Lity Statement: Not applicable. Acknowledgments: S.S.’s perform is supported
Lity Statement: Not applicable. Acknowledgments: S.S.’s operate is supported by grant RSCF 20-71-00133. D.N.’s operate supported by Ministry of science and higher education on the Russian Federation, supplementary agreement N075-02-2020-1542/1, 29 April 2020. A.G.’s work is supported by the mega-grant with the Russian Federation Government N14.Y26.31.0013. Conflicts of Interest: The authors declare no conflict of interest.Mathematics 2021, 9,12 of
mathematicsArticlegeometric Modeling of C-B ier Curve and Surface with Shape ParametersWei Meng , Caiyun Li and Qianqian LiuSchool of Mathematical Sciences, Dalian University of Technology, Panjin 124221, China; [email protected] (W.M.); [email protected] (Q.L.) Correspondence: [email protected]: So as to resolve the problem of geometric style and architectural design of complicated engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-B ier curves and surfaces with shape parameters. Firstly, primarily based on C-B ier basis with parameters, we study the constraints with the manage points with the curves required to be satisfied when connecting them. Moreover, we study the continuity circumstances in between two adjacent C-B ier surfaces with parameters. By the continuity circumstances and unique shape parameters, the curve and surface is often changed simply and be more versatile with out altering its handle points. Thus, by adjusting the values of shape parameters, the curve and surface nonetheless preserve its qualities and geometrical configuration. Some graphical examples make sure that the proposed strategy considerably improves the ability to design and style complicated curves and surfaces and straightforward to implement. Key phrases: C-B ier basis; geometric continuity; parametric continuity; shape parametersCitation: Meng, W.; Li, C.; Liu, Q. Geometric Modeling of C-B ier Curve and Surface with Shape Parameters. Mathematics 2021, 9, 2651. https://doi.org/10.3390/ math9212651 Academic Editor: Maria Lucia Sampoli Received: 13 September 2021 Accepted: 16 October 2021 Published: 20 October1. Introduction Together with the increasingly high specifications for solution style, quite a few items need to carry out the corresponding geometric modeling design and style of curves and surfaces ahead of manufacturing, for instance automobile shell design and style, aircraft wing design and style and individuals wearing footwear, clothes, and so on every day. The study of curve and surface modeling has usually been the core content of CAGD analysis. In sensible application, complex curve and surface modeling are frequently encountered, that is hard to become represented by a curve or a piece of surface. The best way to comprehend the splicing of curves and surfaces, so that they’re hassle-free and YTX-465 Protocol flexible to become Cholesteryl sulfate sodium applied to many curves and surfaces modeling, is the trouble we need to resolve. Classic B ier curves, which can be formed by the classical Bernstein basis functions and manage points, have a lot of exceptional properties like symmetry, terminal properties, partition of unity, non-negativity, linear precision, integral house, convex hull house, etc. We are able to very easily construct any shape by utilizing parametric and geometric continuity constraints on the classical B ier curve, but its drawback is that we can not modify and can not make a little adjustment inside the shape of your curves design without having altering the control points. To overcome this challenge, we study these basis functions that possess shape parameters that help us to create tiny modifications in the shape on the curves ac.
