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
Two data structures for building tetrahedralizations
The Visual Computer: International Journal of Computer Graphics
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)
Structured topological complexes: a feature-based API for non-manifold topologies
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling 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
Real-time and physically realistic simulation of global deformation
ACM SIGGRAPH 99 Conference abstracts 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
Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces
IEEE Transactions on Visualization and Computer Graphics
A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
WBIA '98 Proceedings of the IEEE Workshop on Biomedical Image Analysis
Decomposing non-manifold objects in arbitrary dimensions
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
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
Combinatorial 3-Manifolds from Sets of Tetrahedra
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
Semantic annotation of 3D surface meshes based on feature characterization
SAMT'07 Proceedings of the semantic and digital media technologies 2nd international conference on Semantic Multimedia
Polygon mesh repairing: An application perspective
ACM Computing Surveys (CSUR)
SMI 2013: Steepest descent paths on simplicial meshes of arbitrary dimensions
Computers and Graphics
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We investigate the problem of removing singularities from a non-manifold tetrahedral mesh so as to convert it to a more exploitable manifold representation. Given the twofold combinatorial and geometrical nature of a 3D simplicial complex, we propose two conversion algorithms that, depending on the targeted application, modify either its connectivity only or both its connectivity and its geometry. In the first case, the tetrahedral mesh is converted to a combinatorial 3-manifold, whereas in the second case it becomes a piecewise linear (PL) 3-manifold. For both the approaches, the conversion takes place while using only local modifications around the singularities. We outline sufficient conditions on the mesh to guarantee the feasibility of the approaches and we show how singularities can be both identified and removed according to the configuration of their neighborhoods. Furthermore, besides adapting and extending surface-based approaches to a specific class of full-dimensional simplicial complexes in 3D, we show that our algorithms can be implemented using a flexible data structure for manifold tetrahedral meshes which is suitable for general applications. In order to exclude pathological configurations while providing sound guarantees, the input mesh is required to be a sub-complex of a combinatorial ball; this makes it possible to assume that all the singularities are part of the mesh boundary.