New trigonometric basis possessing denominator shape parameters
type: Item
instance of: scholarly article
title: New trigonometric basis possessing denominator shape parameters
zbMATH Open document ID: 1427.65024
DOI: 10.1155/2018/9569834
author: Xianqiang Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be \(C^2\) continuous for a non-uniform knot vector. For a special value, the generated curves can be \(C^{(2 n - 1)} (n = 1,2, 3, \ldots )\) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be \(C^2\) continuous for a nonuniform knot vector. When given a special value, the related surfaces can be \(C^{(2 n - 1)} (n = 1,2, 3, \ldots )\) continuous for a uniform knot vector. A new class of trigonometric Bernstein-Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein-Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for \(G^1\) continuous jointing two DT BB-like patches over the triangular domain is deduced.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 7019786
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9569834
OpenAlex ID: W2898096247
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Wikidata QID: Q129030983
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description: scientific article; zbMATH DE number 7019786