Predefined functions

As p and scale in pi (π), for all terms where p and q enter directly into formulas for x ,y, z (e.g not in periodic function of the variables), a factor 1/pi (1/π) appears. A factor cos(v*t) indicates that the associated term is animated. Reset redefines t = 0 and hence cos(vt) = 1.

Fixed numbers in the formulas are used to define a reasonable scaling at the start of the simulation for uniform default values of parameters a, b, c (= 0.5).

x_function = p/pi

y_function = q/pi

z_function = cos(v*t)*(a/pi-0.6)*p

Plane

x_function = p/pi

y_function = q/pi

z_function = cos(v*t)*p*q/pi^2

Saddle

x_function = cos(v*t)*a*cos(p)

y_function = b*sin(p)

z_function = c*q/(2*pi)

Cylinder

x_function = a*cos(p)*(1+q/(2*pi)*cos(p/2))

y_function = 2*b*sin(p)*(1+q/(2*pi)*cos(p/2))

z_function = c*q/(pi)*sin(p/2*t)

Möbius strip

x_function = cos(v*t)*a*cos(p)*abs(cos(q))

y_function = cos(v*t)*a*sin(p)*abs(cos(q))

z_function = cos(v*t)*a*sin(q)

Sphere

x_function = a*cos(p)*abs(cos(q))

y_function = cos(v*t)*b*sin(p)*abs(cos(q))

z_function = c*sin(q)

Ellipsoid

x_functio n= a/pi*q*cos(p)*cos(v*t)");

y_function = b/pi*q*sin(p)*cos(v*t)");

z_function = c*q/pi");

Double cone

x_function = (a+0.6*cos(v*t)*b*cos(q))*sin(p)

y_function = (c+0.6*cos(v*t)*b*cos(q))*cos(p)

z_function = 0.6*b*sin(q)

Torus

x_function = 2*(a+0.3*b*cos(q))*sin(p)*cos(p)

y_function = 2*((cos(v*t)^2)*c+0.3*b*cos(q))*cos(p)*cos(p)*cos(p)

z_function = 0.6*b*sin(q)

Torus-8

x_function = (cos(v*t)*c+0.3*b*cos(q))*cos(p)*cos(p)*cos(p)

y_function = (a+0.3*b*cos(q))*sin(p)

z_function = b*0.3*sin(q)

Mouth

x_function = (0.4*c+0.4*b*cos(q))*cos(p)*cos(p)*cos(p)

y_function = (2*a+0.4*b*cos(q))*sin(p)

z_function = cos(v*t)*0.4*b*cos(q)

Boat_1

x_function = (0.4*c+0.4*b*cos(q))*cos(p)*cos(p)*cos(p)

y_function = (2*a+0.4*b*cos(q))*sin(p)

z_function = cos(v*t)*0.4*b*cos(q)*cos(q)

Boat_2