Tensor-product monotonicity preservation

: This paper studies systems of tensor-product functions for which the functions they span are monotonic in any direction when their control nets are monotonic in that direction. It is shown that Bernstein polynomials and B-splines have this property but that totally positive systems in general, such as certain trigonometric and rational bases, do not. AMS subject classification: 65D17, 41A15. Key words: Monotonicity, shape preservation, tensor-product surfaces, Bernstein polynomials, B-splines, trigonometric polynomials, control net.

• Type: Journal
• Year: 1998
• Where: ADCM
• Authors: Michael S. Floater, Juan Manuel Peña
• Keywords: ADCM 1998, Bernstein Polynomials, Paper Studies Systems, Tensor-product Functions