Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An extension of manifold boundary representations to the r-sets
ACM Transactions on Graphics (TOG)
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
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
Non-manifold Multi-tessellation: From Meshes to Iconic Representations of Objects
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
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.
A Combinatorial Analysis of Boundary Data Structure Schemata
IEEE Computer Graphics 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
Topological analysis and characterization of discrete scalar fields
Proceedings of the 11th international conference on Theoretical foundations of computer vision
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In this paper we consider the problem of decomposing a nonmanifold n-dimensional object described by an abstract simplicial complex into an assembly of 'more-regular' components. Manifolds, which would be natural candidates for components, cannot be used to this aim in high dimensions because they are not decidable sets. Therefore, we define d-quasi-manifolds, a decidable superset of the class of combinatorial d-manifolds that coincides with d-manifolds in dimension less or equal than two. We first introduce the notion of d-quasi-manifold complexes, then we sketch an algorithm to decompose an arbitrary complex into an assembly of quasi-manifold components abutting at non-manifold joints. This result provides a rigorous starting point for our future work, which includes designing efficient data structures for non-manifold modeling, as well as defining a notion of measure of shape complexity of such models.