Lossless Geometry Compression for Steady-State and Time-Varying Tetrahedral Meshes

In recent years, new challenges for scientific visualization have emerged as the size of data generated from simulations has grown exponentially. The emerging demand for efficiently storing, transmitting, and visualizing such data in networked environments has motivated research in graphics compression for 3D polygonal models and volumetric datasets. The most general class of volumetric data is irregular-grid volume data represented as a tetrahedral mesh. It has been proposed as an effective means of representing disparate field data that arise in a broad spectrum of scientific applications. Although there has been a significant amount of research done on tetrahedral mesh compression, most techniques reported in the literature have mainly focused on compressing connectivity information, rather than geometry information which consists of vertex-coordinates and data attributes (such as scalar values in our case). As a result, while connectivity compression achieves an impressive compression rate of 1–2 bits per triangle for triangle meshes [5, 4, 1, 6] and 2.04–2.31 bits per tetrahedron for tetrahedral meshes [2, 7], progress made in geometry compression has not been equally impressive. For a tetrahedral mesh, typically about 30 bits per vertex (not including the scalar values) are required after compression [2], and we do not know of any reported results on compressing time-varying fields over irregular grids. Given that the number of tetrahedra in a tetrahedral mesh is typically about 4.5 times the number of vertices and that connectivity compression results in about 2 bits per tetrahedron, it is clear that geometry compression is the bottleneck in the overall graphics compression. The situation gets worse for time-varying datasets where each vertex can have hundreds or even thousands of time-step scalar values. The disparity between bit rates needed for representing connectivity and the geometry gets further amplified when lossless compression is required. Interestingly, whereas almost all connectivity compression techniques are lossless, geometry compression results in the literature almost always include a quantization step which makes them lossy (the only exception is the recent technique of [3] for polygonal meshes). While lossy compression might be acceptable for usual graphics models to produce an approximate visual effect to “fool the eyes,” it is often not acceptable for scientific applications where lossless compression is desired. This is especially true for irregular-grid meshes which represent disparate field data, with more points sampled in regions containing more features. Applying any quantization often results in the collapse between neighboring points which are densely sampled, causing a loss of potentially important features in the data. Moreover, as