Title: Shape improvement of surfaces

(pdf 1.62 MB)

Abstract:

An automatic and local fairing algorithm for bicubic B-spline surfaces is proposed. A local fairness criterion selects the knot, where the spline surface has to be faired. A fairing step is than applied, which locally modifies the control net by a constrained least-squares approximation. It consists of increasing locally the smoothness of the surface from C^2 to C^3. Some extensions of this method are also presented, which show how to build further methods by the same basic fairing principle.

Reference:
Stefanie Hahmann,
Shape improvement of surfaces,
in G. Farin, H. Bieri, G. Brunett, T. DeRose (Eds.), Geometric Modelling,
Computing [Suppl], Vol. 13, Springer-Verlag, 1998, pp. 135-152, (1998)

Example 1:

Unfair surface,
225 control points.

Faired surface after 500 iterations.

Example 2:

Unfair surface,
400 control points.

Faired surface after 5000 iterations.

Example 3:

Unfair surface,
525 control points.

Faired surface after 6000 iterations.

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