Source code for libpysal.cg.standalone

"""
Helper functions for computational geometry in PySAL

"""

__author__ = "Sergio J. Rey, Xinyue Ye, Charles Schmidt, Andrew Winslow"
__credits__ = "Copyright (c) 2005-2009 Sergio J. Rey"

import doctest
import math
import copy
import random
from .shapes import *
from itertools import islice
import scipy.spatial
import numpy as np

EPSILON_SCALER = 3


__all__ = ['bbcommon', 'get_bounding_box', 'get_angle_between', 'is_collinear', 'get_segments_intersect', 'get_segment_point_intersect', 'get_polygon_point_intersect', 'get_rectangle_point_intersect', 'get_ray_segment_intersect', 'get_rectangle_rectangle_intersection', 'get_polygon_point_dist', 'get_points_dist', 'get_segment_point_dist', 'get_point_at_angle_and_dist', 'convex_hull', 'is_clockwise', 'point_touches_rectangle', 'get_shared_segments', 'distance_matrix']


[docs]def bbcommon(bb, bbother): """ Old Stars method for bounding box overlap testing Also defined in pysal.weights._cont_binning Examples -------- >>> b0 = [0,0,10,10] >>> b1 = [10,0,20,10] >>> bbcommon(b0,b1) 1 """ chflag = 0 if not ((bbother[2] < bb[0]) or (bbother[0] > bb[2])): if not ((bbother[3] < bb[1]) or (bbother[1] > bb[3])): chflag = 1 return chflag
[docs]def get_bounding_box(items): """ Find bounding box for a list of geometries Parameters ---------- items: list PySAL shapes Returns ------- Rectangle Examples -------- >>> bb = get_bounding_box([Point((-1, 5)), Rectangle(0, 6, 11, 12)]) >>> bb.left -1.0 >>> bb.lower 5.0 >>> bb.right 11.0 >>> bb.upper 12.0 """ def left(o): if hasattr(o, 'bounding_box'): # Polygon, Ellipse return o.bounding_box.left elif hasattr(o, 'left'): # Rectangle return o.left else: # Point return o[0] def right(o): if hasattr(o, 'bounding_box'): # Polygon, Ellipse return o.bounding_box.right elif hasattr(o, 'right'): # Rectangle return o.right else: # Point return o[0] def lower(o): if hasattr(o, 'bounding_box'): # Polygon, Ellipse return o.bounding_box.lower elif hasattr(o, 'lower'): # Rectangle return o.lower else: # Point return o[1] def upper(o): if hasattr(o, 'bounding_box'): # Polygon, Ellipse return o.bounding_box.upper elif hasattr(o, 'upper'): # Rectangle return o.upper else: # Point return o[1] return Rectangle(min(list(map(left, items))), min(list(map(lower, items))), max(list(map(right, items))), max(list(map(upper, items))))
[docs]def get_angle_between(ray1, ray2): """ Returns the angle formed between a pair of rays which share an origin get_angle_between(Ray, Ray) -> number Parameters ---------- ray1 : a ray forming the beginning of the angle measured ray2 : a ray forming the end of the angle measured Examples -------- >>> get_angle_between(Ray(Point((0, 0)), Point((1, 0))), Ray(Point((0, 0)), Point((1, 0)))) 0.0 """ if ray1.o != ray2.o: raise ValueError('Rays must have the same origin.') vec1 = (ray1.p[0] - ray1.o[0], ray1.p[1] - ray1.o[1]) vec2 = (ray2.p[0] - ray2.o[0], ray2.p[1] - ray2.o[1]) rot_theta = -math.atan2(vec1[1], vec1[0]) rot_matrix = [[math.cos(rot_theta), -math.sin(rot_theta)], [ math.sin(rot_theta), math.cos(rot_theta)]] rot_vec2 = (rot_matrix[0][0] * vec2[0] + rot_matrix[0][1] * vec2[1], rot_matrix[1][0] * vec2[0] + rot_matrix[1][1] * vec2[1]) return math.atan2(rot_vec2[1], rot_vec2[0])
