On scattered data representations using bivariate splines
type: Item
instance of: scholarly article
zbMATH Open document ID: 0970.65014
author: Don Hong
publication date: 2001-10-21T00:00:00Z
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 41-02
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1574924
zbMATH Keywords: bivariate spline
zbMATH Keywords: scattered data representation
zbMATH Keywords: triangulation
zbMATH Keywords: optimal triangulation
zbMATH Keywords: splines on the sphere
zbMATH Keywords: scattered data interpolation
zbMATH Keywords: survey paper
zbMATH Keywords: algorithm
MaRDI profile type: Publication
title: On scattered data representations using bivariate splines
review text: The objective of this survey paper is to present a study of scattered data representations using bivariate polynomial splines. All proofs are omitted.NEWLINENEWLINENEWLINEFirst, results on approximation order of spline spaces over arbitrary triangulations are discussed. In real applications, where the spline degree is required to be low, it is necessary to find an optimal triangulation so that the spline space can achieve the optimal approximation order. The author presents an algorithm to transform an arbitrary triangulation into an optimal triangulation for scattered data representation using quartic \(C^1\) splines.NEWLINENEWLINENEWLINEThen he considers the possibilities of finding optimal triangulations for cubic \(C^1\) splines resp. quadratic \(C^1\) splines. Some interpolation schemes and a stable local basis construction are also presented. Finally, the author describes some results on representing scattered data using splines on sphere and natural splines.NEWLINENEWLINEFor the entire collection see [Zbl 0954.65001].
reviewed by: Manfred Tasche
description: scientific article