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

Princeton University, Princeton NJ

Investigators

Abstract

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