Source code for libpysal.cg.shapes

"""
Computational geometry code for PySAL: Python Spatial Analysis Library.

"""

__author__ = "Sergio J. Rey, Xinyue Ye, Charles Schmidt, Andrew Winslow, Hu Shao"

import math
from .sphere import arcdist

__all__ = ['Point', 'LineSegment', 'Line', 'Ray', 'Chain', 'Polygon',
           'Rectangle', 'asShape']


[docs]def asShape(obj): """ Returns a pysal shape object from obj. obj must support the __geo_interface__. """ if isinstance(obj, (Point, LineSegment, Line, Ray, Chain, Polygon)): return obj if hasattr(obj, '__geo_interface__'): geo = obj.__geo_interface__ else: geo = obj if hasattr(geo, 'type'): raise TypeError('%r does not appear to be a shape object' % (obj)) geo_type = geo['type'].lower() #if geo_type.startswith('multi'): # raise NotImplementedError, "%s are not supported at this time."%geo_type if geo_type in _geoJSON_type_to_Pysal_type: return _geoJSON_type_to_Pysal_type[geo_type].__from_geo_interface__(geo) else: raise NotImplementedError( "%s is not supported at this time." % geo_type)
class Geometry(object): """ A base class to help implement is_geometry and make geometric types extendable. """ def __init__(self): pass
[docs]class Point(Geometry): """ Geometric class for point objects. Attributes ---------- None """
[docs] def __init__(self, loc): """ Returns an instance of a Point object. __init__((number, number)) -> Point Test tag: <tc>#is#Point.__init__</tc> Test tag: <tc>#tests#Point.__init__</tc> Parameters ---------- loc : tuple location (number x-tuple, x > 1) Attributes ---------- Examples -------- >>> p = Point((1, 3)) """ self.__loc = tuple(map(float, loc))
@classmethod def __from_geo_interface__(cls, geo): return cls(geo['coordinates']) @property def __geo_interface__(self): return {'type': 'Point', 'coordinates': self.__loc} def __lt__(self, other): """ Tests if the Point is < another object. __ne__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) < Point((0,1)) False >>> Point((0,1)) < Point((1,1)) True """ return (self.__loc) < (other.__loc) def __le__(self, other): """ Tests if the Point is <= another object. __ne__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) <= Point((0,1)) True >>> Point((0,1)) <= Point((1,1)) True """ return (self.__loc) <= (other.__loc) def __eq__(self, other): """ Tests if the Point is equal to another object. __eq__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) == Point((0,1)) True >>> Point((0,1)) == Point((1,1)) False """ try: return (self.__loc) == (other.__loc) except AttributeError: return False def __ne__(self, other): """ Tests if the Point is not equal to another object. __ne__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) != Point((0,1)) False >>> Point((0,1)) != Point((1,1)) True """ try: return (self.__loc) != (other.__loc) except AttributeError: return True def __gt__(self, other): """ Tests if the Point is > another object. __ne__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) > Point((0,1)) False >>> Point((0,1)) > Point((1,1)) False """ return (self.__loc) > (other.__loc) def __ge__(self, other): """ Tests if the Point is >= another object. __ne__(x) -> bool Parameters ---------- other : an object to test equality against Attributes ---------- Examples -------- >>> Point((0,1)) >= Point((0,1)) True >>> Point((0,1)) >= Point((1,1)) False """ return (self.__loc) >= (other.__loc) def __hash__(self): """ Returns the hash of the Point's location. x.__hash__() -> hash(x) Parameters ---------- None Attributes ---------- Examples -------- >>> hash(Point((0,1))) == hash(Point((0,1))) True >>> hash(Point((0,1))) == hash(Point((1,1))) False """ return hash(self.__loc) def __getitem__(self, *args): """ Return the coordinate for the given dimension. x.__getitem__(i) -> x[i] Parameters ---------- i : index of the desired dimension. Attributes ---------- Examples -------- >>> p = Point((5.5,4.3)) >>> p[0] == 5.5 True >>> p[1] == 4.3 True """ return self.__loc.__getitem__(*args) def __getslice__(self, *args): """ Return the coordinate for the given dimensions. x.__getitem__(i,j) -> x[i:j] Parameters ---------- i : index to start slice j : index to end slice (excluded). Attributes ---------- Examples -------- >>> p = Point((3,6,2)) >>> p[:2] == (3,6) True >>> p[1:2] == (6,) True """ return self.__loc.__getslice__(*args) def __len__(self): """ Returns the number of dimension in the point. __len__() -> int Parameters ---------- None Attributes ---------- Examples -------- >>> len(Point((1,2))) 2 """ return len(self.__loc) def __repr__(self): """ Returns the string representation of the Point __repr__() -> string Parameters ---------- None Attributes ---------- Examples -------- >>> Point((0,1)) (0.0, 1.0) """ return str(self) def __str__(self): """ Returns a string representation of a Point object. __str__() -> string Test tag: <tc>#is#Point.__str__</tc> Test tag: <tc>#tests#Point.__str__</tc> Attributes ---------- Examples -------- >>> p = Point((1, 3)) >>> str(p) '(1.0, 3.0)' """ return str(self.__loc) return "POINT ({} {})".format(*self.__loc)
