A geometrical approach to interpolation on quadric surfaces. (English) Zbl 0813.65040

Jüttler, B.; Dietz, R.

Laurent, Pierre-Jean (ed.) et al., Curves and surfaces in geometric design. Papers from the 2nd international conference on curves and surfaces, held in Chamonix-Mont-Blanc, France, June 10-16, 1993. Wellesley, MA: A K Peters. 251-258 (1994).

Summary: The paper presents a very powerful construction for rational curves and surfaces on quadrics. Based on a result of number theory, a generalization of the stereographic projection is introduced in the case of the unit sphere. With the help of this map, interpolation with spherical rational curves is shown to be a linear problem. The existence of quadratic triangular and biquadratic tensor-product Bézier patches on the sphere interpolating given boundaries is discussed. The final section outlines the extension to arbitrary nondegenerate quadric surfaces.
For the entire collection see [Zbl 0805.00015].

MSC:

65D17

Computer-aided design (modeling of curves and surfaces)

Keywords:

computer-aided design; rational curves and surfaces; stereographic projection; interpolation; tensor-product Bézier patches; quadric surfaces