Nonnegativity of bivariate quadratic functions on a triangle

doi:10.1016/0167-8396(92)90017-J

Computer Aided Geometric Design

Volume 9, Issue 3, August 1992, Pages 195-205

https://doi.org/10.1016/0167-8396(92)90017-J Get rights and content

Abstract

A necessary and sufficient condition for the nonnegativity of a bivariate quadratic defined on a triangle is presented in terms of the Bernstein-Bézier form of the function.

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Citation Excerpt :
Piah et al. [11] have discussed the problem of positivity preserving for scattered data interpolation. Nadler [10], Chang and Sederberg [5] have also discussed the problem of nonnegative interpolation. They have considered nonnegative data arranged over a triangular mesh and have interpolated each triangular patch using a bivariate quadratic function.
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Nonnegativity of bivariate quadratic functions on a triangle

Abstract

J. Approx. Theory

Computer Aided Geometric Design

Computer Aided Geometric Design

Linear Algebra Appl.

Computer Aided Geometric Design