Institute for Data Analysis and Visualization

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sampling points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on ''local feature size'', the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs.