Developable Bézier-like surfaces with multiple shape parameters and its continuity conditions
| Autor: | Huanxin Cao, Guo Wei, Suxia Zhang, Gang Hu |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Developable surface Applied Mathematics 020207 software engineering Bézier curve Basis function 02 engineering and technology Topology Shape parameter Tangential developable Computer Science::Graphics 020901 industrial engineering & automation Position (vector) Modeling and Simulation Duality (projective geometry) 0202 electrical engineering electronic engineering information engineering Projective space Mathematics |
| Zdroj: | Applied Mathematical Modelling. 45:728-747 |
| ISSN: | 0307-904X |
| DOI: | 10.1016/j.apm.2017.01.043 |
| Popis: | To solve the problems of shape adjustment and shape control of developable surfaces, we propose two direct explicit methods for the computer-aided design of developable Bezier-like surfaces with multiple shape parameters. Firstly, with the aim of constructing Bezier-like curves with multiple shape parameters, we present a class of novel Bernstein-like basis functions, which is an extension of classical Bernstein basis functions. Then, according to the important idea of duality between points and planes in 3D projective space, we design the developable Bezier-like surfaces with multiple shape parameters by using control planes with Bernstein-like basis functions. The shape of the developable Bezier-like surfaces can be adjusted by changing their three shape parameters. When the shape parameters take different values, a family of developable Bezier-like surfaces can be constructed and they retain the characteristics of Bezier surfaces. Finally, in order to tackle the problem that most complex developable surfaces in engineering often cannot be constructed by using a single developable surface, we derive the necessary and sufficient conditions for G1 continuity, Farin−Boehm G2 continuity and G2 Beta continuity between two adjacent developable Bezier-like surfaces. In addition, some properties and applications of the developable Bezier-like surfaces are discussed. The modeling examples show that the proposed methods are effective and easy to implement, which greatly improve the problem-solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces. |
| Databáze: | OpenAIRE |
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