588 lines
21 KiB
Python
588 lines
21 KiB
Python
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"""Support for various GEOS geometry operations
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"""
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import sys
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if sys.version_info[0] < 3:
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from itertools import izip
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else:
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izip = zip
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from ctypes import byref, c_void_p, c_double
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from shapely.geos import lgeos
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from shapely.geometry.base import geom_factory, BaseGeometry, BaseMultipartGeometry
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from shapely.geometry import asShape, asLineString, asMultiLineString, Point, MultiPoint,\
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LineString, MultiLineString, Polygon, GeometryCollection
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from shapely.geometry.polygon import orient as orient_
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from shapely.algorithms.polylabel import polylabel
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__all__ = ['cascaded_union', 'linemerge', 'operator', 'polygonize',
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'polygonize_full', 'transform', 'unary_union', 'triangulate',
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'split', 'section']
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class CollectionOperator(object):
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def shapeup(self, ob):
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if isinstance(ob, BaseGeometry):
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return ob
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else:
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try:
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return asShape(ob)
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except ValueError:
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return asLineString(ob)
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def polygonize(self, lines):
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"""Creates polygons from a source of lines
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The source may be a MultiLineString, a sequence of LineString objects,
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or a sequence of objects than can be adapted to LineStrings.
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"""
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source = getattr(lines, 'geoms', None) or lines
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try:
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source = iter(source)
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except TypeError:
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source = [source]
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finally:
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obs = [self.shapeup(l) for l in source]
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geom_array_type = c_void_p * len(obs)
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geom_array = geom_array_type()
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for i, line in enumerate(obs):
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geom_array[i] = line._geom
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product = lgeos.GEOSPolygonize(byref(geom_array), len(obs))
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collection = geom_factory(product)
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for g in collection.geoms:
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clone = lgeos.GEOSGeom_clone(g._geom)
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g = geom_factory(clone)
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g._other_owned = False
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yield g
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def polygonize_full(self, lines):
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"""Creates polygons from a source of lines, returning the polygons
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and leftover geometries.
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The source may be a MultiLineString, a sequence of LineString objects,
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or a sequence of objects than can be adapted to LineStrings.
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Returns a tuple of objects: (polygons, dangles, cut edges, invalid ring
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lines). Each are a geometry collection.
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Dangles are edges which have one or both ends which are not incident on
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another edge endpoint. Cut edges are connected at both ends but do not
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form part of polygon. Invalid ring lines form rings which are invalid
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(bowties, etc).
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"""
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source = getattr(lines, 'geoms', None) or lines
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try:
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source = iter(source)
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except TypeError:
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source = [source]
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finally:
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obs = [self.shapeup(l) for l in source]
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L = len(obs)
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subs = (c_void_p * L)()
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for i, g in enumerate(obs):
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subs[i] = g._geom
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collection = lgeos.GEOSGeom_createCollection(5, subs, L)
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dangles = c_void_p()
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cuts = c_void_p()
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invalids = c_void_p()
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product = lgeos.GEOSPolygonize_full(
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collection, byref(dangles), byref(cuts), byref(invalids))
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return (
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geom_factory(product),
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geom_factory(dangles),
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geom_factory(cuts),
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geom_factory(invalids)
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)
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def linemerge(self, lines):
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"""Merges all connected lines from a source
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The source may be a MultiLineString, a sequence of LineString objects,
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or a sequence of objects than can be adapted to LineStrings. Returns a
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LineString or MultiLineString when lines are not contiguous.
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"""
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source = None
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if hasattr(lines, 'type') and lines.type == 'MultiLineString':
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source = lines
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elif hasattr(lines, '__iter__'):
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try:
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source = asMultiLineString([ls.coords for ls in lines])
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except AttributeError:
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source = asMultiLineString(lines)
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if source is None:
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raise ValueError("Cannot linemerge %s" % lines)
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result = lgeos.GEOSLineMerge(source._geom)
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return geom_factory(result)
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def cascaded_union(self, geoms):
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"""Returns the union of a sequence of geometries
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This method was superseded by :meth:`unary_union`.
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"""
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try:
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L = len(geoms)
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except TypeError:
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geoms = [geoms]
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L = 1
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subs = (c_void_p * L)()
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for i, g in enumerate(geoms):
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subs[i] = g._geom
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collection = lgeos.GEOSGeom_createCollection(6, subs, L)
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return geom_factory(lgeos.methods['cascaded_union'](collection))
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def unary_union(self, geoms):
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"""Returns the union of a sequence of geometries
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This method replaces :meth:`cascaded_union` as the
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prefered method for dissolving many polygons.
