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， 工匠们创造了一个物理原型。 原型随后 根据其机械（可能还有美学）质量进行评估。 然后，将评估结果反馈给设计师，通常 以建议修改零件的形式。 建设 原型的评估是非常昂贵的，所以成本 如果物理原型的数量 可以最小化。 这在很大程度上是通过使用计算机实现的 (i.e.,实体建模系统）在设计某些类型的 机械零件 然而，有一类日益重要的 设计应用，包括汽车车身、船舶 船体和飞机机身，没有看到很大的好处， 实体造型系统 这些应用程序的特点是， 需要紧凑、高效和鲁棒的平滑表示 各种形状。 这项研究旨在更好地了解 设计包含光滑元素的形状的问题和解决方案。 “自由形式”曲线和曲面的使用已经显示出平滑的前景， 设计应用程序，但它们的使用至少在两个 原因：概念复杂性和鲁棒性。 概念问题 复杂性源于当前技术通常 需要大量的数学专业知识才能有效地使用。 鲁棒性不足的事实表明，目前 流行的技术只适用于特殊的几何形状， 情况（例如，当所有曲面片恰好有四个 邻居）。 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形状，并且 这些技术对设计师来说更直观、更自然。 等 系统将不仅使自由形式的设计， 数学上不成熟的设计师， 数学熟练的用户更有效率。

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.