Curves and Surfaces for CAGD, 5th Edition

15

Constructing Polynomial Patches

We have discussed the underlying principles of polynomial patches; now it is time to study how they can be used. First applications of tensor product patches go back to General Motors, and Boeing in the United States, and to Rénault and Citröen in France.

15.1 Ruled Surfaces

One of the most elementary surface-building schemes is this: let two Bézier curves b(u) and c(u) be given by their control polygons b₀, …, b_n and c₀, …, c_n, and find a surface r(u, v) that connects them. The simplest such surface will use a linear type of connection; it is called a ruled surface or lofted surface¹ It is given by

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