Medial axis of polyhedron1

Here is a simple, non-convex polyhedron.

Here are a few views of its medial axis, rendered as trimmed Bezier patches. Most of the sheets are planar, but four are sections of elliptical cones.

Here are a couple of views of the seams, including the edges of the original polyhedron. Most of the seams are line segments, but three are sections of ellipses. (One of the elliptical segments is too small to see here.)

A summary of the structure of the medial axis:
Sheets 15: 11 planar, 4 conical
Seams 12: 9 linear, 3 ellipsoid segments
Junctions 4 internal

Tim Culver
Last modified: Fri May 12 10:15:55 EDT 2000