| 11 |
|
D : field of view (full angle in degrees) |
| 12 |
|
|
| 13 |
|
Inputs: |
| 14 |
< |
iDx, iDy, iDz = uniformly generated sampling vector |
| 14 |
> |
forward = 1 if forward conversion, -1 if reverse |
| 15 |
> |
iDx, iDy, iDz = input sampling vector |
| 16 |
|
|
| 17 |
|
Outputs: |
| 18 |
< |
oDx, oDy, oDz = foveated sample direction (normalized) |
| 18 |
> |
oDx, oDy, oDz = output sample direction (normalized) |
| 19 |
|
|
| 20 |
|
Other variables computed: |
| 21 |
< |
iTheta = original angle to center (radians) |
| 22 |
< |
oTheta = new angle to center (radians) |
| 21 |
> |
iTheta = input angle to center (radians) |
| 22 |
> |
oTheta = output angle to center (radians) |
| 23 |
|
} |
| 24 |
|
|
| 25 |
|
r : PI/360 * D; { half-angle of foveal region in radians } |
| 42 |
|
degen = iDot - cos(.05*PI/180); |
| 43 |
|
|
| 44 |
|
iTheta = acos(iDot); |
| 45 |
+ |
{ quadratic function coefficients mate to linear ramp } |
| 46 |
+ |
qa : (PI - PI/M)/sq(PI - rp); |
| 47 |
+ |
qb : 1/M - 2*PI*r*(M - 1)/sq(PI - rp); |
| 48 |
+ |
qc : (PI - PI/M)/sq(PI/rp - 1); |
| 49 |
|
|
| 50 |
< |
gamma = 1 + sq((iTheta-rp)/(PI-rp)) * (log(M)/(log(PI/(PI-r)) - log(M))); |
| 51 |
< |
|
| 52 |
< |
oTheta = if(rp-iTheta, iTheta/M, (PI-r)*(iTheta/(M*(PI-r)))^gamma); |
| 53 |
< |
|
| 50 |
> |
oTheta = if (forward, |
| 51 |
> |
if(rp-iTheta, iTheta/M, qa*iTheta*iTheta + qb*iTheta + qc), |
| 52 |
> |
if(r-iTheta, iTheta*M, (sqrt(qb*qb - 4*qa*(qc - iTheta)) - qb)/(2*qa)) |
| 53 |
> |
); |
| 54 |
|
{ normalized "up" vector for rotation } |
| 55 |
|
Unf = 1/sqrt(1 - iDot*iDot); |
| 56 |
|
nUx = (nCy*niDz - nCz*niDy)*Unf; |
| 64 |
|
rDy = nCy*rcos + (nUz*nCx - nUx*nCz)*rsin; |
| 65 |
|
rDz = nCz*rcos + (nUx*nCy - nUy*nCx)*rsin; |
| 66 |
|
{ substitute approximation in degenerate case } |
| 67 |
< |
oDx = if(degen, nCx+(niDx-nCx)/M, rDx); |
| 68 |
< |
oDy = if(degen, nCy+(niDy-nCy)/M, rDy); |
| 69 |
< |
oDz = if(degen, nCz+(niDz-nCz)/M, rDz); |
| 67 |
> |
oDx = if(degen, nCx+(niDx-nCx)*if(forward,1/M,M), rDx); |
| 68 |
> |
oDy = if(degen, nCy+(niDy-nCy)*if(forward,1/M,M), rDy); |
| 69 |
> |
oDz = if(degen, nCz+(niDz-nCz)*if(forward,1/M,M), rDz); |
