\i}dSrSSKrSSKJr SSKJr SSKJr SSK J r SSK J r J r Jr SSKJr /S Qr"S S \5r"S S \5r\ S5r\ "/SQ\S9\ S9Sj55r\ "/SQ\S9\ S:Sj55r\ S5r\ S5r\"S5\ S;Sj55r\ S5r\ S;Sj5r\"S5\ S55r\ S5r\ S5r\ S5r \ S S!S".S#j5r!\ S$5r"\ S%5r#\ S&5r$\ S'5r%S(r&S)r'\"S5\ SS1j55r-\ S25r.S3r/\/r0\ S45r1\ S?S5j5r2\ S@S6j5r3\ SS7.S8j5r4g)AzGMethods that yield new objects not derived from set-theoretic analysis.N)lib) ParamEnum)&_oriented_envelope_min_area_vectorized)_orient_polygons_vectorized)deprecate_positionalmultithreading_enabled requires_geos)UnsupportedGEOSVersionError) BufferCapStyleBufferJoinStyleboundarybuffer build_areacentroid clip_by_rect concave_hullconstrained_delaunay_triangles convex_hulldelaunay_trianglesenvelopeextract_unique_points make_validmaximum_inscribed_circleminimum_bounding_circleminimum_clearance_lineminimum_rotated_rectanglenode normalize offset_curveorient_polygonsoriented_envelopepoint_on_surface polygonizepolygonize_fullremove_repeated_pointsreverse segmentizesimplifysnapvoronoi_polygonsc$\rSrSrSrSrSrSrSrg)r 4zEnumeration of buffer cap styles. Attributes ---------- round : int Represents a round cap style. flat : int Represents a flat cap style. square : int Represents a square cap style. N) __name__ __module__ __qualname____firstlineno____doc__roundflatsquare__static_attributes__r0W/var/www/html/kml_chatgpt/mouzaenv/lib/python3.13/site-packages/shapely/constructive.pyr r 4s  E D Fr:r c$\rSrSrSrSrSrSrSrg)r GzEnumeration of buffer join styles. Attributes ---------- round : int Specifies a round join style. mitre : int Specifies a mitre join style. bevel : int Specifies a bevel join style. r-r.r/r0N) r1r2r3r4r5r6mitrebevelr9r0r:r;r r Gs  E E Er:r c 0[R"U40UD6$)a'Return the topological boundary of a geometry. This function will return None for geometrycollections. Parameters ---------- geometry : Geometry or array_like Geometry for which to return the boundary. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import GeometryCollection, LinearRing, LineString, MultiLineString, MultiPoint, Point, Polygon >>> shapely.boundary(Point(0, 0)) >>> shapely.boundary(LineString([(0, 0), (1, 1), (1, 2)])) >>> shapely.boundary(LinearRing([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])) >>> shapely.boundary(Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])) >>> shapely.boundary(MultiPoint([(0, 0), (1, 2)])) >>> shapely.boundary(MultiLineString([[(0, 0), (1, 1)], [(0, 1), (1, 0)]])) >>> shapely.boundary(GeometryCollection([Point(0, 0)])) is None True )rr geometrykwargss r;r r ZsD << +F ++r:) quad_segs cap_style join_style mitre_limit single_sided)categoryFc [U[5(a[RU5n[U[5(a[RU5n[ R "U5(d [S5e[ R "U5(d [S5e[ R "U5(d [S5e[ R "U5(d [S5e[ R "U5(d [S5e[R"UU[ R"U5[ R"U5[ R"U5U[ R"U540UD6$)aCompute the buffer of a geometry for positive and negative buffer distance. The buffer of a geometry is defined as the Minkowski sum (or difference, for negative distance) of the geometry with a circle with radius equal to the absolute value of the buffer distance. The buffer operation always returns a polygonal result. The negative or zero-distance buffer of lines and points is always empty. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the buffer. distance : float or array_like Specifies the circle radius in the Minkowski sum (or difference). quad_segs : int, default 8 Specifies the number of linear segments in a quarter circle in the approximation of circular arcs. cap_style : shapely.BufferCapStyle or {'round', 'square', 'flat'}, default 'round' Specifies the shape of buffered line endings. BufferCapStyle.round ('round') results in circular line endings (see ``quad_segs``). Both BufferCapStyle.square ('square') and BufferCapStyle.flat ('flat') result in rectangular line endings, only BufferCapStyle.flat ('flat') will end at the original vertex, while BufferCapStyle.square ('square') involves adding the buffer width. join_style : shapely.BufferJoinStyle or {'round', 'mitre', 'bevel'}, default 'round' Specifies the shape of buffered line midpoints. BufferJoinStyle.round ('round') results in rounded shapes. BufferJoinStyle.bevel ('bevel') results in a beveled edge that touches the original vertex. BufferJoinStyle.mitre ('mitre') results in a single vertex that is beveled depending on the ``mitre_limit`` parameter. mitre_limit : float, default 5.0 Crops of 'mitre'-style joins if the point is displaced from the buffered vertex by more than this limit. single_sided : bool, default False Only buffer at one side of the geometry. