################################################################################
## Python script for Epitrochoid/Hypotrochoid Spirograph Coding
## Special cases: R=r {limacon} and d=r {epicycloid}
## --
## Developed and coded (2024)
## by Angelea Arnett <aarnett2@huskers.unl.edu>
## Revised (2025)
## by Robert Streubel <streubel@unl.edu>
## --
################################################################################

import numpy as np
import pylab as pp

#R is the radius of your inner ring#
R = 11
#r is the radius of your outer ring#
r = 1.6
#d is the distance from the center of the outer ring to your drawing point#
d = 7.3

#Here we have our starting and ending angle of theta#
start = 0
end = 100*np.pi

"""
This is the coding for the parametric equations.
This also allows for the plotting of the functions.
"""

def Epitrochoid(t,R,r,d):
    return (R+r)*np.cos(t)-d*np.cos((R+r)/r*t), (R+r)*np.sin(t)-d*np.sin((R+r)/r*t)

def Hypotrochoid(t,R,r,d):
    return (R-r)*np.cos(t)+d*np.cos((R-r)/r*t), (R-r)*np.sin(t)-d*np.sin((R-r)/r*t)

t = np.arange(start,end,0.001)

pp.figure()
pp.xlim(-(R+r+d)*1.25,(R+r+d)*1.25)
pp.ylim(-(R+r+d)*1.25,(R+r+d)*1.25)
pp.title("Epitrochoid Spirograph")
for i in range(5)[::-1]:
    pp.plot(*Epitrochoid(t,R,r,d*i/2),label=d*i/2)
pp.legend()

pp.figure()
pp.xlim(-(R+r+d),(R+r+d))
pp.ylim(-(R+r+d),(R+r+d))
pp.title("Hypotrochoid Spirograph")
pp.plot(*Hypotrochoid(t,R,r,d))

pp.figure()
pp.xlim(-(R+r+d)*1.25,(R+r+d)*1.25)
pp.ylim(-(R+r+d)*1.25,(R+r+d)*1.25)
pp.plot(*Epitrochoid(t,R,r,d),label='Epitrochoid')
pp.plot(*Hypotrochoid(t,R,r,d),label='Hypotrochoid')
pp.legend()

pp.show()