Convexity-preserving fairing

Abstract This paper develops a two-stage automatic algorithm for fairing C2-continuous cubic parametric B-splines under convexity, tolerance and end constraints. The first stage is a global procedure, yielding a C2 cubic B-spline which satisfies the local-convexity, local-tolerance and end constraints imposed by the designer. The second stage is a local finefairing procedure employing an iterative knot-removal knotreinsertion technique, which adopts the curvature-slope discontinuity as the fairness measure of a C2 spline. This procedure preserves the convexity and end properties of the output of the first stage and, moreover, it embodies a globaltolerance constraint. The performance of the algorithm is discussed for four data sets.

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