Induced rational parametrisations of special curves

Rational parametrisation of curves and surfaces is a defacto industry standard for computer graphics and shape representation. While it is well known that rational parametrisations of the conic sections exist, and their explicit forms are used in geometric modeling (Hoschek and Lasser, 1993), other classical curves for which rational parametrisations may be determined have received less attention in the literature. This paper presents an elegant method for the explicit computation of rational parametrisations for many 'special' or famous curves. The technique 'induces' a parametrisation of a 'higher' or 'target' curve from a 'primitive' or 'source' curve for which rational parametrisations are known - e.g., the straight line and the conic sections. A number of examples and modeling applications are given.

Keywords:

• Computational Geometry
• Object Modeling