# CrossingCount

CrossingCount[contour,p]

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

# Details • 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 selfintersecting, 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},,{pn-1,pn},{pn,p1}}] and must lie in a plane.

# Examples

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## Basic Examples(1)

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

## Scope(3)

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

Polygon boundary curves:

Polygons with GeoGridPosition:

## Applications(1)

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

## Properties & Relations(1)

WindingCount is an alternate count function:

Introduced in 2019
(12.0)