Let vector u = (Q-P). and let an intersection X on line PQ be of the form:
(1). Then
t > 0 : X is on ray PQ
0 < t < 1 : X is on segment PQ
If t= 0 or 1, P or Q falls on the perimeter of Jerome. I have not yet distinguished these cases as intersections.
Question:What is the rule for drawing segments?
If P or Q falls inside the polygon, it is the endpoint of an orange segment, but should not be included in the intersection list. Also, I calculated intersections in the direction P --> Q, and I don't want to recalculate them from Q, or resort my lists.
Parity: Consider the evaluation of some number k:
(2) GGB: k'= Mod[k,2]
If k is even, k'=0. If k is odd, k'=1. I will call the property even/odd parity. For example, the evaluation
(3) Mod[k, 2] ≟ Mod[m,2]
is true if k, m have the same parity (both even or both odd), and false if their parities differ (one is even and the other odd). If they both go to different parties, I will not measure that quantity, but get out a paper crown and dance.
Then Let k = # intersections on ray PQ, m = # intersections on segment PQ.
Rules:P: If k is odd, P is inside.
Q: If k and m have different parity, Q is inside: