Towards a Geometric-Object-Oriented Language
Towards a Geometric-Object-Oriented Language
复制标题
走向几何面向对象语言
DOI：
10.1007/11615798_9
复制
发表时间：
2004
期刊：
影响因子：
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通讯作者：
Dongming Wang
中科院分区：
文献类型：
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作者：
Tielin Liang;Dongming Wang
本文提出了一种用于符号几何计算、推理和可视化的几何面向对象语言。在这种语言中，几何对象是用不确定的参数数据构造的。启用对这些对象的修改和基本操作。通过施加条件和假设，可以有效地处理简并性和不确定性，并通过声明不同对象之间的关系来制定几何陈述。基于该语言实现的系统将允许用户进行严格的几何计算和推理，并自动证明几何定理并生成几何图表和交互式文档。我们介绍了该语言的总体设计，解释了所提出系统的功能、特性和主要组件，提供了一些函子的规范，报告了我们对系统的初步实现的实验，并讨论了一些遇到的困难和研究问题。
This paper proposes a geometric-object-oriented language for symbolic geometric computation, reasoning, and visualization. In this language, geometric objects are constructed with indefinite parametric data. Modifications and basic operations on these objects are enabled. Degeneracy and uncertainty are handled effectively by means of imposing conditions and assumptions and geometric statements are formulated by declaring relations among different objects. A system implemented on the basis of this language will allow the user to perform geometric computation and reasoning rigorously and to prove geometric theorems and generate geometric diagrams and interactive documents automatically. We present the overall design of the language, explain the capabilities, features, main components of the proposed system, provide specifications for some of its functors, report our experiments with a preliminary implementation of the system, and discuss some encountered difficulties and research problems.