...on mesh compression

Since today's computers do not have the memory or the compute power to efficiently render large data sets on the order of gigabytes in size, scientists have difficulty visualizing and understanding commonly available datasets. To deal with the crippling size of this data, we must find robust and efficient compression algorithms to store, retrieve, render, and probe the data. Ideally, large data sets will be compactly stored offsite in a repository. Whenever some data is needed, only a coarse but very accurate representation will be retrieved. Although very coarse, this initial representation of the data will be detailed enough to serve as a "map" to guide the navigator of this data to desired destinations. A desired destination might be a vortex in a fluid flow or a wavefront in an explosives simulation.

We believe that by coupling semi-regular connectivity meshes with multiresolution mesh compression schemes, we will get the performance gain and the awareness of data behavior that we want. As described earlier, semi-regular meshes have the very desirable features of a hierarchical structure, a smooth parameterization, and a mathematical machinery related to wavelets. The hierarchical structure and smooth parameterization leads immediately to better compression of both mesh connectivity and vertex geometry.

Our work with multiresolution mesh compression schemes is currently in the general setting of irregular connectivity meshes. Irregular meshes lack a hierarchical structure, which is inherent in semi-regular meshes. However, a hierarchical structure can be rapidly built on top of irregular meshes. Although predictive coding of vertices on irregular meshes might not do better than a mesh with smooth parameterization, studying irregular meshes will be useful since ideas learned from the general, irregular setting can always be carried over to the specific, semi-regular setting. In this project, a Dobkin-Kirkpatrick hierarchy will be built on top of an irregular mesh to give it an LOD structure. Two parts need to be addressed: mesh connectivity and vertex geometry. Since connectivity information is currently very well compressed (~1-2 bits/triangle), the focus is on the vertex geometry, which takes up about 80\% of a compressed mesh. We seek better predictors that take into account the non-smooth parameterization of an irregular mesh. Recent ideas on irregular subdivision will be helpful in constructing parameterization dependent predictors for vertex positions, as well as for other continuous data attached to vertices. When considering parameterizations, there are two extremes. One is to fully account for parameterization and the other is to ignore it completely (i.e., assume a smooth parameterization). On irregular meshes, assuming smooth parameterization gives bad predictors. Taking into account the parameterization will give much better predictors, but at the cost of extra bits of information. Work is needed to find the proper balance.