/* en cylindrique : z=1/a*ch((u+b)*a), u étant l'angle polaire  */

#include "colors.inc"
#include "metals.inc"

#declare I_Glass =             
   interior{
      ior 1.51
      caustics 2
      fade_distance 1.5
      fade_power 0.8
   }
#declare T_Glass = texture {
   pigment { color red 0.95 green 0.95 blue 1.0 filter 0.95 }
   finish {
      ambient 0.0
      diffuse 0.0
      reflection 0.05
      phong 0.3
      phong_size 90
   }
}

#declare a=0.165;   // 1.9 ; 0.395 ;
#macro xx(uu) cos(uu) 
#end  
#macro yy(uu) sin(uu) 
#end 
#macro zz(uu) -cosh(uu*a)/a
#end 

// ----------------------
#declare deb=-2.5*pi-0.1;// 0.73 :-pi/2 ; 2.36:-2.5*pi ; 1.6: -1.5*pi
#declare fin=2.5*pi+0.1; // 0.73 :pi/2+0.1;
#declare n=200;         // 0.73 :45   ; 3.6:80 ; 1.6:60
#declare r=0.1;                
#declare pas=(fin-deb)/n;
                      
//----------------------                         
 //Lights, camera, action
camera { orthographic location  < 0,8,-10>
  look_at   < 0,4, 0>
} 

light_source { <-2, 10,-8> color rgb 1  }
light_source { <5, 10, -8> color rgb 1 shadowless }

background{ color White*0.95}
// ---------------------------------------

 union {
  
//---------------------- le fil ----------------    
       #declare uu = deb;                    
sphere_sweep {
  linear_spline
  n+1, // si ça plante il faut ajouter +1 ou -1 
  #while (uu<=fin)
        #declare vv=uu+pas; 
        <xx(uu),yy(uu),zz(uu)>, 0.03
        #declare uu=vv;   
  #end 
  tolerance 0.1             // optional
   texture{ T_Gold_1A }
    finish { diffuse 0.2 ambient 0.6 reflection 0.1 roughness 0.01 specular 0.8 }
        }      
        
 //----------- la tringle horizontale et le clou ------------------       
 union{ cylinder{<xx(deb),yy(deb),zz(deb)>,<xx(fin),yy(fin),zz(fin)> , 0.05}
        cylinder{< (xx(deb)+xx(fin))/2,(yy(deb)+yy(fin))/2,(zz(deb)+zz(fin))/2-0.2>,
                 <(xx(deb)+xx(fin))/2,(yy(deb)+yy(fin))/2,(zz(deb)+zz(fin))/2+0.2>,0.1 }
        sphere{<(xx(deb)+xx(fin))/2,(yy(deb)+yy(fin))/2,(zz(deb)+zz(fin))/2-0.21>,0.1 }
       texture { T_Chrome_4A}
       finish { diffuse 0.2 ambient 0.6 reflection 0.1 roughness 0.01 specular 0.8 }
        }   

//------------- les sphères -----------------------------
#declare r=0.1;

