Bézier nets, convexity and subdivision on higher-dimensional simplices

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• 作者：Goodman ; Tim N.T. ; Peters ; Jö ; rg
• 关键词：Bé ; zier nets ; Convexity ; Subdivision ; Higher-dimensional simplices
• 刊名：Computer Aided Geometric Design
• 出版年：1995
• 出版时间：February, 1995
• 年：1995
• 卷：12
• 期：1
• 页码：53-65
• 全文大小：487 K

文摘

Explicit necessary and sufficient conditions for the convexity of a multivariate Bézier 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 Bézier points on a regular subdivision of a simplex in higher dimensions. This subdivision process preserves the convexity of the Bézier net.