The design and analysis of spatial data structures
The design and analysis of spatial data structures
Octrees for faster isosurface generation
ACM Transactions on Graphics (TOG)
An effective way to represent quadtrees
Communications of the ACM
Multidimensional binary search trees used for associative searching
Communications of the ACM
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Interactive visualization of unstructured grids using hierarchical 3D textures
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
Cell Octrees: A New Data Structure for Volume Modeling and Visualization
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
KD-tree acceleration structures for a GPU raytracer
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Faster Isosurface Ray Tracing Using Implicit KD-Trees
IEEE Transactions on Visualization and Computer Graphics
A semi-Lagrangian contouring method for fluid simulation
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2006 Papers
Interactive k-d tree GPU raytracing
Proceedings of the 2007 symposium on Interactive 3D graphics and games
Fluid Simulation
GigaVoxels: ray-guided streaming for efficient and detailed voxel rendering
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Understanding the efficiency of ray traversal on GPUs
Proceedings of the Conference on High Performance Graphics 2009
Kd-Jump: a Path-Preserving Stackless Traversal for Faster Isosurface Raytracing on GPUs
IEEE Transactions on Visualization and Computer Graphics
Bivariate transfer functions on unstructured grids
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
Implicit and dynamic trees for high performance rendering
Proceedings of Graphics Interface 2011
Interactive particle tracing in time-varying tetrahedral grids
EG PGV'11 Proceedings of the 11th Eurographics conference on Parallel Graphics and Visualization
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We propose a new data representation for octrees and kd-trees that improves upon memory size and algorithm speed of existing techniques. While pointerless approaches exploit the regular structure of the tree to facilitate efficient data access, their memory footprint becomes prohibitively large as the height of the tree increases. Pointerbased trees require memory consumption proportional to the number of tree nodes, thus exploiting the typical sparsity of large trees. Yet, their traversal is slowed by the need to follow explicit pointers across the different levels. Our solution is a pointerless approach that represents each tree level with its own matrix, as opposed to traditional pointerless trees that use only a single vector. This novel data organization allows us to fully exploit the tree's regular structure and improve the performance of tree operations. By using a sparse matrix data structure we obtain a representation that is suited for sparse and dense trees alike. In particular, it uses less total memory than pointer-based trees even when the data set is extremely sparse. We show how our approach is easily implemented on the GPU and illustrate its performance in typical visualization scenarios.