Curves and Surfaces for CAGD, 5th Edition

6

Bézier Curve Topics

6.1 Degree Elevation

Suppose we were designing with Bézier curves as described in Section 4.3, trying to use a Bézier curve of degree n. After modifying the polygon a few times, it may turn out that a degree n curve does not possess sufficient flexibility to model the desired shape. One way to proceed in such a situation is to increase the flexibility of the polygon by adding another vertex to it. As a first step, we might want to add another vertex yet leave the shape of the curve unchanged—this corresponds to raising the degree of the Bézier curve by one. We are thus looking for a curve with control vertices b₀⁽¹⁾, …, b⁽¹⁾_n+1 that describes the same curve as the original polygon b₀, …, b_n.

Using the identities (6.24) ...