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Notes ----- .. deprecated:: 2.1.0 A deprecation warning is shown if ``quad_segs``, ``cap_style``, ``join_style``, ``mitre_limit`` or ``single_sided`` are specified as positional arguments. In a future release, these will need to be specified as keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Point, Polygon, BufferCapStyle, BufferJoinStyle >>> shapely.buffer(Point(10, 10), 2, quad_segs=1) >>> shapely.buffer(Point(10, 10), 2, quad_segs=2) >>> shapely.buffer(Point(10, 10), -2, quad_segs=1) >>> line = LineString([(10, 10), (20, 10)]) >>> shapely.buffer(line, 2, cap_style="square") >>> shapely.buffer(line, 2, cap_style="flat") >>> shapely.buffer(line, 2, single_sided=True, cap_style="flat") >>> line2 = LineString([(10, 10), (20, 10), (20, 20)]) >>> shapely.buffer(line2, 2, cap_style="flat", join_style="bevel") >>> shapely.buffer(line2, 2, cap_style="flat", join_style="mitre") >>> shapely.buffer(line2, 2, cap_style="flat", join_style="mitre", mitre_limit=1) >>> square = Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]) >>> shapely.buffer(square, 2, join_style="mitre") >>> shapely.buffer(square, -2, join_style="mitre") >>> shapely.buffer(square, -5, join_style="mitre") >>> shapely.buffer(line, float("nan")) is None True $quad_segs only accepts scalar valuesz$cap_style only accepts scalar values%join_style only accepts scalar values&mitre_limit only accepts scalar valuesz'single_sided only accepts scalar values) isinstancestrr get_valuer npisscalar TypeErrorrrintcbool_)rBdistancerDrErFrGrHrCs r;rrs@)S!!",,Y7 *c""$..z: ;;y ! !>?? ;;y ! !>?? ;;z " "?@@ ;;{ # #@AA ;;| $ $ABB ::           r:)rDrFrGc [U[5(a[RU5n[R "U5(d [ S5e[R "U5(d [ S5e[R "U5(d [ S5e[R"UU[R"U5[R"U5[R"U540UD6$)a>Return a (Multi)LineString at a distance from the object. For positive distance the offset will be at the left side of the input line. For a negative distance it will be at the right side. In general, this function tries to preserve the direction of the input. Note: the behaviour regarding orientation of the resulting line depends on the GEOS version. With GEOS < 3.11, the line retains the same direction for a left offset (positive distance) or has opposite direction for a right offset (negative distance), and this behaviour was documented as such in previous Shapely versions. Starting with GEOS 3.11, the function tries to preserve the orientation of the original line. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the offset. distance : float or array_like Specifies the offset distance from the input geometry. Negative for right side offset, positive for left side offset. quad_segs : int, default 8 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_limit : float, default 5.0 Crops of 'mitre'-style joins if the point is displaced from the buffered vertex by more than this limit. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Notes ----- .. deprecated:: 2.1.0 A deprecation warning is shown if ``quad_segs``, ``join_style`` or ``mitre_limit`` are specified as positional arguments. In a future release, these will need to be specified as keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString >>> line = LineString([(0, 0), (0, 2)]) >>> shapely.offset_curve(line, 2) >>> shapely.offset_curve(line, -2) rKrLrM) rNrOr rPrQrRrSrrrTdouble)rBrVrDrFrGrCs r;rr sx*c""$..z: ;;y ! !>?? ;;z " "?@@ ;;{ # #@AA        +     r:c 0[R"U40UD6$)aaCompute 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 ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the centroid. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, MultiPoint, Polygon >>> shapely.centroid(Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)])) >>> shapely.centroid(LineString([(0, 0), (2, 2), (10, 10)])) >>> shapely.centroid(MultiPoint([(0, 0), (10, 10)])) >>> shapely.centroid(Polygon()) )rrrAs r;rrYs< << +F ++r:c [SXX4455(d [S5e[R"U[R "U5[R "U5[R "U5[R "U540UD6$)a'Return 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 ---------- geometry : Geometry or array_like The geometry to be clipped. xmin : float Minimum x value of the rectangle. ymin : float Minimum y value of the rectangle. xmax : float Maximum x value of the rectangle. ymax : float Maximum y value of the rectangle. