Geometric design and fabrication of developable Bezier and B-spline surfaces
Geometric design and fabrication of developable Bezier and B-spline surfaces
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DOI：
10.1115/1.2919485
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发表时间：
1994-12
期刊：
影响因子：
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通讯作者：
R. Bodduluri;B. Ravani
中科院分区：
文献类型：
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作者：
R. Bodduluri;B. Ravani
在本文中，我们研究可展曲面的计算机辅助几何设计（CAGD）和制造（CAM）。我们用平面几何来直接表示可展曲面。它使用控制平面来确定表面，该表面是控制平面的贝塞尔曲线或 B 样条插值。在 Bezier 情况下，提出了 de Casteljau 型构造方法，用于可展 Bezier 曲面的几何设计。在B样条情况下，提出了用于可展曲面几何设计的de Boor型构造和Boehm型结插入算法。在可展开表面的制造或加工领域，我们提出了将表面展开为平面以及将平面弯曲为所需可展开表面的简单方法。所提出的方法使用平面和线几何形状，并且消除了求解先前方法中使用的 Riccatti 类型微分方程的需要。使用基于所提出的理论实现的 CAD/CAM 系统生成的示例来说明结果。
In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.