Curves and Surfaces for CAGD, 5th Edition

14

Tensor Product Patches

The first person to consider this class of surfaces for design purposes was probably de Casteljau, who investigated them between 1959 and 1963. The popularity of this type of surface is, however, due to the work of Bézier only slightly later, as documented in Chapter 1. Initially, Bézier patches were only used to approximate a given surface. It took some time for people to realize that any B-spline surface can also be written in piecewise Bézier form.

We will use the example of Bézier patches to demonstrate the tensor product approach to surface patches. Once that principle is developed, it will be trivial to generalize other curve schemes to tensor product surfaces.

14.1 Bilinear Interpolation

In Section 3.1, we studied ...