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Polygon >>> line = LineString([(0, 0), (10, 10)]) >>> shapely.clip_by_rect(line, 0., 0., 1., 1.) >>> polygon = Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]) >>> shapely.clip_by_rect(polygon, 0., 0., 1., 1.) c3N# UHn[R"U5v M g7fN)rQrR).0vals r; clip_by_rect..sD+CCr{{3+Cs#%z.xmin/ymin/xmax/ymax only accepts scalar values)allrSrrrQrX)rBxminyminxmaxymaxrCs r;rrzssL DD+CD D DHII    $ $ $ $     r:z3.11.0c [R"U5(d [S5e[R"U5(d [S5e[R"U[R "U5[R "U540UD6$)a\Compute a concave geometry that encloses an input geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the concave hull. ratio : float, default 0.0 Number in the range [0, 1]. Higher numbers will include fewer vertices in the hull. allow_holes : bool, default False If set to True, the concave hull may have holes. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import MultiPoint, Polygon >>> multi_point = MultiPoint([(0, 0), (0, 3), (1, 1), (3, 0), (3, 3)]) >>> shapely.concave_hull(multi_point, ratio=0.1) >>> shapely.concave_hull(multi_point, ratio=1.0) >>> shapely.concave_hull(Polygon()) zratio must be scalarzallow_holes must be scalar)rQrRrSrrrXrU)rBratio allow_holesrCs r;rrsg< ;;u  .// ;;{ # #455   Hbii&68M XQW XXr:c 0[R"U40UD6$)a Compute the minimum convex geometry that encloses an input geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the convex hull. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import MultiPoint, Polygon >>> shapely.convex_hull(MultiPoint([(0, 0), (10, 0), (10, 10)])) >>> shapely.convex_hull(Polygon()) )rrrAs r;rrs* ??8 .v ..r:c 2[R"XU40UD6$)aFCompute a Delaunay triangulation around the vertices of an input geometry. The output is a geometrycollection containing polygons (default) or linestrings (see ``only_edges``). Returns an empty geometry for input geometries that contain less than 3 vertices. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the Delaunay triangulation. tolerance : float or array_like, default 0.0 Snap input vertices together if their distance is less than this value. only_edges : bool or array_like, default False If set to True, the triangulation will return a collection of linestrings instead of polygons. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Returns ------- GeometryCollection or array of GeometryCollections See Also -------- constrained_delaunay_triangles Examples -------- >>> import shapely >>> from shapely import GeometryCollection, LineString, MultiPoint, Polygon >>> points = MultiPoint([(50, 30), (60, 30), (100, 100)]) >>> shapely.delaunay_triangles(points).normalize() >>> shapely.delaunay_triangles(points, only_edges=True) >>> shapely.delaunay_triangles( ... MultiPoint([(50, 30), (51, 30), (60, 30), (100, 100)]), ... tolerance=2 ... ).normalize() >>> shapely.delaunay_triangles(Polygon([(50, 30), (60, 30), (100, 100), (50, 30)])).normalize() >>> shapely.delaunay_triangles(LineString([(50, 30), (60, 30), (100, 100)])).normalize() >>> shapely.delaunay_triangles(GeometryCollection([])) )rr)rB tolerance only_edgesrCs r;rrsh  ! !(z LV LLr:z3.10.0c 0[R"U40UD6$)aCCompute the constrained Delaunay triangulation of polygons. A constrained Delaunay triangulation requires the edges of the input polygon(s) to be in the set of resulting triangle edges. An unconstrained delaunay triangulation only triangulates based on the vertices, hence triangle edges could cross polygon boundaries. .. versionadded:: 2.1.0 Parameters ---------- geometry : Geometry or array_like **kwargs For other keyword-only arguments, see the `NumPy ufunc docs `_. Returns ------- GeometryCollection or array of GeometryCollections * GeometryCollection of polygons, given polygonal input * Empty GeometryCollection, given non-polygonal input See Also -------- delaunay_triangles Examples -------- >>> import shapely >>> from shapely import MultiPoint, MultiPolygon, Polygon >>> shapely.constrained_delaunay_triangles(Polygon([(10, 10), (20, 40), (90, 90), (90, 10), (10, 10)])) >>> shapely.constrained_delaunay_triangles(Polygon()) >>> shapely.constrained_delaunay_triangles(MultiPolygon([Polygon(((50, 30), (60, 30), (100, 100), (50, 30))), Polygon(((10, 10), (20, 40), (90, 90), (90, 10), (10, 10)))])) >>> shapely.constrained_delaunay_triangles(MultiPolygon()) >>> shapely.constrained_delaunay_triangles(MultiPoint([(50, 30), (51, 30), (60, 30), (100, 100)])) )rrrAs r;rr sZ  - -h A& AAr:c 0[R"U40UD6$)aCompute the minimum bounding box that encloses an input geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the envelope. