/*
 ================================================
 Demonstrating ocal length for a convex lens
 ------------------------------------------------
 Created by Søren Peo Pedersen - see my user page
 at http://da.wikipedia.org/wiki/Bruger:Peo
 ================================================
 */
 
 #declare IndexOfRefraction=1.66;  // Simulated index of refraction
 #declare LineWidth=0.02;          // Width of light beam lines
 
 #switch (1) // edit to 1 for long, 2 for short focal length
 #case (1)
   #declare LR=10;
   #declare VisF=1;
   #break
 #case (2)
   #declare LR=4.4;
   #declare VisF=0;
   #break
 #end
 
 #declare FL=1/(IndexOfRefraction-1)/(2/LR);
 #declare LS=sqrt(LR*LR-5.29)-.05;
 
 #macro DashedLine(L) // White dashed line for annotations
 union {
   #local cnt=0;
   #while (cnt<L)
     box {<-.03,cnt/2,-.02>,<.03,cnt/2+.25,-.021>}
     #local cnt=cnt+1;
   #end
   }
 #end
 
 #macro Beam(Shift)  // Renders one of the nine beams
   #local pX1=LS-sqrt(LR*LR-Shift*Shift);
   #local VI1=asin(Shift/LR);
   #local VO1=-asin(Shift/LR/IndexOfRefraction);
   #local LLa=-tan(VI1+VO1);    
   #local LLb=(Shift-LLa*pX1);
   #local ALa=1+LLa*LLa;
   #local ALb=(2*LS+2*LLa*LLb);
   #local ALc=LS*LS+LLb*LLb-LR*LR;
   #local ALD=ALb*ALb-4*ALa*ALc;
   #local pX2=(-ALb+sqrt(ALD))/(2*ALa);
   #local pY2=sqrt(LR*LR-(pX2+LS)*(pX2+LS))*select(LLa,1,1,-1);
   #local Vud=atan(pY2/(pX2+LS));
   #local VI2=Vud+VO1+VI1;
   #local VO2=-asin(sin(VI2)*IndexOfRefraction);    
   #local DIR=Vud+VO2;
   #local pX3=pX2+50*cos(DIR);
   #local pY3=pY2+50*sin(DIR);
 
   sphere_sweep {
     linear_spline,4,
     <-50,Shift,0>,LineWidth
     <pX1,Shift,0>,LineWidth
     <pX2,pY2,0>,LineWidth
     <pX3,pY3,0>,LineWidth
     pigment {color rgb<1,.95,.8>}
     finish {ambient 1 diffuse 0}
     no_shadow no_reflection        
     translate <0,0,-LineWidth>
     scale <1,1,.5>
     }
 #end
 
 #if (VisF != 0) // Include annotation of "f" length in image?
   union  {
     #object {DashedLine(11) translate <0,-2.8,0>}
     #object {DashedLine( 7) translate <FL-pi/LR,-2.8,0>}
     text {ttf "timesbi.ttf"
       "f",.1,0
       translate <(FL-pi/LR)/2-.3,-3,0>
       }
     triangle {<0,-2.7,0>,<.5,-2.5,0>,<.5,-2.9,0>}
     box {<.5,-2.66,.001>,<(FL-pi/LR)/2-.3,-2.74,0>}
     triangle {<FL-pi/LR,-2.7,0>,<FL-.5-pi/LR,-2.5,0>,<FL-.5-pi/LR,-2.9,0>}
     box {<FL-.5-pi/LR,-2.66,.001>,<(FL-pi/LR)/2+.3,-2.74,0>}
     pigment {color rgb 1} finish {ambient 1 diffuse 0}
     }    
 #end
 
 intersection {  // The lens itself
   sphere {<-LS,0,0>,LR}
   sphere {< LS,0,0>,LR}
   cylinder {<-8,0,0>,<8,0,0>,2.3}
   plane {<0,0,-1>,0}
   pigment {color rgbt <.8,1,.9,.7>}
   finish {phong 1 reflection .1 ambient .5}
   interior {ior IndexOfRefraction}
   }
 
 #object {Beam( 2.0)}  // Beams: The number
 #object {Beam( 1.5)}  // in parenthesis are
 #object {Beam( 1.0)}  // the Y coordinates
 #object {Beam( 0.5)}  // for each beam of
 #object {Beam( 0)}    // light coming in
 #object {Beam(-0.5)}  // from the left
 #object {Beam(-1.0)}
 #object {Beam(-1.5)}
 #object {Beam(-2.0)}
 
 camera {
     location <FL/2,0,-500>
     look_at <FL/2,0,0>
     angle 1
     }
 
 light_source {<100,100,-100> color rgb 1}