Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Free-form deformations with lattices of arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A multiresolution framework for dynamic deformations
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
A new solid subdivision scheme based on box splines
Proceedings of the seventh ACM symposium on Solid modeling and applications
Level of Detail for 3D Graphics
Level of Detail for 3D Graphics
Interpolatory, solid subdivision of unstructured hexahedral meshes
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Smooth subdivision of tetrahedral meshes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
The Half-Edge Tree: A Compact Data Structure for Level-of-Detail Tetrahedral Meshes
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Extension of half-edges for the representation of multiresolution subdivision surfaces
The Visual Computer: International Journal of Computer Graphics
Dynamic local remeshing for elastoplastic simulation
ACM SIGGRAPH 2010 papers
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Computer Aided Geometric Design
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We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms - like filtering or compression - for n-dimensional meshes with arbitrary topologies. We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.