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import GeometryCollection, LineString, MultiPoint, Point >>> shapely.envelope(LineString([(0, 0), (10, 10)])) >>> shapely.envelope(MultiPoint([(0, 0), (10, 10)])) >>> shapely.envelope(Point(0, 0)) >>> shapely.envelope(GeometryCollection([])) )rrrAs r;rrPs2 << +F ++r:c 0[R"U40UD6$)aReturn 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 ---------- geometry : Geometry or array_like Geometry or geometries for which to extract unique points. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, MultiPoint, Point, Polygon >>> shapely.extract_unique_points(Point(0, 0)) >>> shapely.extract_unique_points(LineString([(0, 0), (1, 1), (1, 1)])) >>> shapely.extract_unique_points(Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])) >>> shapely.extract_unique_points(MultiPoint([(0, 0), (1, 1), (0, 0)])) >>> shapely.extract_unique_points(LineString()) )rrrAs r;rrls<  $ $X 8 88r:c 0[R"U40UD6$)aCreate an areal geometry formed by the constituent linework of given geometry. Equivalent of the PostGIS ST_BuildArea() function. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to build an area. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import GeometryCollection, Polygon >>> polygon1 = Polygon([(0, 0), (3, 0), (3, 3), (0, 3), (0, 0)]) >>> polygon2 = Polygon([(1, 1), (1, 2), (2, 2), (1, 1)]) >>> shapely.build_area(GeometryCollection([polygon1, polygon2])) )rrrAs r;rrs. >>( -f --r:lineworkT)methodkeep_collapsedc [R"U5(d [S5e[R"U5(d [S5eUS:Xa'USLa [S5e[R "U40UD6$US:Xa`[R S:a [S5e[R"U[R"S 5[R"U540UD6$[S U35e) aiRepair invalid geometries. Two ``methods`` are available: * the 'linework' algorithm tries to preserve every edge and vertex in the input. It combines all rings into a set of noded lines and then extracts valid polygons from that linework. An alternating even-odd strategy is used to assign areas as interior or exterior. A disadvantage is that for some relatively simple invalid geometries this produces rather complex results. * the 'structure' algorithm tries to reason from the structure of the input to find the 'correct' repair: exterior rings bound area, interior holes exclude area. It first makes all rings valid, then shells are merged and holes are subtracted from the shells to generate valid result. It assumes that holes and shells are correctly categorized in the input geometry. Example: .. plot:: code/make_valid_methods.py When using ``make_valid`` on a Polygon, the result can be a GeometryCollection. For this example this is the case when the 'linework' ``method`` is used. LineStrings in the result are drawn in red. Parameters ---------- geometry : Geometry or array_like Geometry or geometries to repair. method : {'linework', 'structure'}, default 'linework' Algorithm to use when repairing geometry. 'structure' requires GEOS >= 3.10. .. versionadded:: 2.1.0 keep_collapsed : bool, default True For the 'structure' method, True will keep components that have collapsed into a lower dimensionality. For example, a ring collapsing to a line, or a line collapsing to a point. Must be True for the 'linework' method. .. versionadded:: 2.1.0 **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import Polygon >>> polygon = Polygon([(0, 0), (1, 1), (1, 2), (1, 1), (0, 0)]) >>> shapely.is_valid(polygon) False >>> shapely.make_valid(polygon) >>> shapely.make_valid(polygon, method="structure", keep_collapsed=True) >>> shapely.make_valid(polygon, method="structure", keep_collapsed=False) z!method only accepts scalar valuesz)keep_collapsed only accepts scalar valuesrqFz=The 'linework' method does not support 'keep_collapsed=False' structure)r/ rz:The 'structure' method is only available in GEOS >= 3.10.0r-zUnknown method: ) rQrRrS ValueErrorrr geos_versionmake_valid_with_paramsrTrU)rBrrrsrCs r;rrst ;;v  ;<< ;;~ & &CDD  U "O ~~h1&11 ;    j (L )) bggaj"((>": >D  +F8455r:c 0[R"U40UD6$)aBReturn a LineString whose endpoints define the minimum clearance. A geometry's "minimum clearance" is the smallest distance by which a vertex of the geometry could be moved to produce an invalid geometry. If the geometry has no minimum clearance, an empty LineString will be returned. .. versionadded:: 2.1.0 Parameters ---------- geometry : Geometry or array_like Geometry or geometries to determine the minimum clearance line for. **kwargs For other keyword-only arguments, see the `NumPy ufunc docs `_. Examples -------- >>> import shapely >>> from shapely import Polygon >>> poly = Polygon([(0, 0), (10, 0), (10, 10), (5, 5), (0, 10), (0, 0)]) >>> shapely.minimum_clearance_line(poly) See Also -------- minimum_clearance )rrrAs r;rrsB  % %h 9& 99r:c 0[R"U40UD6$)aConvert Geometry to strict normal form (or canonical form). In :ref:`strict canonical form `, the coordinates, rings of a polygon and parts of multi geometries are ordered consistently. Typically useful for testing purposes (for example in combination with ``equals_exact``). Parameters ---------- geometry : Geometry or array_like Geometry or geometries to normalize. