import numpy as np
import os
# helper function
rotMatrix = lambda a: np.array( [[np.cos(a),np.sin(a)], 
                                         [-np.sin(a),np.cos(a)]] )

def vortex(screenpos,i,nletters):
    d = lambda t : 1.0/(0.3+t**8) #damping
    a = i*np.pi/ nletters # angle of the movement
    v = rotMatrix(a).dot([-1,0])
    if i%2 : v[1] = -v[1]
    return lambda t: screenpos+400*d(t)*rotMatrix(0.5*d(t)*a).dot(v)
            
def cascade(screenpos,i,nletters):
    v = np.array([0,-1])
    d = lambda t : 1 if t<0 else abs(np.sinc(t)/(1+t**4))
    return lambda t: screenpos+v*400*d(t-0.15*i)

def arrive(screenpos,i,nletters):
    v = np.array([-1,0])
    d = lambda t : max(0, 3-3*t)
    return lambda t: screenpos-400*v*d(t-0.2*i)
    
def vortexout(screenpos,i,nletters):
    d = lambda t : max(0,t) #damping
    a = i*np.pi/ nletters # angle of the movement
    v = rotMatrix(a).dot([-1,0])
    if i%2 : v[1] = -v[1]
    return lambda t: screenpos+400*d(t-0.1*i)*rotMatrix(-0.2*d(t)*a).dot(v)



import numpy as np
import os
# helper function
rotMatrix = lambda a: np.array( [[np.cos(a),np.sin(a)], 
                                         [-np.sin(a),np.cos(a)]] )

def vortex(screenpos,i,nletters):
    d = lambda t : 1.0/(0.3+t**8) #damping
    a = i*np.pi/ nletters # angle of the movement
    v = rotMatrix(a).dot([-1,0])
    if i%2 : v[1] = -v[1]
    return lambda t: screenpos+400*d(t)*rotMatrix(0.5*d(t)*a).dot(v)
            
def cascade(screenpos,i,nletters):
    v = np.array([0,-1])
    d = lambda t : 1 if t<0 else abs(np.sinc(t)/(1+t**4))
    return lambda t: screenpos+v*400*d(t-0.15*i)

def arrive(screenpos,i,nletters):
    v = np.array([-1,0])
    d = lambda t : max(0, 3-3*t)
    return lambda t: screenpos-400*v*d(t-0.2*i)
    
def vortexout(screenpos,i,nletters):
    d = lambda t : max(0,t) #damping
    a = i*np.pi/ nletters # angle of the movement
    v = rotMatrix(a).dot([-1,0])
    if i%2 : v[1] = -v[1]
    return lambda t: screenpos+400*d(t-0.1*i)*rotMatrix(-0.2*d(t)*a).dot(v)



# helper function #damping # angle of the movement #damping # angle of the movement