Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
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
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
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)
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
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
Efficient compression of non-manifold polygonal meshes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
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
Aspects in Topology-Based Geometric Modeling
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Graphs and Hypergraphs
Update operations on 3D simplicial decompositions of non-manifold objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
A two-level topological decomposition for non-manifold simplicial shapes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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
On converting sets of tetrahedra to combinatorial and PL manifolds
Computer Aided Geometric Design
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
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We address the problem of building valid representations of non-manifold d-dimensional objects through an approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular componems. We first define a standard decomposition of d-dimensional non-manifold objects described by abstract simplicial complexes. This decomposition splits a non-manifold object into components that belong to a well-understood class of objects, that we call initial quasi-manifold. Initial quasi-manifolds cannot be decomposed without cutting them along manifold faces. They form a decidable superset of d-manifolds for d ≥ 3, and coincide with manifolds for d ≤ 2. We then present an algorithm that computes the standard decomposition of a general non-manifold complex. This decomposition is unique, and removes all singularities which can be removed without cutting the complex along its manifold faces.