[docs]class LineSegment(Geometry): """ Geometric representation of line segment objects. Parameters ---------- start_pt : Point Point where segment begins end_pt : Point Point where segment ends Attributes ---------- p1 : Point Starting point p2 : Point Ending point bounding_box : tuple The bounding box of the segment (number 4-tuple) len : float The length of the segment line : Line The line on which the segment lies """
[docs] def __init__(self, start_pt, end_pt): """ Creates a LineSegment object. __init__(Point, Point) -> LineSegment Test tag: <tc>#is#LineSegment.__init__</tc> Test tag: <tc>#tests#LineSegment.__init__</tc> Attributes ---------- None Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) """ self._p1 = start_pt self._p2 = end_pt self._reset_props()
def __str__(self): return "LineSegment(" + str(self._p1) + ", " + str(self._p2) + ")" return "LINESTRING ({} {}, {} {})".format(self._p1[0], self._p1[1], self._p2[0], self._p2[1]) def __eq__(self, other): """ Returns true if self and other are the same line segment Examples -------- >>> l1 = LineSegment(Point((1, 2)), Point((5, 6))) >>> l2 = LineSegment(Point((5, 6)), Point((1, 2))) >>> l1 == l2 True >>> l2 == l1 True """ if not isinstance(other, self.__class__): return False if (other.p1 == self._p1 and other.p2 == self._p2): return True elif (other.p2 == self._p1 and other.p1 == self._p2): return True return False
[docs] def intersect(self, other): """ Test whether segment intersects with other segment Handles endpoints of segments being on other segment Examples -------- >>> ls = LineSegment(Point((5,0)), Point((10,0))) >>> ls1 = LineSegment(Point((5,0)), Point((10,1))) >>> ls.intersect(ls1) True >>> ls2 = LineSegment(Point((5,1)), Point((10,1))) >>> ls.intersect(ls2) False >>> ls2 = LineSegment(Point((7,-1)), Point((7,2))) >>> ls.intersect(ls2) True >>> """ ccw1 = self.sw_ccw(other.p2) ccw2 = self.sw_ccw(other.p1) ccw3 = other.sw_ccw(self.p1) ccw4 = other.sw_ccw(self.p2) return ccw1*ccw2 <= 0 and ccw3*ccw4 <=0
def _reset_props(self): """ HELPER METHOD. DO NOT CALL. Resets attributes which are functions of other attributes. The getters for these attributes (implemented as properties) then recompute their values if they have been reset since the last call to the getter. _reset_props() -> None Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> ls._reset_props() """ self._bounding_box = None self._len = None self._line = False def _get_p1(self): """ HELPER METHOD. DO NOT CALL. Returns the p1 attribute of the line segment. _get_p1() -> Point Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> r = ls._get_p1() >>> r == Point((1, 2)) True """ return self._p1 def _set_p1(self, p1): """ HELPER METHOD. DO NOT CALL. Sets the p1 attribute of the line segment. _set_p1(Point) -> Point Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> r = ls._set_p1(Point((3, -1))) >>> r == Point((3.0, -1.0)) True """ self._p1 = p1 self._reset_props() return self._p1 p1 = property(_get_p1, _set_p1) def _get_p2(self): """ HELPER METHOD. DO NOT CALL. Returns the p2 attribute of the line segment. _get_p2() -> Point Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> r = ls._get_p2() >>> r == Point((5, 6)) True """ return self._p2 def _set_p2(self, p2): """ HELPER METHOD. DO NOT CALL. Sets the p2 attribute of the line segment. _set_p2(Point) -> Point Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> r = ls._set_p2(Point((3, -1))) >>> r == Point((3.0, -1.0)) True """ self._p2 = p2 self._reset_props() return self._p2 p2 = property(_get_p2, _set_p2)
[docs] def is_ccw(self, pt): """ Returns whether a point is counterclockwise of the segment. Exclusive. is_ccw(Point) -> bool Test tag: <tc>#is#LineSegment.is_ccw</tc> Test tag: <tc>#tests#LineSegment.is_ccw</tc> Parameters ---------- pt : point lying ccw or cw of a segment Attributes ---------- Examples -------- >>> ls = LineSegment(Point((0, 0)), Point((5, 0))) >>> ls.is_ccw(Point((2, 2))) True >>> ls.is_ccw(Point((2, -2))) False """ v1 = (self._p2[0] - self._p1[0], self._p2[1] - self._p1[1]) v2 = (pt[0] - self._p1[0], pt[1] - self._p1[1]) return v1[0] * v2[1] - v1[1] * v2[0] > 0
