Short encodings of planar graphs and maps
Discrete Applied Mathematics
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Time/space tradeoffs for polygon mesh rendering
ACM Transactions on Graphics (TOG)
Optimized geometry compression for real-time rendering
VIS '97 Proceedings of the 8th conference on Visualization '97
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
WRAP&Zip decompression of the connectivity of triangle meshes compressed with edgebreaker
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Face fixer: compressing polygon meshes with properties
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
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
Efficient Coding of Non-Triangular Mesh Connectivity
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
3D Compression Made Simple: Edgebreaker with Zip&Wrap on a Corner-Table
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Compressing polygon mesh geometry with parallelogram prediction
Proceedings of the conference on Visualization '02
BLIC: bi-level isosurface compression
Proceedings of the conference on Visualization '02
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Compressing the property mapping of polygon meshes
Graphical Models - Pacific graphics 2001
Out-of-core compression for gigantic polygon meshes
ACM SIGGRAPH 2003 Papers
Compressing hexahedral volume meshes
Graphical Models - Special issue on Pacific graphics 2002
A unified approach for fairing arbitrary polygonal meshes
Graphical Models
Wavelet compression of parametrically coherent mesh sequences
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Geometry prediction for high degree polygons
Proceedings of the 21st spring conference on Computer graphics
Fast reconstruction of Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Algebraic analysis of high-pass quantization
ACM Transactions on Graphics (TOG)
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Connectivity compression for non-triangular meshes by context-based arithmetic coding
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Fast and Efficient Compression of Floating-Point Data
IEEE Transactions on Visualization and Computer Graphics
Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling
ACM Transactions on Algorithms (TALG)
Quick encoding of plane graphs in log 214 bits per edge
Information Processing Letters
Succinct representations of planar maps
Theoretical Computer Science
Fast reconstruction of Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Random accessible hierarchical mesh compression for interactive visualization
SGP '09 Proceedings of the Symposium on Geometry Processing
Technologies for 3D mesh compression: A survey
Journal of Visual Communication and Image Representation
LR: compact connectivity representation for triangle meshes
ACM SIGGRAPH 2011 papers
Planar graphs, via well-orderly maps and trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Adaptive vertex chasing for the lossless geometry coding of 3d meshes
PCM'05 Proceedings of the 6th Pacific-Rim conference on Advances in Multimedia Information Processing - Volume Part I
SMI 2012: Full Progressive compression of manifold polygon meshes
Computers and Graphics
Compression of point-based 3D models by shape-adaptive wavelet coding of multi-height fields
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Triangle mesh compression along the Hamiltonian cycle
The Visual Computer: International Journal of Computer Graphics
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Encoders for triangle mesh connectivity based on enumeration of vertex valences are among the best reported to date. They are both simple to implement and report the best compressed file sizes for a large corpus of test models. Additionally they have recently been shown to be near-optimal since they realize the Tutte entropy bound for all planar triangulations. In this paper we introduce a connectivity encoding method which extends these ideas to 2-manifold meshes consisting of faces with arbitrary degree. The encoding algorithm exploits duality by applying valence enumeration to both the primal and the dual mesh in a symmetric fashion. It generates two sequences of symbols, vertex valences, and face degrees, and encodes them separately using two context-based arithmetic coders. This allows us to exploit vertex or face regularity if present. When the mesh exhibits perfect face regularity (e.g., a pure triangle or quad mesh) or perfect vertex regularity (valence six or four respectively) the corresponding bit rate vanishes to zero asymptotically. For triangle meshes, our technique is equivalent to earlier valence-driven approaches. We report compression results for a corpus of standard meshes. In all cases we are able to show coding gains over earlier coders, sometimes as large as 50%. Remarkably, we even slightly gain over coders specialized to triangle or quad meshes. A theoretical analysis reveals that our approach is near-optimal as we achieve the Tutte entropy bound for arbitrary planar graphs of two bits per edge in the worst case.