_like

See also

is_ccw

Checks if a Geometry is clockwise.

Examples

>>> reverse(Geometry("LINESTRING (0 0, 1 2)"))
<pygeos.Geometry LINESTRING (1 2, 0 0)>
>>> reverse(Geometry("POLYGON ((0 0, 1 0, 1 1, 0 1, 0 0))"))
<pygeos.Geometry POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
>>> reverse(None) is None
True
pygeos.constructive.segmentize(geometry, tolerance, **kwargs)

‘segmentize’ requires at least GEOS 3.10.0

pygeos.constructive.simplify(geometry, tolerance, preserve_topology=False, **kwargs)

Returns a simplified version of an input geometry using the Douglas-Peucker algorithm.

Parameters
geometryGeometry or array_like
tolerancefloat or array_like

The maximum allowed geometry displacement. The higher this value, the smaller the number of vertices in the resulting geometry.

preserve_topologybool

If set to True, the operation will avoid creating invalid geometries.

Examples

>>> line = Geometry("LINESTRING (0 0, 1 10, 0 20)")
>>> simplify(line, tolerance=0.9)
<pygeos.Geometry LINESTRING (0 0, 1 10, 0 20)>
>>> simplify(line, tolerance=1)
<pygeos.Geometry LINESTRING (0 0, 0 20)>
>>> polygon_with_hole = Geometry("POLYGON((0 0, 0 10, 10 10, 10 0, 0 0), (2 2, 2 4, 4 4, 4 2, 2 2))")
>>> simplify(polygon_with_hole, tolerance=4, preserve_topology=True)
<pygeos.Geometry POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0), (2 2, 2 4, 4 4, 4 2...>
>>> simplify(polygon_with_hole, tolerance=4, preserve_topology=False)
<pygeos.Geometry POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0))>
pygeos.constructive.snap(geometry, reference, tolerance, **kwargs)

Snaps an input geometry to reference geometry’s vertices.

The tolerance is used to control where snapping is performed. The result geometry is the input geometry with the vertices snapped. If no snapping occurs then the input geometry is returned unchanged.

Parameters
geometryGeometry or array_like
referenceGeometry or array_like
tolerancefloat or array_like

Examples

>>> point = Geometry("POINT (0 2)")
>>> snap(Geometry("POINT (0.5 2.5)"), point, tolerance=1)
<pygeos.Geometry POINT (0 2)>
>>> snap(Geometry("POINT (0.5 2.5)"), point, tolerance=0.49)
<pygeos.Geometry POINT (0.5 2.5)>
>>> polygon = Geometry("POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0))")
>>> snap(polygon, Geometry("POINT (8 10)"), tolerance=5)
<pygeos.Geometry POLYGON ((0 0, 0 10, 8 10, 10 0, 0 0))>
>>> snap(polygon, Geometry("LINESTRING (8 10, 8 0)"), tolerance=5)
<pygeos.Geometry POLYGON ((0 0, 0 10, 8 10, 8 0, 0 0))>
pygeos.constructive.voronoi_polygons(geometry, tolerance=0.0, extend_to=None, only_edges=False, **kwargs)

Computes a Voronoi diagram from the vertices of an input geometry.

The output is a geometrycollection containing polygons (default) or linestrings (see only_edges). Returns empty if an input geometry contains less than 2 vertices or if the provided extent has zero area.

Parameters
geometryGeometry or array_like
tolerancefloat or array_like

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

extend_toGeometry or array_like

If provided, the diagram will be extended to cover the envelope of this geometry (unless this envelope is smaller than the input geometry).

only_edgesbool or array_like

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

Examples

>>> from pygeos import normalize
>>> points = Geometry("MULTIPOINT (2 2, 4 2)")
>>> normalize(voronoi_polygons(points))
<pygeos.Geometry GEOMETRYCOLLECTION (POLYGON ((3 0, 3 4, 6 4, 6 0, 3 0)), PO...>
>>> voronoi_polygons(points, only_edges=True)
<pygeos.Geometry LINESTRING (3 4, 3 0)>
>>> voronoi_polygons(Geometry("MULTIPOINT (2 2, 4 2, 4.2 2)"), 0.5, only_edges=True)
<pygeos.Geometry LINESTRING (3 4.2, 3 -0.2)>
>>> voronoi_polygons(points, extend_to=Geometry("LINESTRING (0 0, 10 10)"), only_edges=True)
<pygeos.Geometry LINESTRING (3 10, 3 0)>
>>> voronoi_polygons(Geometry("LINESTRING (2 2, 4 2)"), only_edges=True)
<pygeos.Geometry LINESTRING (3 4, 3 0)>
>>> voronoi_polygons(Geometry("POINT (2 2)"))
<pygeos.Geometry GEOMETRYCOLLECTION EMPTY>