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{ RCSid $Id$ } |
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{ |
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Uniform sampling of sphere |
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2/15/2005 G. Ward |
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Define: |
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N - total number of samples |
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i - sample number |
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Constant: |
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N - total number of samples on sphere |
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Input: |
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i - sample number [0,N-1] |
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Output: |
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theta - polar angle (degrees) |
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phi - azimuthal angle (degrees) |
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theta - polar angle (radians) |
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phi - azimuthal angle (radians) |
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Dx - X-component of direction vector |
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Dy - Y-component of direction vector |
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Dz - Z-component of direction vector |
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} |
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S : .7; { jitter amount (0-1) } |
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DEGREE : PI/180; |
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bound(a,x,b) : if(a-x, a, if(x-b, b, x)); |
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Acos(x) : acos(bound(-1,x,1)); |
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Sqrt(x) : if(x, sqrt(x), 0); |
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k : 2*sqrt(PI/N); { k^2 is solid angle of each sample } |
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nalt = floor(sqrt(2/PI*N) + .5); |
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nazi = floor(PI/2*nalt + .5); |
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alpha0 = asin(2/N*(i+.5) - 1); |
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cond = nalt*nazi-.9999 - i; |
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theta = alpha0 + PI/2 + k*S*(rand(.35*i+10.3) - .5); |
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phi = sqrt(PI*N)*alpha0 + k*S*(rand(-.83*i-17.9) - .5); |
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ialt = floor(i/nazi); |
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iazi = i - ialt*nazi; |
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ralt = (ialt + rand(i*.328+.112))/nalt; |
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razi = (iazi + rand(i*-.731+.318))/nazi; |
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rtheta = Acos(Dz); |
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rphi = 2*PI*razi; |
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Dxy = Sqrt(1 - Dz*Dz); |
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theta = rtheta/DEGREE; |
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phi = rphi/DEGREE; |
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Dx = Dxy*cos(rphi); |
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Dy = Dxy*sin(rphi); |
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Dz = 1 - 2*ralt; |
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sint = sin(theta); |
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Dx = cos(phi)*sint; |
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Dy = sin(phi)*sint; |
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Dz = cos(theta); |