[docs]def is_collinear(p1, p2, p3): """ Returns whether a triplet of points is collinear. is_collinear(Point, Point, Point) -> bool Parameters ---------- p1 : a point (Point) p2 : another point (Point) p3 : yet another point (Point) Attributes ---------- Examples -------- >>> is_collinear(Point((0, 0)), Point((1, 1)), Point((5, 5))) True >>> is_collinear(Point((0, 0)), Point((1, 1)), Point((5, 0))) False """ eps = np.finfo(type(p1[0])).eps return (abs((p2[0] - p1[0]) * (p3[1] - p1[1]) - (p2[1] - p1[1]) * (p3[0] - p1[0])) < EPSILON_SCALER * eps)
[docs]def get_segments_intersect(seg1, seg2): """ Returns the intersection of two segments. get_segments_intersect(LineSegment, LineSegment) -> Point or LineSegment Parameters ---------- seg1 : a segment to check intersection for seg2 : a segment to check intersection for Attributes ---------- Examples -------- >>> seg1 = LineSegment(Point((0, 0)), Point((0, 10))) >>> seg2 = LineSegment(Point((-5, 5)), Point((5, 5))) >>> i = get_segments_intersect(seg1, seg2) >>> isinstance(i, Point) True >>> str(i) '(0.0, 5.0)' >>> seg3 = LineSegment(Point((100, 100)), Point((100, 101))) >>> i = get_segments_intersect(seg2, seg3) """ p1 = seg1.p1 p2 = seg1.p2 p3 = seg2.p1 p4 = seg2.p2 a = p2[0] - p1[0] b = p3[0] - p4[0] c = p2[1] - p1[1] d = p3[1] - p4[1] det = float(a * d - b * c) if det == 0: if seg1 == seg2: return LineSegment(seg1.p1, seg1.p2) else: a = get_segment_point_intersect(seg2, seg1.p1) b = get_segment_point_intersect(seg2, seg1.p2) c = get_segment_point_intersect(seg1, seg2.p1) d = get_segment_point_intersect(seg1, seg2.p2) if a and b: # seg1 in seg2 return LineSegment(seg1.p1, seg1.p2) if c and d: # seg2 in seg1 return LineSegment(seg2.p1, seg2.p2) if (a or b) and (c or d): p1 = a if a else b p2 = c if c else d return LineSegment(p1, p2) return None a_inv = d / det b_inv = -b / det c_inv = -c / det d_inv = a / det m = p3[0] - p1[0] n = p3[1] - p1[1] x = a_inv * m + b_inv * n y = c_inv * m + d_inv * n intersect_exists = 0 <= x <= 1 and 0 <= y <= 1 if not intersect_exists: return None return Point((p1[0] + x * (p2[0] - p1[0]), p1[1] + x * (p2[1] - p1[1])))
[docs]def get_segment_point_intersect(seg, pt): """ Returns the intersection of a segment and point. get_segment_point_intersect(LineSegment, Point) -> Point Parameters ---------- seg : a segment to check intersection for pt : a point to check intersection for Attributes ---------- Examples -------- >>> seg = LineSegment(Point((0, 0)), Point((0, 10))) >>> pt = Point((0, 5)) >>> i = get_segment_point_intersect(seg, pt) >>> str(i) '(0.0, 5.0)' >>> pt2 = Point((5, 5)) >>> get_segment_point_intersect(seg, pt2) """ eps = np.finfo(type(pt[0])).eps if is_collinear(pt, seg.p1, seg.p2): if get_segment_point_dist(seg, pt)[0] < EPSILON_SCALER * eps: return pt else: return None vec1 = (pt[0] - seg.p1[0], pt[1] - seg.p1[1]) vec2 = (seg.p2[0] - seg.p1[0], seg.p2[1] - seg.p1[1]) if abs(vec1[0] * vec2[1] - vec1[1] * vec2[0]) < eps: return pt return None
[docs]def get_polygon_point_intersect(poly, pt): """ Returns the intersection of a polygon and point. get_polygon_point_intersect(Polygon, Point) -> Point Parameters ---------- poly : a polygon to check intersection for pt : a point to check intersection for Attributes ---------- Examples -------- >>> poly = Polygon([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))]) >>> pt = Point((0.5, 0.5)) >>> i = get_polygon_point_intersect(poly, pt) >>> str(i) '(0.5, 0.5)' >>> pt2 = Point((2, 2)) >>> get_polygon_point_intersect(poly, pt2) """ def pt_lies_on_part_boundary(pt, vertices): return [i for i in range(-1, len(vertices) - 1) if get_segment_point_dist(LineSegment( vertices[i], vertices[i + 1]), pt)[0] == 0] != [] ret = None if get_rectangle_point_intersect(poly.bounding_box, pt) is None: # Weed out points that aren't even close return None elif [verts for verts in poly._vertices if pt_lies_on_part_boundary(pt, verts)] != []: ret = pt elif [verts for verts in poly._vertices if _point_in_vertices(pt, verts)] != []: ret = pt if poly._holes != [[]]: if [verts for verts in poly.holes if pt_lies_on_part_boundary(pt, verts)] != []: # pt lies on boundary of hole. pass if [verts for verts in poly.holes if _point_in_vertices(pt, verts)] != []: # pt lines inside a hole. ret = None #raise NotImplementedError, 'Cannot compute containment for polygon with holes' return ret
[docs]def get_rectangle_point_intersect(rect, pt): """ Returns the intersection of a rectangle and point. get_rectangle_point_intersect(Rectangle, Point) -> Point Parameters ---------- rect : a rectangle to check intersection for pt : a point to check intersection for Attributes ---------- Examples -------- >>> rect = Rectangle(0, 0, 5, 5) >>> pt = Point((1, 1)) >>> i = get_rectangle_point_intersect(rect, pt) >>> str(i) '(1.0, 1.0)' >>> pt2 = Point((10, 10)) >>> get_rectangle_point_intersect(rect, pt2) """ if rect.left <= pt[0] <= rect.right and rect.lower <= pt[1] <= rect.upper: return pt return None
[docs]def get_ray_segment_intersect(ray, seg): """ Returns the intersection of a ray and line segment. get_ray_segment_intersect(Ray, Point) -> Point or LineSegment Parameters ---------- ray : a ray to check intersection for seg : a line segment to check intersection for Attributes ---------- Examples -------- >>> ray = Ray(Point((0, 0)), Point((0, 1))) >>> seg = LineSegment(Point((-1, 10)), Point((1, 10))) >>> i = get_ray_segment_intersect(ray, seg) >>> isinstance(i, Point) True >>> str(i) '(0.0, 10.0)' >>> seg2 = LineSegment(Point((10, 10)), Point((10, 11))) >>> get_ray_segment_intersect(ray, seg2) """ d = max(math.hypot(seg.p1[0] - ray.o[0], seg.p1[1] - ray.o[1]), math.hypot(seg.p2[0] - ray.o[0], seg.p2[1] - ray.o[1])) + 1 # Upper bound on origin to segment dist (+1) ratio = d / math.hypot(ray.o[0] - ray.p[0], ray.o[1] - ray.p[1]) ray_seg = LineSegment( ray.o, Point((ray.o[0] + ratio * (ray.p[0] - ray.o[0]), ray.o[1] + ratio * (ray.p[1] - ray.o[1])))) return get_segments_intersect(seg, ray_seg)
[docs]def get_rectangle_rectangle_intersection(r0, r1, checkOverlap=True): """ Returns the intersection between two rectangles. Note: Algorithm assumes the rectangles overlap. checkOverlap=False should be used with extreme caution. get_rectangle_rectangle_intersection(r0, r1) -> Rectangle, Segment, Point or None Parameters ---------- r0 : a Rectangle r1 : a Rectangle Attributes ---------- Examples -------- >>> r0 = Rectangle(0,4,6,9) >>> r1 = Rectangle(4,0,9,7) >>> ri = get_rectangle_rectangle_intersection(r0,r1) >>> ri[:] [4.0, 4.0, 6.0, 7.0] >>> r0 = Rectangle(0,0,4,4) >>> r1 = Rectangle(2,1,6,3) >>> ri = get_rectangle_rectangle_intersection(r0,r1) >>> ri[:] [2.0, 1.0, 4.0, 3.0] >>> r0 = Rectangle(0,0,4,4) >>> r1 = Rectangle(2,1,3,2) >>> ri = get_rectangle_rectangle_intersection(r0,r1) >>> ri[:] == r1[:] True """ if checkOverlap: if not bbcommon(r0, r1): #raise ValueError, "Rectangles do not intersect" return None left = max(r0.left, r1.left) lower = max(r0.lower, r1.lower) right = min(r0.right, r1.right) upper = min(r0.upper, r1.upper) if upper == lower and left == right: return Point((left, lower)) elif upper == lower: return LineSegment(Point((left, lower)), Point((right, lower))) elif left == right: return LineSegment(Point((left, lower)), Point((left, upper))) return Rectangle(left, lower, right, upper)