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import MultiLineString >>> line = MultiLineString([[(0, 0), (1, 1)], [(2, 2), (3, 3)]]) >>> shapely.normalize(line) )rrrAs r;rr$s2 == ,V ,,r:c 0[R"U40UD6$)aReturn a point that intersects an input geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute a point on the surface. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, MultiPoint, Polygon >>> shapely.point_on_surface(Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)])) >>> shapely.point_on_surface(LineString([(0, 0), (2, 2), (10, 10)])) >>> shapely.point_on_surface(MultiPoint([(0, 0), (10, 10)])) >>> shapely.point_on_surface(Polygon()) )rr"rAs r;r"r"@s2    3F 33r:c 0[R"U40UD6$)aReturn the fully noded version of the linear input as MultiLineString. Given a linear input geometry, this function returns a new MultiLineString in which no lines cross each other but only touch at and points. To obtain this, all intersections between segments are computed and added to the segments, and duplicate segments are removed. Non-linear input (points) will result in an empty MultiLineString. This function can for example be used to create a fully-noded linework suitable to passed as input to ``polygonize``. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the noded version. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Point >>> line = LineString([(0, 0), (1,1), (0, 1), (1, 0)]) >>> shapely.node(line) >>> shapely.node(Point(1, 1)) )rrrAs r;rr\s@ 88H ' ''r:c 0[R"U40UD6$)a Create 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 ``shapely.multipolygons(shapely.get_parts(shapely.polygonize(geometries)))``. Parameters ---------- geometries : array_like An array of geometries. axis : int 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 See :ref:`NumPy ufunc docs ` for other keyword arguments. Returns ------- GeometryCollection or array of GeometryCollections See Also -------- get_parts, get_geometry polygonize_full node Examples -------- >>> import shapely >>> from shapely import LineString >>> lines = [ ... LineString([(0, 0), (1, 1)]), ... LineString([(0, 0), (0, 1)]), ... LineString([(0, 1), (1, 1)]) ... ] >>> shapely.polygonize(lines) )rr# geometriesrCs r;r#r#sh >>* / //r:c 0[R"U40UD6$)a\Create polygons formed from the linework of a set of Geometries. All extra outputs are returned as well. Polygonizes an array of Geometries that contain linework which represents the edges of a planar graph. Any type of Geometry may be provided as input; only the constituent lines and rings will be used to create the output polygons. This function performs the same polygonization as ``polygonize`` but does not only return the polygonal result but all extra outputs as well. The return value consists of 4 elements: * The polygonal valid output * **Cut edges**: edges connected on both ends but not part of polygonal output * **dangles**: edges connected on one end but not part of polygonal output * **invalid rings**: polygons formed but which are not valid This function returns the geometries within GeometryCollections. Individual geometries can be obtained using ``get_geometry`` to get a single geometry or ``get_parts`` to get an array of geometries. Parameters ---------- geometries : array_like An array of geometries. axis : int Axis along which the geometries are polygonized. The default is to perform a reduction over the last dimension of the input array. A 1D array results in a scalar geometry. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Returns ------- (polygons, cuts, dangles, invalid) tuple of 4 GeometryCollections or arrays of GeometryCollections See Also -------- polygonize Examples -------- >>> import shapely >>> from shapely import LineString >>> lines = [ ... LineString([(0, 0), (1, 1)]), ... LineString([(0, 0), (0, 1), (1, 1)]), ... LineString([(0, 1), (1, 1)]) ... ] >>> shapely.polygonize_full(lines) (, , , ) )rr$rs r;r$r$sv   z 4V 44r:c 0[R"X40UD6$)agReturn a copy of a Geometry with repeated points removed. From the start of the coordinate sequence, each next point within the tolerance is removed. Removing repeated points with a non-zero tolerance may result in an invalid geometry being returned. Parameters ---------- geometry : Geometry or array_like Geometry or geometries to remove repeated points from. tolerance : float or array_like, default=0.0 Use 0.0 to remove only exactly repeated points. