Point in a self-intersecting / complex polygon?

The algorithm described will work fine, cause if you take a look closer at it, you see that it's just the number of crossings that counts. If we start in either "sub-polygon" of the "8" we will cross in worst case the edges 3 times, normally once. And it's true that it's inside.

Otherwise it's outside.

I'm not sure if this is the optimal solution; but the ray-casting algorithm works for any convex polygon. Any polygon can be decomposed into triangles, which are convex. (The double box is not a convex polygon, since if you connect two of the vertices with a line segment, in some cases you will cross over the center edge.) So, to clarify: first decompose the polygon into triangles, then use ray-casting to determine whether the point is inside a triangle.

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