Fast and Local Fairing of B-Spline Curves and Surfaces

Abstract

The paper proposes a fast fairing algorithm for curves and surfaces. It first defines a base algorithm for fairing curves, which is then extended to the surface case, where the isocurves of the surface are faired. The curve fairing process involves the discrete integration of a pseudo-arc-length parameterization of B-spline curves, with a blending and fitting phase concluding the algorithm. In the core of the fairing method, there is a fairness measure introduced in an earlier paper of the authors. This measure is based on the deviation from an ideal or target curvature. A target curvature is a series of smooth curvature values, generated from the original curve or surface. This curve and surface fairing technique is local and semi-automatic, but the user can also designate the region to be faired. The results are illustrated by a few examples on real-life models.