|Ph.D Thesis||Department of Computer Science|
|Supervisor:||Prof. Gotsman Chaim Craig|
3D-mesh is the major representation of 3D objects that is used as an input for graphics rendering engines. Its major elements are geometry and connectivity. The increasing demand for realistic rendering has meant that more and more vertices, edges and faces are added to the mesh, thereby inserting the required fine details. This leads to huge meshes with millions of faces, which are difficult to render and process.
Animation may also be applied to 3D meshes by making the geometry vary from frame to frame. The most realistic animation specifies the position of all the mesh vertices in each frame. Such presentation indeed benefits from the lack of limitations. However, the geometry is multiplied by the number of frames, which produces an even more substantial complexity problem.
In order to make large meshes suitable for rendering and mesh processing, several algorithms were developed that compress and reduce the mesh size.
Spectral tools are commonly used in the field of information theory. This work uses spectral techniques for the compression of 3D meshes. It shows how to generate the spectral bases, transform the mesh geometry with it and use the spectral representation for compression purposes. It also generalizes the spectral tools for use in animation sequences, thereby significantly reducing their size. This work also demonstrates the use of Haar wavelet bases in a fully progressive and lossless compression technique. Finally, this work discusses several techniques and improvements for the parameterization of 3D meshes.