Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An introduction to solid modeling
An introduction to solid modeling
Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Representing geometric structures in d dimensions: topology and order
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
An extension of manifold boundary representations to the r-sets
ACM Transactions on Graphics (TOG)
A boundary representation for form features and non-manifold solid objects
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
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
Converting sets of polygons to manifold surfaces by cutting and stitching
ACM SIGGRAPH 98 Conference abstracts and applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Matchmaker: manifold BReps for non-manifold r-sets
Proceedings of the fifth 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
Out-of-core build of a topological data structure from polygon soup
Proceedings of the sixth ACM symposium on Solid modeling and applications
A multi-resolution topological representation for non-manifold meshes
Proceedings of the seventh ACM symposium on Solid modeling and applications
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
Non-manifold Decomposition in Arbitrary Dimensions
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Representation of non-manifold objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling 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
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
A data structure for non-manifold simplicial d-complexes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
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
A decomposition-based representation for 3D simplicial complexes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computer Aided Geometric Design
Finite Element/Fictitious Domain programming for flows with particles made simple
Advances in Engineering Software
Hi-index | 0.00 |
In this paper, we address the problem of representing and manipulating non-manifold, mixed-dimensional objects described by three-dimensional simplicial complexes embedded in the 3D Euclidean space. We describe the design and the implementation of a new data structure, that we call the non-manifold indexed data structure with adjacencies (NMIA), which can represent any three-dimensional Euclidean simplicial complex compactly, since it encodes only the vertices and the top simplexes of the complex plus a restricted subset of topological relations among simplexes. The NMIA structure supports efficient traversal algorithms which retrieve topological relations in optimal time, and it scales very well to the manifold case. Here, we sketch traversal algorithms, and we compare the NMIA structure with data structures for manifold and regular 3D simplicial complexes.