Practical Aspects of Bézier Triangles

Bézier triangular patches are not only the most natural generalization of Bézier curves, they also offer a variety of applications. They lend themselves easily to patches on spheres or quadrics, and they may be used for scattered data interpolation. Although rectangular patches are traditionally dominating CAD/CAM, some recent applications of triangular patches are in gaming and animation.

18.1 Rational Bézier Triangles

Following the familiar theme of generating rational curve and surface schemes, we define a rational Bézier triangle to be the projection of a polynomial 4D Bézier triangle. We thus have:


where, as usual, the wi are the weights associated with the control vertices bi. For positive ...

Get Curves and Surfaces for CAGD, 5th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.