[mikhailfranco]

To answer the 'Call for comment' about intersecting complex shapes... one simple, fast, general, approximate, discrete method is to use OpenGL to get your GPU to do it for you. Just render the shapes into an off-screen framebuffer, using appropriate logic ops or stencil planes, then read back the final buffer to get a bitmask of the possible positions. To reduce to one estimate of position, find the centroid of the largest contiguous pixel group (flood-fill different seed ids; histogram pixels; select region id with highest count).