Efficient evaluation of multivariate polynomials
type: Item
instance of: scholarly article
title: Efficient evaluation of multivariate polynomials
zbMATH Open document ID: 0606.65007
DOI: 10.1016/0167-8396(86)90018-X
author: Wolfgang Volk
author: Larry L. Schumaker
published in: Computer Aided Geometric Design
publication date: 1986-01-01T00:00:00Z
review text: The authors give an algorithm to evaluate a polynomial of total degree d defined on a triangle T in the plane, \[ p(r,s,t)=\sum^{d}_{i=0}\sum^{i}_{j=0}c_{d-i,i-j,j}\cdot r^{d- i}s^{i-j}t^ j, \] where \(c_{d-i,i-j,j}=(d!/(d-i)!(i-j)!j!)b_{d- i,i-j,j}\), \(0\leq j\leq i\), \(0\leq i\leq d\), and (r,s,t) are the barycentric coordinates of each point in T, and \(b_{ijk}\) are the coefficients in the algorithm of de Casteljau. This algorithm is significantly faster than de Casteljau.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3980352
zbMATH Keywords: de Casteljau algorithm
zbMATH Keywords: data fitting
zbMATH Keywords: Bernstein-Bézier methods
zbMATH Keywords: surfaces
zbMATH Keywords: polynomial evaluation
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
cites work: A survey of curve and surface methods in CAGD
cites work: Q3765102
full work available at URL: 0167-8396(86)90018-x
OpenAlex ID: W2074832341
description: scientific article; zbMATH DE number 3980352