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Bézier patches on quadrics. (English) Zbl 0760.68087

NURBS for curve and surface design, Collect. Pap. SIAM Conf. Geom. Des., Tempe/AZ (USA) 1990, 1-14 (1991).
[For the entire collection see Zbl 0746.00030.]
The authors study triangular quadratic Bézier patches and rectangular biquadratic Bézier patches describing parts of quadrics. With geometric considerations they determine integral triangular quadratic Bézier patches lying on parabolic cylinders, on elliptic or hyperbolic paraboloids. All other quadrics then are projective collinear to these surfaces. Therefore the given results may be extended to rational triangular quadratic Bézier patches on arbitrary quadrics. The same is done first for integral rectangular biquadratic Bézier patches and then for rational patches of the same kind.

MSC:

68U07 Computer science aspects of computer-aided design

Citations:

Zbl 0746.00030
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