Subdivision Surface Based One-Piece Representation

DMS-0310645福华(弗兰克)程这是一个货物孵化奖，由http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.This基金为发展必要的数学理论和几何算法提供资金，以支持基于细分曲面的整体表示，即在设计过程中只用一个细分曲面表示最终对象，无论对象的结构或形状多么复杂。因此，最终表示中的零件数量始终是最小的：一个。本研究主要从表征精化、表征转换和表征连接三个方面进行研究。表示精化的目的是开发新的顶点生成方案和拓扑结构，允许对细分曲面的控制网格进行局部精化，同时保持精化过程的无裂缝特性。表示转换的目的是为不同类型的细分曲面或相同类型但控制网格具有不同拓扑的细分曲面开发转换算法。表示连接的目的是开发直接连接和间接连接技术，这些技术可以迭代地应用于将对象的不同组件表面连接成单个表面。如果成功，本研究的结果将显著缩短自由曲面的构建过程，因为单件表示使布尔运算更有效，从而提高设计工程师的生产率。事实上，除了在整体表示中的作用外，第一方面的结果也将显著改进当前细分曲面理论的艺术。它们不仅包括当前的细化技术作为特例，而且还提供了更强大的网格细化规则，允许对细分曲面进行局部和自适应细化。第二个领域的结果还将使CAD/CAM系统能够将细分曲面作为一种新的、更通用的自由曲面建模工具，因为B-Spline和NURBS是细分曲面的特例。

DMS-0310645Fuhua (Frank) ChengThis is a CARGO incubation award made under solicitation http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.This grant provides funding for the development of necessarymathematical theories and geometric algorithms to supportsubdivision surface based one-piece representation, i.e.,representing the final object in a design process with onlyone subdivision surface, no matter how complicated the object'stopology or shape. Hence, the number of parts in the finalrepresentation is always the minimum: one. The research requiresstudies in three areas: representation refinement, representationconversion and representation joining. The aim for representationrefinement is to develop new vertex generation schemes andtopological structures that allow local refinement of a subdivisionsurface's control mesh while preserving the crack-free property ofthe refining process. The aim for representation conversion is todevelop conversion algorithms for subdivision surfaces of differenttype or subdivision surfaces of the same type but whose controlmeshes are of different topology. The aim for representationjoining is to develop direct and indirect joining techniques thatcan be iteratively applied to join different component surfaces ofan object into a single surface.If successful, the results of this research will significantlyshorten the construction process of a free-from surface becauseone-piece representation makes Boolean operations more efficientand, consequently, increase the productivity of a design engineer.Actually, in addition to their roles in one-piece representation,the results in the first area will also significantly improve thecurrent art of subdivision surface theory. They would not onlyinclude current refinement techniques as special cases, but alsoprovide more powerful mesh refining rules which allow both localand adaptive refinement of subdivision surfaces. The results inthe second area will also make it possible for a CAD/CAM system toinclude subdivision surfaces as a new and yet more general free-formsurface modeling tool because B-splines and NURBS are special casesof subdivision surfaces.