Distance for degree raising and reduction of triangular Bézier surfaces
type: Item
instance of: scholarly article
title: Distance for degree raising and reduction of triangular Bézier surfaces
zbMATH Open document ID: 1032.65020
DOI: 10.1016/S0377-0427(03)00432-1
author: Abedallah Rababah
published in: Journal of Computational and Applied Mathematics
publication date: 2003-10-15T00:00:00Z
review text: Given a triangular Bézier surface of degree \(n\) with specific Bézier points, two other sets of Bézier points are determined: the first set defines the same surface using a basis of degree \(n+1\) (degree raising), while the second set defines the approximative surface of degree \(n-1\) which minimizes the least-squares distances between the old and the new set of points (degree reduction). The formulas for these sets are obtained using the least-squares method, generalized Bernstein polynomials, \(L_2\) and \(l_2\) measures of distance.
reviewed by: Dana Petcu
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1993214
zbMATH Keywords: triangular Bézier surfaces
zbMATH Keywords: degree raising and reduction
zbMATH Keywords: least-squares methods
MaRDI profile type: Publication
cites work: Q4278198
cites work: Distance for Bézier curves and degree reduction
cites work: Polynomial degree reduction in the \(L_2\)-norm equals best Euclidean approximation of Bézier coefficients
cites work: Least squares approximation of Bézier coefficients provides best degree reduction in the \(L_2\)-norm
cites work: Q5722348
cites work: Q3126370
description: scientific article; zbMATH DE number 1993214