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

Advances in Difference Equations

article

Maqsood, Sidra¹  Abbas, Muhammad¹  Miura, Kenjiro T.²  Majeed, Abdul³  Iqbal, Azhar⁴ 

[1] Department of Mathematics, University of Sargodha;Department of Mechanical Engineering, Shizuoka University;Department of Mathematics, University of Education;Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University

关键词: GBT-Bernstein-like polynomial functions;    GBT-Bézier curve;    Properties of GBT-Bézier curves;    Continuities of GBT-Bézier curves;    Shape parameters;   

DOI  :  10.1186/s13662-020-03001-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY