Set of hyperplanes to polyhedron topology

36 Views Asked by At

Problem

By intersection of a set of planes (in three-dimensional space) I constructed an edge-vertex topology structure (see image).

I was able to reconstruct the polygons in this structure by minimum_cycle_basis for each plane (I believe also sometimes called face-cycles). And create a polygon adjacency structure.

The next step would be to reconstruct polyhedra from these polygons. However, I would not know how to.

Attempt

I tried to analyse all cycles in the polygon topology, however many may belong to one of the two polyhedra for each polygon and many do not.

I do know (because all geometry is result of plane intersection) that all polygons and all polyhedra are convex.

Question

How to efficiently find all polyhedra?