Streaming Tetrahedral Volume Meshes

In a streaming mesh format, tetrahedral and the vertices they reference are stored in an interleaved fashion.

This makes it possible to start operating on the data immediately without having to first load all the vertices, as is common practice with standard indexed formats. Furthermore, streaming formats provide explicit information about when vertices are referenced for the last time. This makes it possible to complete operations on these vertices and free the corresponding data structures for immediate reuse. The width of a streaming mesh is the maximal number of vertices that need to be in memory simultaneously. Those are vertices that have already streamed in but have not been finalized yet. The width is the lower bound for the amount of memory needed for processing a streaming mesh since any mesh processing application has to store at least that many vertices simply to dereference the mesh.

The streaming approach to compression relies on the input meshes either being stored or produced in a streaming manner.

The set of example volume meshes that we use to test our compressor, however, does not fulfill these expectations at all.

Not only arethese tetrahedral meshes distributed in conventional, non-streaming formats, they also come with absolutely “un-streamable” element orders, as illustrated by the layout diagrams. The horizontal axis represents the tetrahedral (in the order they occur in the file), and the vertical axis represents the vertices (also echoing their order in the file. The few unclassified data sets that are currently used by the visualization community for performance measurements were created several years ago. Back then, the difficulty of using random access in-core algorithms for producing larger and larger meshes were overcome simply by employing sufficiently powerful computer equipment. But only when there is enough main memory to hold the entire mesh is it possible to output meshes whose vertices and tetrahedral are ordered so “randomly” in the file.

In the near future we anticipate a new generation of meshing algorithms that produces and outputs volume mesh

data in a more coherent fashion. This is a necessity if algorithms are to scale to increasingly large data sets. An algorithm for tetrahedral mesh refinement, for example, could be designed to sweep over the data set and restrict its operation at any time to the currently active set until it achieves the desired element quality. For a mesh generation algorithm operating in this manner, it is natural to output reasonably coherent meshes in a streaming manner. To stream legacy data stored in non-streaming formats or with highly incoherent layouts  describe several conversion strategies.


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