Generalized invariant-geometry conditions for the rational Bézier paths

Abstract

A generalization of Patterson's work on the invariants of the rational Bézier curves, to the case of weight vectors of mixed-sign is presented. It is shown that an additional invariant is required in the general case. The results are viewed from the perspective of the Fundamental Theorem on invariants for Lie groups.

Keywords:

• geometry
• curves
• rational parametrization
• Bézier paths
• invariants

2000 AMS Subject Classifications :

• 14H50
• 14P99
• 14Q05
• 68U05
• 65D17

C.R. Categories :

• I.3.5