Symmetry Analysis of 3D Shapes and its Applications in Computer Graphics

3D 形状的对称性分析及其在计算机图形学中的应用

• 批准号: 0702672
• 负责人: Thomas Funkhouser
• 金额: --
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0702672&HistoricalAwards=false
• 关键词: Symmetry; Analysis; 3D; Shapes; its

Symmetry Analysis of 3D Shapes and its Applications in Computer GraphicsThomas FunkhouserSymmetry is a fundamental property of 3D shape. Understanding an object's symmetries provides insight into its overall shape, its decomposition into parts, its balance of mass, and its possibilities for motion. Meanwhile, symmetry is ubiquitous in our world. Almost all man-made objects exhibit some perfect symmetry, and many organic structures are nearly symmetric and/or composed of nearly symmetric parts (e.g., the bodies of animals). For decades, however, computer graphics researchers have ignored symmetries when designing geometric processing algorithms, instead focusing upon local shape features and/or differential surface properties when manipulating surfaces. As a result, for example, surface reconstruction algorithms produce asymetric meshes for symmetric objects, mesh compression techniques fail to take advantage of approximate symmetries, and mesh completion algorithms fill holes by extrapolating surface properties near their boundaries rather than by copying shape features from symmetric parts. Clearly, methods for analyzing and exploiting the symmetries of an object could greatly improve these and other surface processing applications.The research is accomplishing the following: (1) investigating the theory of symmetry for 3D shapes, (2) developing analysis algorithms for characterizing symmetries of 3D shapes, and (3) demonstrating the utility of symmetry analysis in several computer graphics applications. Expected research results include new multiresolution descriptions of the approximate symmetries of an object and new algorithms that use these descriptions for remeshing, compression, completion, reverse engineering, and editing of 3D meshes. The immediate impact on computer graphics is not only new algorithms for shape analysis, but perhaps also a new way of thinking - understanding and preserving global properties of shape (e.g., symmetry) when editing and processing surfaces, rather than focusing only on local geometric properties. The broader impacts will be felt in other fields that benefit from improved symmetry analysis and in integrated educational activities.

3D图形的对称性分析及其在计算机图形学中的应用对称性是3D图形的一个基本性质。 了解一个物体的对称性可以深入了解它的整体形状，分解成部分，质量平衡以及运动的可能性。 同时，对称性在我们的世界中无处不在。 几乎所有的人造物体都表现出某种完美的对称性，许多有机结构几乎是对称的和/或由几乎对称的部分组成（例如，动物的尸体）。 然而，几十年来，计算机图形学研究人员在设计几何处理算法时忽略了对称性，而是在操纵表面时专注于局部形状特征和/或微分表面特性。 因此，例如，表面重建算法产生对称对象的非对称网格，网格压缩技术未能利用近似对称性，网格完成算法通过外推其边界附近的表面属性来填充孔，而不是通过从对称部分复制形状特征。显然，分析和利用物体的对称性的方法可以极大地改善这些和其他表面处理应用，本研究完成了以下工作：（1）研究三维形状的对称性理论，（2）开发表征三维形状对称性的分析算法，（3）展示对称性分析在几种计算机图形学应用中的实用性。 预期的研究成果包括一个对象的近似对称性的新的多分辨率描述和新的算法，使用这些描述重新网格化，压缩，完成，逆向工程和编辑的3D网格。 对计算机图形学的直接影响不仅是形状分析的新算法，而且可能是一种新的思维方式-理解和保留形状的全局属性（例如，对称），而不是只关注局部几何属性。 更广泛的影响将在其他领域感受到，受益于改进的对称性分析和综合教育活动。