import numpy as np
import matplotlib.pyplot as plt

pi = np.pi
x = np.arange(0,1,0.01)
L = len(x)
# print(x)


def f0(t):
    return [t,np.zeros(len (t))]

def t_vect(t):
    return [ np.ones(len (t)) , np.zeros(len (t)) ]

def n_vect(t):
    return [ np.zeros(len (t)) , np.ones(len (t))  ]
"""
def f0(t):
    return [ np.cos(2*pi*t), np.sin(2*pi*t)]

def t_vect(t):
    return [ -1*np.sin(2*pi*t) , np.cos(2*pi*t) ]

def n_vect(t):
    return [ -1*np.cos(2*pi*t) , -1*np.sin(2*pi*t)  ]
"""
graphe_f0 = f0(x)

N = 4
r = 1

graphe_f1 = graphe_f0 + (1/4)*( -r*np.sin(4*pi*N*x)*t_vect(x) + 2*r*np.sin(2*pi*N*x)*n_vect(x) )

plt.plot( graphe_f0[0], graphe_f0[1] ) # color='navy'
plt.plot( graphe_f1[0], graphe_f1[1] )
plt.show()