import numpy as np
import matplotlib.pyplot as plt

def getSquareY(x):
    if x==-1 or x == 1:
        return 0
    else:
        return 1

getSquareYVectorised = np.vectorize(getSquareY)

def getCircle(x):
    return np.sqrt(1 - np.square(x))

def transform(x,y,t):
    points = np.array([x, y])
    result = t @ points
    return result[0,:], result[1,:]

def plotGridLines(xlim,ylim,t,color,label,linewidth):
    for i in range(xlim[0]-20,xlim[1]+21):
        x = [i,i]
        y = [ylim[0]-20,ylim[1]+20]
        x,y = transform(x,y,t)
        if i == xlim[0]-20:
            plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth,label=label)
        else:
            plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth)
    for i in range(ylim[0]-20,ylim[1]+21):
        y = [i,i]
        x = [xlim[0]-20,xlim[1]+20]
        x,y = transform(x,y,t)
        plt.plot(x,y, color=color,linestyle='dashed',linewidth=linewidth)

def discriminant(t):
    return t[0,0]**2 - 2*t[1,1]*t[0,0] + t[1,1]**2 + 4*t[0,1]*t[1,0]

def getBatman(s=2):
    X = []
    Y = []
    
    # lower
    x = np.linspace(-4, 4, 1600)
    y = np.zeros((0))
    for px in x:
        y = np.append(y,abs(px/2)- 0.09137*px**2 + np.sqrt(1-(abs(abs(px)-2)-1)**2) -3)
    X.append(x/s)
    Y.append(y/s)
    
    # lower left
    x = np.linspace(-7., -4, 300)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, -3*np.sqrt(-(px/7)**2+1))
    X.append(x/s)
    Y.append(y/s)
    
    # lower right
    x = np.linspace(4, 7, 300)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, -3*np.sqrt(-(px/7)**2+1))
    X.append(x/s)
    Y.append(y/s)
    
    # top left
    x = np.linspace(-7, -2.95, 300)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 3*np.sqrt(-(px/7)**2+1))
    X.append(x/s)
    Y.append(y/s)
    
    # top right
    x = np.linspace(2.95, 7, 300)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 3*np.sqrt(-(px/7)**2+1))
    X.append(x/s)
    Y.append(y/s)
    
    # left ear left
    x = np.linspace(-1, -.77, 2)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 9-8*abs(px))
    X.append(x/s)
    Y.append(y/s)
    
    # right ear right
    x = np.linspace(.77, 1, 2)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 9-8*abs(px))
    X.append(x/s)
    Y.append(y/s)
    
    # mid
    x = np.linspace(-.43, .43, 100)
    y = np.zeros((0))
    for px in x:
        y = np.append(y,2)
    X.append(x/s)
    Y.append(y/s)
        
    x = np.linspace(-2.91, -1, 100)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 1.5 - .5*abs(px) - 1.89736*(np.sqrt(3-px**2+2*abs(px))-2) )
    X.append(x/s)
    Y.append(y/s)
    
    x = np.linspace(1, 2.91, 100)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 1.5 - .5*abs(px) - 1.89736*(np.sqrt(3-px**2+2*abs(px))-2) )
    X.append(x/s)
    Y.append(y/s)
    
    x = np.linspace(-.7,-.43, 10)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 3*abs(px)+.75)
    X.append(x/s)
    Y.append(y/s)
    
    x = np.linspace(.43, .7, 10)
    y = np.zeros((0))
    for px in x:
        y = np.append(y, 3*abs(px)+.75)
    X.append(x/s)
    Y.append(y/s)
    
    return X, Y