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 non-uniform density. Excluding the initial data points, any other previous information is not used (as, for example, the topological relations amongst the points or the normal surface at the data points). The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows to reconstruct closed surfaces with any genus and closed surfaces with disconnected