Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters

A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for sh...

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Vydáno v:	Advances in difference equations Ročník 2020; číslo 1; s. 1 - 18
Hlavní autoři:	Maqsood, Sidra, Abbas, Muhammad, Miura, Kenjiro T., Majeed, Abdul, Iqbal, Azhar
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 06.10.2020 SpringerOpen
Témata:	Analysis Applications Continuities of GBT-Bézier curves Difference and Functional Equations Functional Analysis GBT-Bernstein-like polynomial functions GBT-Bézier curve Mathematics Mathematics and Statistics Methods Ordinary Differential Equations Partial Differential Equations Properties of GBT-Bézier curves Shape parameters Topics in Special Functions and q-Special Functions: Theory GBT-Bernstein-like polynomial functions Properties of GBT-Bézier curves Continuities of GBT-Bézier curves GBT-Bézier curve Shape parameters
ISSN:	1687-1847, 1687-1847
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Abstract	A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m . Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The C 3 and G 2 continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling.
AbstractList	A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m . Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The $C^{3}$ C 3 and $G^{2}$ G 2 continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling. Abstract A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m. Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The C 3 $C^{3}$ and G 2 $G^{2}$ continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling. A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new recursive formula in explicit expression is constructed that produces the generalized blended trigonometric Bernstein (or GBT-Bernstein, for short) polynomial functions of degree m . Using these basis functions, generalized blended trigonometric Bézier (or GBT-Bézier, for short) curves with two shape parameters are also constructed, and their geometric features and applications to curve modeling are discussed. The newly created curves share all geometric properties of Bézier curves except the shape modification property, which is superior to the classical Bézier. The C 3 and G 2 continuity conditions of two pieces of GBT-Bézier curves are also part of this study. Moreover, in contrast with Bézier curves, our generalization gives more shape adjustability in curve designing. Several examples are presented to show that the proposed method has high applied values in geometric modeling.
ArticleNumber	550
Author	Maqsood, Sidra Majeed, Abdul Iqbal, Azhar Miura, Kenjiro T. Abbas, Muhammad
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Snippet	A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study, a new... Abstract A Bézier model with shape parameters is one of the momentous research topics in geometric modeling and computer-aided geometric design. In this study,...
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SubjectTerms	Analysis Applications Continuities of GBT-Bézier curves Difference and Functional Equations Functional Analysis GBT-Bernstein-like polynomial functions GBT-Bézier curve Mathematics Mathematics and Statistics Methods Ordinary Differential Equations Partial Differential Equations Properties of GBT-Bézier curves Shape parameters Topics in Special Functions and q-Special Functions: Theory
Title	Geometric modeling and applications of generalized blended trigonometric Bézier curves with shape parameters
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