×

Rational patches on quadric surfaces. (English) Zbl 0814.65020

The authors apply the generalized stereographic projection introduced in an earlier paper [Comput. Aided Geom. Des. 10, No. 3-4, 211-229 (1993; Zbl 0781.65009)] and give explicit formulas for the construction of Bézier patches of degree (2,2) and (2,4) on the sphere and the hyperbolic paraboloid, as well as B-spline curves and surface patches on these surfaces. The (2,4) Bézier patches are needed if one desires the freedom to chose the vertices of the patches arbitrarily on the patch. Any other nondegenerate quadric can be mapped onto one of the standard surfaces by diagonalizing the matrix giving the quadric in homogeneous coordinates.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 0781.65009
PDFBibTeX XMLCite
Full Text: DOI