Compression of Arbitrary Cutting Planes

We present an efficient algorithm for compressing the data necessary to represent an arbitrary cutting plane extracted from a three dimensional curvilinear data set. The cutting plane technique is an important visualization method for time-varying 3D simulation results since the data sets are often so large. An efficient compression algorithm for these cutting planes is especially important when the simulation running on a remote server is being tracked or the data set is stored on a remote server. Various aspects of the visualization process are considered in the algorithm design, such as the inherent data reduction in going from 3D to 2D when generating a cutting plane, the numerical accuracy required in the cutting plane, and the potential to decimate the triangle mesh. After separating each floating point number into mantissa and exponent, a block sorting algorithm and an entropy coding algorithm are used to perform lossless compression. Summary In Computational Field Simulations (CFS), several gigabytes of data are often generated in a single simulation. How to examine all these data quickly and efficiently, and yet grasp all the information, is a unsolved problem for CFS researchers and practicers. A CFS data set is often stored as a 3D structured (curvilinear) grid over space with functional values (temperature, pressure, velocity, momentum, salinity) associated with each point. One way to examine the data is to create cutting planes across this data volume. Algorithms exist to compute both the cutting plane (a surface consisting of triangles) and the data that should be on the cutting planes (usually associated with the vertices of the triangles). Each cutting plane is constructed by determining the intersections of the user-defined cutting plane and the curvilinear CFS grid. The functional value at each of those intersection points is determined by interpolating between known values at the grid points of the curvilinear grid. The triangle connectivity is easily determined since the cells that are sliced are convex hexahedrons. However, numerous degenerate (redundant) and very slender (irrelevant) triangles are often created. Advances in simulation techniques and computational technology now allow us to simulate complicated phenomena at a multitude of spatio-temporal scales with very high accuracy. However, these simulations generate very large datasets and often can only run efficiently on large supercomputers, most of which are located in remote locations, while the research scientists may be located anyway. Unfortunately the communication links to these large computational centers are inferior to the computational power therein. Demand thus arises for techniques to allow scientists to remotely track, steer, and analyze the simulations run on these supercomputers. By eliminating redundant data produced by the standard visualization techniques, separating the floating point numbers into mantissa and exponent to code, and using a block sorting algorithm, we are able to losslessly compress the cutting plane data (geometry and functional values) on the order of 10:1. By adjusting the data accuracy to match the visualization accuracy, even more, albeit lossy, compression can be obtained.