Cyclides in computer aided geometric design
Computer Aided Geometric Design
On cyclides in geometric modeling
Computer Aided Geometric Design
Constructive P th Algebra -Tool for Design,P rametrisation nd Visualisation
EGUK '02 Proceedings of the 20th UK conference on Eurographics
Conversion of dupin cyclide patches into rational biquadratic bézier form
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces
Computer Aided Geometric Design
The Invariant Functions of the Rational Bi-cubic Bézier Surfaces
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
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Dupin cyclides, their applications in geometric modelling and their parametrization using bi-quadratic patches bounded by lines of curvature, have been investigated in recent years by a number of authors such as Martin, de Pont and Sharrock in 1986, Boehm in 1990, Pratt in 1990, and Degen in 1994. However, no completely reliable and general algorithm for the determination of bi-quadratic cyclide patches has appeared in the literature. This paper presents a new approach that produces any required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic geometric constraints or restrictions. Specifically, if a bi-quadratic parametrization exists for the specified region of the cyclide, then it is correctly determined. Explicit formulae are given for the Bernstein weights and vectors of the parametrizations. The method is neither cyclide specific nor specific to the construction of bi-quadratic rational parametrizations-it may therefore be applied to other surfaces and to higher degree rational constructions.