Research Initiation: Symbolic Computer Geometry and Interactive Geometric Design

尽管在人权领域取得了进展， 计算几何和实体建模，只有很少的已经 在交互式计算机辅助设计（CAD）领域取得的成就。 一个具有成本效益的设计系统应该支持交互式用户 比目前的CAD系统更能发挥作用。 之一 这种缺陷的原因是，几何对象是 一直被CAD视为数字表示的对象 系统. 当对象被转换为 这种程序的内部表示。 的理解 几何学是隐含在操纵这些的算法中的。 在数字层面上的对象，而不是在对象层面上。 通过主要研究者的方法，几何物体和 它们的性质可以用符号表示。 因此，我们认为， 这些物体的操作和 操作对于交互式用户是有意义的。 的 主要研究者将开发几何演算， 象征性地操纵几何表达式。 了理论 将开发一个框架来证明正确性和可判定性 几何问题。 将采用的方法是 项重写方法和逻辑编程方法。 这 研究应该会产生更强大的用户界面， 阿尔法一计算机辅助设计系统，开发于 犹他州大学。

Despite the progress that has been made in the field of computational geometry and solid modelling, only little has been achieved in the field of interactive Computer-Aided Design (CAD). A cost-effective design system should support an interactive user in its interaction much more than current CAD systems do. One of the reasons for this deficiency, is that geometric objects are always looked upon as numerically represented objects by CAD systems. Much information is lost when objects are translated to the internal representation of such a program. The understanding of geometry is implicit in the algorithms which manipulate these objects on a numerical level, rather than on an object level. With the Principal Investigator's approach, geometric objects and their properties can be represented symbolically. Therefore, manipulations of such objects and the results of the manipulations are meaningful for the interactive user. The Principal Investigators will develop a geometric calculus for symbolically manipulating geometric expressions. A theoretic framework will be developed to prove correctness and decidability of geometric problems. The approaches to be applied are term-rewriting methods and logic programming methods. This research should result in a more powerful user interface for the Alpha One Computer-Aided Design system, developed at the University of Utah.