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POData structures and algorithms for adaptive "uniform" mesh?
 

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  1. POData structures and algorithms for adaptive "uniform" mesh?
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    <p>I need a data structure for storing float values at an uniformly sampled 3D mesh:</p> <p>x = x0 + ix*dx where 0 &lt;= ix &lt; nx</p> <p>y = y0 + iy*dy where 0 &lt;= iy &lt; ny</p> <p>z = z0 + iz*dz where 0 &lt;= iz &lt; nz</p> <p>Up to now I have used my Array class:</p> <pre><code>Array3D&lt;float&gt; A(nx, ny,nz); A(0,0,0) = 0.0f; // ix = iy = iz = 0 </code></pre> <p>Internally it stores the float values as an 1D array with nx * ny * nz elements.</p> <p>However now I need to represent an mesh with more values than I have RAM, e.g. nx = ny = nz = 2000.</p> <p>I think many neighbour nodes in such an mesh may have similar values so I was thinking if there was some simple way that I could "coarsen" the mesh adaptively.</p> <p>For instance if the 8 (ix,iy,iz) nodes of an cell in this mesh have values that are less than 5% apart; they are "removed" and replaced by just one value; the mean of the 8 values.</p> <p>How could I implement such a data structure in a simple and efficient way?</p> <p>EDIT: thanks Ante for suggesting lossy compression. I think this could work the following way:</p> <pre><code>#define BLOCK_SIZE 64 struct CompressedArray3D { CompressedArray3D(int ni, int nj, int nk) { NI = ni/BLOCK_SIZE + 1; NJ = nj/BLOCK_SIZE + 1; NK = nk/BLOCK_SIZE + 1; blocks = new float*[NI*NJ*NK]; compressedSize = new unsigned int[NI*NJ*NK]; } void setBlock(int I, int J, int K, float values[BLOCK_SIZE][BLOCK_SIZE][BLOCK_SIZE]) { unsigned int csize; blocks[I*NJ*NK + J*NK + K] = compress(values, csize); compressedSize[I*NJ*NK + J*NK + K] = csize; } float getValue(int i, int j, int k) { int I = i/BLOCK_SIZE; int J = j/BLOCK_SIZE; int K = k/BLOCK_SIZE; int ii = i - I*BLOCK_SIZE; int jj = j - J*BLOCK_SIZE; int kk = k - K*BLOCK_SIZE; float *compressedBlock = blocks[I*NJ*NK + J*NK + K]; unsigned int csize = compressedSize[I*NJ*NK + J*NK + K]; float values[BLOCK_SIZE][BLOCK_SIZE][BLOCK_SIZE]; decompress(compressedBlock, csize, values); return values[ii][jj][kk]; } // number of blocks: int NI, NJ, NK; // number of samples: int ni, nj, nk; float** blocks; unsigned int* compressedSize; }; </code></pre> <p>For this to be useful I need a lossy compression that is:</p> <ul> <li>extremely fast, also on small datasets (e.g. 64x64x64)</li> <li>compress quite hard > 3x, never mind if it looses quite a bit of info.</li> </ul> <p>Any good candidates?</p>
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      1. POData structures and algorithms for adaptive "uniform" mesh?
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    1. COSounds like lossy compression of 3D data. Maybe layers can be treated as images and compress independently (e.g. jpg.) Or even to take one coordinate as a time and treat data as a video. I'm not sure, but probably these methods are not so efficient for inquiring of data, since I think they don't work locally.
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    2. COSimilar topic: http://arxiv.org/abs/1303.0270
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