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greg |
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{ RCSid $Id$ } |
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{ |
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Generate rays for a planisphere (a.k.a. stereographic) |
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view projection. This is a type of fisheye projection |
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used in daylighting analysis. We limit ourselves here |
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to square image aspects. |
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2/24/2008 Greg Ward (for Axel Jacobs) |
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Inputs: |
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maxang : Maximum angle (in degrees < 360) |
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x, y = Image position, (0,0)->(1,0) is LL->LR |
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Outputs: |
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dx, dy, dz = Direction vector for image point (x,y) |
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Typical command line: |
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cnt 1024 1024 | rcalc -od -e maxang:180 \ |
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-e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwplanis.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 > planisphere.pic |
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The above directions assume +Z is the view direction, and +Y is the |
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up direction. This isn't very convenient, so an alternate method |
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is provided for other views, delivered via `vwright s < viewfile` |
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like so: |
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cnt 1024 1024 | rcalc -od -e `vwright s < viewfile` \ |
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-e 'maxang:sh' -e 'x=($2+.5)/1024;y=1-($1+.5)/1024' \ |
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-f vwplanis.cal \ |
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-e '$1=spx;$2=spy;$3=spz;$4=Dx;$5=Dy;$6=Dz' \ |
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| rtrace @electric.opt -fdc -x 1024 -y 1024 \ |
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electric.oct > planisphere.pic |
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} |
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amax : PI/180/2*maxang; |
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K : 2*sin(amax)/(1+cos(amax)); |
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sq(x) : x*x; |
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r2 = sq(x-.5) + sq(y-.5); |
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dz = (1 - sq(K)*r2)/(1 + sq(K)*r2); |
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rnorm = sqrt((1 - sq(dz))/r2); |
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dx = rnorm*(x-.5); |
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dy = rnorm*(y-.5); |
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{ Below is where we need `vwright s` paramters } |
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hnorm : 1/sqrt(sq(shx)+sq(shy)+sq(shz)); |
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vnorm : 1/sqrt(sq(svx)+sq(svy)+sq(svz)); |
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Dx = shx*hnorm*dx + svx*vnorm*dy + sdx*dz; |
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Dy = shy*hnorm*dx + svy*vnorm*dy + sdy*dz; |
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Dz = shz*hnorm*dx + svz*vnorm*dy + sdz*dz; |
