Geometric Reasoning for Shape Design

George Turkiyyah, Omar Ghattas

This paper describes a methodology for the design of shapes. 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. A subproblem in the sequence is systematically formulated from a geometric abstraction of current shape, and its objective function, constraints and bounds are dynamically derived. The geometric representation of the shape is adaptive and changes throughout the problem solving process to accommodate the shape change trends that occur. Shape evolution takes place within each subproblem and between subproblems. Intra-subproblem evolution is responsible for geometric modifications while inter-subproblem evolution handles topology modifications. The combination of geometric reasoning and numerical optimization techniques provides a robust and systematic methodology for shape synthesis that can generate new design shapes without relying on heuristic or domain specific knowledge.

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