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 ...