Short encodings of planar graphs and maps
Discrete Applied Mathematics
Arithmetic coding for data compression
Communications of the ACM
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
Real time compression of triangle mesh connectivity
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Counting and random generation of strings in regular languages
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Compressing large polygonal models
Proceedings of the conference on Visualization '01
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Single Resolution Compression of Arbitrary Triangular Meshes with Properties
DCC '99 Proceedings of the Conference on Data Compression
Out-of-core compression for gigantic polygon meshes
ACM SIGGRAPH 2003 Papers
Growth-sensitivity of context-free languages
Theoretical Computer Science - WORDS
A bijection for triangulations of a polygon with interior points and multiple edges
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
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In this work Markov Models are constructed to describe the asymptotic stochastical behavior of regular languages, what allows for optimal arithmetic coding of words from the language. A new method is presented for the optimization of Markov Models such that also constraints are captured that cannot be described within a regular language. The new technique is applied to the encoding of the connectivity graph of triangle meshes of low genus and boundary fraction. The resulting compression rates are up to one percent optimal and the best known upper bound for this class of models.