The conditions of convexity for Bernstein--Bézier surfaces over triangles

Authors:
Zhi Liu;Jie-qing Tan;Xiao-yan Chen;Li Zhang
Affiliations:
School of Mathematics, Hefei University of Technology, Hefei 230009, China and College of Computer and Information, Hefei University of Technology, Hefei 230009, China;School of Mathematics, Hefei University of Technology, Hefei 230009, China and College of Computer and Information, Hefei University of Technology, Hefei 230009, China;School of Mathematics, Hefei University of Technology, Hefei 230009, China;School of Mathematics, Hefei University of Technology, Hefei 230009, China
Venue:
Computer Aided Geometric Design
Year:
2010

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Abstract

This paper derives a convexity condition for Bernstein-Bezier surfaces defined on triangles. The condition for triangular Bezier surfaces to be convex is a linear sufficient condition on the control points. This condition is stronger than that for B-nets to be weak convex, but weaker than known linear conditions. The inequalities in this condition are symmetric with respect to the three barycentric coordinates. Moreover, geometric interpretations are provided. Example shows that this method is feasible and effective in geometric modeling.