Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
An efficient algorithm for CSG to b-rep conversion
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Three-dimensional alpha shapes
VVS '92 Proceedings of the 1992 workshop on Volume visualization
Product operator on cell complexes
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
A model for n-dimensional boundary topology
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Degenerate convex hulls on-line in any fixed dimension
Proceedings of the fourteenth annual symposium on Computational geometry
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Applying parallel processing techniques to classification problems in constructive solid geometry
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the sixth ACM symposium on Solid modeling and applications
Star-vertices: a compact representation for planar meshes with adjacency information
Journal of Graphics Tools
IEEE Computer Graphics and Applications
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
A scalable data structure for three-dimensional non-manifold objects
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Decomposing non-manifold objects in arbitrary dimensions
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Techniques for visualizing 3-dimensional manifolds
VIS '90 Proceedings of the 1st conference on Visualization '90
A bézier-based approach to unstructured moving meshes
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A data structure for non-manifold simplicial d-complexes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Update operations on 3D simplicial decompositions of non-manifold objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Consistency constraints and 3D building reconstruction
Computer-Aided Design
On converting sets of tetrahedra to combinatorial and PL manifolds
Computer Aided Geometric Design
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Signatures of Combinatorial Maps
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
5D data modelling: full integration of 2D/3D space, time and scale dimensions
GIScience'10 Proceedings of the 6th international conference on Geographic information science
Efficient search of combinatorial maps using signatures
Theoretical Computer Science
LR: compact connectivity representation for triangle meshes
ACM SIGGRAPH 2011 papers
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Equivalence between regular n-G-maps and n-surfaces
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Representing topological structures using cell-chains
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Q-Complex: Efficient non-manifold boundary representation with inclusion topology
Computer-Aided Design
Zipper: A compact connectivity data structure for triangle meshes
Computer-Aided Design
The simplex tree: an efficient data structure for general simplicial complexes
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Compact combinatorial maps in 3d
CVM'12 Proceedings of the First international conference on Computational Visual Media
Compact combinatorial maps: A volume mesh data structure
Graphical Models
ImG-complex: graph data model for topology of unstructured meshes
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Using extrusion to generate higher-dimensional GIS datasets
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Modelling higher dimensional data for GIS using generalised maps
ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
Flower modelling using natural interface and 3Gmap L-systems
Proceedings of the 12th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
Database support for unstructured meshes
Proceedings of the VLDB Endowment
Technical note: Linear algebraic representation for topological structures
Computer-Aided Design
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We develop a representation for the topological structure of subdivided manifolds (with and without boundary) of dimension d ≥ 1 which allows straightforward access of the available order information. It is shown that there exists a large amount of ordering information in subdivided manifolds: given a (k-2)-cell in the boundary of a (k+1)-cell, 1 ≤ k ≤ d, all of the k- and (k-1)-cells 'between them' can be ordered 'around' the (k-2)-cell. This includes the usual orderings in 2- and 3-dimensional objects. We introduce the 'cell-tuple structure', a simple, uniform representation of the incidence and ordering information in a subdivided manifold. It includes the quad-edge data structure of Guibas and Stolfi [GS 85] and the facet-edge data structure of Dobkin and Laszlo [DL 87] as special cases in dimensions 2 and 3, respectively.