Introduction to Solid Modeling
Introduction to Solid Modeling
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Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
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Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Vertex-based boundary representation of nonmanifold geometric models
Vertex-based boundary representation of nonmanifold geometric models
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FiberMesh: designing freeform surfaces with 3D curves
ACM SIGGRAPH 2007 papers
Data structures for simplicial complexes: an analysis and a comparison
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IEEE Computer Graphics and Applications
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Offsetting operations on non-manifold topological models
Computer-Aided Design
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Computer-Aided Design
X-maps: An Efficient Model for Non-manifold Modeling
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
EasyToy: Plush Toy Design Using Editable Sketching Curves
IEEE Computer Graphics and Applications
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Technical Section: Topology authentication for CAPD models based on Laplacian coordinates
Computers and Graphics
CAD/Graphics 2013: Sketch2Jewelry: Semantic feature modeling for sketch-based jewelry design
Computers and Graphics
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The interpretation of auxiliary entities as boundary entities in previous non-manifold boundary (NMB) representations may change a model's intended topology and increase the complexity of the corresponding data structure. In this paper, entities appearing in a modeling process are classified into boundary and non-boundary entities. Non-boundary entities are usually embedded into embedding-space entities. These embedding relationships are described by inclusion topology. To support inclusion topology, a new mathematical framework-quasi-cell-complex, as well as a topological data structure-Q-Complex, are proposed. Quasi-cell-complex is an extension of cell-complex with inclusion topology supported. Q-Complex is an NMB representation, in which a new topological entity-embedder is created for inclusion topology and zone/disk is adopted to capture the complete adjacencies around a vertex. Thus, Q-Complex allows full adjacencies, incidence-ordering, and inclusion relationships to be derived, and the efficiency of most basic queries is several times faster than most state-of-the-art NMB representations, without increasing storage. Additionally, the benefits of inclusion topology for shape modeling and feature modeling are explored.