/*Surface de Clebsch ; Equation de hunt
 81*(x^3+y^3+z^3)-189*(x^2*y+x^2*z+y^2*x+y^2*z+z^2*x+z^2*y)+54*x*y*z+
      126*(x*y+x*z+y*z)-9*(x^2+y^2+z^2)-9*(x+y+z)+1 =0
      
7 points de Eckardt à distance finie + 3 couple de droites parallèles( 3 à l'infini )      
*/
#declare a=1 ; 
#include "colors.inc" 

#declare a=4 ; 
 camera { orthographic 
        location <-2.5,0.6,-3>*0.75 look_at<0,0.2,0> }
 
light_source { <-4,5,-10> color White}
light_source { <-5,10,-20> color White shadowless}
light_source { <3,10,-10> color rgb <0.8,0.8,1>*0.5 shadowless}

box {<-20,-1.3,-20>,<5,20,5> 
      pigment {SkyBlue} 
      rotate <0,5, 0>  
        }
union{ 

union { // droites passant par les points Eckardt 
 #declare b=0.08;
 #declare rc= 0.008;
 /*1*/   cylinder{< b,-.3333,-1.*b >,<-1.*b,-.3333,b > ,rc}
/*1*/   cylinder{< 0.,-b-.3333,-b/3 >,<0.,b-.3333,b/3 > ,rc}
/*1*/   cylinder{< -b/3,-b-.3333,0. >,<b/3,b-.3333,0. > ,rc}

/*2*/   cylinder{< -b+.1667,0,b+.1667 >,< b+.1667,0,-b+.1667 > ,rc}//2
/*2*/   cylinder{< -b/3+.1667,0,-b+.1667 >,<b/3+.1667,0,b+.1667 > ,rc}
/*2*/   cylinder{ < -b+.1667,0.,-0.3333*b +.1667>,< b+.1667,0.,0.3333*b +.1667>,rc}

/*3*/   cylinder{< b+.3333,.3333,-1.*b +.3333>,< -b+.3333,.3333,1.*b +.3333>,rc}       
/*3*/   cylinder{< -1.*b+.3333,b+.3333,.3333 >,<b+.3333,-1.*b+.3333,.3333 >,rc}
/*3*/   cylinder{ < .3333,b+.3333,-1.*b+.3333 >,<.3333,-1.*b+.3333,b+.3333 > ,rc}

/*4*/   cylinder{< -2.667*b-.3333,0.,-1.*b >,<2.667*b-.3333,0.,b > ,rc}
/*4*/   cylinder{< -1.*b-.3333,-.3333*b,0. > ,< b-.3333,.3333*b,0. >,rc}
/*4*/   cylinder{< -.3333,b,-b >,< -.3333,-b,b > ,rc}
                
/*5*/   cylinder{ < -1.*b+.1667,b+.1667,0. >,<b+.1667,-b+.1667,0. >,rc}
/*5*/   cylinder{ < -0.3333*b+.1667,-b+.1667,0. >,< 0.3333*b+.1667,b+.1667,0. >,rc}
/*5*/   cylinder{< -1.*b+.1667,-.3333*b+.1667,0. >,<b+.1667,.3333*b+.1667,0. > ,rc}
                    
/*6*/   cylinder{<-b, b,-0.333 >,<b, -b,-0.333 > ,rc}
/*6*/   cylinder{< -.3333*b,0.,-b-.3333 >,< .3333*b,0.,b-.3333 > ,rc}
/*6*/   cylinder{< 0.,-.3333*b,-b-.3333 >,< 0.,.3333*b,b-.3333 > ,rc} 

/*7*/   cylinder{< 0.,-b+.1667,-0.3333*b+.1667 >,< 0.,b+.1667,0.3333*b+.1667 > ,rc}
/*7*/   cylinder{< 0.,b+.1667,-b+.1667 >,< 0.,-b+.1667,b+.1667 > ,rc}
/*7*/   cylinder{< 0.,-.3333*b+.1667,-b+.1667 >,< 0.,.3333*b+.1667,b+.1667 > ,rc}
 pigment{Yellow}
 finish {ambient 0.4 diffuse 0.5 roughness 0.0001 reflection 0.1 specular .8}}


 
union { // points Eckardt 
  #declare rs= 0.02;
 /*1*/   sphere{< 0.,-.3333,0. >,rs }
/*2*/   sphere{< .1667,0.,.1667 >,rs }
/*3*/   sphere{< .3333,.3333,.3333 >,rs }
/*4*/   sphere{< -.3333,0.,0. >,rs }
/*5*/   sphere{< .1667,.1667,0. >,rs }
/*6*/   sphere{< 0.,0.,-.3333 >,rs }
/*7*/   sphere{< 0.,.1667,.1667 >,rs }
 pigment{Blue}
 finish {ambient 0.4 diffuse 0.5 roughness 0.0001 reflection 0.1 specular .8}
 }

union{ // droites entières
	        #declare r=0.002 ; 
                #declare b=4;
                                
