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greg |
1.3 |
{ RCSid $Id: fovsample.cal,v 1.2 2019/04/05 17:17:53 greg Exp $ } |
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greg |
1.1 |
{ |
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Foveated sampling based on central direction vector, |
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magnification factor at center, and central field of view. |
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Greg Ward April 2019 |
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greg |
1.2 |
Preset constants: |
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greg |
1.1 |
Cx, Cy, Cz : central view direction |
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greg |
1.2 |
M : central FOV magnification factor |
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greg |
1.1 |
D : field of view (full angle in degrees) |
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Inputs: |
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iDx, iDy, iDz = uniformly generated sampling vector |
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Outputs: |
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oDx, oDy, oDz = foveated sample direction (normalized) |
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Other variables computed: |
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iTheta = original angle to center (radians) |
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greg |
1.2 |
oTheta = new angle to center (radians) |
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greg |
1.1 |
} |
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greg |
1.2 |
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r : PI/360 * D; { half-angle of foveal region in radians } |
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rp : M * r; { half-angle of mapped boundary } |
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greg |
1.1 |
len(x,y,z) : sqrt(x*x + y*y + z*z); |
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greg |
1.3 |
sq(x) : x*x; |
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greg |
1.2 |
{ normalize central vector } |
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greg |
1.1 |
Clen : len(Cx,Cy,Cz); |
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nCx : Cx/Clen; |
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nCy : Cy/Clen; |
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nCz : Cz/Clen; |
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greg |
1.2 |
{ normalize input direction } |
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greg |
1.1 |
iDnf = 1/len(iDx,iDy,iDz); |
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niDx = iDx*iDnf; |
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niDy = iDy*iDnf; |
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niDz = iDz*iDnf; |
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greg |
1.2 |
{ check for degenerate case (center of fovea) } |
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iDot = nCx*niDx + nCy*niDy + nCz*niDz; |
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degen = iDot - cos(.05*PI/180); |
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greg |
1.1 |
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iTheta = acos(iDot); |
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greg |
1.3 |
gamma = 1 + sq((iTheta-rp)/(PI-rp)) * (log(M)/(log(PI/(PI-r)) - log(M))); |
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greg |
1.1 |
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greg |
1.3 |
oTheta = if(rp-iTheta, iTheta/M, (PI-r)*(iTheta/(M*(PI-r)))^gamma); |
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greg |
1.1 |
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greg |
1.2 |
{ normalized "up" vector for rotation } |
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Unf = 1/sqrt(1 - iDot*iDot); |
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greg |
1.1 |
nUx = (nCy*niDz - nCz*niDy)*Unf; |
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nUy = (nCz*niDx - nCx*niDz)*Unf; |
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nUz = (nCx*niDy - nCy*niDx)*Unf; |
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greg |
1.2 |
{ rotate central vector by oTheta to get new output } |
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rcos = cos(oTheta); |
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rsin = sqrt(1 - rcos*rcos); |
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{ foveated sample direction } |
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greg |
1.3 |
rDx = nCx*rcos + (nUy*nCz - nUz*nCy)*rsin; |
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rDy = nCy*rcos + (nUz*nCx - nUx*nCz)*rsin; |
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rDz = nCz*rcos + (nUx*nCy - nUy*nCx)*rsin; |
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greg |
1.2 |
{ substitute approximation in degenerate case } |
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greg |
1.1 |
oDx = if(degen, nCx+(niDx-nCx)/M, rDx); |
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oDy = if(degen, nCy+(niDy-nCy)/M, rDy); |
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oDz = if(degen, nCz+(niDz-nCz)/M, rDz); |
