Volume of the Intersection of Convex Polyhedra
W. Randolph Franklin (WRF)
Here is how to find the volume (and other mass properties like surface area, moments of inertia, and center of mass) of the intersection of any number of convex polyhedra. It also produces the set of vertices.
- Let F be the combined set of face planes of all the input polyhedra. Each face plane is oriented, so we know the inside side.
- Let P be the set of all intersections of three face planes. P is a superset of the output vertices. For each point p in P, record its position and the three faces that produced it.
- Test each point p in P to against all the face planes f in F. If p is inside every f, then add p to V, the set of actual output vertices.
- If p is exactly on some f, then resolve this degeneracy
with Simulation of Simplicity.
(Details to be added.)
- Compute your desired mass property by applying one of my
local mass property formulae to the elements of V.
(Details to be added.)