Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm

M. Neamtu

doi:10.1016/B978-0-12-438660-0.50056-X

Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm

M. Neamtu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Some possible alternatives to the “classical” subdivision of Bernstein polynomials (i.e., based on utilizing the well known de Casteljau algorithm), are sketched. Our schemes have “asymptotically” lower computational complexities and can be carried out such that the resulting “control points” take the precise values of the polynomial surface being subdivided. For one particular approach, the so called discrete Bernstein basis polynomials are introduced.

Original language	English
Title of host publication	Curves and Surfaces
Editors	Pierre-Jean Laurent, Alain Le Méhauté, Larry L. Schumaker
Publisher	Academic Press
Pages	359-362
Number of pages	4
ISBN (Print)	978-0-12-438660-0
DOIs	https://doi.org/10.1016/B978-0-12-438660-0.50056-X
Publication status	Published - 1991

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10.1016/B978-0-12-438660-0.50056-X

1 Report

Subdividing multivariate polynomials over simplices in Bernstein-Bézier form without de Casteljau algorithm
Neamtu, M., 1990, Enschede: University of Twente. 6 p. (Memorandum; no. 889)
Research output: Book/Report › Report › Professional

Cite this

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title = "Subdividing Multivariate Polynomials Over Simplices in Bernstein-B{\'e}zier Form Without de Casteljau Algorithm",

abstract = "Some possible alternatives to the “classical” subdivision of Bernstein polynomials (i.e., based on utilizing the well known de Casteljau algorithm), are sketched. Our schemes have “asymptotically” lower computational complexities and can be carried out such that the resulting “control points” take the precise values of the polynomial surface being subdivided. For one particular approach, the so called discrete Bernstein basis polynomials are introduced.",

author = "M. Neamtu",

year = "1991",

doi = "10.1016/B978-0-12-438660-0.50056-X",

language = "English",

isbn = "978-0-12-438660-0",

pages = "359--362",

editor = "Pierre-Jean Laurent and \{Le M{\'e}haut{\'e}\}, Alain and Schumaker, \{Larry L.\}",

booktitle = "Curves and Surfaces",

publisher = "Academic Press",

address = "United States",

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T1 - Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm

AU - Neamtu, M.

PY - 1991

Y1 - 1991

N2 - Some possible alternatives to the “classical” subdivision of Bernstein polynomials (i.e., based on utilizing the well known de Casteljau algorithm), are sketched. Our schemes have “asymptotically” lower computational complexities and can be carried out such that the resulting “control points” take the precise values of the polynomial surface being subdivided. For one particular approach, the so called discrete Bernstein basis polynomials are introduced.

AB - Some possible alternatives to the “classical” subdivision of Bernstein polynomials (i.e., based on utilizing the well known de Casteljau algorithm), are sketched. Our schemes have “asymptotically” lower computational complexities and can be carried out such that the resulting “control points” take the precise values of the polynomial surface being subdivided. For one particular approach, the so called discrete Bernstein basis polynomials are introduced.

U2 - 10.1016/B978-0-12-438660-0.50056-X

DO - 10.1016/B978-0-12-438660-0.50056-X

M3 - Conference contribution

SN - 978-0-12-438660-0

SP - 359

EP - 362

BT - Curves and Surfaces

A2 - Laurent, Pierre-Jean

A2 - Le Méhauté, Alain

A2 - Schumaker, Larry L.

PB - Academic Press

ER -

Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm

Abstract

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Research output

Subdividing multivariate polynomials over simplices in Bernstein-Bézier form without de Casteljau algorithm

Cite this