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 is visible, the other one is in the back. Same for edge d. Also, in order to determine what color the current pixel should be, each polygon has a flag which can either be 'in' or 'out', depending upon where on the scanline we currently are. Flags are flipped according to the intersection of the scanline with the edges. Now, as we go from a to d (because all edges are intersected with the scanline at that vertex), this happens: the triangle behind triangle 1 and triangle 1 itself are set 'in', then 2 is set in and 1 is 'out', then 3 is set 'in', 2 is 'out' and finally 3 is 'out' and the one behind it is set 'in', which is not the desired behavior because we only need the triangles which are facing us to be set 'in', the rest should be 'out'. How do process the edges in the Active Edge List (a list of edges that are currently intersected by the scanline) so the right polys are set 'in'?

Also, I should mention that the edges are unique, which means there exists an array of edges in the data structure of the icosahedron which are pointed to by edge pointers in each of the triangles.

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