Catmull-Clark surface fitting for reverse engineering applications

Abstract

Reverse engineering is an approach for reconstructing a computer model from physical object through dimensional measurement and surface modelling. Various mathematical models have be discussed for the representation of free form surfaces in the context of reverse engineering applications. Most of the existing algorithms are, however, mainly developed for fitting isolated surfaces and one must smoothly connect these surfaces afterwards. This paper presents a procedure for simultaneously fitting smoothly connected multiple surfaces from point clouds with arbitrary topology. The final fitted surfaces are represented as Catmull-Clark surfaces, a network of smoothly connected bicubic B-spline surfaces with a finite number of B-spline subdivision surface patches next to extraordinary corner points. The final fitted surfaces are perfect G2 continuous across all surface boundaries except at a finite number of extraordinary points where G1 continuity is obtained. The algorithm is purely a linear least squares fitting procedure without any constraints.