__abstract:__

Unstructured hexahedral volume meshes are of particular interest for visualization
and simulation applications. They allow regular tiling of the three-dimensional
space and show good numerical behaviour in finite element computations. Beside
such appealing properties, volume meshes take up huge amounts of space when stored
in a raw format. In this paper we present a technique for encoding connectivity and
geometry of unstructured hexahedral volume meshes.

For connectivity compression, we extend the idea of coding with degrees as pioneered
by Touma and Gotsman to volume meshes. Hexahedral connectivity is coded as a sequence
of edge degrees. This naturally exploits the regularity of typical hexahedral meshes.
We achieve compression rates of around 1.5 bits per hexahedron (bph) that go down to
0.18 bph for regular meshes. On our test meshes the average connectivity compression
ratio is 1:162.

For geometry compression, we perform simple parallelogram prediction on uniformly
quantized vertices within the side of a hexahedron. Tests show an average geometry
compression ratio of 1:3.7 at a quantization level of 16 bits.

__main contributions:__

__publication:__

---> appeared also as a journal version in Graphical Models, Volume 65, Issue 4, pages 239-257, July 2003.

__related publications:__

__downloads:__

__hindsights:__

The described data structure for compression is unnecessarily bloated. A more efficient
implementation would separate the data structure into a static part that stores hexahedral
connectivity and a dynamic part that maintains the hull. The described prediction for the
position of the last vertex of a hexahedron (by far the most frequent case) should be replaced
by the more efficient Lorenzo
prediction. This improves geometry compression rates further
and is already implemented in the available source code.

__funding:__