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 | References | Similar Articles | Additional Information

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

Email:
mif@math.sintef.no

**J. M. Peña**

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

Email:
jmpena@posta.unizar.es

DOI:
http://dx.doi.org/10.1090/S0025-5718-99-01176-X

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