"""Support for various GEOS geometry operations """ import sys if sys.version_info[0] < 3: from itertools import izip else: izip = zip from ctypes import byref, c_void_p, c_double from shapely.geos import lgeos from shapely.geometry.base import geom_factory, BaseGeometry, BaseMultipartGeometry from shapely.geometry import asShape, asLineString, asMultiLineString, Point, MultiPoint,\ LineString, MultiLineString, Polygon, GeometryCollection from shapely.geometry.polygon import orient as orient_ from shapely.algorithms.polylabel import polylabel __all__ = ['cascaded_union', 'linemerge', 'operator', 'polygonize', 'polygonize_full', 'transform', 'unary_union', 'triangulate', 'split', 'section'] class CollectionOperator(object): def shapeup(self, ob): if isinstance(ob, BaseGeometry): return ob else: try: return asShape(ob) except ValueError: return asLineString(ob) def polygonize(self, lines): """Creates polygons from a source of lines The source may be a MultiLineString, a sequence of LineString objects, or a sequence of objects than can be adapted to LineStrings. """ source = getattr(lines, 'geoms', None) or lines try: source = iter(source) except TypeError: source = [source] finally: obs = [self.shapeup(l) for l in source] geom_array_type = c_void_p * len(obs) geom_array = geom_array_type() for i, line in enumerate(obs): geom_array[i] = line._geom product = lgeos.GEOSPolygonize(byref(geom_array), len(obs)) collection = geom_factory(product) for g in collection.geoms: clone = lgeos.GEOSGeom_clone(g._geom) g = geom_factory(clone) g._other_owned = False yield g def polygonize_full(self, lines): """Creates polygons from a source of lines, returning the polygons and leftover geometries. The source may be a MultiLineString, a sequence of LineString objects, or a sequence of objects than can be adapted to LineStrings. Returns a tuple of objects: (polygons, dangles, cut edges, invalid ring lines). Each are a geometry collection. Dangles are edges which have one or both ends which are not incident on another edge endpoint. Cut edges are connected at both ends but do not form part of polygon. Invalid ring lines form rings which are invalid (bowties, etc). """ source = getattr(lines, 'geoms', None) or lines try: source = iter(source) except TypeError: source = [source] finally: obs = [self.shapeup(l) for l in source] L = len(obs) subs = (c_void_p * L)() for i, g in enumerate(obs): subs[i] = g._geom collection = lgeos.GEOSGeom_createCollection(5, subs, L) dangles = c_void_p() cuts = c_void_p() invalids = c_void_p() product = lgeos.GEOSPolygonize_full( collection, byref(dangles), byref(cuts), byref(invalids)) return ( geom_factory(product), geom_factory(dangles), geom_factory(cuts), geom_factory(invalids) ) def linemerge(self, lines): """Merges all connected lines from a source The source may be a MultiLineString, a sequence of LineString objects, or a sequence of objects than can be adapted to LineStrings. Returns a LineString or MultiLineString when lines are not contiguous. """ source = None if hasattr(lines, 'type') and lines.type == 'MultiLineString': source = lines elif hasattr(lines, '__iter__'): try: source = asMultiLineString([ls.coords for ls in lines]) except AttributeError: source = asMultiLineString(lines) if source is None: raise ValueError("Cannot linemerge %s" % lines) result = lgeos.GEOSLineMerge(source._geom) return geom_factory(result) def cascaded_union(self, geoms): """Returns the union of a sequence of geometries This method was superseded by :meth:`unary_union`. """ try: L = len(geoms) except TypeError: geoms = [geoms] L = 1 subs = (c_void_p * L)() for i, g in enumerate(geoms): subs[i] = g._geom collection = lgeos.GEOSGeom_createCollection(6, subs, L) return geom_factory(lgeos.methods['cascaded_union'](collection)) def unary_union(self, geoms): """Returns the union of a sequence of geometries This method replaces :meth:`cascaded_union` as the prefered method for dissolving many polygons. """ try: L = len(geoms) except TypeError: geoms = [geoms] L = 1 subs = (c_void_p * L)() for i, g in enumerate(geoms): subs[i] = g._geom collection = lgeos.GEOSGeom_createCollection(6, subs, L) return geom_factory(lgeos.methods['unary_union'](collection)) operator = CollectionOperator() polygonize = operator.polygonize polygonize_full = operator.polygonize_full linemerge = operator.linemerge cascaded_union = operator.cascaded_union unary_union = operator.unary_union def triangulate(geom, tolerance=0.0, edges=False): """Creates the Delaunay triangulation and returns a list of geometries The source may be any geometry type. All vertices of the geometry will be used as the points of the triangulation. From the GEOS documentation: tolerance is the snapping tolerance used to improve the robustness of the triangulation computation. A tolerance of 0.0 specifies that no snapping will take place. If edges is False, a list of Polygons (triangles) will be returned. Otherwise the list of LineString edges is returned. """ func = lgeos.methods['delaunay_triangulation'] gc = geom_factory(func(geom._geom, tolerance, int(edges))) return [g for g in gc.geoms] class ValidateOp(object): def __call__(self, this): return lgeos.GEOSisValidReason(this._geom) validate = ValidateOp() def transform(func, geom): """Applies `func` to all coordinates of `geom` and returns a new geometry of the same type from the transformed coordinates. `func` maps x, y, and optionally z