Energy, fairness, and a counterexample
Computer-Aided Design
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The NURBS book (2nd ed.)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Local Energy Fairing of B-spline Curves
Geometric Modelling, Dagstuhl, Germany, 1993
Hierarchical surface fairing with constraints
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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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.