Control point based exact description of a class of closed curves and surfaces
type: Item
instance of: scholarly article
title: Control point based exact description of a class of closed curves and surfaces
zbMATH Open document ID: 1244.65027
author: Ágoston Róth
author: Imre Juhász
published in: Computer Aided Geometric Design
publication date: 2011-03-22T00:00:00Z
review text: The authors consider closed parametric curves and surfaces based on cyclic basis functions which were introduced by \textit{Á. Róth}, \textit{I. Juhász}, \textit{J. Schicho} and \textit{M. Hoffmann} [Comput. Aided Geom. Des. 26, No. 5, 528--546 (2009; Zbl 1205.65345)] as an alternative for say \(B\)-spline functions. Cyclic basis functions are trigonometric polynomials and thus allow for exact representations of a wide class of famous closed curves and surfaces. In this paper explicit formulas for the control points (coefficients of the representations) are given and illustrated by several examples including epi- and hypocycloids, Lissajous curves, torus knots, or surfaces of revolution, as well as the Roman surface of Steiner. Moreover, the authors describe by explicit formulas the transformation between the basis of cyclic functions and the standard basis of trigonometric polynomials, and show that partial derivatives of cyclic curves/surfaces are cyclic curves/surfaces.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 5869102
zbMATH Keywords: cyclic curves
zbMATH Keywords: cyclic surfaces
zbMATH Keywords: closed curves
zbMATH Keywords: closed surfaces
zbMATH Keywords: basis transformation
zbMATH Keywords: \(B\)-spline functions
zbMATH Keywords: control points
zbMATH Keywords: epi- and hypocycloids
zbMATH Keywords: Lissajous curves
zbMATH Keywords: torus knots
zbMATH Keywords: surfaces of revolution
zbMATH Keywords: surface of Steiner
MaRDI profile type: Publication
full work available at URL: j.cagd.2009.11.005
OpenAlex ID: W2129054912
cites work: A class of Bézier-like curves
cites work: Q4256595
cites work: Q4278198
cites work: An orthogonal basis for the hyperbolic hybrid polynomial space
cites work: Shape preserving representations in computer aided geometric design
cites work: A cyclic basis for closed curve and surface modeling
cites work: Nuat B-spline curves
cites work: Optimal properties of the uniform algebraic trigonometric B-splines
cites work: C-curves: An extension of cubic curves
cites work: Two different forms of C-B-splines
cites work: Unifying C-curves and H-curves by extending the calculation to complex numbers
DOI: 10.1016/J.CAGD.2009.11.005
description: scientific article; zbMATH DE number 5869102