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Mathematics of Computation

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Monotonicity preservation on triangles

Authors: Michael S. Floater and J. M. Peña
Journal: Math. Comp. 69 (2000), 1505-1519
MSC (1991): Primary 41A10, 65D17; Secondary 41A63
Published electronically: May 20, 1999
MathSciNet review: 1677482
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Abstract: It is well known that Bernstein polynomials on triangles preserve monotonicity. In this paper we define and study three kinds of monotonicity preservation of systems of bivariate functions on a triangle. We characterize and compare several of these systems and derive some geometric applications.

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Additional Information

Michael S. Floater
Affiliation: SINTEF Applied Mathematics, P.O. Box 124 Blindern, 0314 Oslo, NORWAY

J. M. Peña
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio de Mate- máticas, Planta 1a, 50009 Zaragoza, SPAIN

Keywords: Monotonicity, shape preservation, bivariate Bernstein polynomials, control net
Received by editor(s): May 27, 1997
Received by editor(s) in revised form: December 7, 1998
Published electronically: May 20, 1999
Additional Notes: The authors were supported in part by the EU project CHRX-CT94-0522.
Article copyright: © Copyright 2000 American Mathematical Society