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"""
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try:
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L = len(geoms)
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except TypeError:
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geoms = [geoms]
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L = 1
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subs = (c_void_p * L)()
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for i, g in enumerate(geoms):
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subs[i] = g._geom
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collection = lgeos.GEOSGeom_createCollection(6, subs, L)
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return geom_factory(lgeos.methods['unary_union'](collection))
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operator = CollectionOperator()
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polygonize = operator.polygonize
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polygonize_full = operator.polygonize_full
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linemerge = operator.linemerge
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cascaded_union = operator.cascaded_union
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unary_union = operator.unary_union
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def triangulate(geom, tolerance=0.0, edges=False):
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"""Creates the Delaunay triangulation and returns a list of geometries
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The source may be any geometry type. All vertices of the geometry will be
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used as the points of the triangulation.
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From the GEOS documentation:
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tolerance is the snapping tolerance used to improve the robustness of
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the triangulation computation. A tolerance of 0.0 specifies that no
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snapping will take place.
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If edges is False, a list of Polygons (triangles) will be returned.
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Otherwise the list of LineString edges is returned.
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"""
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func = lgeos.methods['delaunay_triangulation']
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gc = geom_factory(func(geom._geom, tolerance, int(edges)))
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return [g for g in gc.geoms]
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class ValidateOp(object):
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def __call__(self, this):
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return lgeos.GEOSisValidReason(this._geom)
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validate = ValidateOp()
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def transform(func, geom):
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"""Applies `func` to all coordinates of `geom` and returns a new
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geometry of the same type from the transformed coordinates.
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`func` maps x, y, and optionally z to output xp, yp, zp. The input
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parameters may iterable types like lists or arrays or single values.
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The output shall be of the same type. Scalars in, scalars out.
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Lists in, lists out.
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For example, here is an identity function applicable to both types
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of input.
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def id_func(x, y, z=None):
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return tuple(filter(None, [x, y, z]))
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g2 = transform(id_func, g1)
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A partially applied transform function from pyproj satisfies the
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requirements for `func`.
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from functools import partial
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import pyproj
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project = partial(
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pyproj.transform,
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pyproj.Proj(init='epsg:4326'),
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pyproj.Proj(init='epsg:26913'))
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g2 = transform(project, g1)
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Lambda expressions such as the one in
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g2 = transform(lambda x, y, z=None: (x+1.0, y+1.0), g1)
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also satisfy the requirements for `func`.
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"""
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if geom.is_empty:
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return geom
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if geom.type in ('Point', 'LineString', 'LinearRing', 'Polygon'):
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# First we try to apply func to x, y, z sequences. When func is
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# optimized for sequences, this is the fastest, though zipping
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# the results up to go back into the geometry constructors adds
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# extra cost.
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try:
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if geom.type in ('Point', 'LineString', 'LinearRing'):
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return type(geom)(zip(*func(*izip(*geom.coords))))
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elif geom.type == 'Polygon':
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shell = type(geom.exterior)(
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zip(*func(*izip(*geom.exterior.coords))))
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holes = list(type(ring)(zip(*func(*izip(*ring.coords))))
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for ring in geom.interiors)
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return type(geom)(shell, holes)
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# A func that assumes x, y, z are single values will likely raise a
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# TypeError, in which case we'll try again.
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except TypeError:
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if geom.type in ('Point', 'LineString', 'LinearRing'):
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return type(geom)([func(*c) for c in geom.coords])
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elif geom.type == 'Polygon':
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shell = type(geom.exterior)(
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[func(*c) for c in geom.exterior.coords])
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holes = list(type(ring)([func(*c) for c in ring.coords])
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for ring in geom.interiors)
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return type(geom)(shell, holes)
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elif geom.type.startswith('Multi') or geom.type == 'GeometryCollection':
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return type(geom)([transform(func, part) for part in geom.geoms])
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else:
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raise ValueError('Type %r not recognized' % geom.type)
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def nearest_points(g1, g2):
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"""Returns the calculated nearest points in the input geometries
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The points are returned in the same order as the input geometries.
