// ---------------------------
//  The Steiner roman surface
//  is an emmbedding of P_2
//  into R^3.
//  The algebraic surface
//  containing the image
//  contains three lines.
// ---------------------------

//  image size

height=200;
width =200;

double  w2=sqrt(2.0);
double  Pi=2*arccos(0);

//  tetrahedral coodinates

poly p=1-z-w2*x;
poly q=1-z+w2*x;
poly r=1+z+w2*y;
poly s=1+z-w2*y;

//  rotation

rot_x=0.2;
rot_y=0.6;
rot_z=0.94+Pi;

//  scaling 

double  sf = 1.4;

scale_x=sf;
scale_y=sf;
scale_z=sf;

radius=9.5;

spec_z=30;
perspective=central;
antialiasing=4;

//  light

illumination=ambient_light+
             diffuse_light+
             reflected_light+
             transmitted_light;

ambient=20;
smoothness=30;
transparence=0;

light1_x=-100;
light1_y=100;
light1_z=100;
light1_vol=100;

light3_x=100;
light3_y=20;
light3_z=50;
light3_vol=20;

light8_x=0;
light8_y=100;
light8_z=30;
light8_vol=40;

poly steiner=x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z;
surface=steiner;

//  our new way to draw lines
//  as intersection of planes

transparence2=100;
transmitted2 =0;
transparence3=100;
transmitted3 =0;
transparence4=100;
transmitted4 =0;

//  this are the three planes
 
surface2=x-y;
surface3=y-z;
surface4=z+x;

clear_screen;
draw_surface;

curve_width = 4.0;
curve_red   = surface_red;
curve_blue  = surface_blue;
curve_green = surface_green;

//  draw z-axis x=y=0

surface_n=2;
plane=x+y;
cut_with_plane;

//  draw x-axis y=z=0

surface_n=3;
plane=y+z;
cut_with_plane;

// draw y-axis x=z=0

surface_n=4;
plane=z-x;
cut_with_plane;

filename="steiner.ras";
color_file_format=sun;
save_color_image;