[docs] def is_cw(self, pt): """ Returns whether a point is clockwise of the segment. Exclusive. is_cw(Point) -> bool Test tag: <tc>#is#LineSegment.is_cw</tc> Test tag: <tc>#tests#LineSegment.is_cw</tc> Parameters ---------- pt : point lying ccw or cw of a segment Attributes ---------- Examples -------- >>> ls = LineSegment(Point((0, 0)), Point((5, 0))) >>> ls.is_cw(Point((2, 2))) False >>> ls.is_cw(Point((2, -2))) True """ v1 = (self._p2[0] - self._p1[0], self._p2[1] - self._p1[1]) v2 = (pt[0] - self._p1[0], pt[1] - self._p1[1]) return v1[0] * v2[1] - v1[1] * v2[0] < 0
[docs] def sw_ccw(self, pt): """ Sedgewick test for pt being ccw of segment Returns ------- 1 if turn from self.p1 to self.p2 to pt is ccw -1 if turn from self.p1 to self.p2 to pt is cw -1 if the points are collinear and self.p1 is in the middle 1 if the points are collinear and self.p2 is in the middle 0 if the points are collinear and pt is in the middle """ p0 = self.p1 p1 = self.p2 p2 = pt dx1 = p1[0] - p0[0] dy1 = p1[1] - p0[1] dx2 = p2[0] - p0[0] dy2 = p2[1] - p0[1] if dy1*dx2 < dy2*dx1: return 1 if dy1*dx2 > dy2*dx1: return -1 if (dx1*dx2 < 0 or dy1*dy2 <0): return -1 if dx1*dx1 + dy1*dy1 >= dx2*dx2 + dy2*dy2: return 0 else: return 1
[docs] def get_swap(self): """ Returns a LineSegment object which has its endpoints swapped. get_swap() -> LineSegment Test tag: <tc>#is#LineSegment.get_swap</tc> Test tag: <tc>#tests#LineSegment.get_swap</tc> Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> swap = ls.get_swap() >>> swap.p1[0] 5.0 >>> swap.p1[1] 6.0 >>> swap.p2[0] 1.0 >>> swap.p2[1] 2.0 """ return LineSegment(self._p2, self._p1)
@property def bounding_box(self): """ Returns the minimum bounding box of a LineSegment object. Test tag: <tc>#is#LineSegment.bounding_box</tc> Test tag: <tc>#tests#LineSegment.bounding_box</tc> bounding_box -> Rectangle Attributes ---------- Examples -------- >>> ls = LineSegment(Point((1, 2)), Point((5, 6))) >>> ls.bounding_box.left 1.0 >>> ls.bounding_box.lower 2.0 >>> ls.bounding_box.right 5.0 >>> ls.bounding_box.upper 6.0 """ if self._bounding_box is None: # If LineSegment attributes p1, p2 changed, recompute self._bounding_box = Rectangle( min([self._p1[0], self._p2[0]]), min([ self._p1[1], self._p2[1]]), max([self._p1[0], self._p2[0]]), max([self._p1[1], self._p2[1]])) return Rectangle( self._bounding_box.left, self._bounding_box.lower, self._bounding_box.right, self._bounding_box.upper) @property def len(self): """ Returns the length of a LineSegment object. Test tag: <tc>#is#LineSegment.len</tc> Test tag: <tc>#tests#LineSegment.len</tc> len() -> number Attributes ---------- Examples -------- >>> ls = LineSegment(Point((2, 2)), Point((5, 2))) >>> ls.len 3.0 """ if self._len is None: # If LineSegment attributes p1, p2 changed, recompute self._len = math.hypot(self._p1[0] - self._p2[0], self._p1[1] - self._p2[1]) return self._len @property def line(self): """ Returns a Line object of the line which the segment lies on. Test tag: <tc>#is#LineSegment.line</tc> Test tag: <tc>#tests#LineSegment.line</tc> line() -> Line Attributes ---------- Examples -------- >>> ls = LineSegment(Point((2, 2)), Point((3, 3))) >>> l = ls.line >>> l.m 1.0 >>> l.b 0.0 """ if self._line == False: dx = self._p1[0] - self._p2[0] dy = self._p1[1] - self._p2[1] if dx == 0 and dy == 0: self._line = None elif dx == 0: self._line = VerticalLine(self._p1[0]) else: m = dy / float(dx) b = self._p1[1] - m * self._p1[0] # y - mx self._line = Line(m, b) return self._line
class VerticalLine(Geometry): """ Geometric representation of verticle line objects. Attributes ---------- x : float x-intercept """ def __init__(self, x): """ Returns a VerticalLine object. __init__(number) -> VerticalLine Parameters ---------- x : the x-intercept of the line Attributes ---------- Examples -------- >>> ls = VerticalLine(0) >>> ls.m inf >>> ls.b nan """ self._x = float(x) self.m = float('inf') self.b = float('nan') def x(self, y): """ Returns the x-value of the line at a particular y-value. x(number) -> number Parameters ---------- y : the y-value to compute x at Attributes ---------- Examples -------- >>> l = VerticalLine(0) >>> l.x(0.25) 0.0 """ return self._x def y(self, x): """ Returns the y-value of the line at a particular x-value. y(number) -> number Parameters ---------- x : the x-value to compute y at Attributes ---------- Examples -------- >>> l = VerticalLine(1) >>> l.y(1) nan """ return float('nan')
[docs]class Line(Geometry): """ Geometric representation of line objects. Attributes ---------- m : float slope b : float y-intercept """
[docs] def __init__(self, m, b): """ Returns a Line object. __init__(number, number) -> Line Test tag: <tc>#is#Line.__init__</tc> Test tag: <tc>#tests#Line.__init__</tc> Parameters ---------- m : the slope of the line b : the y-intercept of the line Attributes ---------- Examples -------- >>> ls = Line(1, 0) >>> ls.m 1.0 >>> ls.b 0.0 """ if m == float('inf') or m == float('inf'): raise ArithmeticError('Slope cannot be infinite.') self.m = float(m) self.b = float(b)
[docs] def x(self, y): """ Returns the x-value of the line at a particular y-value. x(number) -> number Parameters ---------- y : the y-value to compute x at Attributes ---------- Examples -------- >>> l = Line(0.5, 0) >>> l.x(0.25) 0.5 """ if self.m == 0: raise ArithmeticError('Cannot solve for X when slope is zero.') return (y - self.b) / self.m
[docs] def y(self, x): """ Returns the y-value of the line at a particular x-value. y(number) -> number Parameters ---------- x : the x-value to compute y at Attributes ---------- Examples -------- >>> l = Line(1, 0) >>> l.y(1) 1.0 """ if self.m == 0: return self.b return self.m * x + self.b
[docs]class Ray: """ Geometric representation of ray objects. Attributes ---------- o : Point Origin (point where ray originates) p : Point Second point on the ray (not point where ray originates) """
[docs] def __init__(self, origin, second_p): """ Returns a ray with the values specified. __init__(Point, Point) -> Ray Parameters ---------- origin : the point where the ray originates second_p : the second point specifying the ray (not the origin) Attributes ---------- Examples -------- >>> l = Ray(Point((0, 0)), Point((1, 0))) >>> str(l.o) '(0.0, 0.0)' >>> str(l.p) '(1.0, 0.0)' """ self.o = origin self.p = second_p
[docs]class Chain(Geometry): """ Geometric representation of a chain, also known as a polyline. Attributes ---------- vertices : list List of Points of the vertices of the chain in order. len : float The geometric length of the chain. """
[docs] def __init__(self, vertices): """ Returns a chain created from the points specified. __init__(Point list or list of Point lists) -> Chain Parameters ---------- vertices : list -- Point list or list of Point lists. Attributes ---------- Examples -------- >>> c = Chain([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((2, 1))]) """ if isinstance(vertices[0], list): self._vertices = [part for part in vertices] else: self._vertices = [vertices] self._reset_props()
@classmethod def __from_geo_interface__(cls, geo): if geo['type'].lower() == 'linestring': verts = [Point(pt) for pt in geo['coordinates']] elif geo['type'].lower() == 'multilinestring': verts = [list(map(Point, part)) for part in geo['coordinates']] else: raise TypeError('%r is not a Chain'%geo) return cls(verts) @property def __geo_interface__(self): if len(self.parts) == 1: return {'type': 'LineString', 'coordinates': self.vertices} else: return {'type': 'MultiLineString', 'coordinates': self.parts} def _reset_props(self): """ HELPER METHOD. DO NOT CALL. Resets attributes which are functions of other attributes. The getters for these attributes (implemented as properties) then recompute their values if they have been reset since the last call to the getter. _reset_props() -> None Attributes ---------- Examples -------- >>> ls = Chain([Point((1, 2)), Point((5, 6))]) >>> ls._reset_props() """ self._len = None self._arclen = None self._bounding_box = None @property def vertices(self): """ Returns the vertices of the chain in clockwise order. vertices -> Point list Attributes ---------- Examples -------- >>> c = Chain([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((2, 1))]) >>> verts = c.vertices >>> len(verts) 4 """ return sum([part for part in self._vertices], []) @property def parts(self): """ Returns the parts of the chain. parts -> Point list Attributes ---------- Examples -------- >>> c = Chain([[Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))],[Point((2,1)),Point((2,2)),Point((1,2)),Point((1,1))]]) >>> len(c.parts) 2 """ return [[v for v in part] for part in self._vertices] @property def bounding_box(self): """ Returns the bounding box of the chain. bounding_box -> Rectangle Attributes ---------- Examples -------- >>> c = Chain([Point((0, 0)), Point((2, 0)), Point((2, 1)), Point((0, 1))]) >>> c.bounding_box.left 0.0 >>> c.bounding_box.lower 0.0 >>> c.bounding_box.right 2.0 >>> c.bounding_box.upper 1.0 """ if self._bounding_box is None: vertices = self.vertices self._bounding_box = Rectangle( min([v[0] for v in vertices]), min([v[1] for v in vertices]), max([v[0] for v in vertices]), max([v[1] for v in