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Joined: Mar 2010
31-03-2010, 11:12 PM

Meshes are dominantly used to represent 3D models as they fit well with graphics rendering hardware. Features such as volume, moments, and Fourier transform coeffi- cients need to be calculated from the mesh representation efficiently. In this paper, we propose an algorithm to cal- culate these features without transforming the mesh into other representations such as the volumetric representa- tion. To calculate a feature for a mesh, we show that we can first compute it for each elementary shape such as a triangle or a tetrahedron, and then add up all the values for the mesh. The algorithm is simple and efficient, with many potential applications.
Presented By:
Cha Zhang and Tsuhan Chen
Dept. of Electrical and Computer Engineering, Carnegie Mellon University


3D scene/object browsing is becoming more and more popular as it engages people with much richer experience than 2D images. The Virtual Reality Modeling Language (VRML) , which uses mesh models to represent the 3D content, is rapidly becoming the standard file format for the delivery of 3D contents across the Internet. Tradition- ally, in order to fit graphics rendering hardware well, a VRML file models the surface of a virtual object or envi- ronment with a collection of 3D geometrical entities, such as vertices and polygons. In many applications, there is a high demand to calcu- late some important features for a mesh model, e.g., the volume of the model, the moments of the model, or even the Fourier transform coefficients of the model. One ex- ample application is the search and retrieval of 3D models in a database 2 3 . Another example is shape analysis and object recognition . Intuitively, we may calculate these features by first transforming the 3D mesh model into its volumetric representation and then finding these features in the voxel space. However, transforming a 3D mesh model into its volumetric representation is a time- consuming task, in addition to a large storage requirement
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