Perceptual organization and the representation of natural form
Artificial Intelligence
An extension of manifold boundary representations to the r-sets
ACM Transactions on Graphics (TOG)
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Converting sets of polygons to manifold surfaces by cutting and stitching
ACM SIGGRAPH 98 Conference abstracts and applications
Matchmaker: manifold BReps for non-manifold r-sets
Proceedings of the fifth ACM symposium on Solid modeling and applications
A mathematical model for boundary representations of n-dimensional geometric objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
A discourse on geometric feature recognition from CAD models
Journal of Computing and Information Science in Engineering
Parametric and Feature Based CAD/Cam: Concepts, Techniques, and Applications
Parametric and Feature Based CAD/Cam: Concepts, Techniques, and Applications
Representation of non-manifold objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Decomposing non-manifold objects in arbitrary dimensions
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Computing and Visualizing a Graph-Based Decomposition for Non-manifold Shapes
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
A semantic web environment for digital shapes understanding
SAMT'07 Proceedings of the semantic and digital media technologies 2nd international conference on Semantic Multimedia
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
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Modeling and understanding complex non-manifold shapes is a key issue in shape analysis. Geometric shapes are commonly discretized as two- or three-dimensional simplicial complexes embedded in the 3D Euclidean space. The topological structure of a nonmanifold simplicial shape can be analyzed through its decomposition into a collection of components with a simpler topology. Here, we present a topological decomposition of a shape at two different levels, with different degrees of granularity. We discuss the topological properties of the components at each level, and we present algorithms for computing such decompositions. We investigate the relations among the components, and propose a graph-based representation for such relations.