| 1 |
greg |
1.1 |
{ |
| 2 |
|
|
Generate rays for a parabolic view projection -- |
| 3 |
|
|
i.e., a round image that when projected downwards |
| 4 |
|
|
in parallel onto a parabolic reflector results in |
| 5 |
|
|
a panoramic view from the paraboloid's focal point. |
| 6 |
|
|
|
| 7 |
|
|
The forward view direction corresponding to the top |
| 8 |
|
|
of the image is always +Y, and the up direction is |
| 9 |
|
|
always +Z. |
| 10 |
|
|
|
| 11 |
|
|
9/8/98 Greg Ward Larson |
| 12 |
|
|
|
| 13 |
|
|
Inputs: |
| 14 |
|
|
maxalt : Maximum altitude (in degrees) |
| 15 |
|
|
x, y = Image position, (0,0)->(1,0) is LL->LR |
| 16 |
|
|
|
| 17 |
|
|
Outputs: |
| 18 |
|
|
dx, dy, dz = Direction vector for image point (x,y) |
| 19 |
|
|
|
| 20 |
|
|
Typical command line: |
| 21 |
|
|
cnt 1024 1024 | rcalc -e maxalt:25 \ |
| 22 |
|
|
-e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwparab.cal \ |
| 23 |
|
|
-e '$1=25.5;$2=12;$3=5;$4=dx;$5=dy;$6=dz' \ |
| 24 |
|
|
| rtrace @electric.opt -fac -x 1024 -y 1024 \ |
| 25 |
|
|
electric.oct > pan.pic |
| 26 |
|
|
} |
| 27 |
|
|
amax : PI/180*maxalt; |
| 28 |
|
|
F0 : .5/cos(amax) - .5*tan(amax); { dist. btwn. parabola and directrix } |
| 29 |
|
|
xr = 2*x - 1; |
| 30 |
|
|
yr = 2*y - 1; |
| 31 |
|
|
r2 = xr*xr + yr*yr; |
| 32 |
|
|
r = sqrt(r2); { never actually needed } |
| 33 |
|
|
z = r2/(4*F0) + F0; |
| 34 |
|
|
zo = r2/(4*F0) - F0; |
| 35 |
|
|
sin_alt = zo/z; |
| 36 |
|
|
cos_alt = r/z; |
| 37 |
|
|
dx = xr/z; { same as xr/r*cos_alt } |
| 38 |
|
|
dy = yr/z; { same as yr/r*cos_alt } |
| 39 |
|
|
dz = zo/z; { same as sin_alt } |
