// ---------------------
//  The cyclide:
//  a quartic surface
//  with singular conic
// ---------------------

//  image size

width=300;
height=300;

//  constants

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

//  light

illumination = ambient_light +
               diffuse_light +
               reflected_light +
               transmitted_light;

ambient=20;

smoothness=30;
diffuse=60;
reflected=70;
transmitted=0;
transparence=0;

diffuse2=diffuse;
reflected2=reflected;
transmitted2=0;
transparence2=100;
thickness2=0;

light1_x=-173;
light1_y=100;
light1_z=100;
light1_vol=80;
light1_red=255;
light1_green=255;
light1_blue=255;

light2_x=173;
light2_y=100;
light2_z=80;
light2_vol=0;

light3_x=0;
light3_y=-80;
light3_z=80;
light3_vol=20;

//   since the image will be dithered 
//   the background is set to white

background_red  =255;
background_blue =255;
background_green=255;

radius=9.5;

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

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

curve_width=3;

double  sf = 0.15;
scale_x=sf;
scale_y=sf;
scale_z=sf;

//  equation

double a1=3;
double a2=1;
double a3=2;
double c=1;

poly zyklide=(x^2+y^2+(-1))^2 +
    z^2*(a1*x^2 +  a2*y^2 +a3*(-1) + c*z^2);

//  rotation

rot_y=Pi/180*70;
rot_x=Pi/180*10;
rot_z=Pi/180*0;

epsilon=0.0000001;
root_finder=d_chain_newton;

//  draw the singular conic by cutting the sphere
//  of surface2 with the plane z=0

surface=zyklide;
surface2=x^2+y^2+z^2-1.0;

clear_screen;
draw_surface;

//  draw the singular conic

plane=z;
surf_nr=2;
cut_with_plane;

dither_surface;