Octree Encoding- used in Computational Methods

Octree Encoding- used in Computational Methods

• 1.
  Presentation on Octree Encoding PresentedBy: Aditya Deshpande Guided By: Prof. G. D. Korwar VISHWAKARMA INSTITUTE OF TECHNOLOGY, PUNE
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  Introduction Octrees are hierarchicaltree structures that describe each region of 3D space as nodes. When compared with the basic voxel representation, octrees reduce storage requirements for 3D objects. It also provides a convenient representation for storing information about object interiors. Octree encoding procedure is an extension of the quadtree encoding of 2D images
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  • An octreeis a tree data structure in which each internal node has exactly eight children. • Octrees are most often used to partition a three dimensional space by recursively subdividing it into eight octants. • Octrees are the three-dimensional analogue of quadtrees. • The name is formed from oct + tree, but note that it is normally written "octree" with only one "t". • Octrees are often used in 3D graphics and 3D game engines. • The use of octrees for 3D computer graphics was pioneered by Donald Meagher at Rensselaer Polytechnic Institute, in a 1980 Octrees - Intro
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  Octrees are hierarchicaltree structures used to represent solid objects Octrees are particularly useful in applications that require cross sectional views for example medical applications Octrees are typically used when the interior of objects is important Octrees
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  • Octrees arebased on a two-dimensional representation scheme called quadtree encoding • Quadtree encoding divides a square region of space into four equal areas until homogeneous regions are found • These regions can then be arranged in a tree Octrees & Quadtrees
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  Quadtree Examples 1
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  Quadtree Examples 2
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  • Quadtree encodingsprovide considerable savings in storage when large colour areas exist in a region of space • An octree takes the same approach as quadtrees, but divides a cube region of 3D space into octants • Each region within an octree is referred to as a volume element or voxel • Division is continued until homogeneous regions are discovered Octree
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  Octree (cont…)
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  • In 3dimensions regions can be considered to be homogeneous in terms of colour, material type, density or any other physical characteristics • Voxels also have the unique possibility of being empty Octree (cont…)
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  Octree Examples
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  Octree Representation of3D Data (a) Example 3-dimensional object; (b) its octree block decomposition; and (c) its tree representation.
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  1. 3D computergraphics 2. Spatial indexing 3. Nearest neighbour search 4. Efficient collision detection in three dimensions 5. View frustum culling 6. Fast Multipole Method 7. Unstructured grid 8. Finite element analysis 9. Sparse voxel octree 10. State estimation 11. Set estimation Applications