基于混合网格向量值细分曲面可计算光滑性研究

项目名称： 基于混合网格向量值细分曲面可计算光滑性研究

项目编号： No.11301504

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 李保滨

作者单位： 中国科学院大学

项目金额： 22万元

中文摘要： 计算机辅助几何设计中的细分曲面方法是快速、高效地设计三维形体绘制和展示的重要技术手段。基于混合网格细分曲面方法可以实现多种拓扑几何特征三维形体逼真表示，但仍未能解决在降低算法复杂性同时提高极限曲面光滑性的问题。本项目拟将向量值特征引入混合网格细分方法中，提出一种基于混合网格向量值细分曲面方法。并在分析加细模型特点的基础上，建立模型与小波分析领域中非齐次向量值加细方程的对应关系，借助调和分析中函数空间刻画的相关理论，结合数值分析中联合谱半径迭代算法，探寻并建立其极限曲面光滑性刻画理论以及相应的实现算法。本研究工作有望解决已有基于混合网格细分方法的局限性，提供一种低复杂度、高光滑性的三维形体绘制方法，并且可计算光滑性刻画也将为深入研究小波函数及曲面多尺度分析等应用奠定坚实的理论基础。

中文关键词： 细分曲面；向量值细分曲面；非齐次向量值加细方程；基于混合网格细分曲面方法；向量小波

英文摘要： Subdivision surface is an important technical means for quickly and effectively drawing and displaying three dimensional forms, modellings with the aid of computer in Graphics. Recently, the study and consruction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision strats with a control net consisting of both quads and triangles, and produces finer and finer meshes with quads and triangles. The use of the quad/triangle structure for surface design is motivated by the fact that in CAD modelling, the designers often want to model certain regions with quad meshes and others with triangle meshes to get beeter vivid visul quality of subdivision surface with variety of topological geometry. This project will explore how to introduce the vector-valued feature into the hybrid mesh subdivision method, and study the vector-valued subdivision surface based on quad/triangle grid and its computable smoothness of the limit surface. The whole research process is arranged as following roughly. First, we will show that vector-valued quad/triangle subdivision scheme can be derived from an nonhomogeneous refinement equation which is famous in the field of harmonic analysis and wavelet analysis, and establish an one-to-one relation between them. Secondly, with the help of some results abou

英文关键词： Subdivision scheme；Vector-valued subdivision scheme；Nonhomogeneous vector-valued refinement equation；Quad/triangle subdivision scheme；Multiwavelets