Presidential Young Investigator Awards: Robust and Intuitive Surface Design Methods

传统上，机械零件的设计是由设计师或工程师创建零件的详细图纸，然后让工匠创建物理原型。原型随后根据其机械(可能还有美学)质量进行评估。然后，评估的结果被反馈给设计者，通常是以对零件的建议修改的形式。原型的建造和评估非常昂贵，因此如果物理原型的数量能够降到最低，设计成本就可以大大降低。这在很大程度上是通过在某些类型的机械部件的设计中使用计算机(即实体建模系统)来实现的。然而，有一类日益重要的设计应用程序，包括汽车车身、船体和飞机机身的设计，并没有从实体建模系统中看到巨大的好处。这些应用的特点是需要对平滑变化的形状进行紧凑、高效和稳健的表示。这项研究致力于更好地了解包含平滑元素的形状设计的问题和解决方案。“自由形式”曲线和曲面的使用在流畅的设计应用方面显示出了希望，但它们的使用受到阻碍，至少有两个原因：概念复杂和健壮性。概念复杂性的问题源于这样一个事实，即当前的技术通常需要大量的数学专业知识才能有效地使用。当前流行的技术仅适用于特殊的几何情况(例如，当所有曲面片恰好有四个相邻面片时)，这一事实证明了健壮性不足。该项目正在开发技术，使自由形式的设计系统适用于更广泛的几何情况，并使设计人员更直观和自然的技术。这样的系统不仅会让不懂数学的设计师能够接触到自由形式的设计，还会让精通数学的用户更有效率。

Mechanical parts have traditionally been designed by having a designer or engineer create detailed drawings of the part, then having a craftsmen create a physical prototype. The prototype is subsequently evaluated based on its mechanical (and possibly aesthetic) qualities. The results of this evaluation are then fed back to the designer, often in the form of suggested modifications to the part. The construction and evaluation of prototypes is extremely expensive, so the cost of design can be dramatically reduced if the number of physical prototypes can be minimized. This has largely been achieved by using computers (i.e., solid modeling systems) in the design of certain types of mechanical parts. However, there is a class of increasingly important design applications, including the design of automobile bodies, ship hulls, and airplane fuselages, that have not seen great benefits from solid modeling systems. These applications are characterized by their need for compact, efficient, and robust representations of smoothly varying shapes. This research is concerned with providing a better understanding of the problems and solutions of designing shapes containing smooth elements. The use of "free-form" curves and surfaces has shown promise for smooth design applications, but their use has been hindered for at least two reasons: conceptual complexity and robustness. The issue of conceptual complexity stems from the fact that current techniques typically require a great deal of mathematical expertise to use effectively. Insufficient robustness is demonstrated by the fact that currently popular techniques are applicable only in special geometrical situations (for instance, when all surface patches have exactly four neighbors). The project is developing techniques to make free-form design systems applicable in a wider variety of geometrical situations, and also techniques that are more intuitive and natural for designers. Such systems would not only make free-form design accessible to mathematically unsophisticated designers, they would make mathematically proficient users more productive.