Conditions for unique graph realizations
SIAM Journal on Computing
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
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
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Face fixer: compressing polygon meshes with properties
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A fast multi-scale method for drawing large graphs
AVI '00 Proceedings of the working conference on Advanced visual interfaces
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Efficient Coding of Non-Triangular Mesh Connectivity
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
SwingWrapper: Retiling triangle meshes for better edgebreaker compression
ACM Transactions on Graphics (TOG)
On the optimality of spectral compression of mesh data
ACM Transactions on Graphics (TOG)
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Mesh analysis via breadth-first traversal
Proceedings of the 48th Annual Southeast Regional Conference
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
SMI 2011: Full Paper: Parallel computation of spherical parameterizations for mesh analysis
Computers and Graphics
Proceedings of Graphics Interface 2012
Graph drawing by subspace optimization
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Graphics Interaction: 5-6-7 Meshes: Remeshing and analysis
Computers and Graphics
Geometry curves: A compact representation for 3D shapes
Graphical Models
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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We describe a method to visualize the connectivity graph of a mesh using a natural embedding in 3D space. This uses a 3D shape representation that is based solely on mesh connectivity --- the connectivity shape. Given a connectivity, we define its natural geometry as a smooth embedding in space with uniform edge lengths and describe efficient techniques to compute it. Our main contribution is to demonstrate that a surprising amount of geometric information is implicit in the connectivity.We also show how to generate connectivity shapes that approximate given 3D shapes. Potential applications of connectivity shapes to modeling and mesh coding are described.