Convexity-preserving fairing

This paper develops a two-stage automatic algorithm for fairing C-2-continuous cubic parametric B-splines under convexity, tolerance and end constraints. The first stage is a global procedure, yielding a C-2 cubic B-spline which satisfies the local-convexity, local-tolerance and end constraints imposed by the designer. The second stage is a local fine-fairing procedure employing an iterative knot-removal knot-reinsertion technique, which adopts the curvature-slope discontinuity as the fairness measure of a C-2 spline. This procedure preserves the convexity and end properties of the output of the first stage and, moreover, it embodies a global-tolerance constraint. The performance of the algorithm is discussed for four data sets. Copyright (C) 1996 Elsevier Science Ltd