高精度常平均曲率曲面建模理论与应用研究

项目名称： 高精度常平均曲率曲面建模理论与应用研究

项目编号： No.61572288

项目类型： 面上项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 周元峰

作者单位： 山东大学

项目金额： 16万元

中文摘要： 本项目提出了一种构造高精度常平均曲率（Constant Mean Curvature，简称CMC）曲面的统一优化框架，为构造高质量离散曲面模型尤其是自然曲面模型提供新的解决方案和思路。该类型曲面在建筑造型、物理模拟等领域具有广泛的应用背景，本项目将以以上领域的应用需求为中心，展开曲面模型的构造理论和算法研究。主要研究内容包括：1)研究CMC曲面的几何属性，建立一个统一的高精度、带约束CMC曲面构造及优化理论框架；2)研究多约束情况下CMC曲面构造目标函数的有效优化方法；3)研究带有物理属性约束及精确体积控制下的CMC曲面构造；4)带约束CMC曲面的应用。研究范围涉及理论与方法、技术和原型系统。项目主要目标是为解决高精度、带约束CMC曲面建模及应用问题提供新理论和方法，并提供一系列简单、高效和鲁棒的技术，为上述领域中的相关理论和算法问题的解决提供新的思路和手段，具有很好的理论意义和应用价值。

中文关键词： 常平均曲率曲面；建模；高精度；测地距离；超像素

英文摘要： In this proposal, we present a uniform optimization framework for constructing accurate constant mean curvature (CMC for short) surfaces. This framework can supply new solutions and thoughts for high quality discrete meshes modeling for approximating constant mean curvature surfaces which are natural surfaces. This kind of surfaces have wide application background in architecture modeling, physical simulation area, and so on. We will focus on the application expanding in these areas and study CMC surfaces modeling theories in this project. This project will take a systematic research to this argument, including: (1) Study the geometric properties of CMC surface, we will present a uniform framework for accurate and flexible Constant Mean Curvature surfaces discrete modeling; (2) Efficient optimizing method is studied to solve this constrained optimization energy function for constructing CMC surfaces; (3) The accurate volume control with physical property constraints CMC surface construction; (4) The applications of CMC surfaces with constraints. The research include theories, methods, technologies and prototype system. This project will give new theories and methods for accurate and flexible CMC surfaces modeling. The completion of the project will provide new theories and methods for solving the construction of

英文关键词： Constant mean curvature surface；modelling；high quality；geodesic distance；superpixels