Affiliation:
1. Univ. of Washington, Seattle
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Graphics and Computer-Aided Design
Reference12 articles.
1. General distortion of an ensemble of biparametric surfaces;B~ZIER P;Comput.-Aided Des.,1978
2. A survey of curve and surface methods in CAGD
3. Triangular Bernstein-Bézier patches
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