[docs]def get_polygon_point_dist(poly, pt): """ Returns the distance between a polygon and point. get_polygon_point_dist(Polygon, Point) -> number Parameters ---------- poly : a polygon to compute distance from pt : a point to compute distance from Attributes ---------- Examples -------- >>> poly = Polygon([Point((0, 0)), Point((1, 0)), Point((1, 1)), Point((0, 1))]) >>> pt = Point((2, 0.5)) >>> get_polygon_point_dist(poly, pt) 1.0 >>> pt2 = Point((0.5, 0.5)) >>> get_polygon_point_dist(poly, pt2) 0.0 """ if get_polygon_point_intersect(poly, pt) is not None: return 0.0 part_prox = [] for vertices in poly._vertices: part_prox.append(min([get_segment_point_dist(LineSegment(vertices[i], vertices[i + 1]), pt)[0] for i in range(-1, len(vertices) - 1)])) return min(part_prox)
[docs]def get_points_dist(pt1, pt2): """ Returns the distance between a pair of points. get_points_dist(Point, Point) -> number Parameters ---------- pt1 : a point pt2 : the other point Attributes ---------- Examples -------- >>> get_points_dist(Point((4, 4)), Point((4, 8))) 4.0 >>> get_points_dist(Point((0, 0)), Point((0, 0))) 0.0 """ return math.hypot(pt1[0] - pt2[0], pt1[1] - pt2[1])
[docs]def get_segment_point_dist(seg, pt): """ Returns the distance between a line segment and point and distance along the segment of the closest point on the segment to the point as a ratio of the length of the segment. get_segment_point_dist(LineSegment, Point) -> (number, number) Parameters ---------- seg : a line segment to compute distance from pt : a point to compute distance from Attributes ---------- Examples -------- >>> seg = LineSegment(Point((0, 0)), Point((10, 0))) >>> pt = Point((5, 5)) >>> get_segment_point_dist(seg, pt) (5.0, 0.5) >>> pt2 = Point((0, 0)) >>> get_segment_point_dist(seg, pt2) (0.0, 0.0) """ src_p = seg.p1 dest_p = seg.p2 # Shift line to go through origin points_0 = pt[0] - src_p[0] points_1 = pt[1] - src_p[1] points_2 = 0 points_3 = 0 points_4 = dest_p[0] - src_p[0] points_5 = dest_p[1] - src_p[1] segment_length = get_points_dist(src_p, dest_p) # Meh, robustness...maybe should incorporate this into a more general # approach later if segment_length == 0: return (get_points_dist(pt, src_p), 0) u_x = points_4 / segment_length u_y = points_5 / segment_length inter_x = u_x * u_x * points_0 + u_x * u_y * points_1 inter_y = u_x * u_y * points_0 + u_y * u_y * points_1 src_proj_dist = get_points_dist((0, 0), (inter_x, inter_y)) dest_proj_dist = get_points_dist((inter_x, inter_y), (points_4, points_5)) if src_proj_dist > segment_length or dest_proj_dist > segment_length: src_pt_dist = get_points_dist( (points_2, points_3), (points_0, points_1)) dest_pt_dist = get_points_dist( (points_4, points_5), (points_0, points_1)) if src_pt_dist < dest_pt_dist: return (src_pt_dist, 0) else: return (dest_pt_dist, 1) else: return (get_points_dist((inter_x, inter_y), (points_0, points_1)), src_proj_dist / segment_length)
