# 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:
else:
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