import numpy as np
import scipy.integrate as spi
import matplotlib.pylab as plt
%matplotlib inline

#-- Alpha parameters should be given in degrees
def calphas(s, alpha, l = 1, k = 1, phi = 0):
    
    #-- Convert alpha and phi into radians
    alpha_rad = alpha * np.pi / 180.
    phi_rad = phi * np.pi / 180.
    
    return np.cos(alpha_rad * np.cos(2 * np.pi * k * s / l + phi_rad))

def salphas(s, alpha, l = 1, k = 1, phi = 0):
    
    #-- Convert alpha into radians
    alpha_rad = alpha * np.pi / 180.
    phi_rad = phi * np.pi / 180.
    
    return np.sin(alpha_rad * np.cos(2 * np.pi * k * s / l + phi_rad))


#-- Scalar functions. Variable s is a real number
def serp_x_scalar (s, alpha, l = 1, k = 1, phi = 0):
    return spi.quad(calphas, 0, s, args =(alpha, l, k, phi) )

def serp_y_scalar (s, alpha, l = 1, k = 1, phi = 0):
    return spi.quad(salphas, 0, s, args =(alpha, l, k, phi) )

def serp (s, alpha = 45, l = 1, k = 1, phi = 0):
    """Serpenoid curve
       Inputs:
         - alpha : winding angle (in degrees)
         - l : Curve length
         - k : Number of undulations
       S is the variable (it is an array). The x,y arrays are returned
    """
    
    #-- Results
    x = []
    y = []
    
    for i, vs in enumerate(s):
        x.append(serp_x_scalar(vs, alpha, l, k, phi)[0])
        y.append(serp_y_scalar(vs, alpha, l, k, phi)[0])
    return x,y


#-- Obtener los puntos a lo largo de la curva
s = np.linspace(0, 1, 100)

#-- Obtener las coordenadas x,y
x, y = serp(s, alpha = 60, l = 1, k = 1)

#-- Dibujar la curva
plt.plot(x, y, linewidth = 3)
plt.grid()
plt.axis('equal')
plt.show()

from IPython.html import widgets # Widget definitions
from IPython.display import display # Used to display widgets in the notebook

widget_alpha = widgets.FloatSliderWidget()
widget_alpha.min = 0.0
widget_alpha.max = 121
widget_alpha.description = "Alpha"
widget_alpha.value = 60

widget_k = widgets.FloatSliderWidget()
widget_k.min = 0.1
widget_k.max = 20
widget_k.description = "k"
widget_k.value = 1


def draw_serp():
    #-- Obtener los puntos a lo largo de la curva
    s = np.linspace(0, 1, 100)

    #-- Obtener las coordenadas x,y
    x, y = serp(s, alpha = widget_alpha.value, l = 1, k = widget_k.value)

    #-- Dibujar la curva
    plt.plot(x, y, linewidth = 3)
    plt.grid()
    plt.axis('equal')
    plt.show()
    
    
button_draw = widgets.ButtonWidget(description="Draw!")


def on_button_draw_clicked(b):
    draw_serp()

button_draw.on_click(on_button_draw_clicked)    

display(widget_alpha)
display(widget_k)
display(button_draw)
draw_serp()