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{ RCSid $Id$ } |
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{ |
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< |
Uniform sampling of sphere |
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Jittered sampling of a sphere |
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2/15/2005 G. Ward |
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Constant: |
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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 (radians) |
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phi - azimuthal angle (radians) |
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theta - polar angle (0-PI) |
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phi_un - azimuthal angle (unnormalized) |
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phi - azimuthal angle (0-2*PI) |
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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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k : 2*sqrt(PI/N); { k^2 is solid angle of each sample } |
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mod(n,d) : n - floor(n/d)*d; |
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alpha0 = asin(2/N*(i+.5) - 1); |
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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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phi_un = sqrt(PI*N)*alpha0 + k*S*(rand(-.83*i-17.9) - .5); |
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phi = mod(phi_un, 2*PI); |
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sint = sin(theta); |
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Dx = cos(phi)*sint; |
