Affiliation:
1. Purdue Univ., West Lafayette, IN
Abstract
Polynomials of the total degree
d
in
m
variables have a geometrically intuitive representation in the Bernstein-Be´zier form defined over an
m
-dimensional simplex. The two algorithms given in this article evaluate the Bernstein-Be´zier form on a large number of points corresponding to a regular partition of the simplicial domain. The first algorithm is an adaptation of isoparametric evaluation. The second is a subdivision algorithm. In contrast to de Casteljau's algorithm, both algorithms have a cost of evaluation per point that is linear in the degree regardless of the number of variables. To demonstrate practicality, implementations of both algorithms on a triangular domain are compared with generic implementations of six algorithms in the literature.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference26 articles.
1. BOE~M W. 1983. Subdividing multivariato splinog. Comput. Aided Des_ 15 6 (Nov. L 345-352. BOE~M W. 1983. Subdividing multivariato splinog. Comput. Aided Des_ 15 6 (Nov. L 345-352.
2. A survey of curve and surface methods in CAGD
3. DE BOOR C. 1987. B-form basics In Geometrzc Modehng: Appl~catzons and New Trends G Farin Ed. SIAM Philadelphia Pa. DE BOOR C. 1987. B-form basics In Geometrzc Modehng: Appl~catzons and New Trends G Farin Ed. SIAM Philadelphia Pa.
4. DE BooR C. 1978. A Practical Guide to Spl~nes. Applied Mathematical Sciences. Vol. 27. Springer New York. DE BooR C. 1978. A Practical Guide to Spl~nes. Applied Mathematical Sciences. Vol. 27. Springer New York.
5. DE CASTELJAU F. 1959. Courbes et surfaces ~ p61es. Andr~ Cztroen Automobzles. Paris 1963. CONTE S. D. AND DE BOOR C. 1980. Elementary Numerzcal Analyszs. 3rd ed. McGraw-Hill New York DE CASTELJAU F. 1959. Courbes et surfaces ~ p61es. Andr~ Cztroen Automobzles. Paris 1963. CONTE S. D. AND DE BOOR C. 1980. Elementary Numerzcal Analyszs. 3rd ed. McGraw-Hill New York
Cited by
18 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献