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Polygon >>> shapely.remove_repeated_points(LineString([(0,0), (0,0), (1,0)]), tolerance=0) >>> shapely.remove_repeated_points(Polygon([(0, 0), (0, .5), (0, 1), (.5, 1), (0,0)]), tolerance=.5) )rr%rBrkrCs r;r%r%s<  % %h DV DDr:c 0[R"U40UD6$)aReturn 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 ---------- geometry : Geometry or array_like Geometry or geometries to reverse the coordinates of. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. See Also -------- is_ccw : Checks if a Geometry is clockwise. Examples -------- >>> import shapely >>> from shapely import LineString, Polygon >>> shapely.reverse(LineString([(0, 0), (1, 2)])) >>> shapely.reverse(Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)])) >>> shapely.reverse(None) is None True )rr&rAs r;r&r&s@ ;;x *6 **r:c 0[R"X40UD6$)aAdd vertices to line segments based on maximum segment length. Additional vertices will be added to every line segment in an input geometry so that segments are no longer than the provided maximum segment length. New vertices will evenly subdivide each segment. Only linear components of input geometries are densified; other geometries are returned unmodified. Parameters ---------- geometry : Geometry or array_like Geometry or geometries to segmentize. max_segment_length : float or array_like Additional vertices will be added so that all line segments are no longer than this value. Must be greater than 0. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Polygon >>> line = LineString([(0, 0), (0, 10)]) >>> shapely.segmentize(line, max_segment_length=5) >>> polygon = Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]) >>> shapely.segmentize(polygon, max_segment_length=5) >>> shapely.segmentize(None, max_segment_length=5) is None True )rr')rBmax_segment_lengthrCs r;r'r'8sH >>( A& AAr:preserve_topologyc lU(a[R"X40UD6$[R"X40UD6$)a/Return a simplified version of an input geometry. The Douglas-Peucker algorithm is used to simplify the geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries to simplify. tolerance : float or array_like The maximum allowed geometry displacement. The higher this value, the smaller the number of vertices in the resulting geometry. preserve_topology : bool, default True By default (True), the operation will avoid creating invalid geometries (checking for collapses, ring-intersections, etc), but this is computationally more expensive. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Notes ----- .. deprecated:: 2.1.0 A deprecation warning is shown if ``preserve_topology`` is specified as a positional argument. This will need to be specified as a keyword argument in a future release. Examples -------- >>> import shapely >>> from shapely import LineString, Polygon >>> line = LineString([(0, 0), (1, 10), (0, 20)]) >>> shapely.simplify(line, tolerance=0.9) >>> shapely.simplify(line, tolerance=1) >>> polygon_with_hole = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]] ... ) >>> shapely.simplify(polygon_with_hole, tolerance=4, preserve_topology=True) >>> shapely.simplify(polygon_with_hole, tolerance=4, preserve_topology=False) )rsimplify_preserve_topologyr()rBrkrrCs r;r(r(hs2`--hLVLL||H:6::r:c 2[R"XU40UD6$)a Snap the vertices and segments of the geometry to vertices of the reference. Vertices and segments of the input geometry are snapped to vertices of the reference geometry, returning a new geometry; the input geometries are not modified. The result geometry is the input geometry with the vertices and segments snapped. If no snapping occurs then the input geometry is returned unchanged. The tolerance is used to control where snapping is performed. Where possible, this operation tries to avoid creating invalid geometries; however, it does not guarantee that output geometries will be valid. It is the responsibility of the caller to check for and handle invalid geometries. Because too much snapping can result in invalid geometries being created, heuristics are used to determine the number and location of snapped vertices that are likely safe to snap. These heuristics may omit some potential snaps that are otherwise within the tolerance. Parameters ---------- geometry : Geometry or array_like Geometry or geometries to snap. reference : Geometry or array_like Geometry or geometries to snap to. tolerance : float or array_like The maximum distance between the input and reference geometries for snapping to occur. A value of 0 will snap only identical points. