Bivariate cubic B-splines relative to cross-cut triangulations
type: Item
instance of: scholarly article
title: Bivariate cubic B-splines relative to cross-cut triangulations
zbMATH Open document ID: 0567.41013
author: Charles K. Chui
author: Ren-Hong Wang
published in: Chinese Annals of Mathematics. Series B
publication date: 1983-01-01T00:00:00Z
review text: In this paper we prove that there are no locally supported bivariate \(C^{k-1}\) spline functions of degree k on cross-cut grid partitioned regions with no more than three lines meeting at a common vertex. We also give explicit expressions of bivariate \(C^ 1\) cubic B-spline with smallest local support on cross-cut triangular grid partitioned regions where each vertex is the intersection of three lines. Properly normalized, these B-splines are proved to be uniquely determined and form a partition of unity. Furthermore, the corresponding variation diminishing bivariate spline operators are proved to preserve all linear polynomials of two variables. These facts enable us to give error estimates for approximation by bivariate \(C^ 1\) cubic splines for functions of class C, \(C^ 1\) and \(C^ 2\).
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 3905153
zbMATH Keywords: bivariate spline functions
zbMATH Keywords: B-splines
zbMATH Keywords: error estimates
zbMATH Keywords: cubic splines
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3905153