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"""
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seq = lgeos.methods['nearest_points'](g1._geom, g2._geom)
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if seq is None:
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if g1.is_empty:
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raise ValueError('The first input geometry is empty')
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else:
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raise ValueError('The second input geometry is empty')
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x1 = c_double()
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y1 = c_double()
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x2 = c_double()
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y2 = c_double()
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lgeos.GEOSCoordSeq_getX(seq, 0, byref(x1))
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lgeos.GEOSCoordSeq_getY(seq, 0, byref(y1))
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lgeos.GEOSCoordSeq_getX(seq, 1, byref(x2))
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lgeos.GEOSCoordSeq_getY(seq, 1, byref(y2))
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p1 = Point(x1.value, y1.value)
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p2 = Point(x2.value, y2.value)
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return (p1, p2)
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def snap(g1, g2, tolerance):
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"""Snap one geometry to another with a given tolerance
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Vertices of the first geometry are snapped to vertices of the second
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geometry. The resulting snapped geometry is returned. The input geometries
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are not modified.
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Parameters
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----------
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g1 : geometry
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The first geometry
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g2 : geometry
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The second geometry
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tolerence : float
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The snapping tolerance
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Example
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-------
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>>> square = Polygon([(1,1), (2, 1), (2, 2), (1, 2), (1, 1)])
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>>> line = LineString([(0,0), (0.8, 0.8), (1.8, 0.95), (2.6, 0.5)])
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>>> result = snap(line, square, 0.5)
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>>> result.wkt
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'LINESTRING (0 0, 1 1, 2 1, 2.6 0.5)'
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"""
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return(geom_factory(lgeos.methods['snap'](g1._geom, g2._geom, tolerance)))
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def shared_paths(g1, g2):
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"""Find paths shared between the two given lineal geometries
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Returns a GeometryCollection with two elements:
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- First element is a MultiLineString containing shared paths with the
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same direction for both inputs.
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- Second element is a MultiLineString containing shared paths with the
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opposite direction for the two inputs.
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Parameters
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----------
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g1 : geometry
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The first geometry
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g2 : geometry
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The second geometry
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"""
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if not isinstance(g1, LineString):
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raise TypeError("First geometry must be a LineString")
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if not isinstance(g2, LineString):
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raise TypeError("Second geometry must be a LineString")
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return(geom_factory(lgeos.methods['shared_paths'](g1._geom, g2._geom)))
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class SplitOp(object):
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@staticmethod
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def _split_polygon_with_line(poly, splitter):
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"""Split a Polygon with a LineString"""
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assert(isinstance(poly, Polygon))
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assert(isinstance(splitter, LineString))
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union = poly.boundary.union(splitter)
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# some polygonized geometries may be holes, we do not want them
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# that's why we test if the original polygon (poly) contains
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# an inner point of polygonized geometry (pg)
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return [pg for pg in polygonize(union) if poly.contains(pg.representative_point())]
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@staticmethod
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def _split_line_with_line(line, splitter):
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"""Split a LineString with another (Multi)LineString or (Multi)Polygon"""
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# if splitter is a polygon, pick it's boundary
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if splitter.type in ('Polygon', 'MultiPolygon'):
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splitter = splitter.boundary
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assert(isinstance(line, LineString))
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assert(isinstance(splitter, LineString) or isinstance(splitter, MultiLineString))
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if splitter.crosses(line):
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# The lines cross --> return multilinestring from the split
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return line.difference(splitter)
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elif splitter.relate_pattern(line, '1********'):
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# The lines overlap at some segment (linear intersection of interiors)
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raise ValueError('Input geometry segment overlaps with the splitter.')
