
546 Chapter 11 Curves
n. For small degree n, the number of multiplications can be reduced by computing
intermediate products of powers of t and 1 − t, but this optimization is not con-
sidered at the moment in the operation count. Multiplying a polynomial coefficient
times control point requires three multiplications. Given n + 1 terms, the number of
required multiplications is (n + 1)(n + 3).Therearen + 1 3D terms to sum for a to-
tal of 3n additions. The total operation count for a single B
´
ezier curve evaluation is
n
2
+ 7n + 3 operations.
Using the barycentric form of a B
´
ezier curve, evaluation is possible by using the
de Casteljau algorithm (a good ...