Automated Geometry Reasoning and Diagram Constructing

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This project is concerned with automated geometry diagram constructing or geometric constraint solving, which is to draw a declaratively-described diagram or an engineering drawing automatically. This kind of work is central to much of the current work of developing intelligent and parametric CAD systems and interactive constraint-based graphic systems.Successful methods of automated geometry theorem proving and discovering which have been developed in recent years will be extended to methods of automated geometry diagram constructing, which in turn will be applied to the areas of intelligent CAD (computer aided design) and CAI (computer aided instruction).New techniques for geometry constraint solving will be developed to advance the state of the art for CAD research and to provide better CAI systems. New automated reasoning techniques will be explored for developing faster and more powerful automated diagram constructing methods by using more geometry predicates, introducing new drawing tools, and extending the 2D method to 3D. The basis of the proposed research is the work on automated generation of human-readable proofs in geometry. The global propagation method for automated generation of construction steps of geometry diagrams shows that the proposed work is feasible and may lead to significant improvement of the performance of CAD systems. Various optimization techniques, such as global optimization methods and multi-objective optimization methods will be used to develop more stable, flexible, and powerful numerical methods of geometric constraint solving.New symbolic computation techniques will be used to enhance the power of constraint solving systems in certain special cases. These techniques include block triangulation and elimination theories based on vector and geometric invariants.Finally, integration techniques will be studied and used to build more practical and intelligent CAD and CAI systems by incorporation all the above methods.