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

这项奋进的目标是制定一种方法， 三维形状的设计受一般几何 和机械性能要求。 从初始 形状，使用几何推理内核来生成和控制 一系列数值优化子问题，收敛到 最终设计（拓扑和相关几何）， 与初始形状有很大不同。 几何 形状的表示是自适应的， 解决问题的过程，以适应形状变化的趋势， 发生. 几何推理与数值计算的结合 优化技术有望提供一个强大的， 形状合成系统方法，可以产生新的 设计形状而不依赖于启发式或特定领域 知识

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.