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{ RCSid $Id$ } |
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{ |
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Generate rays for a parabolic view projection -- |
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i.e., a round image that when projected downwards |
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in parallel onto a parabolic reflector results in |
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a panoramic view from the paraboloid's focal point. |
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|
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The forward view direction corresponding to the top |
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of the image is always +Y, and the up direction is |
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always +Z. |
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|
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9/8/98 Greg Ward Larson |
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|
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Inputs: |
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maxalt : Maximum altitude (in degrees) |
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x, y = Image position, (0,0)->(1,0) is LL->LR |
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|
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Outputs: |
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dx, dy, dz = Direction vector for image point (x,y) |
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|
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Typical command line: |
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cnt 1024 1024 | rcalc -od -e maxalt:25 \ |
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-e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwparab.cal \ |
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-e '$1=25.5;$2=12;$3=5;$4=dx;$5=dy;$6=dz' \ |
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| rtrace @electric.opt -fdc -x 1024 -y 1024 \ |
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electric.oct > pan.pic |
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} |
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amax : PI/180*maxalt; |
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F0 : .5/cos(amax) - .5*tan(amax); { dist. btwn. parabola and directrix } |
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xr = 2*x - 1; |
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yr = 2*y - 1; |
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r2 = xr*xr + yr*yr; |
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r = sqrt(r2); { never actually needed } |
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z = r2/(4*F0) + F0; |
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zo = r2/(4*F0) - F0; |
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sin_alt = zo/z; |
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cos_alt = r/z; |
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dx = xr/z; { same as xr/r*cos_alt } |
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dy = yr/z; { same as yr/r*cos_alt } |
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dz = zo/z; { same as sin_alt } |
