Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Introduction to Solid Modeling
Introduction to Solid Modeling
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
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
A generalized Euler-Poincare´ equation
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Boolean set operations on non-manifold boundary representation objects
Computer-Aided Design - Beyond solid modelling
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
A model for n-dimensional boundary topology
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Bubble mesh: automated triangular meshing of non-manifold geometry by sphere packing
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Offsetting operations on non-manifold boundary representation models with simple geometry
Proceedings of the fifth ACM symposium on Solid modeling and applications
An Editable Nonmanifold Boundary Representation
IEEE Computer Graphics and Applications
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Vertex-based boundary representation of nonmanifold geometric models
Vertex-based boundary representation of nonmanifold geometric models
A multi-resolution topological representation for non-manifold meshes
Proceedings of the seventh ACM symposium on Solid modeling and applications
Representation of non-manifold objects
SM '03 Proceedings of the eighth 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
A concise b-rep data structure for stratified subanalytic 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
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
Computational Geometry: Theory 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
Delaunay refinement for piecewise smooth complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Representing non-manifold geometric objects in n dimensions: incidence, order, and shape
ISCGAV'06 Proceedings of the 6th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
On converting sets of tetrahedra to combinatorial and PL manifolds
Computer Aided Geometric Design
Interaction interfaces in proteins via the Voronoi diagram of atoms
Computer-Aided Design
Design automation for customized apparel products
Computer-Aided Design
Oversimplified euler operators for a non-oriented, non-manifold b-rep data structure
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Topological operators on cell complexes in arbitrary dimensions
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Finite Element/Fictitious Domain programming for flows with particles made simple
Advances in Engineering Software
Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions
Computer Vision and Image Understanding
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Non-manifold boundary representations have gained a great deal of popularity in recent years and various representation schemes have been proposed because they allow an even wider range of objects for various applications than conventional manifold representations. However, since these schemes are mainly interested in describing sufficient adjacency relationships of topological entities, the models represented in these schemes occupy too much storage space redundantly although they are very efficient in answering queries on topological adjacency relationships. Storage requirement can arise as a crucial problem in models in which topological data is more dominant than geometric data, such as tessellated or mesh models.To solve this problem, in this paper, we propose a compact non-manifold boundary representation, called the partial entity structure, which allows the reduction of the storage size to half that of the radial edge structure, which is known as a time efficient non-manifold data structure, while allowing full topological adjacency relationships to be derived without loss of efficiency. This representation contains not only the conventional primitive entities like the region, face, edge, and vertex, but also the partial topological entities such as the partial-face, partial-edge, and partial-vertex for describing non-manifold conditions at vertices, edges, and faces. In order to verify the time and storage efficiency of the partial entity structure, the time complexity of basic query procedures and the storage requirement for typical geometric models are derived and compared with those of existing schemes. Furthermore, a set of the generalized Euler operators and typical high-level modeling capabilities such as Boolean operations are also implemented to confirm that our data structure is sound and easy to be manipulated.