/* eq. développée = x+y+z-x^2-2*x*y-y^2+5*x^2*y-x*y^2+z^2+4*y^2*z-2*y*z^2+4*z^2*x-2*z*x^2-2*x^3-2*y^3-2*z^3 Plans de Sylvester : [[-2*x+y = 0, 2*x-y = 0], [-2*y+z = 0, 2*y-z = 0], [-2*z+x = 0, -x+2*z = 0], [1+z = 0, -z-1 = 0], [x+y-1 = 0, -x-y+1 = 0]] Eckardt (10) = {[-1/4, -1/2, -1], [0, 0, 0], [-2, -4, -1], [1/3, 2/3, 4/3], [-2, 3, -1], [1/3, 2/3, -1], [3/2, -1/2, -1], [1/3, 2/3, 1/6], [-2, -1/2, -1], [4/5, 1/5, 2/5]} Dr. diagonales (15) : [[t, 2*t, -3*t], [t, 2*t, -1/2+2*t], [-1+t, -2+2*t, t], [-3*t, t, 2*t], [1/2+3/2*t, t, 2*t], [-1+2*t, t, 2*t], [2*t, -3*t, t], [2*t, -1+3*t, t], [2*t, t+1/2, t], [t, -2*t-1, -1], [t+2, t, -1], [-1+2*t, t, -1], [-1+t, 2-t, t], [1/2-t, t+1/2, t], [1-t, t, -3*t+1]] Dr. de Sclafli (12) : [[17/2*t-7/2*5^(1/2)*t+7/2*5^(1/2)-15/2, 4*t-7/2-2*5^(1/2)*t+3/2*5^(1/2), t], [5/38+9/19*t+9/38*5^(1/2)+1/19*5^(1/2)*t, 9/38+21/38*t+1/38*5^(1/2)+15/38*5^(1/2)*t, t], [-3/2*t-1/5*5^(1/2)-9/10*5^(1/2)*t, 3/10*5^(1/2)-2/5*5^(1/2)*t-1/2, t], [-3*t+11/2+5/2*5^(1/2)-5^(1/2)*t, -3/2*t+5+2*5^(1/2)-3/2*5^(1/2)*t, t], [1/22+1/2*5^(1/2)*t-1/2*t-3/22*5^(1/2), 3/11+1/2*5^(1/2)*t-1/2*t+2/11*5^(1/2), t], [4/11+3/22*t-9/22*5^(1/2)*t-1/11*5^(1/2), -5/22+27/22*t+7/22*5^(1/2)*t-7/22*5^(1/2), t]] [[17/2*t+7/2*5^(1/2)*t-7/2*5^(1/2)-15/2, 4*t-7/2+2*5^(1/2)*t-3/2*5^(1/2), t], [5/38-9/38*5^(1/2)-1/19*5^(1/2)*t+9/19*t, 9/38-1/38*5^(1/2)-15/38*5^(1/2)*t+21/38*t, t], [-3/2*t+1/5*5^(1/2)+9/10*5^(1/2)*t, -3/10*5^(1/2)+2/5*5^(1/2)*t-1/2, t], [-3*t+11/2-5/2*5^(1/2)+5^(1/2)*t, -3/2*t+5-2*5^(1/2)+3/2*5^(1/2)*t, t], [1/22-1/2*5^(1/2)*t-1/2*t+3/22*5^(1/2), 3/11-1/2*5^(1/2)*t-1/2*t-2/11*5^(1/2), t], [4/11+3/22*t+9/22*5^(1/2)*t+1/11*5^(1/2), -5/22+27/22*t-7/22*5^(1/2)*t+7/22*5^(1/2), t]] suite -2,5,-2,-1,-1,0,-2,4,0,1,-2,4,-1,-2,0,1,-2,1,1,0 */ #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 { <-4,10,-10> color White} // shadowless light_source { <-5,3,-20> color White shadowless} light_source { <3,10,-10> color rgb <0.8,0.8,1>*0.5 shadowless} /*background{White}*/ box {<-20,-1.3,-50>,<4,20,5> pigment {SkyBlue} // Yellow rotate <0,+10, 0> } union{ // axes ---------------------- /* #declare g=3 ; #declare r1=0.03; #declare k=4;// longueur fleche=k*r1 #declare co=1.8;// rayon base=co*r1 union{ cylinder{ <-g/2,0,0>,,r1 } cone{ ,co*r1,,0 } pigment { Red }//transmit 0.3} } union{ cylinder{ <0,-g/2,0>,<0,g,0>,r1 } cone{ <0,g,0>,co*r1,<0,g+k*r1,0>,0 } pigment { Green }//transmit 0.3} } union{ cylinder{<0,0,-g/2>,<0,0,g>,r1 } cone{ <0,0,g>,co*r1,<0,0,g+k*r1>,0 } pigment { Blue }//transmit 0.3} } //plans de Sylvester <-2,1,0><0,-2,1><-1,0,2><0,0,1,1 > <1,1,0,1/sqrt(2)> // plane{<-2,1,0>,0 pigment{Magenta }} //1 // plane{<0,-2,1>,0 pigment{Magenta }}//2 // plane{<-1,0,2>,0 pigment{Magenta }} //3 // plane{<0,0,1>,-1 pigment{Magenta }} //4 // plane{<1,1,0>,1/sqrt(2) pigment{Magenta }} //5 triangle{ <.333,.667,1.33><.333,.667,-1><-2.,-4.,-1> pigment{ Yellow*1.5 transmit 0.4 }} //1 triangle{ <.333,.667,1.33><-2.,-.5,-1><1.5,-.5,-1> pigment{Green*1.5 transmit 0.4 }} //2 triangle{ <.8,.2,.4><-2.,-.5,-1><-2.,3.,-1> pigment{ Magenta transmit 0.5}} //3 triangle{ <-2.,-4.,-1><-2.,3.,-1><1.5,-.5,-1> pigment{ Black transmit 0.5}} //4 triangle{ <.333,.667,1.33><-2.,3.,-1> <1.5,-.5,-1>pigment{ Pink transmit 0.5}} //5 */ union{ // points de Eckardt #declare r=0.06; sphere{< -.250,-.500,-1. > ,r } //1 sphere{< 0.,0.,0. > ,r } //2 sphere{< -2.,-4.,-1. > ,r } //3 sphere{< .333,.667,1.33 > ,r } //4 sphere{< -2.,3.,-1. > ,r } //5 sphere{< .333,.667,-1. > ,r } //6 sphere{< 1.50,-.500,-1. > ,r } //7 sphere{< .333,.667,.167 > ,r } //8 sphere{< -2.,-.500,-1. > ,r } //9 sphere{< .800,.200,.400 > ,r } //10 pigment{Cyan*1.3} finish {ambient 0.4 diffuse 0.6 roughness 0.001 reflection 0 specular .8} } union{ // droites diagonales #declare r=0.02 ; #declare b=4; cylinder{< -1.*b,-2.*b,3.*b >, ,r } //1 cylinder{< -1.*b,-2.*b,-.500-2.*b >, ,r } //2 cylinder{< -1.-1.*b,-2.-2.*b,-1.*b >,<-1.+b,-2.+2.*b,b > ,r } //3 cylinder{< 3.*b,-1.*b,-2.*b >,<-3.*b,b,2.*b > ,r } //4 cylinder{< .500-1.50*b,-1.*b,-2.*b >,<.500+1.50*b,b,2.*b > ,r } //5 cylinder{< -1.-2.*b,-1.*b,-2.*b >,<-1.+2.*b,b,2.*b > ,r } //6 cylinder{< -2.*b,3.*b,-1.*b >,<2.*b,-3.*b,b > ,r } //7 cylinder{< -2.*b,-1.-3.*b,-1.*b >,<2.*b,-1.+3.*b,b > ,r } //8 cylinder{< -2.*b,-1.*b+.500,-1.*b >,<2.*b,b+.500,b > ,r } //9 cylinder{< -1.*b,-1.+2.*b,-1. >, ,r } //10 cylinder{< -1.*b+2.,-1.*b,-1. >, ,r } //11 cylinder{< -1.-2.*b,-1.*b,-1. >,<-1.+2.*b,b,-1. > ,r } //12 cylinder{< -1.-1.*b,b+2.,-1.*b >,<-1.+b,-1.*b+2.,b > ,r } //13 cylinder{< b+.500,-1.*b+.500,-1.*b >,<-1.*b+.500,b+.500,b > ,r } //14 cylinder{< 1.+b,-1.*b,3.*b+1. >,<1.-1.*b,b,-3.*b+1. > ,r } //15 pigment{Yellow} } union{ // droites Sclafli 1 cylinder{< -.66*b+.34,.48*b-.14,-1.*b >,<.66*b+.34,-.48*b-.14,b > ,r } //1 cylinder{< .663-.592*b,.296-1.44*b,-1.*b >,<.663+.592*b,.296+1.44*b,b > ,r } //2 cylinder{< 3.52*b-.448,.172+.896*b,-1.*b >,<-3.52*b-.448,.172-.896*b,b > ,r } //3 cylinder{< 5.24*b+11.1,4.86*b+9.48,-1.*b >,<-5.24*b+11.1,-4.86*b+9.48,b > ,r } //4 cylinder{< -.260-.620*b,.681-.620*b,-1.*b >,<-.260+.620*b,.681+.620*b,b > ,r } //5 cylinder{< .160+.780*b,-.939-1.94*b,-1.*b >,<.160-.780*b,-.939+1.94*b,b > ,r } //6 pigment{Red} } union{ // droites Sclafli 2 cylinder{< -16.3*b-15.3,-8.48*b-6.86,-1.*b >,<16.3*b-15.3,8.48*b-6.86,b > ,r } //1 cylinder{< -.399-.356*b,.178+.332*b,-1.*b >,<-.399+.356*b,.178-.332*b,b > ,r } //2 cylinder{< -.52*b+.448,-1.17-.896*b,-1.*b >,<.52*b+.448,-1.17+.896*b,b > ,r } //3 cylinder{< .76*b-.10,-1.86*b+.52,-1.*b >,<-.76*b-.10,1.86*b+.52,b > ,r } //4 cylinder{< .350+1.62*b,-.135+1.62*b,-1.*b >,<.350-1.62*b,-.135-1.62*b,b > ,r } //5 cylinder{< .568-1.05*b,.485-.518*b,-1.*b >,<.568+1.05*b,.485+.518*b,b > ,r } //6 pigment{Blue} } /* */ poly{3,<-2,5,-2,-1,-1,0,-2,4,0,1,-2,4,-1,-2,0,1,-2,1,1,0> pigment{White*0.63 transmit 0.35}//} finish {ambient 0.4 diffuse 0.5 roughness 0.001 reflection 0.1 specular .8} }//fin poly clipped_by { sphere{ < -0.4,-0.50,0 > ,5. scale < 0.7,0.95,0.9> translate < -0,0.2,0.2 > } }// < 0.6,1,0.6> < -0,0.5,0.5 > bounded_by { clipped_by } rotate <-50,120,25 > scale 0.4 //0.43 translate <0,0.15,0> } 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> }