Variational Design and Fairing of Spline Surfaces

Variational principles have become quite popular in the design of free form surfaces. Among others they are used for fairing purposes. The choice of the ‘right’ fairness functional is a crucial step. There is always a tradeoff between high quality and computational effort. In this paper we present fairness functionals that allow fairing efficiently, i.e., produce high quality surfaces in a reasonable amount of time. These functionals can be considered as simplified thin plate energy functionals for parametric surfaces or as simplified MVC functionals.

[1]  Dieter Lasser,et al.  Grundlagen der geometrischen Datenverarbeitung , 1989 .

[2]  Matthias Eck,et al.  Local Energy Fairing of B-spline Curves , 1993, Geometric Modelling.

[3]  Carlo H. Séquin,et al.  Functional optimization for fair surface design , 1992, SIGGRAPH.

[4]  Carlo H. Séquin,et al.  Scale‐Invariant Minimum‐Cost Curves: Fair and Robust Design Implements , 1993, Comput. Graph. Forum.

[5]  Hans Hagen,et al.  Variational Surface Design and Surface Interrogation , 1993, Comput. Graph. Forum.

[6]  Tony DeRose,et al.  Parametric surface interpolation , 1992, IEEE Computer Graphics and Applications.

[7]  Gerald E. Farin,et al.  Curvature and the fairness of curves and surfaces , 1989, IEEE Computer Graphics and Applications.

[8]  G. Greiner.  Surface construction based on variational principles , 1994 .

[9]  E. T. Y. Lee.  Energy, fairness, and a counterexample , 1990, Comput. Aided Des..

[10]  N. Lott,et al.  Method for fairing B-spline surfaces , 1988 .

[11]  Hans Hagen,et al.  Automatic smoothing with geometric surface patches , 1987, Comput. Aided Geom. Des..