BEZIER NETS, CONVEXITY AND SUBDIVISION ON HIGHER-DIMENSIONAL SIMPLICES

被引：6

作者：

GOODMAN, TNT

PETERS, J

机构：

[1] PURDUE UNIV,DEPT COMP SCI,W LAFAYETTE,IN 47907

[2] UNIV DUNDEE,DEPT MATH & COMP SCI,DUNDEE DD1 4HN,SCOTLAND

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1995年 / 12卷 / 01期

基金：

美国国家科学基金会;

关键词：

BEZIER NETS; CONVEXITY; SUBDIVISION; HIGHER-DIMENSIONAL SIMPLICES;

D O I：

10.1016/0167-8396(93)E0057-K

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Explicit necessary and sufficient conditions for the convexity of a multivariate Bezier net are given. These are used to show that the Bernstein polynomial of a function on a simplex preserves a strong form of convexity, that takes the generating directions of the simplex into account. Moreover, an efficient algorithm is presented for computing the Bezier points on a regular subdivision of a simplex in higher dimensions. This subdivision process preserves the convexity of the Bezier net.

引用

页码：53 / 65

页数：13

共 13 条

[1] THE CONVEXITY OF BERNSTEIN POLYNOMIALS OVER TRIANGLES [J].

CHANG, GZ ;

DAVIS, PJ .

JOURNAL OF APPROXIMATION THEORY, 1984, 40 (01) :11-28

[2]

Dahmen W., 1988, STUD SCI MATH HUNG, V23, P265

[3]

de Boor C., 1987, GEOMETRIC MODELING

[4]

Goodman T. N. T., 1991, Computer-Aided Geometric Design, V8, P175, DOI 10.1016/0167-8396(91)90043-B

[5]

Goodman T.N.T., 1991, MATH BALKANICA, V5, P129

[6] VARIATION DIMINISHING PROPERTIES OF BERNSTEIN POLYNOMIALS ON TRIANGLES [J].

GOODMAN, TNT .

JOURNAL OF APPROXIMATION THEORY, 1987, 50 (02) :111-126

[7]

GOODMAN TNT, 1989, MATH METHODS CAGD, P249

[8]

Grandine T. A., 1989, Computer-Aided Geometric Design, V6, P181, DOI 10.1016/0167-8396(89)90022-8

[9]

LORENTZ GG, 1953, MATH EXPOSITIONS

[10]

PETERS J, 1994, EVALUATION APPROXIMA

← 1 2 →