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New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces
This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at http://dx.doi.org/10.1016/j.amc.2013.09.039New minimal bounds are derived for the magnitudes of the derivatives of the rational Bézier paths and the rational rectangular Bézier surface
patches of arbitrary degree, which improve previous work of this type in many
cases. Moreover, our new bounds are explicitly given by simple and closed-form expressions. An important advantage of the closed-form expressions is
that they allow us to prove that our bounds are sharp under certain well-
defined conditions. Some numerical examples, highlighting the potential of
the new bounds in providing improved estimates, are given in an appendix