New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces

Neal Bez; Helmut Bez

doi:10.1016/j.amc.2013.09.039

New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces

Neal Bez, Helmut Bez

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

231 Downloads (Pure)

Abstract

New 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.

Original language	English
Pages (from-to)	475-479
Journal	Applied Mathematics and Computation
Volume	225
DOIs	https://doi.org/10.1016/j.amc.2013.09.039
Publication status	Published - 2013

Access to Document

10.1016/j.amc.2013.09.039

Bez_Applied Mathematics and Computation_2013
NOTICE: 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 in Applied Mathematics and Computation Volume 225, 1 December 2013, Pages 475–479 DOI: http://dx.doi.org/10.1016/j.amc.2013.09.039
Accepted author manuscript, 87.5 KBLicence: None: All rights reserved

Cite this

@article{aa0421d2af244c71be742e74d137ad07,

title = "New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces",

abstract = "New minimal bounds are derived for the magnitudes of the derivatives of the rational B{\'e}zier paths and the rational rectangular B{\'e}zier 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.",

author = "Neal Bez and Helmut Bez",

year = "2013",

doi = "10.1016/j.amc.2013.09.039",

language = "English",

volume = "225",

pages = "475--479",

journal = "Applied Mathematics and Computation ",

issn = "0096-3003",

publisher = "Elsevier",

}

TY - JOUR

T1 - New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces

AU - Bez, Neal

AU - Bez, Helmut

PY - 2013

Y1 - 2013

N2 - New 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.

AB - New 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.

U2 - 10.1016/j.amc.2013.09.039

DO - 10.1016/j.amc.2013.09.039

M3 - Article

SN - 0096-3003

VL - 225

SP - 475

EP - 479

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

New minimal bounds for the derivatives of rational Bezier paths and rational rectangular Bezier surfaces

Abstract

Access to Document

Fingerprint

Cite this