Lossless Compression of Hexahedral Meshes

Abstract

Many science and engineering applications use high-resolution unstructured hexahedral meshes to model solid 3D shapes for finite element simulations. These simulations frequently dump the mesh and associated fields to disk for subsequent analysis, which involves the transfer of huge volumes of data. To reduce requirements on disk space and bandwidth, we propose efficient schemes for lossless online compression of hexahedral mesh geometry and connectivity. Our approach is to use hash-based value predictors to transform the mesh connectivity list into a more compact byte-aligned stream of symbols that can then be efficiently compressed using conventional text compressors such as gzip. Our scheme is memory efficient, fast, and simple to implement, and yields 1-3 orders of magnitude reduction on a set of benchmark meshes. For geometry and field coding, we derive a set of local spectral predictors optimized for each possible configuration of previously encoded and thus available vertices within a hexahedron. Combined with lossless floating-point residual coding, this approach improves considerably upon prior predictive geometry coding schemes.

Streaming compression of hexahedral meshes

“…In Table 2 we list the compression rates of our scheme on different models and compare them to those of [7], [14] and [15]. As expected, our rates are worse than those of degree-based methods since we compress the hexahedra in their original order.…”

“…In Table 2 we list our geometry compression rates across our set of test meshes side by side with those of [7] and [15]. For fair comparison we use a newer version of [7] that also uses spectral prediction.…”

“…Lindstrom and Isenburg [15] propose a radically different compressor that neither reorders vertices nor hexahedra and is therefore completely lossless. It also handles nonmanifold meshes or degenerate elements.…”

“…Three algorithms have been published on the subject of hexahedral mesh compression [7,14,15]. Isenburg and Alliez [7] extend the concept of degree coding (that was introduced by Touma and Gotsman for triangle meshes [19]) to compress the connectivity of hexahedral meshes.…”

“…The fundamental assumption of all compression schemes (except [15]) is that the particular order in which mesh vertices and mesh elements are stored does not need to be preserved. Most schemes firs construct the mesh connectivity graph, traverse it in some deterministic manner, and encode vertices and elements as they are encountered-thereby reordering them.…”