Construction of spherical spline quasi-interpolants based on blossoming
type: Item
instance of: scholarly article
title: Construction of spherical spline quasi-interpolants based on blossoming
zbMATH Open document ID: 1203.65026
author: M. J. Ibáñez
author: A. Lamnii
author: H. Mraoui
author: D. Sbibih
published in: Journal of Computational and Applied Mathematics
publication date: 2010-04-21T00:00:00Z
review text: The authors study the important problem of fitting scattered data on sphere-like surfaces by means of quasi-interpolation methods. First, some Marsden identities for quadratic spherical Powell-Sabin splines are obtained using blossoms (polar forms). Then the functional coefficients of quasi-interpolating splines are computed by evaluating the blossom values of a chosen local approximation operator at certain points. Various families of discrete and differential quasi-interpolants are constructed that are exact on quadratic spherical Bernstein-Bézier polynomials or on the whole space of spherical Powell-Sabin splines. Error bounds for these methods are presented, along with two numerical examples using data from the Marschner-Lobb test function and from ultrasound images of the human heart.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 5696569
zbMATH Keywords: quadratic spherical splines
zbMATH Keywords: quasi-interpolation
zbMATH Keywords: Powell-Sabin triangulation
zbMATH Keywords: Bézier-Bernstein representation
zbMATH Keywords: fitting scattered data
zbMATH Keywords: blossoms
zbMATH Keywords: error bounds
zbMATH Keywords: numerical examples
zbMATH Keywords: Marschner-Lobb test function
zbMATH Keywords: ultrasound images of the human heart
reviewed by: Aurelian Bejancu
MaRDI profile type: Publication
full work available at URL: j.cam.2009.12.010
OpenAlex ID: W2053197486
cites work: Scattered Data Fitting on Surfaces Using Projected Powell-Sabin Splines
cites work: Quadratic spherical spline quasi-interpolants on Powell-Sabin partitions
cites work: Spline approximation by quasiinterpolants
cites work: Local spline approximation methods
cites work: Quasi-interpolation projectors for box splines
cites work: Quadratic spline quasi-interpolants on Powell-Sabin partitions
cites work: Quasi-interpolation by quadratic piecewise polynomials in three variables
cites work: Local quasi-interpolation by cubic C1 splines on type-6 tetrahedral partitions
cites work: Bernstein-Bézier polynomials on spheres and sphere-like surfaces
cites work: Fitting scattered data on sphere-like surfaces using spherical splines
cites work: Modeling sphere-like manifolds with spherical Powell-Sabin B-splines
cites work: Blossoming and knot insertion algorithms for B-spline curves
cites work: Symmetric recursive algorithms for surfaces: B-patches and the de Boor algorithm for polynomials over triangles
cites work: Polar forms and quadratic spline quasi-interpolants on Powell-Sabin partitions
cites work: Near-best quasi-interpolants associated with \(H\)-splines on a three-direction mesh
cites work: Q3839098
cites work: Hybrid Bézier patches on sphere-like surfaces
cites work: Spline Functions on Triangulations
cites work: On the approximation order of splines on spherical triangulations
DOI: 10.1016/J.CAM.2009.12.010
description: scientific article; zbMATH DE number 5696569