Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Introduction to Solid Modeling
Introduction to Solid Modeling
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Two data structures for building tetrahedralizations
The Visual Computer: International Journal of Computer Graphics
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision
Mathematics of Computation
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Grow & fold: compression of tetrahedral meshes
Proceedings of the fifth ACM symposium on Solid modeling and applications
Tetrahedral mesh compression with the cut-border machine
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Implant sprays: compression of progressive tetrahedral mesh connectivity
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Directed edges—A scalable representation for triangle meshes
Journal of Graphics Tools
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
On-the-Fly rendering of losslessly compressed irregular volume data
Proceedings of the conference on Visualization '00
An out-of-core method for computing connectivities of large unstructured meshes
EGPGV '02 Proceedings of the Fourth Eurographics Workshop on Parallel Graphics and Visualization
TetFusion: an algorithm for rapid tetrahedral mesh simplification
Proceedings of the conference on Visualization '02
Interactive view-dependent rendering of large isosurfaces
Proceedings of the conference on Visualization '02
Star-vertices: a compact representation for planar meshes with adjacency information
Journal of Graphics Tools
Simplification of Tetrahedral Meshes with Error Bounds
IEEE Transactions on Visualization and Computer Graphics
WBIA '98 Proceedings of the IEEE Workshop on Biomedical Image Analysis
A scalable data structure for three-dimensional non-manifold objects
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Multiresolution Tetrahedral Meshes: An Analysis and a Comparison
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Texture-Encoded Tetrahedral Strips
VV '04 Proceedings of the 2004 IEEE Symposium on Volume Visualization and Graphics
TetStreamer: Compressed Back-to-Front Transmission of Delaunay Tetrahedra Meshes
DCC '05 Proceedings of the Data Compression Conference
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
The Half-Edge Tree: A Compact Data Structure for Level-of-Detail Tetrahedral Meshes
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
View-dependent tetrahedral meshing and rendering
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
CHF: A Scalable Topological Data Structure for Tetrahedral Meshes
SIBGRAPI '05 Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Streaming compression of tetrahedral volume meshes
GI '06 Proceedings of Graphics Interface 2006
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Streaming Simplification of Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Random-Accessible Compressed Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
The PR-star octree: a spatio-topological data structure for tetrahedral meshes
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Explicit array-based compact data structures for triangulations
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Q-Complex: Efficient non-manifold boundary representation with inclusion topology
Computer-Aided Design
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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The Corner Table (CT) promoted by Rossignac et al. provides a simple and efficient representation of triangle meshes, storing 6 integer references per triangle (3 vertex references in the V table and 3 references to opposite corners in the O table that accelerate access to adjacent triangles). The Compact Half Face (CHF) proposed by Lage et al. extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the V table and 4 in the O table). We call it the Vertex Opposite Table (VOT) and propose a sorted variation, SVOT, which does not require any additional storage and yet provides, for each vertex, a reference to an incident corner from which an incident tetrahedron may be recovered and the star of the vertex may be traversed at a constant cost per visited element. We use a set of powerful wedge-based operators for querying and traversing the mesh. Finally, inspired by tetrahedral mesh encoding techniques used by Weiler et al. and by Szymczak and Rossignac, we propose our Sorted O Table (SOT) variation, which eliminates the V table completely and hence reduces storage requirements by 50% to only 4 references and 9 bits per tetrahedron, while preserving the vertex-to-incident-corner references and supporting our wedge operators with a linear average cost.