"""
Functions for calculating geometry.
"""
from typing import cast
from arcade import PointList
_PRECISION = 2
[docs]def are_polygons_intersecting(poly_a: PointList,
poly_b: PointList) -> bool:
"""
Return True if two polygons intersect.
:param PointList poly_a: List of points that define the first polygon.
:param PointList poly_b: List of points that define the second polygon.
:Returns: True or false depending if polygons intersect
:rtype bool:
"""
for polygon in (poly_a, poly_b):
for i1 in range(len(polygon)):
i2 = (i1 + 1) % len(polygon)
projection_1 = polygon[i1]
projection_2 = polygon[i2]
normal = (projection_2[1] - projection_1[1],
projection_1[0] - projection_2[0])
min_a, max_a, min_b, max_b = (None,) * 4
for poly in poly_a:
projected = normal[0] * poly[0] + normal[1] * poly[1]
if min_a is None or projected < min_a:
min_a = projected
if max_a is None or projected > max_a:
max_a = projected
for poly in poly_b:
projected = normal[0] * poly[0] + normal[1] * poly[1]
if min_b is None or projected < min_b:
min_b = projected
if max_b is None or projected > max_b:
max_b = projected
if cast(float, max_a) <= cast(float, min_b) or cast(float, max_b) <= cast(float, min_a):
return False
return True
# Point in polygon function from https://www.geeksforgeeks.org/how-to-check-if-a-given-point-lies-inside-a-polygon/
# Given three collinear points p, q, r,
# the function checks if point q lies
# on line segment 'pr'
def _on_segment(p: tuple, q: tuple, r: tuple) -> bool:
if ((q[0] <= max(p[0], r[0])) & (q[0] >= min(p[0], r[0])) & (q[1] <= max(p[1], r[1])) & (q[1] >= min(p[1], r[1]))):
return True
return False
# To find orientation of ordered triplet (p, q, r).
# The function returns following values
# 0 --> p, q and r are collinear
# 1 --> Clockwise
# 2 --> Counterclockwise
def _orientation(p: tuple, q: tuple, r: tuple) -> int:
val = (((q[1] - p[1]) * (r[0] - q[0])) - ((q[0] - p[0]) * (r[1] - q[1])))
if val == 0:
return 0
if val > 0:
return 1 # Collinear
else:
return 2 # Clock or counterclock
def _do_intersect(p1, q1, p2, q2):
# Find the four orientations needed for
# general and special cases
o1 = _orientation(p1, q1, p2)
o2 = _orientation(p1, q1, q2)
o3 = _orientation(p2, q2, p1)
o4 = _orientation(p2, q2, q1)
# General case
if (o1 != o2) and (o3 != o4):
return True
# Special Cases
# p1, q1 and p2 are collinear and
# p2 lies on segment p1q1
if (o1 == 0) and (_on_segment(p1, p2, q1)):
return True
# p1, q1 and p2 are collinear and
# q2 lies on segment p1q1
if (o2 == 0) and (_on_segment(p1, q2, q1)):
return True
# p2, q2 and p1 are collinear and
# p1 lies on segment p2q2
if (o3 == 0) and (_on_segment(p2, p1, q2)):
return True
# p2, q2 and q1 are collinear and
# q1 lies on segment p2q2
if (o4 == 0) and (_on_segment(p2, q1, q2)):
return True
return False
# Returns true if the point p lies
# inside the polygon[] with n vertices
[docs]def is_point_in_polygon(x: float, y: float, polygon_point_list) -> bool:
p = x, y
n = len(polygon_point_list)
# There must be at least 3 vertices
# in polygon
if n < 3:
return False
# Create a point for line segment
# from p to infinite
extreme = (10000, p[1])
# To count number of points in polygon
# whose y-coordinate is equal to
# y-coordinate of the point
decrease = 0
count = i = 0
while True:
next_item = (i + 1) % n
if polygon_point_list[i][1] == p[1]:
decrease += 1
# Check if the line segment from 'p' to
# 'extreme' intersects with the line
# segment from 'polygon[i]' to 'polygon[next]'
if (_do_intersect(polygon_point_list[i],
polygon_point_list[next_item],
p, extreme)):
# If the point 'p' is collinear with line
# segment 'i-next', then check if it lies
# on segment. If it lies, return true, otherwise false
if _orientation(polygon_point_list[i], p,
polygon_point_list[next_item]) == 0:
return not _on_segment(polygon_point_list[i], p,
polygon_point_list[next_item])
count += 1
i = next_item
if i == 0:
break
# Reduce the count by decrease amount
# as these points would have been added twice
count -= decrease
# Return true if count is odd, false otherwise
return count % 2 == 1