CrossingPolygon
CrossingPolygon[{p1,p2,…,pn}]
gives a Polygon representing all points for which a ray from the point in any direction in the plane crosses the line segments {p1,p2},…,{pn-1,pn},{pn,p1} an odd number of times.
CrossingPolygon[{{p11,p12,…},{p21,p22,…},…}]
gives a Polygon from the line segments {p11,p12},…,{p21,p22},….
Details and Options


- CrossingPolygon is also known as even–odd filling rule.
- A point is in CrossingPolygon if a ray starting at that point to infinity in any direction will cross the boundary curves an odd number of times. The number of ray crossings is given by CrossingCount.
- The number of ray crossings is given below for each region.
- CrossingPolygon is used to define a polygon from possibly self-intersecting closed curves.
- CrossingPolygon[{p1,p2,…,pn}] is effectively equivalent to Polygon[{p1,p2,…,pn}].
- CrossingPolygon[{{p11,p12,…},{p21,p22,…},…}] is, in general, different than Polygon[{{p11,p12,…},{p21,p22,…},…}] since the former will use the ray crossing rule for all closed curves {pi1,pi2,…}. The latter is the union of polygons Polygon[{pi1,pi2,…}].
- The points pi can have any length but must all lie in a plane.
- CrossingPolygon takes the same options as Polygon.
-
VertexColors Automatic vertex colors to be interpolated VertexNormals Automatic effective vertex normals for shading VertexTextureCoordinates None coordinates for textures



List of all options

Examples
open allclose allBasic Examples (2)
Scope (11)
Basic Uses (5)
Self-Intersecting Contours (3)
CrossingPolygon works on self-intersecting contours:
Multiple Contours (3)
Options (6)
VertexNormals (1)
VertexTextureCoordinates (3)
Texture mapping with 2D polygons:
Texture mapping with 3D polygons:
Repeat a texture by using non-unified texture coordinate values:
Texture mapping is preceded by VertexColors:
Applications (3)
Properties & Relations (3)
CrossingPolygon is effectively equivalent to Polygon for a single contour:
CrossingPolygon is, in general, different than Polygon for multiple intersecting contours:
WindingPolygon is an alternate polygon constructor:
Possible Issues (1)
The points in CrossingPolygon must all lie on a plane:

Text
Wolfram Research (2019), CrossingPolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/CrossingPolygon.html.
CMS
Wolfram Language. 2019. "CrossingPolygon." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CrossingPolygon.html.
APA
Wolfram Language. (2019). CrossingPolygon. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CrossingPolygon.html