Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An extension of manifold boundary representations to the r-sets
ACM Transactions on Graphics (TOG)
Shapes and implementations in three-dimensional geometry
Shapes and implementations in three-dimensional geometry
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
Directed edges—A scalable representation for triangle meshes
Journal of Graphics Tools
Proceedings of the sixth ACM symposium on Solid modeling and applications
Out-of-core build of a topological data structure from polygon soup
Proceedings of the sixth ACM symposium on Solid modeling and applications
Tools for Triangulations and Tetrahedrizations
Scientific Visualization, Overviews, Methodologies, and Techniques
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
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Data structures for simplicial complexes: an analysis and a comparison
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
On converting sets of tetrahedra to combinatorial and PL manifolds
Computer Aided Geometric Design
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We define a new representation for non-manifold 3D shapes described by three-dimensional simplicial complexes, that we call the Double-Level Decomposition (DLD) data structure. The DLD data structure is based on a unique decomposition of the simplicial complex into nearly manifold parts, and encodes the decomposition in an efficient and powerful two-level representation. It is compact, and it supports efficient topological navigation through adjacencies. It also provides a suitable basis for geometric reasoning on non-manifold shapes. We describe an algorithm to decompose a 3D simplicial complex into nearly manifold parts. We discuss how to build the DLD data structure from a description of a 3D complex as a collection of tetrahedra, dangling triangles and wire edges, and we present algorithms for topological navigation. We present a thorough comparison with existing representations for 3D simplicial complexes.