Presidential Young Investigator Award: High-Dimensional Paradigm in Geometric Design

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Industrial computer-aided design and manufacturing packages live in the three-dimensional arena and it is assumed that solid objects are homogeneous and isotropic. These underlying assumptions are becoming invalid with the recent developments of new materials such as composite, and emerging manufacturing technologies such as plasma spray. Moreover, engineers are starting to integrate materials in the process of inhomogeneous structure design. A high-dimensional paradigm in geometric design will be developed to capture, visualize and assist in the design and manufacturing of inhomogeneous structures. Specific emphasis will be placed on scientific foundations for high-dimensional geometric representation and manufacturing integration.