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Šír, Zbyněk; Gravesen, Jens; Jüttler, Bert

Curves and surfaces represented by polynomial support functions. (English) Zbl 1134.68062

Theor. Comput. Sci. 392, No. 1-3, 141-157 (2008).
Summary: This paper studies shapes (curves and surfaces) which can be described by (piecewise) polynomial support functions. The class of these shapes is closed under convolutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for the approximation of general curves and surfaces by them. Based on the rich theory of spherical spline functions, this leads to computational techniques for rational curves and surfaces with rational offsets, which can deal with shapes without inflections/parabolic points.

Cited in 16 Documents

MSC:

68U07 Computer science aspects of computer-aided design
41A15 Spline approximation
65D07 Numerical computation using splines

Keywords:

polynomial support function; approximation by spherical splines; offset surfaces; convolutions
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References:

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