Quasi-Bézier Curves with Shape Parameters

Quasi-Bézier Curves with Shape Parameters

The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding Quasi-Bézier curves were constructed step-by-step in this paper, using the method of undetermined coefficients. The series of Quasi-Bézier curves had geometric and affine invari...

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Main Author: Jun Chen
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/171392
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spelling doaj-4d5a5198d33840b084af0ec9aa6f74eb2020-11-24T21:03:03ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/171392171392Quasi-Bézier Curves with Shape ParametersJun Chen0Faculty of Science, Ningbo University of Technology, Ningbo 315211, ChinaThe universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding Quasi-Bézier curves were constructed step-by-step in this paper, using the method of undetermined coefficients. The series of Quasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpoints, and shape adjustability while maintaining the control points. Various existing Quasi-Bézier curves became special cases in the series. The obvious geometric significance of shape parameters made the adjustment of the geometrical shape easier for the designer. The numerical examples indicated that the algorithm was valid and can easily be applied.http://dx.doi.org/10.1155/2013/171392
collection DOAJ
language English
format Article
sources DOAJ
author Jun Chen
spellingShingle Jun Chen
Quasi-Bézier Curves with Shape Parameters
Journal of Applied Mathematics
author_facet Jun Chen
author_sort Jun Chen
title Quasi-Bézier Curves with Shape Parameters
title_short Quasi-Bézier Curves with Shape Parameters
title_full Quasi-Bézier Curves with Shape Parameters
title_fullStr Quasi-Bézier Curves with Shape Parameters
title_full_unstemmed Quasi-Bézier Curves with Shape Parameters
title_sort quasi-bézier curves with shape parameters
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding Quasi-Bézier curves were constructed step-by-step in this paper, using the method of undetermined coefficients. The series of Quasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpoints, and shape adjustability while maintaining the control points. Various existing Quasi-Bézier curves became special cases in the series. The obvious geometric significance of shape parameters made the adjustment of the geometrical shape easier for the designer. The numerical examples indicated that the algorithm was valid and can easily be applied.
url http://dx.doi.org/10.1155/2013/171392
work_keys_str_mv AT junchen quasibeziercurveswithshapeparameters
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