Compact 3D Representations
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The need to compactly represent 3D data is motivated by the ever-increasing size of these data. Furthermore, for large data sets it is useful to randomly access and process a small part of the data. In this thesis we propose two methods of compactly representing 3D data while allowing random access. The first is the multiresolution sphere-packing tree (MSP-tree). The MSP-tree is a multiresolution 3D hierarchy on regular grids based on sphere-packing arrangements. The grids of the MSP-tree compactly represent underlying point-sampled data by using more efficient grids than existing methods while maintaining high granularity and a hierarchical structure that allows random access. The second is distance-ranked random-accessible mesh compression (DR-RAMC). DR-RAMC is a lossless simplicial mesh compressor that allows random access and decompression of the mesh data based on a spatial region-of-interest. DR-RAMC encodes connectivity based on relative proximity of vertices to each other and organizes both this proximity data and vertex coordinates using a k-d tree. DR-RAMC is insensitive to a variety of topological mesh problems (e.g. holes, handles, non-orientability) and can compress simplicial meshes of any dimension embedded in spaces of any dimension. Testing of DR-RAMC shows competitive compression rates for triangle meshes and first-ever random accessible compression rates for tetrahedral meshes.