Computing minimal distances on polyhedral surfaces

Abstract

The authors implement an algorithm that finds minimal (geodesic) distances on a three-dimensional polyhedral surface. The algorithm is intrinsically parallel, in as much as it deals with all nodes simultaneously, and is simple to implement. Although exponential in complexity, it can be used with a companion gradient-descent surface-flattening algorithm that produces an optimal flattening of a polyhedral surface. Together, these two algorithms have made it possible to obtain accurate flattening of biological surfaces consisting of several thousand triangular faces (monkey visual cortex) by providing a characterization of the distance geometry of these surfaces. The authors propose this approach as a pragmatic solution to characterizing the surface geometry of the complex polyhedral surfaces which are encountered in the cortex of vertebrates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>