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, Point, Polygon, MultiPoint >>> point = Point(0.5, 2.5) >>> target_point = Point(0, 2) >>> shapely.snap(point, target_point, tolerance=1) >>> shapely.snap(point, target_point, tolerance=0.49) >>> polygon = Polygon([(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)]) >>> shapely.snap(polygon, Point(8, 10), tolerance=5) >>> shapely.snap(polygon, LineString([(8, 10), (8, 0)]), tolerance=5) You can snap one line to another, for example to clean imprecise coordinates: >>> line1 = LineString([(0.1, 0.1), (0.49, 0.51), (1.01, 0.89)]) >>> line2 = LineString([(0, 0), (0.5, 0.5), (1.0, 1.0)]) >>> shapely.snap(line1, line2, 0.25) Snapping also supports Z coordinates: >>> point1 = Point(0.1, 0.1, 0.5) >>> multipoint = MultiPoint([(0, 0, 1), (0, 0, 0)]) >>> shapely.snap(point1, multipoint, 1) Snapping to an empty geometry has no effect: >>> shapely.snap(line1, LineString([]), 0.25) Snapping to a non-geometry (None) will always return None: >>> shapely.snap(line1, None, 0.25) is None True Only one vertex of a polygon is snapped to a target point, even if all vertices are equidistant to it, in order to prevent collapse of the polygon: >>> poly = shapely.box(0, 0, 1, 1) >>> poly >>> shapely.snap(poly, Point(0.5, 0.5), 1) )rr))rB referencerkrCs r;r)r)sh 88H =f ==r:) extend_torlorderedc USLa0[RS:a[S[R35e[R"XX#U40UD6$)aF Compute 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 ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the Voronoi diagram. tolerance : float or array_like, default 0.0 Snap input vertices together if their distance is less than this value. extend_to : Geometry 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_edges : bool or array_like, default False If set to True, the triangulation will return a collection of linestrings instead of polygons. ordered : bool or array_like, default False If set to True, polygons within the GeometryCollection will be ordered according to the order of the input vertices. Note that this may slow down the computation. Requires GEOS >= 3.12.0. .. versionadded:: 2.1.0 **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Notes ----- .. deprecated:: 2.1.0 A deprecation warning is shown if ``extend_to``, ``only_edges`` or ``ordered`` are specified as positional arguments. In a future release, these will need to be specified as keyword arguments. Examples -------- >>> import shapely >>> from shapely import LineString, MultiPoint, Point >>> points = MultiPoint([(2, 2), (4, 2)]) >>> shapely.voronoi_polygons(points).normalize() >>> shapely.voronoi_polygons(points, only_edges=True) >>> shapely.voronoi_polygons(MultiPoint([(2, 2), (4, 2), (4.2, 2)]), 0.5, only_edges=True) >>> shapely.voronoi_polygons(points, extend_to=LineString([(0, 0), (10, 10)]), only_edges=True) >>> shapely.voronoi_polygons(LineString([(2, 2), (4, 2)]), only_edges=True) >>> shapely.voronoi_polygons(Point(2, 2)) >>> shapely.voronoi_polygons(points, ordered=True) Fr/ rz7Ordered Voronoi polygons require GEOS >= 3.12.0, found )rrxr geos_version_stringr*)rBrkrrlrrCs r;r*r*sa~e 0 0: =) ,,- /     YG ?E r:c 0[R"U40UD6$r\)rr!rAs r;_oriented_envelope_geosrGs   4V 44r:c V[RS:a[nO[nU"U40UD6$)aNCompute the oriented envelope (minimum rotated rectangle) of the input geometry. The oriented envelope encloses an input geometry, such that the resulting rectangle has minimum area. Unlike envelope this rectangle is not constrained to be parallel to the coordinate axes. If the convex hull of the object is a degenerate (line or point) this degenerate is returned. The starting point of the rectangle is not fixed. You can use :func:`~shapely.normalize` to reorganize the rectangle to :ref:`strict canonical form ` so the starting point is always the lower left point. ``minimum_rotated_rectangle`` is an alias for ``oriented_envelope``. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the oriented envelope. