Surface Schemes for Three-Dimensional Design Space

三维立体设计空间是用于三维几何建模应用的先进设计工作站，由主机、三维立体显示系统和能够感知用户每个手指的位置和方向的最先进的输入设备组成。设计空间平滑地变化复杂的表面形状，如汽车车身，飞机机身和电话外壳。为了支持这种类型的设计，必须找到能够描述任意拓扑的一阶或二阶光滑形状的表面表示方案；曲面方案应具有高效的可计算性，并支持连续的精细化设计。不幸的是，现有的表面表示方案无法满足这些标准。本研究涉及具有上述特征的新方案的开发。这种曲面方案不仅可以在交互式三维设计中使用，还可以在各种数据拟合问题中找到重要的应用。

The Three-Dimensional Solid Design Space is an advanced design workstation for three-dimensional geometric modeling applications, composed of a host computer, a three-dimensional stereoscopic display system, and a state-of-the-art input device capable of sensing the position and orientation of each of the user's fingers. The Design Space smoothly varying complex surface shapes such as car bodies, airplane fuselages, and telephone casings. To support this type of design, a surface representation scheme must be found that is capable of describing either first or second order smooth shapes of arbitrary topology; the surface scheme should be efficiently computable and support successive refinement design. Unfortunately, existing surface representation schemes fail to meet these standards. This research deals with the development of new schemes that possess the characteristics listed above. Such surface schemes will not only enjoy use in interactive three- dimensional design, they will also find important applications in a variety of data fitting problems.