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
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
A feature-based approach for smooth surfaces
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Offsetting operations on non-manifold boundary representation models with simple geometry
Proceedings of the fifth ACM symposium on Solid modeling and applications
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
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
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
Feature-based multiresolution modeling of solids
ACM Transactions on Graphics (TOG)
Update operations on 3D simplicial decompositions of non-manifold objects
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Euler operators for stratified objects with incomplete boundaries
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Solid and physical modeling with chain complexes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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
Offsetting operations on non-manifold topological models
Computer-Aided Design
Modeling complex heterogeneous objects with non-manifold heterogeneous cells
Computer-Aided Design
Manifoldization of β-shapes in O(n) time
Computer-Aided Design
CW complexes: topological mainframe for numerical representations of objects
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Manifoldization of β-shapes by topology operators
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Q-Complex: Efficient non-manifold boundary representation with inclusion topology
Computer-Aided Design
Finite Element/Fictitious Domain programming for flows with particles made simple
Advances in Engineering Software
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Many studies of solid models based on 2-manifolds have been done. However, a manifold solid model is not powerful enough, because a regularized Boolean operation may yield a non-manifold result. Furthermore, a solid model can basically represent only one closed volume, and cannot handle volumes, surfaces, and curves simultaneously. A non-manifold topology model is expected to be a break-through in solving these problems. Several representations and Euler operations for non-manifold topology were suggested recently. But, the representations capable of representing volumes with dangling edges and faces were determined in a rather ad hoc manner, so that there have been no discussions on sufficiency or efficiency. Also, the operations were not complete in the sense of manipulating all types of data entities. We propose a data structure and two classes of operations, focusing on neighborhood relationship, as well as boundary information. The data structure is both sufficient and efficient for describing adjacency ordering. The operations are able to manipulate all types of data entities maintaining satisfaction of a certain set of consistency conditions.