Shape-adjustable developable generalized blended trigonometric Bézier surfaces and their applications

Advances in Difference Equations

卷:2021

Abdul Majeed¹  Sidra Maqsood²  Tahir Nazir²  Muhammad Abbas²  Gang Hu³  Kenjiro T. Miura⁴ 

[1] Department of Mathematics, Division of Science and Technology, University of Education;

[2] Department of Mathematics, University of Sargodha;

[3] Department of Mathematics, Xi’an University of Technology;

[4] Department of Mechanical Engineering, Shizuoka University;

关键词: GBTB basis functions;    Shape control of developable GBT-Bézier curve;    Developable GBT-Bézier surfaces;    Duality;    Enveloping developable GBT-Bézier surfaces;    Spine curve developable GBT-Bézier surfaces;   

DOI  :  10.1186/s13662-021-03614-3

来源: DOAJ

【 摘 要 】

Abstract Developable surfaces have a vital part in geometric modeling, architectural design, and material manufacturing. Developable Bézier surfaces are the important tools in the construction of developable surfaces, but due to polynomial depiction and having no shape parameter, they cannot describe conics exactly and can only handle a few shapes. To tackle these issues, two straightforward techniques are proposed to the computer-aided design of developable generalized blended trigonometric Bézier surfaces (for short, developable GBT-Bézier surfaces) with shape parameters. A developable GBT-Bézier surface is established by making a collection of control planes with generalized blended trigonometric Bernstein-like (for short, GBTB) basis functions on duality principle among points and planes in 4D projective space. By changing the values of shape parameters, a group of developable GBT-Bézier surfaces that preserves the features of the developable GBT-Bézier surfaces can be generated. Furthermore, for a continuous connection among these developable GBT-Bézier surfaces, the necessary and sufficient G 1 $G^{1}$ and G 2 $G^{2}$ (Farin–Boehm and beta) continuity conditions are also defined. Some geometric designs of developable GBT-Bézier surfaces are illustrated to show that the suggested scheme can settle the shape and position adjustment problem of developable Bézier surfaces in a better way than other existing schemes. Hence, the suggested scheme has not only all geometric features of current curve design schemes but surpasses their imperfections which are usually faced in engineering.

【 授权许可】

Unknown