vertices])) return self._bounding_box @property def len(self): """ Returns the geometric length of the chain. len -> number Attributes ---------- Examples -------- >>> c = Chain([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((2, 1))]) >>> c.len 3.0 >>> c = Chain([[Point((0, 0)), Point((1, 0)), Point((1, 1))],[Point((10,10)),Point((11,10)),Point((11,11))]]) >>> c.len 4.0 """ def dist(v1, v2): return math.hypot(v1[0] - v2[0], v1[1] - v2[1]) def part_perimeter(part): return sum([dist(part[i], part[i + 1]) for i in range(len(part) - 1)]) if self._len is None: self._len = sum([part_perimeter(part) for part in self._vertices]) return self._len @property def arclen(self): """ Returns the geometric length of the chain computed using arcdistance (meters). len -> number Attributes ---------- Examples -------- """ def part_perimeter(part): return sum([arcdist(part[i], part[i + 1]) * 1000. for i in range(len(part) - 1)]) if self._arclen is None: self._arclen = sum( [part_perimeter(part) for part in self._vertices]) return self._arclen @property def segments(self): """ Returns the segments that compose the Chain """ return [[LineSegment(a, b) for (a, b) in zip(part[:-1], part[1:])] for part in self._vertices]
class Ring(Geometry): """ Geometric representation of a Linear Ring Linear Rings must be closed, the first and last point must be the same. Open rings will be closed. This class exists primarily as a geometric primitive to form complex polygons with multiple rings and holes. The ordering of the vertices is ignored and will not be altered. Parameters ---------- vertices : list -- a list of vertices Attributes __________ vertices : list List of Points with the vertices of the ring len : int Number of vertices perimeter : float Geometric length of the perimeter of the ring bounding_box : Rectangle Bounding box of the ring area : float area enclosed by the ring centroid : tuple The centroid of the ring defined by the 'center of gravity' or 'center or mass' _quad_tree_structure : object The quad tree structure for the ring. This structure could help test if a point is inside the ring """ def __init__(self, vertices): if vertices[0] != vertices[-1]: vertices = vertices[:] + vertices[0:1] #raise ValueError, "Supplied vertices do not form a closed ring, the first and last vertices are not the same" self.vertices = tuple(vertices) self._perimeter = None self._bounding_box = None self._area = None self._centroid = None self._quad_tree_structure = None def __len__(self): return len(self.vertices) @property def len(self): return len(self) @staticmethod def dist(v1, v2): return math.hypot(v1[0] - v2[0], v1[1] - v2[1]) @property def perimeter(self): if self._perimeter is None: dist = self.dist v = self.vertices self._perimeter = sum([dist(v[i], v[i + 1]) for i in range(-1, len(self) - 1)]) return self._perimeter @property def bounding_box(self): """ Returns the bounding box of the ring bounding_box -> Rectangle Examples -------- >>> r = Ring([Point((0, 0)), Point((2, 0)), Point((2, 1)), Point((0, 1)), Point((0,0))]) >>> r.bounding_box.left 0.0 >>> r.bounding_box.lower 0.0 >>> r.bounding_box.right 2.0 >>> r.bounding_box.upper 1.0 """ if self._bounding_box is None: vertices = self.vertices x = [v[0] for v in vertices] y = [v[1] for v in vertices] self._bounding_box = Rectangle(min(x), min(y), max(x), max(y)) return self._bounding_box @property def area(self): """ Returns the area of the ring. area -> number Examples -------- >>> r = Ring([Point((0, 0)), Point((2, 0)), Point((2, 1)), Point((0, 1)), Point((0,0))]) >>> r.area 2.0 """ return abs(self.signed_area) @property def signed_area(self): if self._area is None: vertices = self.vertices x = [v[0] for v in vertices] y = [v[1] for v in vertices] N = len(self) A = 0.0 for i in range(N - 1): A += (x[i] + x[i + 1]) * \ (y[i] - y[i + 1]) A = A * 0.5 self._area = -A return self._area @property def centroid(self): """ Returns the centroid of the ring. centroid -> Point Notes ----- The centroid returned by this method is the geometric centroid. Also known as the 'center of gravity' or 'center of mass'. Examples -------- >>> r = Ring([Point((0, 0)), Point((2, 0)), Point((2, 1)), Point((0, 1)), Point((0,0))]) >>> str(r.centroid) '(1.0, 0.5)' """ if self._centroid is None: vertices = self.vertices x = [v[0] for v in vertices] y = [v[1] for v in vertices] A = self.signed_area N = len(self) cx = 0 cy = 0 for i in range(N - 1): f = (x[i] * y[i + 1] - x[i + 1] * y[i]) cx += (x[i] + x[i + 1]) * f cy += (y[i] + y[i + 1]) * f cx = 1.0 / (6 * A) * cx cy = 1.0 / (6 * A) * cy self._centroid = Point((cx, cy)) return self._centroid def build_quad_tree_structure(self): """ Build the quad tree structure for this ring. Once the structure is built, speed for testing if a point is inside the ring will be inscreased significantly. :return: """ self._quad_tree_structure = QuadTreeStructureSingleRing(self) def contains_point(self, point): """ Point containment using winding number Implementation based on: http://www.engr.colostate.edu/~dga/dga/papers/point_in_polygon.pdf """ if self._quad_tree_structure is None: x, y = point # bbox check if x < self.bounding_box.left: return False if x > self.bounding_box.right: return False if y < self.bounding_box.lower: return False if y > self.bounding_box.upper: return False rn = len(self.vertices) xs = [ self.vertices[i][0] - point[0] for i in range(rn) ] ys = [ self.vertices[i][1] - point[1] for i in range(rn) ] w = 0 for i in range(len(self.vertices) - 1): yi = ys[i] yj = ys[i+1] xi = xs[i] xj = xs[i+1] if yi*yj < 0: r = xi + yi * (xj-xi) / (yi - yj) if r > 0: if yi < 0: w += 1 else: w -= 1 elif yi==0 and xi > 0: if yj > 0: w += 0.5 else: w -= 0.5 elif yj == 0 and xj > 0: if yi < 0: w += 0.5 else: w -= 0.5 if w==0: return False else: return True else: return self._quad_tree_structure.contains_point(point)
[docs]class Polygon(Geometry): """ Geometric representation of polygon objects. Attributes ---------- vertices : list List of Points with the vertices of the Polygon in clockwise order len : int Number of vertices including holes perimeter : float Geometric length of the perimeter of the Polygon bounding_box : Rectangle Bounding box of the polygon bbox : List [left, lower, right, upper] area : float Area enclosed by the polygon centroid : tuple The 'center of gravity', i.e. the mean point of the polygon. """
[docs] def __init__(self, vertices, holes=None): """ Returns a polygon created from the objects specified. __init__(Point list or list of Point lists, holes list ) -> Polygon Parameters ---------- vertices : list -- a list of vertices or a list of lists of vertices. holes : list -- a list of sub-polygons to be considered as holes. is_quad_tree_structure_built : bool -- record if the quad tree structure has been built for this polygon. This quad tree structure could help speed up the contains_point test Attributes ---------- Examples -------- >>> p1 = Polygon([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))]) """ self._part_rings = [] self._hole_rings = [] def clockwise(part): if standalone.is_clockwise(part): return part[:] else: return part[::-1] vl = list(vertices) if isinstance(vl[0], list): self._part_rings = list(map(Ring, vertices)) self._vertices = [clockwise(part) for part in vertices] else: self._part_rings = [Ring(vertices)] self._vertices = [clockwise(vertices)] if holes is not None and holes != []: if isinstance(holes[0], list): self._hole_rings = list(map(Ring, holes)) self._holes = [clockwise(hole) for hole in holes] else: self._hole_rings = [Ring(holes)] self._holes = [clockwise(holes)] else: self._holes = [[]] self._reset_props()
@classmethod def __from_geo_interface__(cls, geo): """ While pysal does not differentiate polygons and multipolygons GEOS,Shapely and geoJSON do. In GEOS, etc, polygons may only have a single exterior ring, all other parts are holes. MultiPolygons are simply a list of polygons. """ geo_type = geo['type'].lower() if geo_type == 'multipolygon': parts = [] holes = [] for polygon in geo['coordinates']: verts = [[Point(pt) for pt in part] for part in polygon] parts += verts[0:1] holes += verts[1:] if not holes: holes = None return cls(parts, holes) else: verts = [[Point(pt) for pt in part] for part in geo['coordinates']] return cls(verts[0:1], verts[1:]) @property def __geo_interface__(self): if len(self.parts) > 1: geo = {'type': 'MultiPolygon', 'coordinates': [[ part] for part in self.parts]} if self._holes[0]: geo['coordinates'][0] += self._holes return geo if self._holes[0]: return {'type': 'Polygon', 'coordinates': self._vertices + self._holes} else: return {'type': 'Polygon', 'coordinates': self._vertices} def _reset_props(self): self._perimeter = None self._bounding_box = None self._bbox = None self._area = None self._centroid = None self._len = None def __len__(self): return self.len @property def len(self): """ Returns the number of vertices in the polygon. len -> int Attributes ---------- Examples -------- >>> p1 = Polygon([Point((0, 0)), Point((0, 1)), Point((1, 1)), Point((1, 0))]) >>> p1.len 4 >>> len(p1) 4 """ if self._len is None: self._len = len(self.vertices) return self._len @property def vertices(self): """ Returns