// ----------------------------------
//  The Barth sextic: 
//  a degree 6 surface with 65
//  ordinary double points
//  and symmetry of the icosahedron
// ----------------------------------

//  image size

width = 500;
height = 500;
 
//  fix rotation

rot_x=0.2;
rot_y=-0.33;
rot_z=-3.33;

//  fix scaling

double sf = 0.25;
 
scale_x=sf;
scale_y=sf;
scale_z=sf;

//  fix position and perspective

spec_z = 25.0;
perspective=central;
radius=9.0;

//  fix light

surface_red  =inside_red;
surface_green=inside_green;
surface_blue =inside_blue;

ambient=20;
diffuse=60;
reflected=60;

smoothness=14;
 
light1_x=100;
light1_y=100;
light1_z=100;
light1_vol=80;
 
light2_x=100;
light2_y= 20;
light2_z= 50;
light2_vol=50;
 
light3_x=-100;
light3_y= 100;
light3_z=-100;
light3_vol=0;

//  define the sextic
 
double t=(1+sqrt(5))/2;
 
poly f1=t^2*x^2-y^2;
poly f2=t^2*y^2-z^2;
poly f3=t^2*z^2-x^2;
 
poly g =(x^2+y^2+z^2-1)^2;
 
surface=4*f1*f2*f3-(1+2*t)*g;


epsilon=0.0001;
iterations=30;

//  draw it

clear_screen;
draw_surface;