Projective Transformations of the Parameter of a Bernstein-Bézier Curve

Abstract

The definitions of polynomial and rational Bernstein-Bézier curves are reviewed and extended to include homogeneous parametrizations. Then the effects of a projective transformation of the parameter space are described in terms of a group representation. This representation is used to answer the following questions: (1) If the control points are held fixed, when do two different sets of weights determine the same rational curve? (2) How do we find the control points for a subdivision of the original curve?. © 1985, ACM. All rights reserved.