[docs]def get_point_at_angle_and_dist(ray, angle, dist): """ Returns the point at a distance and angle relative to the origin of a ray. get_point_at_angle_and_dist(Ray, number, number) -> Point Parameters ---------- ray : the ray which the angle and distance are relative to angle : the angle relative to the ray at which the point is located dist : the distance from the ray origin at which the point is located Attributes ---------- Examples -------- >>> ray = Ray(Point((0, 0)), Point((1, 0))) >>> pt = get_point_at_angle_and_dist(ray, math.pi, 1.0) >>> isinstance(pt, Point) True >>> round(pt[0], 8) -1.0 >>> round(pt[1], 8) 0.0 """ v = (ray.p[0] - ray.o[0], ray.p[1] - ray.o[1]) cur_angle = math.atan2(v[1], v[0]) dest_angle = cur_angle + angle return Point((ray.o[0] + dist * math.cos(dest_angle), ray.o[1] + dist * math.sin(dest_angle)))
[docs]def convex_hull(points): """ Returns the convex hull of a set of points. convex_hull(Point list) -> Polygon Parameters ---------- points : a list of points to compute the convex hull for Attributes ---------- Examples -------- >>> points = [Point((0, 0)), Point((4, 4)), Point((4, 0)), Point((3, 1))] >>> convex_hull(points) [(0.0, 0.0), (4.0, 0.0), (4.0, 4.0)] """ points = copy.copy(points) lowest = min(points, key=lambda p: (p[1], p[0])) points.remove(lowest) points.sort(key=lambda p: math.atan2(p[1] - lowest[1], p[0] - lowest[0])) stack = [lowest] def right_turn(p1, p2, p3): # Returns if p1 -> p2 -> p3 forms a 'right turn' vec1 = (p2[0] - p1[0], p2[1] - p1[1]) vec2 = (p3[0] - p2[0], p3[1] - p2[1]) return vec2[0] * vec1[1] - vec2[1] * vec1[0] >= 0 for p in points: stack.append(p) while len(stack) > 3 and right_turn(stack[-3], stack[-2], stack[-1]): stack.pop(-2) return stack
[docs]def is_clockwise(vertices): """ Returns whether a list of points describing a polygon are clockwise or counterclockwise. is_clockwise(Point list) -> bool Parameters ---------- vertices : a list of points that form a single ring Examples -------- >>> is_clockwise([Point((0, 0)), Point((10, 0)), Point((0, 10))]) False >>> is_clockwise([Point((0, 0)), Point((0, 10)), Point((10, 0))]) True >>> v = [(-106.57798, 35.174143999999998), (-106.583412, 35.174141999999996), (-106.58417999999999, 35.174143000000001), (-106.58377999999999, 35.175542999999998), (-106.58287999999999, 35.180543), (-106.58263099999999, 35.181455), (-106.58257999999999, 35.181643000000001), (-106.58198299999999, 35.184615000000001), (-106.58148, 35.187242999999995), (-106.58127999999999, 35.188243), (-106.58138, 35.188243), (-106.58108, 35.189442999999997), (-106.58104, 35.189644000000001), (-106.58028, 35.193442999999995), (-106.580029, 35.194541000000001), (-106.57974399999999, 35.195785999999998), (-106.579475, 35.196961999999999), (-106.57922699999999, 35.198042999999998), (-106.578397, 35.201665999999996), (-106.57827999999999, 35.201642999999997), (-106.57737999999999, 35.201642999999997), (-106.57697999999999, 35.201543000000001), (-106.56436599999999, 35.200311999999997), (-106.56058, 35.199942999999998), (-106.56048, 35.197342999999996), (-106.56048, 35.195842999999996), (-106.56048, 35.194342999999996), (-106.56048, 35.193142999999999), (-106.56048, 35.191873999999999), (-106.56048, 35.191742999999995), (-106.56048, 35.190242999999995), (-106.56037999999999, 35.188642999999999), (-106.56037999999999, 35.187242999999995), (-106.56037999999999, 35.186842999999996), (-106.56037999999999, 35.186552999999996), (-106.56037999999999, 35.185842999999998), (-106.56037999999999, 35.184443000000002), (-106.56037999999999, 35.182943000000002), (-106.56037999999999, 35.181342999999998), (-106.56037999999999, 35.180433000000001), (-106.56037999999999, 35.179943000000002), (-106.56037999999999, 35.178542999999998), (-106.56037999999999, 35.177790999999999), (-106.56037999999999, 