Title: Shape improvement of surfaces

(pdf 1.62 MB)


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.

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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