the vertices of the polygon in clockwise order. vertices -> Point list Attributes ---------- Examples -------- >>> p1 = Polygon([Point((0, 0)), Point((0, 1)), Point((1, 1)), Point((1, 0))]) >>> len(p1.vertices) 4 """ return sum([part for part in self._vertices], []) + sum([part for part in self._holes], []) @property def holes(self): """ Returns the holes of the polygon in clockwise order. holes -> Point list Attributes ---------- Examples -------- >>> p = Polygon([Point((0, 0)), Point((10, 0)), Point((10, 10)), Point((0, 10))], [Point((1, 2)), Point((2, 2)), Point((2, 1)), Point((1, 1))]) >>> len(p.holes) 1 """ return [[v for v in part] for part in self._holes] @property def parts(self): """ Returns the parts of the polygon in clockwise order. parts -> Point list Attributes ---------- Attributes ---------- Examples -------- >>> p = Polygon([[Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))], [Point((2,1)),Point((2,2)),Point((1,2)),Point((1,1))]]) >>> len(p.parts) 2 """ return [[v for v in part] for part in self._vertices] @property def perimeter(self): """ Returns the perimeter of the polygon. perimeter() -> number Attributes ---------- Examples -------- >>> p = Polygon([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))]) >>> p.perimeter 4.0 """ def dist(v1, v2): return math.hypot(v1[0] - v2[0], v1[1] - v2[1]) def part_perimeter(part): return sum([dist(part[i], part[i + 1]) for i in range(-1, len(part) - 1)]) if self._perimeter is None: self._perimeter = (sum([part_perimeter(part) for part in self._vertices]) + sum([part_perimeter(hole) for hole in self._holes])) return self._perimeter @property def bbox(self): """ Returns the bounding box of the polygon as a list See also bounding_box """ if self._bbox is None: self._bbox = [ self.bounding_box.left, self.bounding_box.lower, self.bounding_box.right, self.bounding_box.upper] return self._bbox @property def bounding_box(self): """ Returns the bounding box of the polygon. bounding_box -> Rectangle Attributes ---------- Examples -------- >>> p = Polygon([Point((0, 0)), Point((2, 0)), Point((2, 1)), Point((0, 1))]) >>> p.bounding_box.left 0.0 >>> p.bounding_box.lower 0.0 >>> p.bounding_box.right 2.0 >>> p.bounding_box.upper 1.0 """ if self._bounding_box is None: vertices = self.vertices self._bounding_box = Rectangle( min([v[0] for v in vertices]), min([v[1] for v in vertices]), max([v[0] for v in vertices]), max([v[1] for v in vertices])) return self._bounding_box @property def area(self): """ Returns the area of the polygon. area -> number Attributes ---------- Examples -------- >>> p = Polygon([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))]) >>> p.area 1.0 >>> p = Polygon([Point((0, 0)), Point((10, 0)), Point((10, 10)), Point((0, 10))],[Point((2,1)),Point((2,2)),Point((1,2)),Point((1,1))]) >>> p.area 99.0 """ def part_area(part_verts): area = 0 for i in range(-1, len(part_verts) - 1): area += (part_verts[i][0] + part_verts[i + 1][0]) * \ (part_verts[i][1] - part_verts[i + 1][1]) area = area * 0.5 if area < 0: area = -area return area return (sum([part_area(part) for part in self._vertices]) - sum([part_area(hole) for hole in self._holes])) @property def centroid(self): """ Returns the centroid of the polygon centroid -> Point Notes ----- The centroid returned by this method is the geometric centroid and respects multipart polygons with holes. Also known as the 'center of gravity' or 'center of mass'. Examples -------- >>> p = Polygon([Point((0, 0)), Point((10, 0)), Point((10, 10)), Point((0, 10))], [Point((1, 1)), Point((1, 2)), Point((2, 2)), Point((2, 1))]) >>> p.centroid (5.0353535353535355, 5.0353535353535355) """ CP = [ring.centroid for ring in self._part_rings] AP = [ring.area for ring in self._part_rings] CH = [ring.centroid for ring in self._hole_rings] AH = [-ring.area for ring in self._hole_rings] A = AP + AH cx = sum([pt[0] * area for pt, area in zip(CP + CH, A)]) / sum(A) cy = sum([pt[1] * area for pt, area in zip(CP + CH, A)]) / sum(A) return cx, cy
[docs] def build_quad_tree_structure(self): """ Build the quad tree structure for this polygon. Once the structure is built, speed for testing if a point is inside the ring will be inscreased significantly. :return: """ for ring in self._part_rings: ring.build_quad_tree_structure() for ring in self._hole_rings: ring.build_quad_tree_structure() self.is_quad_tree_structure_built = True
