Bézier representation for quadric surface patches

Abstract

Quadric surfaces such as cylinders and spheres play an important role in CAD. This paper describes a new method for creating triangular surface patches on a quadric surface. The surface patches are defined using a restricted type of quadratic Bézier control polyhedron. The control polyhedron and the resulting quadric surface patch satisfy all of the standard properties of parametric Bézier surfaces, including interpolation of the corners of the control polyhedron and the convex hull property. A new technique for creating a C 1 mesh of these quadric surface patches is also introduced.