Subdivision Surface Based One-Piece Representation

dms03010645fuhua (Frank) cheng这是一项CARGO孵化奖，根据征求http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.This资助为必要的数学理论和几何算法的发展提供资金，以支持基于细分表面的整体表示，即在设计过程中仅用一个细分表面表示最终对象，无论对象的拓扑或形状有多复杂。因此，最终表示中的部分数量总是最小的：一个。本研究需要从表征细化、表征转换和表征联接三个方面进行研究。表示细化的目的是开发新的顶点生成方案和拓扑结构，允许细分表面控制网格的局部细化，同时保留细化过程的无裂纹特性。表示转换的目的是开发不同类型的细分曲面或相同类型的细分曲面但控制网格具有不同拓扑结构的转换算法。表示连接的目的是开发直接和间接连接技术，这些技术可以迭代地应用于将对象的不同组件表面连接到单个表面。如果成功，这项研究的结果将大大缩短自由曲面的施工过程，因为整体表示使布尔运算更有效，从而提高设计工程师的生产力。实际上，除了它们在整体表现方面的作用外，第一个领域的结果也将显著改善当前细分表面理论的艺术。它们不仅包括当前的细化技术作为特殊情况，而且还提供更强大的网格细化规则，允许局部和自适应细分表面的细化。第二个领域的结果也将使CAD/CAM系统有可能包括细分曲面作为一个新的，但更一般的自由曲面建模工具，因为b样条和NURBS是细分曲面的特殊情况。

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.