Research Initiation: Symbolic Computer Geometry and Interactive Geometric Design

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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.