/*1*/   cylinder{< b,-.3333,-1.*b >,<-1.*b,-.3333,b > ,r } 
/*2*/   cylinder{< b+.3333,0.,-1.*b >,<-1.*b+.3333,0.,b > ,r } 
/*3*/   cylinder{< b+.6667,.3333,-1.*b >,<-1.*b+.6667,.3333,b > ,r } 
/*4*/   cylinder{< 2.927*b+.2696,1.309*b+.637e-1,-1.*b >,<-2.927*b+.2696,-1.309*b+.637e-1,b > ,r } 
/*5*/   cylinder{< -1.*b,-.3333*b+.1111,0. >,<b,.3333*b+.1111,0. > ,r } 
/*6*/   cylinder{< 5.236*b+2.285,2.236*b+.8727,-1.*b >,<-5.236*b+2.285,-2.236*b+.8727,b > ,r } 
/*7*/   cylinder{< -2.342*b+.2412,.4472*b+.3903,-1.*b >,<2.342*b+.2412,-.4472*b+.3903,b > ,r } 
/*8*/   cylinder{< -3.*b-.3333,0.,-1.*b >,<3.*b-.3333,0.,b > ,r } 
/*9*/   cylinder{< -2.236*b+.1273,.764*b+.49e-1,-1.*b >,<2.236*b+.1273,-.764*b+.49e-1,b > ,r } 
/*10*/   cylinder{< -1.*b,b+.6667,.3333 >,<b,-1.*b+.6667,.3333 > ,r } 
/*11*/   cylinder{< -1.*b,b+.3333,0. >,<b,-1.*b+.3333,0. > ,r } 
/*12*/   cylinder{< -1.*b,b,-.3333 >,<b,-1.*b,-.3333 > ,r } 
/*13*/   cylinder{< .4472*b+.3903,-2.342*b+.2412,-1.*b >,<-.4472*b+.3903,2.342*b+.2412,b > ,r } 
/*14*/   cylinder{< .764*b+.49e-1,-2.236*b+.1273,-1.*b >,<-.764*b+.49e-1,2.236*b+.1273,b > ,r } 
/*15*/   cylinder{< 0.,-3.*b-.3333,-1.*b >,<0.,3.*b-.3333,b > ,r } 
/*16*/   cylinder{< -1.*b,-3.*b-.3333,0. >,<b,3.*b-.3333,0. > ,r } 
/*17*/   cylinder{< 1.309*b+.637e-1,2.927*b+.2696,-1.*b >,<-1.309*b+.637e-1,-2.927*b+.2696,b > ,r } 
/*18*/   cylinder{< 2.236*b+.8727,5.236*b+2.285,-1.*b >,<-2.236*b+.8727,-5.236*b+2.285,b > ,r } 
/*19*/   cylinder{< -.3333,b,-1.*b >,<-.3333,-1.*b,b > ,r } 
/*20*/   cylinder{< 0.,b+.3333,-1.*b >,<0.,-1.*b+.3333,b > ,r } 
/*21*/   cylinder{< .3333,b+.6667,-1.*b >,<.3333,-1.*b+.6667,b > ,r } 
/*22*/   cylinder{< -.4472*b-.569e-1,.342*b+.9217e-1,-1.*b >,<.4472*b-.569e-1,-.342*b+.9217e-1,b > ,r } 
/*23*/   cylinder{< -.3333*b+.1111,0.,-1.*b >,<.3333*b+.1111,0.,b > ,r } 
/*24*/   cylinder{< -.427*b-.1030,.1910*b+.4363,-1.*b >,<.427*b-.1030,-.1910*b+.4363,b > ,r } 
/*25*/   cylinder{< .1910*b+.4363,-.427*b-.1030,-1.*b >,<-.1910*b+.4363,.427*b-.1030,b > ,r } 
/*26*/   cylinder{< 0.,-.3333*b+.1111,-1.*b >,<0.,.3333*b+.1111,b > ,r } 
/*27*/   cylinder{< .342*b+.9217e-1,-.4472*b-.569e-1,-1.*b >,<-.342*b+.9217e-1,.4472*b-.569e-1,b > ,r } 
        pigment{Red} 
 	}
	poly{3, < 81,-189,-189,-9,-189,54,126,-189,126,-9,81,-189,-9,-189,126,-9,81,-9,-9,1 >  
	      pigment{White*0.6 transmit 0.2} 
	      finish {ambient 0.4 diffuse 0.5 roughness 0.001 reflection 0.02 specular .8} 
	       	}//fin poly

	clipped_by { sphere{ < 0,0,0 > , 0.8  translate < 0,0,0 > } } 
	bounded_by { clipped_by }
        rotate <-30,-180,-27>
 	scale 2.5 
        translate <0,0.,0>  
}

  
text {	ttf "times.ttf" "AE"
        0.5,0 
        pigment { Cyan*1.2 }
        scale 0.08
        rotate <0,40,0> 
        translate <1.9,-1.3,-0.4> }