Tessellation, Fairing, Shape Design, and Trimming Techniques for Subdivision Surface based Modeling

该项目将开发必要的几何算法和设计技术，以支持计算机自动产品实现(CAD/CAM)应用中基于细分曲面的建模。细分曲面已经在几个商业系统中用作基本体，例如AliasIWavefront的Maya、Pixar的Rederman、Nichiman的Mirai和Microspace的Lightwave 3D。然而，由于在曲面细分、曲面光顺、形状设计和曲面裁剪等方面缺乏必要的几何算法和建模技术，它们还没有被用作CAD/CAM系统中的主要曲面表示。这些算法和技术非常重要，因为它们将成为CAD/CAM系统中用于下一代曲面表示的许多基于细分曲面的建模操作的构建块。具体研究内容包括：通过误差控制技术和自适应细化技术进行曲面细分；通过光顺性指示方法和曲面不规则性自动检测和校正技术进行曲面自动光顺；通过基于插值法的形状设计和控制网格处理方法进行形状设计；以及新的曲面修剪曲线表示方案，以避免过高的计算要求。所提出的研究将在基于细分曲面的建模方面取得重大进展，为有限元过程提供一种精确而有效的输入，同时还解决了可制造性问题。设计工程师将被提供有效的工具来将曲面雕刻成以前从未创建过的所需形状。这预计将通过新的布尔运算来实现，以形成更复杂的对象。所生成的工具有望在支持用于CAD/CAM产品设计和开发的下一代曲面表示方面更加可靠。随着这些研究成果的整合，几何设计和自由形式实体造型的研究生课程将得到加强。

This project will develop the necessary geometric algorithms and design technologies that support subdivision surface based modeling in computer automated product realization (CAD/CAM) applications. Subdivision surfaces have already been used as primitives in several commercial systems such as AliasIWavefront's Maya, Pixar's Rederman, Nichiman's Mirai, and Microspace' Lightwave 3D. However they have not been used as a major surface representation in CAD/CAM systems as yet because the necessary geometric algorithms and modeling techniques in surface tessellation, surface fairing, shape design and surface trimming are still lacking. These algorithms and technologies are important as they will be the building blocks of many subdivision surface based modeling operations for next generation surface representation in CAD/CAM systems. Specific research will address surface tessellation through error control techniques and adaptive refinement techniques; automatic surface fairing through fairness indicating methods and automatic surface irregularity detecting and correcting techniques; shape design through interpolation-based shape design and control mesh manipulation methods; and new surface trimming curve representation schemes to avoid excessive computational requirements. The proposed research will provide significant advancement in subdivision surface based modeling, with a precise and efficient way to generate input to the finite element process while also addressing manufacturability issues. Design engineers will be provided with effective tools to sculpt a surface into a desired shape that has not been created before. This is expected to be accomplished through the new Boolean operations to form more complicated objects. The resulting tools are expected to be more reliable in supporting next generation surface representation for CAD/CAM product design and development. Graduate courses in both Geometric Design and Freeform Solid Modeling will be enhanced with the integration of these research results.