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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Vydané v:Advances in difference equations Ročník 2020; číslo 1; s. 1 - 18
Hlavní autori: Maqsood, Sidra, Abbas, Muhammad, Miura, Kenjiro T., Majeed, Abdul, Iqbal, Azhar
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 06.10.2020
SpringerOpen
Predmet:
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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Issue 1
Keywords GBT-Bernstein-like polynomial functions
Properties of GBT-Bézier curves
Continuities of GBT-Bézier curves
GBT-Bézier curve
Shape parameters
Language English
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PublicationYear 2020
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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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