Tetrahedral mesh compression with the cut-border machine

In recent years, substantial progress has been achieved in the area of volume visualization on irregular grids, which is mainly based on tetrahedral meshes. Even moderately fine tetrahedral meshes consume several mega-bytes of storage. For archivation and transmission compression algorithms are essential. In scientific applications lossless compression schemes are of primary interest. This paper introduces a new lossless compression scheme for the connectivity of tetrahedral meshes. Our technique can handle all tetrahedral meshes in three dimensional euclidean space even with non manifold border. We present compression and decompression algorithms which consume for reasonable meshes linear time in the number of tetrahedra. The connectivity is compressed to less than 2.4 bits per tetrahedron for all measured meshes. Thus a tetrahedral mesh can almost be reduced to the vertex coordinates, which consume in a common representation about one quarter of the total storage space. We complete our work with solutions for the compression of vertex coordinates and additional attributes, which might be attached to the mesh.