CrossingCount

gives a count of the number of times a ray starting from the point p crosses the closed curve contour.

Details and Options

CrossingCount is also known as crossing number.
CrossingCount is typically used to determine the inclusion of a point in a polygon.

If the closed curve contour is self‐intersecting, CrossingCount[contour,p] gives the minimal count among all rays starting from the point p.

The closed curve contour is typically a collection of line segments Line[{{p₁,p₂},…,{p_n-1,p_n},{p_n,p₁}}] and must lie in a plane.

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Count how many times a ray starting from the point crosses the closed-curve contour:

Count how many times a ray starting from the point crosses the closed-curve contour:

Polygon boundary curves:

Color points based on the crossing count of a point in the given polygon:

WindingCount is an alternate count function:

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