On the injectivity of Wachspress and mean value mappings between convex polygons
type: Item
instance of: scholarly article
title: On the injectivity of Wachspress and mean value mappings between convex polygons
zbMATH Open document ID: 1184.65024
author: Jiří Kosinka
author: Michael S. Floater
published in: Advances in Computational Mathematics
publication date: 2010-02-25T00:00:00Z
full work available at URL: http://hdl.handle.net/10852/10495
review text: The injectivity of Wachspress [cf. \textit{E. L. Wachspress}, A rational finite element basis (1975; Zbl 0322.65001)] and mean value mappings between planar convex polygons is investigated in this paper. Wachspress and mean value coordinates represent two generalizations of triangular barycentric coordinates to convex polygons and are used for construction of mappings between planar polygons. Mappings between planar polygons are widely used in image warping for deformation of the curve which is associated with the polygon. Therefore, the problem of injectivity is very important because it is necessary to ensure the same number of self-intersections on the original and deformed curve. The proof that Wachspress mappings are always injective is given and the examples of mean value mappings that are not injective when the polygons have five or more vertices are shown in this paper.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 26B10
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 5675107
zbMATH Keywords: Injectivity
zbMATH Keywords: convex polygons mapping
zbMATH Keywords: barycentric coordinates
zbMATH Keywords: Wachspress coordinates
zbMATH Keywords: mean value coordinates
zbMATH Keywords: self-intersection
zbMATH Keywords: warping
zbMATH Keywords: curve deformation
MaRDI profile type: Publication
OpenAlex ID: W2046338268
Wikidata QID: Q122937740
cites work: Totally positive matrices
cites work: Convexity of rational curves and total positivity
cites work: Global convexity of curves and polygons
cites work: Transfinite mean value interpolation
cites work: Total positivity and convexity preservation
cites work: Mean value coordinates
cites work: A general construction of barycentric coordinates over convex polygons
cites work: Mean value coordinates in 3D
cites work: Pseudo-Harmonic Interpolation on Convex Domains
cites work: Mappings with Non-Vanishing Jacobian
cites work: Generalized Barycentric Coordinates on Irregular Polygons
cites work: A unified, integral construction for coordinates over closed curves
cites work: A rational finite element basis
cites work: Barycentric coordinates for convex polytopes
cites work: Barycentric coordinates for convex sets
DOI: 10.1007/S10444-008-9098-Z
description: scientific article; zbMATH DE number 5675107