BEZIER NETS, CONVEXITY AND SUBDIVISION ON HIGHER-DIMENSIONAL SIMPLICES

Authors
GOODMAN TNT PETERS J
Citation
Tnt. Goodman et J. Peters, BEZIER NETS, CONVEXITY AND SUBDIVISION ON HIGHER-DIMENSIONAL SIMPLICES, Computer aided geometric design, 12(1), 1995, pp. 53-65
Citations number
13
Categorie Soggetti
Computer Sciences",Mathematics,"Computer Science Software Graphycs Programming
Journal title
Computer aided geometric design → ACNP
ISSN journal
01678396
Volume
12
Issue
1
Year of publication
1995
Pages
53 - 65
Database
ISI
SICI code
0167-8396(1995)12:1<53:BNCASO>2.0.ZU;2-W
Abstract
Explicit necessary and sufficient conditions for the convexity of a mu ltivariate Bezier net are given. These are used to show that the Berns tein polynomial of a function on a simplex preserves a strong form of convexity, that takes the generating directions of the simplex into ac count. Moreover, an efficient algorithm is presented for computing the Bezier points on a regular subdivision of a simplex in higher dimensi ons. This subdivision process preserves the convexity of the Bezier ne t.