Computing Minimal Distances on Arbitrary Polyhedral Surfaces

摘要

We have implemented an algorithm that makes iterative use of the law of cosines to find all the minimal (geodesic) distances in an arbitrary (that is, non-convex) three-dimensional polyhedral surface. The algorithm is intrinsically parallel, inasmuch as it deals with all nodes simultaneously. It has let us obtain very satisfactory flattening of biological (monkey visual cortex) surfaces consisting of several thousand triangular faces, by providing a full characterization of the distance geometry of these surfaces. (KR)