# Progressive Lossless Compression of Arbitrary Simplicial Complexes

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifol'' or nearly manifold''. We propose here a progressive geometry compression scheme which can handle manifold models as well as triangle soups'' and 3D tetrahedral meshes. The method is lossless when the decompression is complete which is extremely important in some domains such as medical or finite element. While most existing methods enumerate the vertices of the mesh in an order depending on the connectivity, we use a kd-tree technique which does not depend on the connectivity. Then we compute a compatible sequence of meshes which can be encoded using edge expansion and vertex split. The main contributions of this paper are: the idea of using the kd-tree encoding of the geometry to drive the construction of a sequence of meshes, an improved coding of the edge expansion and vertex split since the vertices to split are implicitly defined, a prediction scheme which reduces the code for simplices incident to the split vertex, and a new generalization of the edge expansion operation to tetrahedral meshes.
Document type :
Journal articles

https://hal.inria.fr/inria-00167216
Contributor : Olivier Devillers <>
Submitted on : Thursday, August 16, 2007 - 4:09:21 PM
Last modification on : Wednesday, September 18, 2019 - 4:36:03 PM
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### Citation

Pierre-Marie Gandoin, Olivier Devillers. Progressive Lossless Compression of Arbitrary Simplicial Complexes. ACM Transactions on Graphics, Association for Computing Machinery, 2002, 21 (Siggraph'2002 Conference proceedings), pp.372-379. ⟨10.1145/566654.566591⟩. ⟨inria-00167216⟩

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