Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational 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
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Structural operators for modeling 3-manifolds
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Converting sets of polygons to manifold surfaces by cutting and stitching
ACM SIGGRAPH 98 Conference abstracts and applications
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Matchmaker: manifold BReps for non-manifold r-sets
Proceedings of the fifth ACM symposium on Solid modeling and applications
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
Proceedings of the sixth ACM symposium on Solid modeling and applications
Simplification of Tetrahedral Meshes with Error Bounds
IEEE Transactions on Visualization and Computer Graphics
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
Time-Critical Rendering of Irregular Grids
SIBGRAPI '00 Proceedings of the 13th Brazilian Symposium on Computer Graphics and Image Processing
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
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Equivalence between Closed Connected n-G-Maps without Multi-Incidence and n-Surfaces
Journal of Mathematical Imaging and Vision
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We address the problem of updating non-manifold mixed-dimensional objects, described by three-dimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a simplicial complex. We examine the effect of such operations on a 3D simplicial complex, and we describe algorithms for edge collapse and vertex split on a compact representation of a 3D simplicial complex, that we call the Non-Manifold Indexed data structure with Adjacencies (NMIA). We also discuss how to encode the information needed for performing a vertex split and an edge collapse on a 3D simplicial complex. The encoding of such information together with the algorithms for updating the NMIA data structure form the basis for defining progressive as well as multi-resolution representations for objects described by 3D simplicial complexes and for extracting variable-resolution object descriptions.