35.177143999999998), (-106.56037999999999, 35.175643999999998), (-106.56037999999999, 35.174444000000001), (-106.56037999999999, 35.174043999999995), (-106.560526, 35.174043999999995), (-106.56478, 35.174043999999995), (-106.56627999999999, 35.174143999999998), (-106.566541, 35.174144999999996), (-106.569023, 35.174157000000001), (-106.56917199999999, 35.174157999999998), (-106.56938, 35.174143999999998), (-106.57061499999999, 35.174143999999998), (-106.57097999999999, 35.174143999999998), (-106.57679999999999, 35.174143999999998), (-106.57798, 35.174143999999998)] >>> is_clockwise(v) True """ if len(vertices) < 3: return True area = 0.0 ax, ay = vertices[0] for bx, by in vertices[1:]: area += ax * by - ay * bx ax, ay = bx, by bx, by = vertices[0] area += ax * by - ay * bx return area < 0.0
def ccw(vertices): """ Returns whether a list of points is counterclockwise >>> ccw([Point((0, 0)), Point((10, 0)), Point((0, 10))]) True >>> ccw([Point((0, 0)), Point((0, 10)), Point((10, 0))]) False """ if is_clockwise(vertices): return False else: return True def seg_intersect(a, b, c, d): """ Tests if two segments (a,b) (c,d) intersect >>> a = Point((0,1)) >>> b = Point((0,10)) >>> c = Point((-2,5)) >>> d = Point((2,5)) >>> e = Point((-3,5)) >>> seg_intersect(a, b, c, d) True >>> seg_intersect(a, b, c, e) False """ if ccw([a, c, d]) == ccw([b, c, d]): return False elif ccw([a, b, c]) == ccw([a, b, d]): return False else: return True def _point_in_vertices(pt, vertices): """ HELPER METHOD. DO NOT CALL. Returns whether a point is contained in a polygon specified by a sequence of vertices. _point_in_vertices(Point, Point list) -> bool Parameters ---------- Attributes ---------- Examples -------- >>> _point_in_vertices(Point((1, 1)), [Point((0, 0)), Point((10, 0)), Point((0, 10))]) True """ def neg_ray_intersect(p1, p2, p3): # Returns whether a ray in the negative-x direction from p3 intersects the segment between if not min(p1[1], p2[1]) <= p3[1] <= max(p1[1], p2[1]): return False if p1[1] > p2[1]: vec1 = (p2[0] - p1[0], p2[1] - p1[1]) else: vec1 = (p1[0] - p2[0], p1[1] - p2[1]) vec2 = (p3[0] - p1[0], p3[1] - p1[1]) return vec1[0] * vec2[1] - vec2[0] * vec1[1] >= 0 vert_y_set = set([v[1] for v in vertices]) while pt[1] in vert_y_set: pt = (pt[0], pt[1] + -1e-14 + random.random( ) * 2e-14) # Perturb the location very slightly inters = 0 for i in range(-1, len(vertices) - 1): v1 = vertices[i] v2 = vertices[i + 1] if neg_ray_intersect(v1, v2, pt): inters += 1 return inters % 2 == 1
[docs]def point_touches_rectangle(point, rect): """ Returns True if the point is in the rectangle or touches it's boundary. point_touches_rectangle(point, rect) -> bool Parameters ---------- point : Point or Tuple rect : Rectangle Examples -------- >>> rect = Rectangle(0,0,10,10) >>> a = Point((5,5)) >>> b = Point((10,5)) >>> c = Point((11,11)) >>> point_touches_rectangle(a,rect) 1 >>> point_touches_rectangle(b,rect) 1 >>> point_touches_rectangle(c,rect) 0 """ chflag = 0 if point[0] >= rect.left and point[0] <= rect.right: if point[1] >= rect.lower and point[1] <= rect.upper: chflag = 1 return chflag