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else:
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# The lines do not cross --> return collection with identity line
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return [line]
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@staticmethod
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def _split_line_with_point(line, splitter):
|
||
|
|
"""Split a LineString with a Point"""
|
||
|
|
|
||
|
|
assert(isinstance(line, LineString))
|
||
|
|
assert(isinstance(splitter, Point))
|
||
|
|
|
||
|
|
# check if point is in the interior of the line
|
||
|
|
if not line.relate_pattern(splitter, '0********'):
|
||
|
|
# point not on line interior --> return collection with single identity line
|
||
|
|
# (REASONING: Returning a list with the input line reference and creating a
|
||
|
|
# GeometryCollection at the general split function prevents unnecessary copying
|
||
|
|
# of linestrings in multipoint splitting function)
|
||
|
|
return [line]
|
||
|
|
elif line.coords[0] == splitter.coords[0]:
|
||
|
|
# if line is a closed ring the previous test doesn't behave as desired
|
||
|
|
return [line]
|
||
|
|
|
||
|
|
# point is on line, get the distance from the first point on line
|
||
|
|
distance_on_line = line.project(splitter)
|
||
|
|
coords = list(line.coords)
|
||
|
|
# split the line at the point and create two new lines
|
||
|
|
current_position = 0.0
|
||
|
|
for i in range(len(coords)-1):
|
||
|
|
point1 = coords[i]
|
||
|
|
point2 = coords[i+1]
|
||
|
|
dx = point1[0] - point2[0]
|
||
|
|
dy = point1[1] - point2[1]
|
||
|
|
segment_length = (dx ** 2 + dy ** 2) ** 0.5
|
||
|
|
current_position += segment_length
|
||
|
|
if distance_on_line == current_position:
|
||
|
|
# splitter is exactly on a vertex
|
||
|
|
return [
|
||
|
|
LineString(coords[:i+2]),
|
||
|
|
LineString(coords[i+1:])
|
||
|
|
]
|
||
|
|
elif distance_on_line < current_position:
|
||
|
|
# splitter is between two vertices
|
||
|
|
return [
|
||
|
|
LineString(coords[:i+1] + [splitter.coords[0]]),
|
||
|
|
LineString([splitter.coords[0]] + coords[i+1:])
|
||
|
|
]
|
||
|
|
return [line]
|
||
|
|
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def _split_line_with_multipoint(line, splitter):
|
||
|
|
"""Split a LineString with a MultiPoint"""
|
||
|
|
|
||
|
|
assert(isinstance(line, LineString))
|
||
|
|
assert(isinstance(splitter, MultiPoint))
|
||
|
|
|
||
|
|
chunks = [line]
|
||
|
|
for pt in splitter.geoms:
|
||
|
|
new_chunks = []
|
||
|
|
for chunk in filter(lambda x: not x.is_empty, chunks):
|
||
|
|
# add the newly split 2 lines or the same line if not split
|
||
|
|
new_chunks.extend(SplitOp._split_line_with_point(chunk, pt))
|
||
|
|
chunks = new_chunks
|
||
|
|
|
||
|
|
return chunks
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
def split(geom, splitter):
|
||
|
|
"""
|
||
|
|
Splits a geometry by another geometry and returns a collection of geometries. This function is the theoretical
|
||
|
|
opposite of the union of the split geometry parts. If the splitter does not split the geometry, a collection
|
||
|
|
with a single geometry equal to the input geometry is returned.
|
||
|
|
The function supports:
|
||
|
|
- Splitting a (Multi)LineString by a (Multi)Point or (Multi)LineString or (Multi)Polygon
|
||
|
|
- Splitting a (Multi)Polygon by a LineString
|
||
|
|
|
||
|
|
It may be convenient to snap the splitter with low tolerance to the geometry. For example in the case
|
||
|
|
of splitting a line by a point, the point must be exactly on the line, for the line to be correctly split.
|
||
|
|
When splitting a line by a polygon, the boundary of the polygon is used for the operation.
|
||
|
|
When splitting a line by another line, a ValueError is raised if the two overlap at some segment.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
geom : geometry
|
||
|
|
The geometry to be split
|
||
|
|
splitter : geometry
|
||
|
|
The geometry that will split the input geom
|
||
|
|
|
||
|
|
Example
|
||
|
|
-------
|
||
|
|
>>> pt = Point((1, 1))
|
||
|
|
>>> line = LineString([(0,0), (2,2)])
|
||
|
|
>>> result = split(line, pt)
|
||
|
|
>>> result.wkt
|
||
|
|
'GEOMETRYCOLLECTION (LINESTRING (0 0, 1 1), LINESTRING (1 1, 2 2))'
|
||
|
|
"""
|
||
|
|
|
||
|
|
if geom.type in ('MultiLineString', 'MultiPolygon'):
|
||
|
|
return GeometryCollection([i for part in geom.geoms for i in SplitOp.split(part, splitter).geoms])
|
||
|
|
|
||
|
|
elif geom.type == 'LineString':
|
||
|
|
if splitter.type in ('LineString', 'MultiLineString', 'Polygon', 'MultiPolygon'):
|
||
|
|
split_func = SplitOp._split_line_with_line
|
||
|
|
elif splitter.type in ('Point'):
|
||
|
|
split_func = SplitOp._split_line_with_point
|
||
|
|
elif splitter.type in ('MultiPoint'):
|
||
|
|
split_func = SplitOp._split_line_with_multipoint
|
||
|
|
else:
|
||
|
|
raise ValueError("Splitting a LineString with a %s is not supported" % splitter.type)
|
||
|
|
|
||
|
|
elif geom.type == 'Polygon':
|
||
|
|
if splitter.type == 'LineString':
|
||
|
|
split_func = SplitOp._split_polygon_with_line
|
||
|
|
else:
|
||
|
|
raise ValueError("Splitting a Polygon with a %s is not supported" % splitter.type)
|
||
|
|
|
||
|
|
else:
|
||
|
|
raise ValueError("Splitting %s geometry is not supported" % geom.type)
|
||
|
|
|
||
|
|
return GeometryCollection(split_func(geom, splitter))
|
||
|
|
|
||
|
|
split = SplitOp.split
|
||
|
|
|
||
|
|
|
||
|
|
def substring(geom, start_dist, end_dist, normalized=False):
|
||
|
|
"""Return a line segment between specified distances along a linear geometry.
