Abstract
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.
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Floater, M.S., Peña, J. Tensor-product monotonicity preservation. Advances in Computational Mathematics 9, 353–362 (1998). https://doi.org/10.1023/A:1018906027191
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DOI: https://doi.org/10.1023/A:1018906027191