Subdivision Surface Based One-Piece Representation

基于细分曲面的一件式表示

• 批准号: 0310645
• 负责人: Fuhua (Frank) Cheng
• 金额: $ 9.99万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-05-15 至 2006-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0310645&HistoricalAwards=false
• 关键词: Subdivision; Surface; Based; Piece; Representation

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.

DMS-0310645 Fuhua（Frank）Cheng这是一个在http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.This募捐下获得的CARGO孵化奖，为开发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单件表示，即，在设计过程中，无论对象的拓扑或形状多么复杂，都可以仅用一个细分曲面来表示最终对象。因此，最终表示中的部分数量总是最小的：1。 本研究需要从表征细化、表征转换和表征连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，允许局部细化细分曲面的控制网格，同时保持细化过程的无裂纹属性。 表示转换的目的是为不同类型的细分曲面或同一类型但其控制网格具有不同拓扑结构的细分曲面开发转换算法。 表示连接的目的是开发直接和间接连接技术，可以迭代地应用这些技术将物体的不同组成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表面的构建过程，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。实际上，第一个领域的研究结果除了在整体表示中发挥作用外，还将显著地改进现有的细分曲面理论。 它们不仅将当前的细分技术作为特例，而且还提供了更强大的网格细分规则，允许局部和自适应细分曲面。 在第二个领域的结果也将使它有可能为CAD/CAM系统，包括细分曲面作为一个新的，但更一般的自由曲面造型工具，因为B样条和NURBS是特殊情况下细分曲面。