I understand how the PiP algorithm works on a high level, but I am having a little bit of a hard time understanding this implementation (from here) works, specifically what the math of second part of the if statement is doing. Thanks in advance for any help.
def point_in_polygon(polygon, point):
"""
Raycasting Algorithm to find out whether a point is in a given polygon.
Performs the even-odd-rule Algorithm to find out whether a point is in a given polygon.
This runs in O(n) where n is the number of edges of the polygon.
*
:param polygon: an array representation of the polygon where polygon[i][0] is the x Value of the i-th point and polygon[i][1] is the y Value.
:param point: an array representation of the point where point[0] is its x Value and point[1] is its y Value
:return: whether the point is in the polygon (not on the edge, just turn < into <= and > into >= for that)
"""
# A point is in a polygon if a line from the point to infinity crosses the polygon an odd number of times
odd = False
# For each edge (In this case for each point of the polygon and the previous one)
i = 0
j = len(polygon) - 1
while i < len(polygon) - 1:
i = i + 1
# If a line from the point into infinity crosses this edge
# One point needs to be above, one below our y coordinate
# ...and the edge doesn't cross our Y corrdinate before our x coordinate (but between our x coordinate and infinity)
if (((polygon[i][1] > point[1]) != (polygon[j][1] > point[1])) and (point[0] < (
(polygon[j][0] - polygon[i][0]) * (point[1] - polygon[i][1]) / (polygon[j][1] - polygon[i][1])) +
polygon[i][0])):
# Invert odd
odd = not odd
j = i
# If the number of crossings was odd, the point is in the polygon
return odd
