Subharmonicity and convexity properties of Bernstein polynomials and Bézier nets on triangles

This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It...

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Bibliographic Details
Published in:Computer aided geometric design 1999-05, Vol.16 (4), p.287-300
Main Authors: Lorente-Pardo, J, Sablonniere, P, Serrano-Perez, M C
Format: Article
Language:English
Subjects:
Axial convexity
Bernstein polynomials
Bézier nets
Convexity
Exact sciences and technology
Interpolation
curve fitting
Mathematical methods in physics
Numerical approximation and analysis
Physics
Polyhedral convexity
Subharmonicity
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Summary:This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true.
ISSN:0167-8396
1879-2332
DOI:10.1016/S0167-8396(98)00050-8