Towards a New Generation of Robust CAD/CAM Systems

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The object of this project is to advance the state of knowledge in robustly representing, interrogating and manipulating the geometry of complex objects using imprecise/discrete computer arithmetic and developing the necessary theory and algorithms which can form the basis for CAD/CAM systems of the future. This theory will involve primarily concepts of interval arithmetic and conditioning from numerical analysis as well as concepts of stability from differential topology, of simplicial complex theory from algebraic topology, and basic concepts of differential geometry, all applied in computational geometry representations and algorithms. Specific objectives are: To analyze how interval non-uniform rational B-spline curves and surface patches can be used to obtain robust machine realizations of flexible free-form boundaries for solids in a modeling system for complex objects. To develop methods which allow stable Boolean operations. To investigate how local stability properties of adjacencies resulting from Boolean operations. To investigate how local stability properties of adjacencies resulting from Boolean operations can be integrated in a global topological generalized Boundary Representation cell- tuple structure, so as to obtain consistent geometric results which remain compatible with a variable numerical resolution. To obtain a reliable classification of cases where the resulting information of the system is uncertain and those cases where the answer is specific.