The conditions of convexity for Bernstein-Bézier surfaces over triangles

DOI10.1016/j.cagd.2010.05.004zbMath1210.65043OpenAlexW1988474928MaRDI QIDQ631039

Xiao-yan Chen, Zhi Liu, Jie-qing Tan, Li Zhang

Publication date: 22 March 2011

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2010.05.004

zbMATH Keywords

control pointsgeometric modelingconvexity conditiontriangular Bézier surfaceB-netsBernstein-Bézier surfaces

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (2)

Convexity-preserving scattered data interpolation scheme using side-vertex method ⋮ Convexity preserving splines over triangulations

Cites Work

• The convexity of Bernstein polynomials over triangles
• Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces
• An improved condition for the convexity of Bernstein-Bézier surfaces over triangles
• A new proof for the convexity of the Bernstein-Bézier surfaces over triangles
• Convexity preserving interpolation
• The invariance of weak convexity conditions of \(B\)-nets with respect to subdivision
• Linear convexity conditions for rectangular and triangular Bernstein-Bézier surfaces
• Convex preserving scattered data interpolation using bivariate \(C^1\) cubic splines
• Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm \(L_{2}\)
• On the existence of biharmonic tensor-product Bézier surface patches
• On the convexity of parametric Bézier triangular surfaces
• Unnamed Item

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