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

这项工作的目标是开发一种满足一般几何和机械行为要求的三维形状设计方法。从初始形状开始，使用几何推理核来生成和控制收敛到最终设计(拓扑和相关几何)的一系列数值优化子问题，该最终设计可能与初始形状显著不同。形状的几何表示是自适应的，并在整个问题解决过程中进行更改，以适应发生的形状更改趋势。几何推理和数值优化技术的结合有望为形状合成提供一种健壮和系统的方法，可以在不依赖启发式或领域特定知识的情况下生成新的设计形状。

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.