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Scanline filling of polygons that share edges and vertices

In this picture (a perspective projection of an icosahedron), the scanline (red) intersects that vertex at the top. In an icosahedron each edge belongs to two triangles. From edge a, only one triangle ...
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Greiner-Hormann clipping problem

I have a set of planar polygons in 3D space defined by their vertices in counterclockwise order. Let's define the 'positive face' as being the face of the 3D polygon such as when observed, the ...