《基于约束的CAD.doc》由会员分享，可在线阅读，更多相关《基于约束的CAD.doc（10页珍藏版）》请在金锄头文库上搜索。
1、基于约束的CAD 1 一 Christoph M. Hoffmann 克里斯托夫米霍夫曼 Department of Computer Science 计算机科学系 Purdue University 普渡大学 West Lafayette, IN 47907 西拉斐特，在47907 Abstract 抽象 CAD systems have become parametric, basing shape design on constraints and design CAD系统已成为参数，造型设计基础和设计上的限制 feature operations. 功能操作。 We review th
2、e development of constraint-based parametric CAD, 我们回顾了CAD开发的基于约束的参数化， explaining some of the foundational issues as well as giving an outlook on possible future 说明一些问题的基础，以及提供一个可能的前景 directions of development. 方向发展。 Keywords: CAD, geometric constraints, design features, parametric CAD, shape editin
3、g, 关键词：CAD，几何约束，设计特点，参数化CAD，形状编辑， semantics. 语义。 1. 1。 Introduction and Historical Development 介绍和历史发展 Computer-Aided Design (CAD) began in the mid 1970s with two competing approaches. 计算机辅助设计（CAD）1970年中期的做法与两个相互竞争的。 The Constructive Solid Geometry (CSG) approach by Requicha and Voelcker, then at th
4、e 在建构实体几何（CSG）的沃尔克办法雷基沙和，然后在 University of Rochester, conceptualized a CAD model as an expression; 1. 罗切斯特大学，概念化作为表达式的CAD模型; 1。 The operations of 的运营 expressions were rigid-body motions and regularized Boolean set operations (union, intersection 表达刚体运动，正规化布尔集合运算（并，交 and difference), and whose operan
5、ds were instantiated simple primitives. 和差异），而且其操作数的实例简单的原语。 Initially the primitives 最初的原语 were block, cylinder, cone and sphere, with the subsequent addition of the torus as primitive. 有块，圆筒，圆锥和球体原始，与环面为随后的增补。 The 该 primitives were parameterized, for example the cylinder by diameter and height. 原语
6、的参数例如，对于缸直径和高度。 The Boundary Representation (Brep) approach by Braid, then in Cambridge, England, 边界代表（Brep）编织办法，然后在剑桥，英国， conceptualized a CAD model as a quilt of surface patches; 2. 概念化的曲面的CAD模型作为被子; 2。 The patches were joined at edges 这些补丁都加入了在边缘 and vertices and enclosing a solid shape by a 2-ma
7、nifold without boundary. 和顶点并随信附上了坚实的形状由一个2流形无边界。 The patches could 这些补丁可以 be, in the simplest case, polygons. Building complex shapes could be done by regularized 有情况下，最简单的多边形。大厦复杂的形状可以通过正规化 Boolean operations on two Brep solids, suitably positioned by rigid-body motions. 布尔运算两个Brep固体，适当运动定位的刚体。 Bo
8、th approaches sought to represent solids. 这两种方法要代理固体。 Early on, a key application considered was modeling 在早期，一个主要的程序审议的建模 objects for discrete manufacturing, hence early papers restricted to shapes that were 离散制造业的物体，形状，因此被限制在早期文件 manufacturable and excluding solids such as the one shown in Figure
9、1. 可制造和排除固体，如在一个图1所示。 1 一 Work supported in part by NSF grants DMS-013098, DCNS-0216131, DHER-0227828, DSC-0325227, 工作支持部分由美国国家科学基金会资助的DMS - 013098，DCNS公司- 0216131，DHER - 0227828，数码相机- 0325227， DCMS-0443148, and by an IBM Faculty Scholar award. 磁控溅射- 0443148，由IBM和学院学者奖。 Figure 1: Nonmanifold solid c
10、onsidered not manufacturable 图1：不考虑制造的非流形稳固 Other considerations included extending the allowed operations on solids, such as rounding, 其他考虑因素包括扩大业务进行固体所允许的，如四舍五入， chamfering, shelling, and so on. 倒角，炮击等。 Some extending operations, such as rounding and filleting, are easily stipulated and 有些扩展业务嵌缝，如
11、四舍五入，并很容易和规定 straightforwardly implemented for Brep solids, but they are not so easy to deal with for CSG 直截了当地实施Brep固体，但他们不那么容易对付南玻集团与 solids. 固体。 Uniform radius rounding and filleting was considered by Rossignac 3 who 均匀圆，圆角半径是认为Rossignac 3谁 approximated the surfaces that arise in this context by
12、CSG primitives. 近似的表面基元出现在南玻这方面的。 The semantics of representing, manipulating and reasoning about solids was also considered early 该代表的语义，操纵和固体推理也被认为是早期 on. 上。 Tech memo 28 by Requicha 4 set forth a rigorous semantics for CSG. 技术备忘录28雷基沙4提出了严格的语义南玻。 Comparable 可比 attempts at providing a rigorous sem
13、antics for Breps fell short in that it would have required exact Breps企图提供一个严格的语义不及，因为它会需要确切 arithmetic and representational convention for parametric patches that even to-date are not used. 算术和最新的代表性甚至公约参数补丁不使用。 Nevertheless, the greater flexibility of Breps in accommodating new operations and ulti
14、mately 然而，更大的灵活性，可容纳Breps新的行动，并最终 offering greater (practical) flexibility for shape representation persuaded applications to go with 提供更多的（实践）代表的灵活性，形状一起去说服申请 Breps and live with the semantic shortcomings of that representation. Breps和生活与该代表的语义缺陷。 Inroads into converting 进军改建 between the two repres
15、entations were made, in particular by Shapiro and Vossler 5. 双方进行了交涉，特别是在由夏皮罗和沃斯勒5。 They give 他们给 rise to profound mathematical issues when converting Brep to CSG. 产生深刻的数学问题，以南玻转换时Brep。 The opposite conversion, 相反的转换， CSG to Brep, was accomplished early-on and is a solved problem (subject to numeric
16、al issues); 南玻到Brep，是完成早期的，是解决问题（受数值问题）; 6. 6。 Summarizing, the two initial approaches to CAD differed in practical expressiveness and in the 总结，这两个最初的计算机辅助设计方法不同，在实际表现和 ease with which to prove rigorously properties of the solids so represented. 轻而易举地证明严格固体性质，以便代表。 Applications 应用 employed the approaches to model sp
