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

工业计算机辅助设计和制造软件包 生活在三维竞技场中，并假设固体 物体是均匀的和各向同性的。 该等相关 随着最近的事态发展， 复合材料等新材料和新兴制造业 等离子喷涂等技术。 此外，工程师 开始在非均匀的过程中整合材料， 结构设计 几何设计中的高维范式 将被开发来捕捉，可视化和协助设计 和非均匀结构的制造。 具体重点 将建立在科学基础上， 几何表示和制造集成。

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.