Curves and Surfaces for CAGD, 5th Edition

16

Composite Surfaces

Tensor product Bézier patches were under development in the early 1960s; at about the same time, people started to think about piecewise surfaces. One of the first publications was de Boor’s work on bicubic splines [136] in 1962. Almost simultaneously, and apparently unaware of de Boor’s work, J. Ferguson [231] implemented piecewise bicubics at Boeing. His method was used extensively, although it had the serious flaw of using only zero corner twist vectors. An excellent account of the early industrial use of piecewise bicubics is the article by G. Peters [462].

16.1 Smoothness and Subdivision

Let x(u, v) and y(u, v) be two patches, defined over [u_I–1, u_I] × [v_J, v_J+1] and [u_I, u_I+1] × [v_J, v_J+1], respectively. They are ...