Good degree reduction of Bézier curves using Jacobi polynomials (Q1591965)

The authors use the constrained Jacobi polynomial instead of the constrained Chebyshev polynomial as error function for degree reduction with \(C^1\)-continuity [cf. \textit{M. A. Lachance}, Rocky Mt. J. Math. 21, No. 1, 473-488 (1991; Zbl 0763.65008)]. Although the degree reduction is not the best approximation, it has the advantage that its coefficients are expressed explicitly. The authors also present the uniform error bounds of the constrained Jacobi polynomial and a subdivision scheme for degree reduction within given tolerance. An application of the method to a Bézier curve of degree six is also illustrated.