|
||
|
|
|
||
|
|
Negative distance values are taken as measured in the reverse
|
||
|
|
direction from the end of the geometry. Out-of-range index
|
||
|
|
values are handled by clamping them to the valid range of values.
|
||
|
|
If the start distances equals the end distance, a point is being returned.
|
||
|
|
If the normalized arg is True, the distance will be interpreted as a
|
||
|
|
fraction of the geometry's length.
|
||
|
|
"""
|
||
|
|
|
||
|
|
assert(isinstance(geom, LineString))
|
||
|
|
|
||
|
|
# Filter out cases in which to return a point
|
||
|
|
if start_dist == end_dist:
|
||
|
|
return geom.interpolate(start_dist, normalized)
|
||
|
|
elif not normalized and start_dist >= geom.length and end_dist >= geom.length:
|
||
|
|
return geom.interpolate(geom.length, normalized)
|
||
|
|
elif not normalized and -start_dist >= geom.length and -end_dist >= geom.length:
|
||
|
|
return geom.interpolate(0, normalized)
|
||
|
|
elif normalized and start_dist >= 1 and end_dist >= 1:
|
||
|
|
return geom.interpolate(1, normalized)
|
||
|
|
elif normalized and -start_dist >= 1 and -end_dist >= 1:
|
||
|
|
return geom.interpolate(0, normalized)
|
||
|
|
|
||
|
|
start_point = geom.interpolate(start_dist, normalized)
|
||
|
|
end_point = geom.interpolate(end_dist, normalized)
|
||
|
|
|
||
|
|
min_dist = min(start_dist, end_dist)
|
||
|
|
max_dist = max(start_dist, end_dist)
|
||
|
|
if normalized:
|
||
|
|
min_dist *= geom.length
|
||
|
|
max_dist *= geom.length
|
||
|
|
|
||
|
|
if start_dist < end_dist:
|
||
|
|
vertex_list = [(start_point.x, start_point.y)]
|
||
|
|
else:
|
||
|
|
vertex_list = [(end_point.x, end_point.y)]
|
||
|
|
coords = list(geom.coords)
|
||
|
|
for p in coords:
|
||
|
|
pd = geom.project(Point(p))
|
||
|
|
if min_dist < pd < max_dist:
|
||
|
|
vertex_list.append(p)
|
||
|
|
elif pd >= max_dist:
|
||
|
|
break
|
||
|
|
if start_dist < end_dist:
|
||
|
|
vertex_list.append((end_point.x, end_point.y))
|
||
|
|
else:
|
||
|
|
vertex_list.append((start_point.x, start_point.y))
|
||
|
|
# reverse direction result
|
||
|
|
vertex_list = reversed(vertex_list)
|
||
|
|
|
||
|
|
return LineString(vertex_list)
|
||
|
|
|
||
|
|
|
||
|
|
def clip_by_rect(geom, xmin, ymin, xmax, ymax):
|
||
|
|
"""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.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
geom : geometry
|
||
|
|
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
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Requires GEOS >= 3.5.0
|
||
|
|
New in 1.7.
|
||
|
|
"""
|
||
|
|
if geom.is_empty:
|
||
|
|
return geom
|
||
|
|
result = geom_factory(lgeos.methods['clip_by_rect'](geom._geom, xmin, ymin, xmax, ymax))
|
||
|
|
return result
|
||
|
|
|
||
|
|
|
||
|
|
def orient(geom, sign=1.0):
|
||
|
|
if isinstance(geom, BaseMultipartGeometry):
|
||
|
|
return geom.__class__(
|
||
|
|
list(
|
||
|
|
map(
|
||
|
|
lambda geom: orient(geom, sign),
|
||
|
|
geom.geoms,
|
||
|
|
)
|
||
|
|
)
|
||
|
|
)
|
||
|
|
if isinstance(geom, (Polygon,)):
|
||
|
|
return orient_(geom, sign)
|
||
|
|
return geom
|