[docs] def contains_point(self, point): """ Test if polygon contains point Examples -------- >>> p = Polygon([Point((0,0)), Point((4,0)), Point((4,5)), Point((2,3)), Point((0,5))]) >>> p.contains_point((3,3)) 1 >>> p.contains_point((0,6)) 0 >>> p.contains_point((2,2.9)) 1 >>> p.contains_point((4,5)) 0 >>> p.contains_point((4,0)) 0 >>> Handles holes >>> p = Polygon([Point((0, 0)), Point((0, 10)), Point((10, 10)), Point((10, 0))], [Point((2, 2)), Point((4, 2)), Point((4, 4)), Point((2, 4))]) >>> p.contains_point((3.0,3.0)) False >>> p.contains_point((1.0,1.0)) True >>> Notes ----- Points falling exactly on polygon edges may yield unpredictable results """ for ring in self._hole_rings: if ring.contains_point(point): return False for ring in self._part_rings: if ring.contains_point(point): return True return False
[docs]class Rectangle(Geometry): """ Geometric representation of rectangle objects. Attributes ---------- left : float Minimum x-value of the rectangle lower : float Minimum y-value of the rectangle right : float Maximum x-value of the rectangle upper : float Maximum y-value of the rectangle """
[docs] def __init__(self, left, lower, right, upper): """ Returns a Rectangle object. __init__(number, number, number, number) -> Rectangle Parameters ---------- left : the minimum x-value of the rectangle lower : the minimum y-value of the rectangle right : the maximum x-value of the rectangle upper : the maximum y-value of the rectangle Attributes ---------- Examples -------- >>> r = Rectangle(-4, 3, 10, 17) >>> r.left #minx -4.0 >>> r.lower #miny 3.0 >>> r.right #maxx 10.0 >>> r.upper #maxy 17.0 """ if right < left or upper < lower: raise ArithmeticError('Rectangle must have positive area.') self.left = float(left) self.lower = float(lower) self.right = float(right) self.upper = float(upper)
def __bool__(self): """ ___nonzero__ is used "to implement truth value testing and the built-in operation bool()" -- http://docs.python.org/reference/datamodel.html Rectangles will evaluate to Flase if they have Zero Area. >>> r = Rectangle(0,0,0,0) >>> bool(r) False >>> r = Rectangle(0,0,1,1) >>> bool(r) True """ return bool(self.area) def __eq__(self, other): if other: return self[:] == other[:] return False def __add__(self, other): x, y, X, Y = self[:] x1, y2, X1, Y1 = other[:] return Rectangle(min(self.left, other.left), min(self.lower, other.lower), max(self.right, other.right), max(self.upper, other.upper)) def __getitem__(self, key): """ >>> r = Rectangle(-4, 3, 10, 17) >>> r[:] [-4.0, 3.0, 10.0, 17.0] """ l = [self.left, self.lower, self.right, self.upper] return l.__getitem__(key)
[docs] def set_centroid(self, new_center): """ Moves the rectangle center to a new specified point. set_centroid(Point) -> Point Parameters ---------- new_center : the new location of the centroid of the polygon Attributes ---------- Examples -------- >>> r = Rectangle(0, 0, 4, 4) >>> r.set_centroid(Point((4, 4))) >>> r.left 2.0 >>> r.right 6.0 >>> r.lower 2.0 >>> r.upper 6.0 """ shift = (new_center[0] - (self.left + self.right) / 2, new_center[1] - (self.lower + self.upper) / 2) self.left = self.left + shift[0] self.right = self.right + shift[0] self.lower = self.lower + shift[1] self.upper = self.upper + shift[1]
[docs] def set_scale(self, scale): """ Rescales the rectangle around its center. set_scale(number) -> number Parameters ---------- scale : the ratio of the new scale to the old scale (e.g. 1.0 is current size) Attributes ---------- Examples -------- >>> r = Rectangle(0, 0, 4, 4) >>> r.set_scale(2) >>> r.left -2.0 >>> r.right 6.0 >>> r.lower -2.0 >>> r.upper 6.0 """ center = ((self.left + self.right) / 2, (self.lower + self.upper) / 2) self.left = center[0] + scale * (self.left - center[0]) self.right = center[0] + scale * (self.right - center[0]) self.lower = center[1] + scale * (self.lower - center[1]) self.upper = center[1] + scale * (self.upper - center[1])
@property def area(self): """ Returns the area of the Rectangle. area -> number Attributes ---------- Examples -------- >>> r = Rectangle(0, 0, 4, 4) >>> r.area 16.0 """ return (self.right - self.left) * (self.upper - self.lower) @property def width(self): """ Returns the width of the Rectangle. width -> number Attributes ---------- Examples -------- >>> r = Rectangle(0, 0, 4, 4) >>> r.width 4.0 """ return self.right - self.left @property def height(self): """ Returns the height of the Rectangle. height -> number Examples -------- >>> r = Rectangle(0, 0, 4, 4) >>> r.height 4.0 """ return self.upper - self.lower
_geoJSON_type_to_Pysal_type = {'point': Point, 'linestring': Chain, 'multilinestring': Chain, 'polygon': Polygon, 'multipolygon': Polygon} from . import standalone # moving this to top breaks unit tests ! from .polygonQuadTreeStructure import QuadTreeStructureSingleRing