I am interested in finding software to compute the exact medial axis (or your term of choice!) of a 3D polyhedra. I imagine the output would be a list of triangular faces, possibly edges, and vertices, representing the junctions, sheets, and seams of the medial surface. Ideally I would like something that could handle all polyhedra, including concave shapes (at which point triangular faces are not sufficient) but I would be very happy to find something that could handle convex polyhedra.
Let me tell first about the softwares I am aware of:
There are various "approximate" methods available that assume that the shape I am transforming is a complicated surface and that by scattering dense points over the surface.
One of these methods is the powercrust software provided by http://www.cs.ucdavis.edu/~amenta/powercrust.html
(Although how points files should be defined for this software so as to handle concave cases correctly, I am not sure)
Another approximate method is integrated into Tight Cocone (http://www.cse.ohio-state.edu/~tamaldey/cocone.html). This, again, densely distributes points on a surface and uses a voronoi diagram to converge to the medial axis. There is an "improved medial axis for CAD models" version, that takes advantage of the fact that the surface is exactly known. However, this improved model is not incorporated into the distributed code.
There is a Matlab Code, for example, "skeleton in 3D", by Gianni Schena (http://www.mathworks.com/matlabcentral/fileexchange/4917-skeleton-in-3d) that use a couple simple methods based on distance transform. Still approximate.
Apparently approximate methods can suffer from certain types of numerical instability, giving the surface "spikes". Also, they generate a very large data structure of faces and vertices. What I want is an exact representation of the medial axis/surface of a polyhedron (like a cube) which should have a very simple and small data structure.
In [2004, Culver, Keyser, and Manocha, Exact Computation of the Medial Axis of a Polyhedron], a method for computing the exact medial axis of a polyhedron was published. However, I cannot find any software where somebody has actually implemented this method.
Anybody know anything, or have something to add to my little foray into 3D medial surface softwares?
