# Constructive operations¶

boundary(geometry, **kwargs)

Returns the topological boundary of a geometry.

Parameters
geometryGeometry or array_like

This function will return None for geometrycollections.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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
```

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).

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

cap_style{‘round’, ‘square’, ‘flat’}, default ‘round’

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’}, default ‘round’

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, default 5.0

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

single_sidedbool, default False

Only buffer at one side of the geometry.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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, 11.414 8.586, 10 8, 8.586 8.586, 8 10, 8.5...>
>>> 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, 21.828 9, 21 8.172, 10 8, 10...>
>>> 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
```
build_area(geometry, **kwargs)

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

Note

‘build_area’ requires at least GEOS 3.8.0.

Equivalent of the PostGIS ST_BuildArea() function.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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))>
```
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
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
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

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

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

Computes the minimum convex geometry that encloses an input geometry.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
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, default 0.0

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

only_edgesbool or array_like, default False

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

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
envelope(geometry, **kwargs)

Computes the minimum bounding box that encloses an input geometry.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
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
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
make_valid(geometry, **kwargs)

Repairs invalid geometries.

Note

‘make_valid’ requires at least GEOS 3.8.0.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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))>
```
minimum_bounding_circle(geometry, **kwargs)

Computes the minimum bounding circle that encloses an input geometry.

Note

‘minimum_bounding_circle’ requires at least GEOS 3.8.0.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`minimum_bounding_radius`

Examples

```>>> minimum_bounding_circle(Geometry("POLYGON ((0 0, 0 10, 10 10, 10 0, 0 0))"))
<pygeos.Geometry POLYGON ((12.071 5, 11.935 3.621, 11.533 2.294, 10.879 1.07...>
>>> minimum_bounding_circle(Geometry("LINESTRING (1 1, 10 10)"))
<pygeos.Geometry POLYGON ((11.864 5.5, 11.742 4.258, 11.38 3.065, 10.791 1.9...>
>>> minimum_bounding_circle(Geometry("MULTIPOINT (2 2, 4 2)"))
<pygeos.Geometry POLYGON ((4 2, 3.981 1.805, 3.924 1.617, 3.831 1.444, 3.707...>
>>> minimum_bounding_circle(Geometry("POINT (0 1)"))
<pygeos.Geometry POINT (0 1)>
>>> minimum_bounding_circle(Geometry("GEOMETRYCOLLECTION EMPTY"))
<pygeos.Geometry POLYGON EMPTY>
```
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
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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))>
```
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.

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

join_style{‘round’, ‘bevel’, ‘mitre’}, default ‘round’

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, default 5.0

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

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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)>
```
oriented_envelope(geometry, **kwargs)

Computes the oriented envelope (minimum rotated rectangle) that encloses an input geometry.

Note

‘oriented_envelope’ requires at least GEOS 3.6.0.

Unlike envelope this rectangle is not constrained to be parallel to the coordinate axes. If the convex hull of the object is a degenerate (line or point) this degenerate is returned.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> oriented_envelope(Geometry("MULTIPOINT (0 0, 10 0, 10 10)"))
<pygeos.Geometry POLYGON ((0 0, 5 -5, 15 5, 10 10, 0 0))>
>>> oriented_envelope(Geometry("LINESTRING (1 1, 5 1, 10 10)"))
<pygeos.Geometry POLYGON ((1 1, 3 -1, 12 8, 10 10, 1 1))>
>>> oriented_envelope(Geometry("POLYGON ((1 1, 15 1, 5 10, 1 1))"))
<pygeos.Geometry POLYGON ((15 1, 15 10, 1 10, 1 1, 15 1))>
>>> oriented_envelope(Geometry("LINESTRING (1 1, 10 1)"))
<pygeos.Geometry LINESTRING (1 1, 10 1)>
>>> oriented_envelope(Geometry("POINT (2 2)"))
<pygeos.Geometry POINT (2 2)>
>>> oriented_envelope(Geometry("GEOMETRYCOLLECTION EMPTY"))
<pygeos.Geometry POLYGON EMPTY>
```
point_on_surface(geometry, **kwargs)

Returns a point that intersects an input geometry.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```
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.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Returns
GeometryCollection or array of GeometryCollections

`get_parts`, `get_geometry`
`polygonize_full`

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)))>
```
polygonize_full(geometries, **kwargs)

Creates polygons formed from the linework of a set of Geometries and return all extra outputs as well.

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.

This function performs the same polygonization as `polygonize` but does not only return the polygonal result but all extra outputs as well. The return value consists of 4 elements:

• The polygonal valid output

• Cut edges: edges connected on both ends but not part of polygonal output

• dangles: edges connected on one end but not part of polygonal output

• invalid rings: polygons formed but which are not valid

This function returns the geometries within GeometryCollections. Individual geometries can be obtained using `get_geometry` to get a single geometry or `get_parts` to get an array of 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.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Returns
(polgyons, cuts, dangles, invalid)

tuple of 4 GeometryCollections or arrays of GeometryCollections

Examples

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

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

Note

‘reverse’ requires at least GEOS 3.7.0.

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
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`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
```
segmentize(geometry, tolerance, **kwargs)

Adds vertices to line segments based on tolerance.

Note

‘segmentize’ requires at least GEOS 3.10.0.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
geometryGeometry or array_like
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> line = Geometry("LINESTRING (0 0, 0 10)")
>>> segmentize(line, tolerance=5)
<pygeos.Geometry LINESTRING (0 0, 0 5, 0 10)>
>>> poly = Geometry("POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0))")
>>> segmentize(poly, tolerance=5)
<pygeos.Geometry POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
>>> segmentize(None, tolerance=5) is None
True
```
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, default False

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

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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))>
```
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
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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))>
```
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, default 0.0

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

extend_toGeometry or array_like, optional

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, default False

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

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

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>
```