Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
Computing
Progressive simplicial complexes
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Multidimensional binary search trees used for associative searching
Communications of the ACM
Wavelet-based multiresolution with n√2 subdivision
Computing - Geometric modelling dagstuhl 2002
A granular three dimensional multiresolution transform
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
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Sphere packing arrangements are frequently found in nature, exhibiting efficient space-filling and energy minimization properties. Close sphere packings provide a tight, uniform, and highly symmetric spatial sampling at a single resolution. We introduce the Multiresolution Sphere Packing Tree (MSP-tree): a hierarchical spatial data structure based on sphere packing arrangements suitable for 3D space representation and selective refinement. Compared to the commonly used octree, MSP-tree offers three advantages: a lower fanout (a factor of four compared to eight), denser packing (about 24% denser), and persistence (sphere centers at coarse resolutions persist at finer resolutions). We present MSP-tree both as a region-based approach that describes the refinement mechanism succintly and intuitively, and as a lattice-based approach better suited for implementation. The MSP-tree offers a robust, highly symmetric tessellation of 3D space with favorable image processing properties.