A geometric-based convection approach of 3-D reconstruction

Surface reconstruction algorithms produce piece-wise linear approximations of a surface S from a finite, sufficiently dense, subset of its points. In this paper, we present a fast algorithm for surface reconstruction from scattered data sets. This algorithm is inspired of an existing numerical convection scheme developed by Zhao, Osher and Fedkiw. Unlike this latter, the result of our algorithm does not depend on the precision of a (rectangular- ) grid. The reconstructed surface is simply a set of oriented faces located into the 3D Delaunay triangulation of the points. It is the result of the evolution of an oriented pseudo-surface. The representation of the evolving pseudo-surface uses an appropriate data structure together with operations that allow deformation and topological changes of it. The presented algorithm can handle complicated topologies and, unlike most of the others schemes, it involves no heuristic. The complexity of that method is that of the 3D Delaunay triangulation of the points. We present results of this algorithm which turned out to be efficient even in presence of noise.