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Fast Computation of Polynomial Data Points Over Simplicial Face Values

Tareq Hamadneh (), Hassan Al-Zoubi () and Saleh Ali Alomari ()
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Tareq Hamadneh: Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan
Hassan Al-Zoubi: Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman 11733, Jordan
Saleh Ali Alomari: #x2020;Faculty of Science and Information Technology, Jadara University, Irbid, Jordan

Journal of Information & Knowledge Management (JIKM), 2020, vol. 19, issue 01, 1-13

Abstract: Polynomial functions F of degree m have a form in the Bernstein basis defined over l-dimensional simplex W. The Bernstein coefficients exhibit a number of special properties. The function F can be optimised by the smallest and largest Bernstein coefficients (enclosure bounds) over W. By a proper choice of barycentric subdivision steps of W, we prove the inclusion property of Bernstein enclosure bounds. To this end, we provide an algorithm that computes the Bernstein coefficients over subsimplices. These coefficients are collected in an l-dimensional array in the field of computer-aided geometric design. Such a construct is typically classified as a patch. We show that the Bernstein coefficients of F over the faces of a simplex coincide with the coefficients contained in the patch.

Keywords: Bernstein expansion; simplex; computing of range values; inclusion of bounds; face values (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219649220400018

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