Parametrization for surface fitting in reverse engineering

Abstract

Given four boundary curves and a set of random points lying on a surface patch, a method for assigning parameters to these points is presented. The algorithm uses various base surfaces to project the points onto these surfaces to recover the parameters based on the surfaces' underlying parametrization. Several techniques for speeding up the time consuming projection process are also presented. A thinning method is introduced as well to select a subset of the points that may have been sampled at a much higher rate than necessary. The thinning is based on the geometry of the base surface and relies on a meaningful geometric tolerance. © 2001 Elsevier Science Ltd.