import numpy as np
import matplotlib.pyplot as plt

def interp2_normalized(f00, f10, f01, f11, x, y):
    a00 = f00
    a10 = f10 - f00
    a01 = f01 - f00
    a11 = f11 - f10 - f01 + f00
    return a00 + a10*x + a01*y + a11*x*y

def interp2(x0, y0, x1, y1, f00, f10, f01, f11, x, y):
    x_n = (x - x0)/(x1 - x0)
    y_n = (y - y0)/(y1 - y0)
    return interp2_normalized(f00, f10, f01, f11, x_n, y_n)

if __name__ == '__main__':
    f00, f10, f01, f11 = 0, 1, 2, -3
    N = 101
    F = np.zeros((N,N))
    for i in range(N):
        for j in range(N):
            F[i,j] = interp2_normalized(f00, f10, f01, f11, i/(N-1), j/(N-1))
    
    plt.figure()
    plt.imshow(F)
    plt.colorbar()
    plt.show()