Polyhedral approximation of 3-D objects without holes

Abstract An efficient way of building a polyhedral approximation of a set of points in 3-D space is described. The points are the vertices of a planar graph embedded in a surface of genus 0 and are obtained by a laser range finder. The technique presented here is a generalization of an existing algorithm (R. Duda and P. Hart, Pattern Classification and Scene Analysis, Wiley-Interscience, New York 1973) for the polygonal approximation of a simple curve in 2-D space.