Closed rational trigonometric curves and surfaces
type: Item
instance of: scholarly article
title: Closed rational trigonometric curves and surfaces
zbMATH Open document ID: 1194.65032
author: Imre Juhász
author: Ágoston Róth
published in: Journal of Computational and Applied Mathematics
publication date: 2010-06-22T00:00:00Z
review text: A general method of obtaining a set of basis functions is presented in order to describe curves as combinations of control points and basis functions. The starting point is in a set of basis functions and a set of corresponding weights. The basis functions are normalized by their weighted sum, obtaining a new set of basis functions, which is called, in this paper, quotient bases. Representatives of quotient bases are the rational Bernstein and B-spline functions. Several properties of rational curves/surfaces are shown to hold for this general case. Further, the rational counterpart of cyclic curves/surfaces is specified. Some applications show how rational trigonometric basis can be used for the exact description of some famous closed curves and surfaces: lemniscate of Bernoulli, Zhukovsky airfoil profile, Boy surface, Dupin cyclide.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 5724558
zbMATH Keywords: cyclic curves/surfaces
zbMATH Keywords: closed curves/surfaces
zbMATH Keywords: rational curves/surfaces
zbMATH Keywords: rational trigonometric polynomials
zbMATH Keywords: quotient basis
zbMATH Keywords: control points
zbMATH Keywords: rational Bernstein and B-spline functions
zbMATH Keywords: lemniscate of Bernoulli
zbMATH Keywords: Zhukovsky airfoil profile
zbMATH Keywords: Boy surface
zbMATH Keywords: Dupin cyclide
MaRDI profile type: Publication
full work available at URL: j.cam.2010.03.009
OpenAlex ID: W1970819854
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DOI: 10.1016/J.CAM.2010.03.009
description: scientific article; zbMATH DE number 5724558