Quadratic-cycloidal curves
type: Item
instance of: scholarly article
title: Quadratic-cycloidal curves
zbMATH Open document ID: 1043.65031
DOI: 10.1023/A:1025813919473
author: Esmeralda Mainar
author: J. M. Peña
published in: Advances in Computational Mathematics
publication date: 2004-03-15T00:00:00Z
review text: For a given \(\alpha\), such that \(0<\alpha< 2\pi\), normalized B-basis for the space \(Q ([0,\alpha]) \equiv \) span \(\{1, t, t^2, \)cos \( t , \)sin \(t \}, t \in [0,\alpha]\) is known [see \textit{E. Mainar, J. M. Peña}, and \textit{J. Sánchez-Reyes}, Comput. Aided Geom. Des. 18, No. 1, 37--60 (2001; Zbl 0972.68157)]. Assuming \(0<\alpha<\pi\) and using the elements of the foregoing B-basis, a quadratic-cycloidal (QC)-spline segment is defined in terms of a new basis which is shown to be normalized total positive.This enables the authors to derive some shape preserving properties of QC-splines. It is also shown that as \(\alpha\) tends to zero, the limit of a QC-B-spline curve approaches a B-spline curve of degree 4.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 2057588
zbMATH Keywords: quadratic cycloidal curve
zbMATH Keywords: normalised B-basis
zbMATH Keywords: QC-splines
zbMATH Keywords: shape preserving properties
zbMATH Keywords: C-curves
zbMATH Keywords: B-splines
zbMATH Keywords: B-algorithms
zbMATH Keywords: total positivity QC-curves
MaRDI profile type: Publication
full work available at URL: a:1025813919473
OpenAlex ID: W2062173419
Recommended article: Quasiregular curves
Recommended article: Pythagorean-hodograph cycloidal curves
Recommended article: Q3832683
Recommended article: Q5192858
Recommended article: Quadratic trigonometric polynomial curves with a shape parameter
Recommended article: Cyclic quadrilaterals and smooth Jordan curves
Recommended article: Q4294458
Recommended article: Piecewise quadratic trigonometric polynomial curves
description: scientific article; zbMATH DE number 2057588