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Linear Correlations between Spatial and Normal Noise in Triangle Meshes
Jan. 2013 (vol. 19 no. 1)
pp. 4555
ASCII Text  x  
Ying Yang, N. Peyerimhoff, I. Ivrissimtzis, "Linear Correlations between Spatial and Normal Noise in Triangle Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 1, pp. 4555, Jan., 2013.  
BibTex  x  
@article{ 10.1109/TVCG.2012.106, author = { Ying Yang and N. Peyerimhoff and I. Ivrissimtzis}, title = {Linear Correlations between Spatial and Normal Noise in Triangle Meshes}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {19}, number = {1}, issn = {10772626}, year = {2013}, pages = {4555}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.106}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Linear Correlations between Spatial and Normal Noise in Triangle Meshes IS  1 SN  10772626 SP45 EP55 EPD  4555 A1  Ying Yang, A1  N. Peyerimhoff, A1  I. Ivrissimtzis, PY  2013 KW  mesh generation KW  approximation theory KW  computational geometry KW  average normal distortion KW  linear correlations KW  spatial noise KW  normal noise KW  triangle meshes KW  uniform noise KW  dithered vertex quantization KW  mesh vertices KW  Noise KW  Quantization KW  Degradation KW  Upper bound KW  Linear approximation KW  Rendering (computer graphics) KW  normal noise KW  mesh generation KW  approximation theory KW  computational geometry KW  average normal distortion KW  linear correlations KW  spatial noise KW  normal noise KW  triangle meshes KW  uniform noise KW  dithered vertex quantization KW  mesh vertices KW  Noise KW  Quantization KW  Degradation KW  Upper bound KW  Linear approximation KW  Rendering (computer graphics) KW  vertex quantization KW  Triangle mesh VL  19 JA  IEEE Transactions on Visualization and Computer Graphics ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2012.106
We study the relationship between the noise in the vertex coordinates of a triangle mesh and normal noise. First, we compute in closed form the expectation for the angle θ between the new and the old normal when uniform noise is added to a single vertex of a triangle. Next, we propose and experimentally validate an approximation and lower and upper bounds for θ when uniform noise is added to all three vertices of the triangle. In all cases, for small amounts of spatial noise that do not severely distort the mesh, there is a linear correlation between θ and simple functions of the heights of the triangles and thus, θ can be computed efficiently. The addition of uniform spatial noise to a mesh can be seen as a dithered quantization of its vertices. We use the obtained linear correlations between spatial and normal noise to compute the level of dithered quantization of the mesh vertices when a tolerance for the average normal distortion is given.
Index Terms:
mesh generation,approximation theory,computational geometry,average normal distortion,linear correlations,spatial noise,normal noise,triangle meshes,uniform noise,dithered vertex quantization,mesh vertices,Noise,Quantization,Degradation,Upper bound,Linear approximation,Rendering (computer graphics),normal noise,mesh generation,approximation theory,computational geometry,average normal distortion,linear correlations,spatial noise,normal noise,triangle meshes,uniform noise,dithered vertex quantization,mesh vertices,Noise,Quantization,Degradation,Upper bound,Linear approximation,Rendering (computer graphics),vertex quantization,Triangle mesh
Citation:
Ying Yang, N. Peyerimhoff, I. Ivrissimtzis, "Linear Correlations between Spatial and Normal Noise in Triangle Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 1, pp. 4555, Jan. 2013, doi:10.1109/TVCG.2012.106
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