PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
type: Item
instance of: scholarly article
title: PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
zbMATH Open document ID: 1215.65032
author: Sumit K. Garg
published in: Journal of Computational and Applied Mathematics
publication date: 2010-11-30T00:00:00Z
review text: PDE surfaces result as a solution of partial differential equations (PDEs). In this article, two general PDEs with constant coefficients of second-order and fourth-order are investigated to create harmonic and biharmonic triangular Bézier surfaces with prescribed set of control points. It is shown that two lines of control points must be given for a harmonic triangular Bézier surface and four lines of control points must be given for biharmonic triangular Bézier surface. Moreover, a second-order and a fourth-order isotropic operator is studied and introduced to overcome the non-isotropy of the harmonic and the biharmonic equations over triangular Bézier surfaces. The method of modelling PDE triangular Bézier surfaces suggested in this article is useful in geometric modelling and computer graphics for creating smooth surfaces by prescribed a set of control points. The results can be used in various physical application areas, too.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 5821385
zbMATH Keywords: PDE surface
zbMATH Keywords: Bézier surface
zbMATH Keywords: rectangular Bézier surface
zbMATH Keywords: triangular Bézier surface
zbMATH Keywords: harmonic surface
zbMATH Keywords: biharmonic surface
zbMATH Keywords: isotropic surface
zbMATH Keywords: Laplacian operator
zbMATH Keywords: bi-Laplacian operator
MaRDI profile type: Publication
full work available at URL: j.cam.2010.07.020
OpenAlex ID: W2059732884
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DOI: 10.1016/J.CAM.2010.07.020
description: scientific article; zbMATH DE number 5821385