Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane

Abstract

This paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows one to reconstruct closed surfaces with arbitrary genus and closed surfaces with disconnected shells.