A Combined Geometric Reasoning/Numerical Optimization Methodology for Three Dimensional Shape Synthesis

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The objective of this endeavor is to develop a methodology for the design of three dimensional shapes subject to general geometric and mechanical behavior requirements. Starting from an initial shape, a geometric reasoning kernel is used to generate and control a sequence of numerical optimization subproblems that converges to a final design (a topology and associated geometry) that can be significantly different from the starting shape. The geometric representation of the shape is adaptive and changes throughout the problem solving process to accommodate the shape change trends that occur. The combination of geometric reasoning and numerical optimization techniques is expected to provide a robust and systematic methodology for shape synthesis that can generate new design shapes without relying on heuristic or domain specific knowledge.