Design and shape adjustment of developable surfaces

Min Zhou; Junqing Yang; Hongchan Zheng; Weijie Song

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Design and shape adjustment of developable surfaces

机译：可显影表面的设计和形状调整

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摘要

This paper presents two direct explicit methods of computer-aided design for developable surfaces. The developable surfaces are designed by using control planes with C-Bezier basis functions. The shape of developable surfaces can be adjusted by using a control parameter. When the parameter takes on different values, a family of developable surfaces can be constructed and they keep the characteristics of Bezier surfaces. The thesis also discusses the properties of designed developable surfaces and presents geometric construction algorithms, including the de Casteljau algorithm, the Farin-Boehm construction for G~2 continuity, and the G~2 Beta restricted condition algorithm. The techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design, but go beyond the limitations of traditional approaches in designing developable surfaces and resolve problems frequently encountered in engineering by adjusting the position and shape of developable surfaces.

机译：本文介绍了两种直接显式的计算机辅助设计方法，用于可展开曲面。通过使用具有C-Bezier基函数的控制平面来设计可显影表面。可显影表面的形状可以通过使用控制参数来调整。当参数采用不同的值时，可以构造一系列可展开曲面，并且这些曲面保留了Bezier曲面的特性。本文还讨论了可设计曲面的性质，并提出了几何构造算法，包括de Casteljau算法，G〜2连续性的Farin-Boehm构造以及G〜2 Beta限制条件算法。本文中用于可展开曲面的几何设计技术具有曲线设计现有方法的所有特征，但在设计可展开曲面时超越了传统方法的局限性，并通过调整可展开曲面的位置和形状来解决工程中经常遇到的问题表面。

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来源
《Applied Mathematical Modelling》 |2013年第6期|3789-3801|共13页
作者
Min Zhou; Junqing Yang; Hongchan Zheng; Weijie Song;
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作者单位

College of Science, Northwestern Polytechnical University, Xi'an 710072, PR China;

Department of Computer Engineering, Xi'an Aerotechnical College, Xi'an 710077, PR China;

College of Science, Northwestern Polytechnical University, Xi'an 710072, PR China;

College of Science, Northwestern Polytechnical University, Xi'an 710072, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Developable surface; C-Bezier basis function; Duality; Control plane; Control parameter Geometric construction algorithm;

机译：可显影的表面;C-Bezier基函数;二元性控制平面控制参数几何构造算法;

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2. Shape-Adjustable Generalized Bézier Rotation Surfaces with Multiple Shape Parameters [J] . Gang Hu, Guo Wei, Junli Wu Results in mathematics . 2017,第3期

机译：具有多种形状参数的形状可调的通用Bézier旋转曲面
3. Computer-Aided Design of Developable Surfaces: Designing with Developable Surfaces [J] . Francisco Perez-Arribas, Leonardo Fernandez -Jambrina Journal of Computers . 2018,第10期

机译：可开发表面的计算机辅助设计：使用可开发表面设计
4. CREATING SHAPES WITH DEVELOPABLE SURFACES IN AN INTUITIVE AND CONSTRUCTIVE DESIGN PROCESS [C] . Oliver Niewiadomski International Conference on Geometry and Graphics . 2013

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7. Shape Design of Curved Surface of Membrane Structure Using Developable Surface [O] . Jinglan Cui, Makoto Ohsaki 2018

机译：使用可开发表面的膜结构曲面的形状设计

Design and shape adjustment of developable surfaces

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