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import GeometryCollection, LineString, MultiPoint, Point, Polygon >>> shapely.oriented_envelope(MultiPoint([(0, 0), (10, 0), (10, 10)])).normalize() >>> shapely.oriented_envelope(LineString([(1, 1), (5, 1), (10, 10)])).normalize() >>> shapely.oriented_envelope(Polygon([(1, 1), (15, 1), (5, 10), (1, 1)])).normalize() >>> shapely.oriented_envelope(LineString([(1, 1), (10, 1)])).normalize() >>> shapely.oriented_envelope(Point(2, 2)) >>> shapely.oriented_envelope(GeometryCollection([])) r)rrxrr)rBrCfs r;r!r!Ls-V *$ 2 # X   r:c 0[R"U40UD6$)aCompute the minimum bounding circle that encloses an input geometry. Parameters ---------- geometry : Geometry or array_like Geometry or geometries for which to compute the minimum bounding circle. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- >>> import shapely >>> from shapely import GeometryCollection, LineString, MultiPoint, Point, Polygon >>> shapely.minimum_bounding_circle( ... Polygon([(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)]) ... ) >>> shapely.minimum_bounding_circle(LineString([(1, 1), (10, 10)])) >>> shapely.minimum_bounding_circle(MultiPoint([(2, 2), (4, 2)])) >>> shapely.minimum_bounding_circle(Point(0, 1)) >>> shapely.minimum_bounding_circle(GeometryCollection([])) See Also -------- minimum_bounding_radius, maximum_inscribed_circle )rrrAs r;rrsB  & &x :6 ::r:c UcSnO,[R"U5(aUS:a [S5e[R"X40UD6$)aFind the largest circle that is fully contained within the input geometry. Constructs the "maximum inscribed circle" (MIC) for a polygonal geometry, up to a specified tolerance. The MIC is determined by a point in the interior of the area which has the farthest distance from the area boundary, along with a boundary point at that distance. In the context of geography the center of the MIC is known as the "pole of inaccessibility". A cartographic use case is to determine a suitable point to place a map label within a polygon. The radius length of the MIC is a measure of how "narrow" a polygon is. It is the distance at which the negative buffer becomes empty. The function supports polygons with holes and multipolygons. Returns a two-point linestring, with the first point at the center of the inscribed circle and the second on the boundary of the inscribed circle. .. versionadded:: 2.1.0 Parameters ---------- geometry : Geometry or array_like tolerance : float or array_like, optional Stop the algorithm when the search area is smaller than this tolerance. When not specified, uses `max(width, height) / 1000` per geometry as the default. **kwargs For other keyword-only arguments, see the `NumPy ufunc docs `_. Examples -------- >>> import shapely >>> from shapely import Polygon >>> poly = Polygon([(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)]) >>> shapely.maximum_inscribed_circle(poly) See Also -------- minimum_bounding_circle rz'tolerance' should be positive)rQrRrwrrrs r;rrsGX Y  IM9::  ' ' Fv FFr:c 0[R"X40UD6$r\)rr )rB exterior_cwrCs r;_orient_polygons_geosrs   x ? ??r:)rc V[RS:a[nO[nU"X40UD6$)aEnforce a ring orientation on all polygonal elements in the input geometry. Forces (Multi)Polygons to use a counter-clockwise orientation for their exterior ring, and a clockwise orientation for their interior rings (or the oppposite if ``exterior_cw=True``). Also processes geometries inside a GeometryCollection in the same way. Other geometries are returned unchanged. .. versionadded:: 2.1.0 Parameters ---------- geometry : Geometry or array_like Geometry or geometries to orient consistently. exterior_cw : bool, default False If True, exterior rings will be clockwise and interior rings will be counter-clockwise. **kwargs See :ref:`NumPy ufunc docs ` for other keyword arguments. Examples -------- A polygon with both shell and hole having clockwise orientation: >>> from shapely import Polygon, orient_polygons >>> polygon = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]], ... ) >>> polygon By default, the exterior ring is oriented counter-clockwise and the holes clockwise: >>> orient_polygons(polygon) Asking for the opposite orientation: >>> orient_polygons(polygon, exterior_cw=True) r)rrxrr)rBrrCrs r;r r s-^ *$ ' ! X -f --r:)r6r6@F)rr6r)rF)r)T)rNFFr\)F)5r5numpyrQshapelyr shapely._enumr%shapely.algorithms._oriented_envelopershapely.algorithms.cgarshapely.decoratorsrrr shapely.errorsr __all__r r r DeprecationWarningrrrrrrrrrrrrrrr"rr#r$r%r&r'r(r)r*rr!rrrrr r0r:r;rsbM#X> 7! HY&i&!,!,ZK r  r|.9KEHGGT,,@..bx Y YF//.3M3Mlx+B+B\,,699@..2#-dU6U6p : :F--6446((D40n;5|xEE>++Dx"B"B\*+6HI1;J1;hS>S>~*5GGLBBJ55/!d. ; ;F/G/Gd@@-22.2.r: