Representations for Rigid Solids: Theory, Methods, and Systems
Representations for Rigid Solids: Theory, Methods, and Systems
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DOI：
10.1145/356827.356833
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发表时间：
1980-12
期刊：
影响因子：
--
通讯作者：
A. Requicha
中科院分区：
文献类型：
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作者：
A. Requicha
在机械和土木工程、建筑、计算机图形学、计算机视觉以及其他处理空间现象的领域，基于计算机的刚性固体物体几何建模系统正变得越来越重要。这种系统的核心是符号结构（表示），它指定了模拟物理实体的“抽象实体”（欧几里得空间的子集）。表示是计算对象有用属性的过程的数据源。体现固体表示的系统的种类和用途正在迅速增长，但在评估当前设计、指定未来系统应该表现的特征以及设计满足这些规范的系统方面的困难也在迅速增加。本文解决了许多这些困难，提供了一个连贯的观点，基于健全的理论原则，什么是目前已知的固体的表示。本文共分为三个部分。第一部分介绍了一个简单的数学框架，用于表征表征的某些重要方面，例如，它们的语义（几何）完整性。第二部分使用框架来描述和比较所有已知的表示实体的主要方案。第三部分简要介绍了现有的几何建模系统，然后将本文提出的概念应用于多表示几何建模系统的高级设计，该系统的可靠性和通用性超过了目前工业计算机辅助设计和制造中使用的系统。
Computer-based systems for modehng the geometry of rigid solid objects are becoming increasingly important in mechanical and civil engineering, architecture, computer graphics, computer vision, and other fields that deal with spatial phenomena. At the heart of such systems are symbol structures (representations) designating "abstract solids" (subsets of Euclidean space) that model physical solids. Representations are the sources of data for procedures which compute useful properties of objects. The variety and uses of systems embodying representations of solids are growing rapidly, but so are the difficulties in assessing current designs, specifying the characteristics that future systems should exhibit, and designing systems t9 meet such specifications. This paper resolves many of these difficulties by providing a coherent view, based on sound theoretical principles, of what is presently known about the representation of solids. The paper is divided into three parts. The first introduces a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) integrity. The second part uses the framework to describe and compare all of the major knownschemes fo~ representing solids. The third part briefly surveys extant geometric modeling systems and then applies the concepts developed in the paper to the high-level design of a multiple*representation geometric modeling system which exhibits a level of reliability and versatility supermr to that of systems currently used in industrial computer-aided design and manufacturing.