"""
Author: Piotr A. Zolnierczuk (zolnierczukp at ornl dot gov)
 
Based on a paper by:
Drawing an elephant with four complex parameters
Jurgen Mayer, Khaled Khairy, and Jonathon Howard,
Am. J. Phys. 78, 648 (2010), DOI:10.1119/1.3254017
"""
import numpy as np
 
# elephant parameters
p1, p2, p3, p4 = (50 - 30j, 18 +  8j, 12 - 10j, -14 - 60j )
p5 = 40 + 20j # wiggle factor and eyepiece
 
def fourier(t, C):
    f = np.zeros(t.shape)
    A, B = C.real, C.imag
    for k in range(len(C)):
        f = f + A[k]*np.cos(k*t) + B[k]*np.sin(k*t)
    return f
 
def elephant(t, p1, p2, p3, p4, p5):
    npar = 6
    Cx = np.zeros((npar,), dtype='complex')
    Cy = np.zeros((npar,), dtype='complex')
 
    Cx[1] = p1.real*1j
    Cx[2] = p2.real*1j
    Cx[3] = p3.real
    Cx[5] = p4.real
 
    Cy[1] = p4.imag + p1.imag*1j
    Cy[2] = p2.imag*1j
    Cy[3] = p3.imag*1j
 
    x = np.append(fourier(t,Cx), [-p5.imag])
    y = np.append(fourier(t,Cy), [p5.imag])
 
    # wiggle the trunk (
    trunk_i = y>40
    x_trunk = x[trunk_i]
    N_trunk = len(x_trunk)
#    x[trunk_i] = x_trunk * concatenate([linspace(1,p5.real,floor(N_trunk/2.0)), 
#                                        linspace(p5.real,1,ceil(N_trunk/2.0))])
    x[trunk_i] = x_trunk + concatenate([linspace(0,p5.real,floor(N_trunk/2.0)), 
                                        linspace(p5.real,0,ceil(N_trunk/2.0))])
    return x,y

def plot_elephant(wiggle=40, p4_real=14, t_p=1.0):
    p1, p2, p3, p4 = (50 - 30j, 18 +  8j, 12 - 10j, - p4_real - 60j )
    p5 = wiggle + 20j
    t = np.linspace(0,2*np.pi,1000)
    x, y = elephant(t, p1, p2, p3, p4, p5)
    
    fig, ax = plt.subplots(figsize=(10, 7))
    ax.plot(y,-x,'.')
    
    #x_p, y_p = elephant(array(t_p/1000.0*2*pi), p1, p2, p3, p4, p5)
    #ax.plot(y_p,-x_p,'ro')
    
    ax.set_xlim(-80, 100)
    ax.set_ylim(-80, 100)
    fig.suptitle('elephant with wiggle parameter = ' + str(wiggle))
    return fig

#fig = plot_elephant(wiggle=0.5)
#plot_elephant(wiggle=10, p4_real=10)

from ipywidgets import StaticInteract, RangeWidget, RadioWidget
StaticInteract(plot_elephant, wiggle=RangeWidget(0,40,5))