Optimal multilevel iterative methods for adaptive grids
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Symbolic local refinement of tetrahedral grids
Journal of Symbolic Computation
Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
Complex-valued contour meshing
Proceedings of the 7th conference on Visualization '96
Interactive view-dependent rendering of large isosurfaces
Proceedings of the conference on Visualization '02
Terrain Simplification Simplified: A General Framework for View-Dependent Out-of-Core Visualization
IEEE Transactions on Visualization and Computer Graphics
Estimating the in/out function of a surface represented by points
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Constant-Time Navigation in Four-Dimensional Nested Simplicial Meshes
SMI '04 Proceedings of the Shape Modeling International 2004
Parallel Volume Segmentation with Tetrahedral Adaptive Grid
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Real-Time Optimal Adaptation for Planetary Geometry and Texture: 4-8 Tile Hierarchies
IEEE Transactions on Visualization and Computer Graphics
Some combinatorial Lemmas in topology
IBM Journal of Research and Development
Multiresolution interval volume meshes
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach [Mau95] have been widely used in 2D and 3D as multi-resolution models of terrains and three-dimensional scalar fields, They are an alternative to octree representation since they allow generating crack-free representations of the underlying field. On the other hand, this method generates conforming meshes only when all simplices sharing the bisection edge are subdivided concurrently. Thus, efficient representations have been proposed in 2D and 3D based on a clustering of the simplices sharing a common longest edge in what is called a diamond. These representations exploit the regularity of the vertex distribution and the diamond structure to yield an implicit encoding of the hierarchical and geometric relationships among the triangles and tetrahedra, respectively. Here, we analyze properties of d-dimensional diamonds to better understand the hierarchical and geometric relationships among the simplices generated by Maubach's bisection scheme and derive closed-form equations for the number of vertices, simplices, parents and children of each type of diamond. We exploit these properties to yield an implicit pointerless representation for d-dimensional diamonds and reduce the number of required neighbor-finding accesses from O(d!) to O(d).