[docs]def get_shared_segments(poly1, poly2, bool_ret=False): """ Returns the line segments in common to both polygons. get_shared_segments(poly1, poly2) -> list Parameters ---------- poly1 : a Polygon poly2 : a Polygon Attributes ---------- Examples -------- >>> from libpysal.cg.shapes import Polygon >>> x = [0, 0, 1, 1] >>> y = [0, 1, 1, 0] >>> poly1 = Polygon( list(map(Point,zip(x,y))) ) >>> x = [a+1 for a in x] >>> poly2 = Polygon( list(map(Point,zip(x,y))) ) >>> get_shared_segments(poly1, poly2, bool_ret=True) True """ #get_rectangle_rectangle_intersection inlined for speed. r0 = poly1.bounding_box r1 = poly2.bounding_box wLeft = max(r0.left, r1.left) wLower = max(r0.lower, r1.lower) wRight = min(r0.right, r1.right) wUpper = min(r0.upper, r1.upper) segmentsA = set() common = list() partsA = poly1.parts for part in poly1.parts + [p for p in poly1.holes if p]: if part[0] != part[-1]: # not closed part = part[:] + part[0:1] a = part[0] for b in islice(part, 1, None): # inlining point_touches_rectangle for speed x, y = a # check if point a is in the bounding box intersection if x >= wLeft and x <= wRight and y >= wLower and y <= wUpper: x, y = b # check if point b is in the bounding box intersection if x >= wLeft and x <= wRight and y >= wLower and y <= wUpper: if a > b: segmentsA.add((b, a)) else: segmentsA.add((a, b)) a = b for part in poly2.parts + [p for p in poly2.holes if p]: if part[0] != part[-1]: # not closed part = part[:] + part[0:1] a = part[0] for b in islice(part, 1, None): # inlining point_touches_rectangle for speed x, y = a if x >= wLeft and x <= wRight and y >= wLower and y <= wUpper: x, y = b if x >= wLeft and x <= wRight and y >= wLower and y <= wUpper: if a > b: seg = (b, a) else: seg = (a, b) if seg in segmentsA: common.append(LineSegment(*seg)) if bool_ret: return True a = b if bool_ret: if len(common) > 0: return True else: return False return common
[docs]def distance_matrix(X, p=2.0, threshold=5e7): """Calculate a distance matrix XXX Needs optimization/integration with other weights in pysal Parameters ---------- X : numpy.ndarray An n by k array where n is the number of observations and k is the number of dimensions (2 for x,y). p : float Minkowski p-norm distance metric parameter: 1<=p<=infinity 2: Euclidean distance 1: Manhattan distance threshold : positive integer If (n**2)*32 > threshold use scipy.spatial.distance_matrix instead of working in RAM, this is roughly the amount of RAM (in bytes) that will be used. Returns ------- D : numpy.ndarray An n by m p-norm distance matrix. Examples -------- >>> x, y = [r.flatten() for r in np.indices((3, 3))] >>> data = np.array([x, y]).T >>> d = distance_matrix(data) >>> np.array(d) array([[0. , 1. , 2. , 1. , 1.41421356, 2.23606798, 2. , 2.23606798, 2.82842712], [1. , 0. , 1. , 1.41421356, 1. , 1.41421356, 2.23606798, 2. , 2.23606798], [2. , 1. , 0. , 2.23606798, 1.41421356, 1. , 2.82842712, 2.23606798, 2. ], [1. , 1.41421356, 2.23606798, 0. , 1. , 2. , 1. , 1.41421356, 2.23606798], [1.41421356, 1. , 1.41421356, 1. , 0. , 1. , 1.41421356, 1. , 1.41421356], [2.23606798, 1.41421356, 1. , 2. , 1. , 0. , 2.23606798, 1.41421356, 1. ], [2. , 2.23606798, 2.82842712, 1. , 1.41421356, 2.23606798, 0. , 1. , 2. ], [2.23606798, 2. , 2.23606798, 1.41421356, 1. , 1.41421356, 1. , 0. , 1. ], [2.82842712, 2.23606798, 2. , 2.23606798, 1.41421356, 1. , 2. , 1. , 0. ]]) """ if X.ndim == 1: X.shape = (X.shape[0], 1) if X.ndim > 2: msg = "Should be 2D point coordinates: %s dimensions present." % X.ndim raise TypeError(msg) n, k = X.shape if (n ** 2) * 32 > threshold: return scipy.spatial.distance_matrix(X, X, p) else: M = np.ones((n, n)) D = np.zeros((n, n)) for col in range(k): x = X[:, col] xM = x * M dx = xM - xM.T if p % 2 != 0: dx = np.abs(dx) dx2 = dx ** p D += dx2 D = D ** (1.0 / p) return D