[general]
name = Kleinbottle1;
comments = Klein's bottle (kleinsche Flaeche), bottle shape parametrization. Felix Christian Klein (1849-1925).;
a1_min = 0;
a1_max = 360;
a1_steps = 40;
a2_min = 0; 
a2_max = 360;
a2_steps = 40;

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

[param]
name = b;
title = Height;
default = 3;
min = 0.01;
max = 10;

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


[formula]
I1 = linstep(180.0000001,180,A1); 
I2 = 1 - I1;
S1 = sin(A1);
C1 = cos(A1);
S2 = sin(A2);
C2 = cos(A2);
r = c * (1 - C1 / 2);
/*
a = 3;
b = 4;
c = 2;
*/

X = I1 * ((a * (1 + S1) + r * C2) * C1) + I2 * (a * (1 + S1) * C1 - r * C2);
Y = I1 * ((b + r * C2) * S1) + I2 * (b * S1);
Z = r * S2;

[preset]
name = default;
a = 1;
b = 3;
c = 1;
a1_min = 0;
a1_max = 360;
a1_steps = 40;
a2_min = 0; 
a2_max = 360;
a2_steps = 40;