Degree reduction of Bézier curves by uniform approximation with endpoint interpolation (Q1902434)

The authors adapt the economization method of \textit{C. Lanczos} [Trigonometric interpolation of empirical and analytical functions, J. Math. Physics, Massachusetts Inst. Technol. 17, 123-199 (1938; Zbl 0020.01301)] to Bézier splines. They present two algorithms replacing \(n\)th degree curves by \((n- 1)\)st degree curves, a direct economization and one that produces the best uniform approximation with endpoint interpolation. They give the complete algorithm with proofs, and show comparisons of their methods with that of \textit{M. A. Watkins} and \textit{A. J. Worsey} [Comput. Aided Des. 20, No. 7, 398-405 (1988; Zbl 0658.65014)] as well as examples of multidegree reductions.