RIA: Cyclides as Blending Surfaces in Geometric Modeling

RIA：几何建模中作为混合曲面的循环

• 批准号: 9410707
• 负责人: Ching-Kuang Shene
• 金额: $ 5.73万
• 依托单位: Northern Michigan University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9410707&HistoricalAwards=false
• 关键词: RIA; Cyclides; Blending; Surfaces; Geometric

9410707 Shene Using a geometric approach, this project aims to completely solve the problem of using Dupin cyclides as blending surfaces for all pairs of CSG primitives, and to explore the possibility that other tractable surfaces, such as the cyclide family, can be used for blending purpose. Initially, the project will investigate the role of Dupin cyclides as blending surfaces for CSG primitives. This includes construction algorithms and characterization results for each pair of CSG primitives and their generalizations. Since constructions are based on the geometric characteristics, not on implicit/parametric equations, the construction algorithms would be more robust. Next, various generalizations of Dupin cyclides (e.g., projective cyclides, general cyclides and quartics with a double conics) will be examined to see if there are viable and tractable classes of lower degree algebraic surfaces for blending purpose. Techniques from descriptive, algebraic and differential geometry will be used to study the geometry of these surface classes and to develop efficient construction algorithms. Finally, some fundamental issues of general blending surface construction will be considered by looking at the connection between the geometry of the intersection curve, the clipping curves, and the blending surfaces. ***

9410707 Shene使用几何方法，该项目旨在完全解决使用Dupin cyclides作为所有CSG基元对的混合曲面的问题，并探索其他易处理曲面（如cyclide族）可用于混合目的的可能性。 最初，该项目将研究Dupin cycrides作为CSG图元的混合曲面的作用。 这包括每对CSG基元及其泛化的构造算法和表征结果。 由于构造是基于几何特征，而不是基于隐式/参数方程，因此构造算法将更鲁棒。 接下来，各种推广的Dupin循环（例如，投影圆线、一般圆线及具有双二次曲线的四次曲线），以探讨是否有可行及易于处理的低次代数曲面类别可供混合之用。 技术从描述，代数和微分几何将被用来研究这些表面类的几何形状，并制定有效的建设算法。 最后，一般的过渡曲面构造的一些基本问题将被认为是通过查看相交曲线，裁剪曲线和过渡曲面的几何之间的连接。 ***