RIA: Cyclides as Blending Surfaces in Geometric Modeling

点击翻译按钮获取中文摘要

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. ***