Newer theory and more robust algorithms for computer-aided design of developable surfaces
Newer theory and more robust algorithms for computer-aided design of developable surfaces
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发表时间：
2005-04
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通讯作者：
B. Konesky
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作者：
B. Konesky
在设计中使用可展曲面具有工程重要性，因为它们可以相对容易地制造出来。如何使表面可显影的问题并不新鲜。通常的技术是通过使用两条空间曲线来定义曲面的边缘。首先创建这些空间曲线，然后在可展开的约束下，在空间曲线之间构造一组规则。设计可展曲面的现有算法存在一个问题，即倾向于包括曲面的不可展部分：回归区域。提出了一种更可靠的可展曲面生成方法。该方法的关键是用法向线来定义可展曲面。法线准线的形状定义了所得到的可展开曲面。定义了从一对空间曲线计算法向线形状的算法。实现了相邻可展曲面的相交和平面布局的生成。本文介绍了1987年前后开始的研究和开发。算法采用ANSI c++编程语言和商用计算机辅助设计与制造（CAD和CAM）软件程序实现。
The use of developable surfaces in design is of engineering importance because of the relative ease with which they can be manufactured. The problem of how to make surfaces developable is not new. The usual technique is by using two space curves, defining the edges of the surface. These are first created, and then a set of rulings are constructed between the space curves under the constraint of being developable. A problem with existing algorithms for designing developable surfaces is the tendency to include nondevelopable portions of the surface: areas of regression. A more reliable solution to the problem of creating a developable surface is presented. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the resulting developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. Intersecting adjacent developable surfaces and generating the flat plate layouts were also accomplished. This paper presents research and development that started around 1987. The algorithms were implemented using ANSI C++ programming language and commercial computer-aided design and manufacturing (CAD and CAM) software programs.