[general]
name = Dupin;
comments = Dupin's Cyclide. Pierre Charles Francois Dupin (1784-1873).;
a1_min = 0;
a1_max = 360;
a1_steps = 60;
a2_min = 0; 
a2_max = 360;
a2_steps = 60;

[param]
name = a;
title = a;
default = 1;
min = 0.01;
max = 10;

[param]
name = b;
title = b;
default = 1;
min = 0.01;
max = 1;

[param]
name = c;
title = c;
default = 0;
min = 0.01;
max = 10;

[param]
name = d;
title = d;
default = 1;
min = 0.01;
max = 10;


[formula]
I0 = linstep(0.000001,0,a-c); 
I1 = 1 - I0;
T1 = 1 / (I1 * (a - c * cos(A1) * cos(A2)) + I0 * 0.000001);

X = (d * (c - a * cos(A1) * cos(A2)) + b*b * cos(A1)) * T1;
Y = (b * sin(A2) * (c * cos(A1) - d)) * T1;
Z = -(b * sin(A1) * (a - d * cos(A2))) * T1;


[preset]
name = Torus (a = b);
a = 1;
b = 1;
c = 0;
d = 0.5;
a1_min = 0;
a1_max = 360;
a1_steps = 60;
a2_min = 0; 
a2_max = 360;
a2_steps = 60;


[preset]
name = Symmetric Crescents (0 = d < c);
a = 1;
b = 1;
c = 0.5;
d = 0;

[preset]
name = Crescents (0 < d < c);
a = 1;
b = 1;
c = 0.5;
d = 0.1;

[preset]
name = Single Crescent (b = d);
a = 1;
b = 0.8;
c = 0.6;
d = 0.8;

[preset]
name = Spindle Cyclide (d > a);
a = 1;
b = 1;
c = 0;
d = 1.5;