I am currently looking for a method for pulling a polyhedron to the xy-plane. This means, that an arbitrary polyhedron (i.e. with holes and concavities) is not simply projected to the xy-plane, but "melts/sinks down" filling holes and lateral concavities, just as if strong gravity pulled it down to the surface. The resulting polyhedron has the same volume and the same projection to the xy-plane as the original.
The goal is to find a way to calculate the "thickness" of the polyhedron in the z-direction for a given x/y coordinate (a function thickness(x, y)), which could be determined easily from the resulting polyhedron.
With a "flattened" polyhedron you have a set of plane equations which make up the "top" of the polyhedron. Then you just have to insert x/y into the appropriate plane equation to get the height, which equals the thickness.
Or is there a better way to achieve this?