to output xp, yp, zp. The input parameters may iterable types like lists or arrays or single values. The output shall be of the same type. Scalars in, scalars out. Lists in, lists out. For example, here is an identity function applicable to both types of input. def id_func(x, y, z=None): return tuple(filter(None, [x, y, z])) g2 = transform(id_func, g1) A partially applied transform function from pyproj satisfies the requirements for `func`. from functools import partial import pyproj project = partial( pyproj.transform, pyproj.Proj(init='epsg:4326'), pyproj.Proj(init='epsg:26913')) g2 = transform(project, g1) Lambda expressions such as the one in g2 = transform(lambda x, y, z=None: (x+1.0, y+1.0), g1) also satisfy the requirements for `func`. """ if geom.is_empty: return geom if geom.type in ('Point', 'LineString', 'LinearRing', 'Polygon'): # First we try to apply func to x, y, z sequences. When func is # optimized for sequences, this is the fastest, though zipping # the results up to go back into the geometry constructors adds # extra cost. try: if geom.type in ('Point', 'LineString', 'LinearRing'): return type(geom)(zip(*func(*izip(*geom.coords)))) elif geom.type == 'Polygon': shell = type(geom.exterior)( zip(*func(*izip(*geom.exterior.coords)))) holes = list(type(ring)(zip(*func(*izip(*ring.coords)))) for ring in geom.interiors) return type(geom)(shell, holes) # A func that assumes x, y, z are single values will likely raise a # TypeError, in which case we'll try again. except TypeError: if geom.type in ('Point', 'LineString', 'LinearRing'): return type(geom)([func(*c) for c in geom.coords]) elif geom.type == 'Polygon': shell = type(geom.exterior)( [func(*c) for c in geom.exterior.coords]) holes = list(type(ring)([func(*c) for c in ring.coords]) for ring in geom.interiors) return type(geom)(shell, holes) elif geom.type.startswith('Multi') or geom.type == 'GeometryCollection': return type(geom)([transform(func, part) for part in geom.geoms]) else: raise ValueError('Type %r not recognized' % geom.type) def nearest_points(g1, g2): """Returns the calculated nearest points in the input geometries The points are returned in the same order as the input geometries. """ seq = lgeos.methods['nearest_points'](g1._geom, g2._geom) if seq is None: if g1.is_empty: raise ValueError('The first input geometry is empty') else: raise ValueError('The second input geometry is empty') x1 = c_double() y1 = c_double() x2 = c_double() y2 = c_double() lgeos.GEOSCoordSeq_getX(seq, 0, byref(x1)) lgeos.GEOSCoordSeq_getY(seq, 0, byref(y1)) lgeos.GEOSCoordSeq_getX(seq, 1, byref(x2)) lgeos.GEOSCoordSeq_getY(seq, 1, byref(y2)) p1 = Point(x1.value, y1.value) p2 = Point(x2.value, y2.value) return (p1, p2) def snap(g1, g2, tolerance): """Snap one geometry to another with a given tolerance Vertices of the first geometry are snapped to vertices of the second geometry. The resulting snapped geometry is returned. The input geometries are not modified. Parameters ---------- g1 : geometry The first geometry g2 : geometry The second geometry tolerence : float The snapping tolerance Example ------- >>> square = Polygon([(1,1), (2, 1), (2, 2), (1, 2), (1, 1)]) >>> line = LineString([(0,0), (0.8, 0.8), (1.8, 0.95), (2.6, 0.5)]) >>> result = snap(line, square, 0.5) >>> result.wkt 'LINESTRING (0 0, 1 1, 2 1, 2.6 0.5)' """ return(geom_factory(lgeos.methods['snap'](g1._geom, g2._geom, tolerance))) def shared_paths(g1, g2): """Find paths shared between the two given lineal geometries Returns a GeometryCollection with two elements: - First element is a MultiLineString containing shared paths with the same direction for both inputs. - Second element is a MultiLineString containing shared paths with the opposite direction for the two inputs. Parameters ---------- g1 : geometry The first geometry g2 : geometry The second geometry """ if not isinstance(g1, LineString): raise TypeError("First geometry must be a LineString") if not isinstance(g2, LineString): raise TypeError("Second geometry must be a LineString") return(geom_factory(lgeos.methods['shared_paths'](g1._geom, g2._geom))) class SplitOp(object): @staticmethod def _split_polygon_with_line(poly, splitter): """Split a Polygon with a LineString""" assert(isinstance(poly, Polygon)) assert(isinstance(splitter, LineString)) union = poly.boundary.union(splitter) # some polygonized geometries may be holes, we do not want them # that's why we test if the original polygon (poly) contains # an inner point of polygonized geometry (pg) return [pg for pg in polygonize(union) if poly.contains(pg.representative_point())] @staticmethod def _split_line_with_line(line, splitter): """Split a LineString with another (Multi)LineString or (Multi)Polygon""" # if splitter is a polygon, pick it's boundary if splitter.type in ('Polygon', 'MultiPolygon'): splitter = splitter.boundary assert(isinstance(line, LineString)) assert(isinstance(splitter, LineString) or isinstance(splitter, MultiLineString)) if splitter.crosses(line): # The lines cross --> return multilinestring from the split return line.difference(splitter) elif splitter.relate_pattern(line, '1********'): # The lines overlap at some segment (linear intersection of interiors) raise ValueError('Input geometry segment overlaps with the splitter.') else: # The lines do not cross --> return collection with identity line return [line] @staticmethod 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