#declare pts=array[141][3]
{{-.9983e-1,-.995,-12.07},{-.2046e-1,-.9998,-11.94},{.5905e-1,-.9983,-11.80},{.1382,-.9904,-11.67},{.2164,-.9763,-11.54},
{.2933,-.956,-11.41},{.3684,-.9297,-11.29},{.4411,-.8975,-11.16},{.511,-.8596,-11.04},{.5777,-.8163,-10.92},{.6407,-.7678,-10.80},
{.6997,-.7145,-10.69},{.7594,-.6506,-10.56},{.8134,-.5817,-10.44},{.8611,-.5084,-10.32},{.9022,-.4313,-10.20},
{.9365,-.3508,-10.08},{.9635,-.2676,-9.964},{.9832,-.1824,-9.850},{.9954,-.9576e-1,-9.739},{1.,.3352e-3,-9.620},
{.9953,.9643e-1,-9.502},{.9815,.1916,-9.387},{.9585,.2851,-9.274},{.9267,.3758,-9.164},{.8863,.4632,-9.056},{.8377,.5462,-8.950},
{.7813,.6241,-8.847},{.711,.7032,-8.736},{.6327,.7744,-8.627},{.5473,.8369,-8.521},{.4558,.8901,-8.418},{.3592,.9333,-8.317},
{.2586,.966,-8.219},{.1551,.9879,-8.123},{.4980e-1,.9988,-8.030},{-.6659e-1,.9978,-7.930},{-.1821,.9833,-7.833},
{-.2951,.9555,-7.739},{-.4041,.9147,-7.648},{-.5076,.8616,-7.560},{-.6043,.7967,-7.475},{-.6928,.7211,-7.392},{-.7719,.6358,-7.312},
{-.8468,.5319,-7.227},{-.9078,.4194,-7.146},{-.9539,.3,-7.067},{-.9844,.1757,-6.992},{-.9988,.4846e-1,-6.920},
{-.9968,-.7953e-1,-6.851},{-.9785,-.2062,-6.785},{-.9441,-.3295,-6.722},{-.8943,-.4475,-6.662},{-.8298,-.558,-6.605},
{-.7432,-.669,-6.546},{-.6419,-.7668,-6.490},{-.5278,-.8493,-6.438},{-.4033,-.9151,-6.389},{-.2708,-.9626,-6.344},
{-.1329,-.9911,-6.302},{.7586e-2,-1.,-6.263},{.148,-.989,-6.228},{.2854,-.9584,-6.197},{.4172,-.9088,-6.168},{.5407,-.8412,-6.143},
{.6535,-.757,-6.122},{.7533,-.6577,-6.103},{.8382,-.5454,-6.088},{.9065,-.4223,-6.076},{.9568,-.2908,-6.068},{.9881,-.1535,-6.063},
{.9999,-.1320e-1,-6.061},{.9919,.1274,-6.062},{.9641,.2654,-6.067},{.9173,.3982,-6.074},{.8523,.5231,-6.086},{.7704,.6376,-6.100},
{.6732,.7395,-6.118},{.5627,.8267,-6.139},{.441,.8975,-6.163},{.3106,.9505,-6.191},{.174,.9847,-6.222},{.3399e-1,.9994,-6.256},
{-.1067,.9943,-6.294},{-.2453,.9694,-6.336},{-.379,.9254,-6.380},{-.5052,.863,-6.428},{-.6214,.7835,-6.480},{-.7253,.6884,-6.535},
{-.8148,.5798,-6.593},{-.8881,.4596,-6.656},{-.9439,.3303,-6.721},{-.9809,.1944,-6.791},{-.9985,.5476e-1,-6.864},
{-.9974,-.7197e-1,-6.933},{-.9803,-.1975,-7.005},{-.9474,-.3199,-7.080},{-.8994,-.4372,-7.158},{-.8368,-.5474,-7.239},
{-.7609,-.6489,-7.324},{-.6727,-.7399,-7.411},{-.5737,-.8191,-7.502},{-.4655,-.885,-7.596},{-.3498,-.9368,-7.694},
{-.2409,-.9706,-7.784},{-.1288,-.9917,-7.878},{-.1498e-1,-.9999,-7.974},{.9899e-1,-.9951,-8.073},{.2117,-.9773,-8.175},
{.3216,-.9469,-8.280},{.4274,-.9041,-8.387},{.5275,-.8495,-8.498},{.6119,-.791,-8.600},{.6898,-.724,-8.705},{.7604,-.6495,-8.812},
{.823,-.5681,-8.922},{.8769,-.4807,-9.034},{.9215,-.3883,-9.149},{.9565,-.2917,-9.266},{.9814,-.1921,-9.387},{.9949,-.1007,-9.497},
{1.,-.8409e-2,-9.610},{.9965,.8394e-1,-9.724},{.9845,.1756,-9.842},{.9641,.2657,-9.961},{.9354,.3536,-10.08},{.8988,.4384,-10.21},
{.8545,.5195,-10.33},{.8028,.5962,-10.46},{.7505,.6609,-10.58},{.693,.7209,-10.70},{.6307,.776,-10.82},{.564,.8258,-10.95},
{.4934,.8698,-11.07},{.4194,.9078,-11.20},{.3425,.9395,-11.33},{.2633,.9647,-11.46},{.1822,.9833,-11.60},{.1081,.9941,-11.72},
{.3342e-1,.9994,-11.85},{-.4145e-1,.9991,-11.97}}

   union{ 
  #declare uu =0;   //deb ; 
  #while (uu<=140)     //fin)
        #declare vv=uu+2; 
        sphere{ <pts[uu][0],pts[uu][1],pts[uu][2]>, r}  // (ligne A)
// pour avoir des perles régulièrement espacées à l'aide d'un tableau de points calculés avec Maple             
//sinon utiliser :   sphere{<xx(uu),yy(uu),zz(uu)>, r} à la place de la (ligne A)
// mais les perles ne seront pas régulières              
       #declare uu=vv;   
  #end 
  sphere{<xx(fin),yy(fin),zz(fin)>, r}
        texture{ T_Chrome_5A }
        finish { diffuse 0.2 ambient 0.6 reflection 0.2 roughness 0.0001 specular 0.8 }
   }/**/
//----------------- le cylindre support ----------------

#declare bas=-5.7 ;  //1.9:-0.1 ;0.395 :-2.4 ; 0.2 :
cylinder{<0,0,bas><0,0,zz(fin)+0.2>,1-r
        pigment{ color Red }
        finish { diffuse 0.2 ambient 0.6 reflection 0.1 roughness 0.0001 specular 0.8 }                 
}
// -----------------------------------------------------
// support en plexiglass
          
cylinder {  <0,0,bas>,<0,0,bas+0.35>,1.8
          texture { T_Glass}
          interior { I_Glass}
          finish { diffuse 0.2 ambient 0.6 reflection 0.1 roughness 0.0001 specular 0.8 }                         
 }     
// ---------------------------------------

scale 1.45          
rotate  <90,60,0 >  // 0.74 :<90,60,0 > ; 2.36:<90,50,0 > ; 0.395:<90,-40,0 >
translate <0,bas-2.6,0>    // 0.73 :<0,-0.8,0> ; 0.4 :-0.8 ; 0.2 :-
}