Composing Bézier simplexes
Author:
Open Access
- 1 July 1988
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 7 (3) , 198-221
Abstract
This paper describes two algorithms for solving the following general problem: Given two polynomial maps f: R n ↦ R N and S R N ↦ R d in Bézier simplex form, find the composition map S = S ° f in Bézier simplex form (typically, n ≤ N ≤ d ≤ 3). One algorithm is more appropriate for machine implementation, while the other provides somewhat more geometric intuition. The composition algorithms can be applied to the following problems: evaluation, subdivision, and polynomial reparameterization of Bézier simplexes; joining Bézier curves with geometric continuity of arbitrary order; and the determination of the control nets of Bézier curves and triangular Bézier surface patches after they have undergone free-form deformations.Keywords
This publication has 4 references indexed in Scilit:
- Free-form deformation of solid geometric models1986
- Triangular Bernstein-Bézier patchesComputer Aided Geometric Design, 1986
- A survey of curve and surface methods in CAGDComputer Aided Geometric Design, 1984
- Using degenerate Bézier triangles and tetrahedra to subdivide Bézier curvesComputer-Aided Design, 1982