Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An introduction to solid modeling
An introduction to solid modeling
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Directed edges—A scalable representation for triangle meshes
Journal of Graphics Tools
Proceedings of the sixth ACM symposium on Solid modeling and applications
A scalable data structure for three-dimensional non-manifold objects
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
3D Compression Made Simple: Edgebreaker with Zip&Wrap on a Corner-Table
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Geometric algorithms and data representation for solid freeform fabrication
Geometric algorithms and data representation for solid freeform fabrication
A data structure for non-manifold simplicial d-complexes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
CHF: A Scalable Topological Data Structure for Tetrahedral Meshes
SIBGRAPI '05 Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
X-maps: An Efficient Model for Non-manifold Modeling
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
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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We propose a compact, dimension-independent data structure for manifold, non-manifold and non-regular simplicial complexes, that we call the Generalized Indexed Data Structure with Adjacencies (IA^@?data structure). It encodes only top simplices, i.e. the ones that are not on the boundary of any other simplex, plus a suitable subset of the adjacency relations. We describe the IA^@? data structure in arbitrary dimensions, and compare the storage requirements of its 2D and 3D instances with both dimension-specific and dimension-independent representations. We show that the IA^@? data structure is more cost effective than other dimension-independent representations and is even slightly more compact than the existing dimension-specific ones. We present efficient algorithms for navigating a simplicial complex described as an IA^@? data structure. This shows that the IA^@? data structure allows retrieving all topological relations of a given simplex by considering only its local neighborhood and thus it is a more efficient alternative to incidence-based representations when information does not need to be encoded for boundary simplices.