import matplotlib.pyplot as plt
import numpy as np
(L1, Lo1) = (23.211144, 72.6833273)
(L2, Lo2) = (23.211170, 72.685835)
(L3, Lo3) = (23.209616, 72.685929)
(L4, Lo4) = (23.209530, 72.683318)
(L5, Lo5) = (23.209997, 72.685008)
(X1, Y1) = (83, 70)
(X2, Y2) = (620, 61)
(X3, Y3) = (640, 427)
(X4, Y4) = (80, 444)
(X5, Y5) = (441, 337)
## Quintic Lagrangian Interpolation
def LX(X):
w_X = ((X - X2) * (X - X3) * (X - X4) * (X - X5)) / ((X1 - X2) * (X1 - X3) * (X1 - X4) * (X1 - X5))
w_X1 = ((X - X1) * (X - X3) * (X - X4) * (X - X5)) / ((X2 - X1) * (X2 - X3) * (X2 - X4) * (X2 - X5))
w_X2 = ((X - X1) * (X - X2) * (X - X4) * (X - X5)) / ((X3 - X1) * (X3 - X2) * (X3 - X4) * (X3 - X5))
w_X3 = ((X - X1) * (X - X2) * (X - X3) * (X - X5)) / ((X4 - X1) * (X4 - X2) * (X4 - X3) * (X4 - X5))
w_X4 = ((X - X1) * (X - X2) * (X - X3) * (X - X4)) / ((X5 - X1) * (X5 - X2) * (X5 - X3) * (X5 - X4))
return (w_X*Lo1) + (w_X1*Lo2) + (w_X2*Lo3) + (w_X3*Lo4) + (w_X4*Lo5)
def LY(Y):
w_Y = ((Y - Y2) * (Y - Y3) * (Y - Y4) * (Y - Y5)) / ((Y1 - Y2) * (Y1 - Y3) * (Y1 - Y4) * (Y1 - Y5))
w_Y1 = ((Y - Y1) * (Y - Y3) * (Y - Y4) * (Y - Y5)) / ((Y2 - Y1) * (Y2 - Y3) * (Y2 - Y4) * (Y2 - Y5))
w_Y2 = ((Y - Y1) * (Y - Y2) * (Y - Y4) * (Y - Y5)) / ((Y3 - Y1) * (Y3 - Y2) * (Y3 - Y4) * (Y3 - Y5))
w_Y3 = ((Y - Y1) * (Y - Y2) * (Y - Y3) * (Y - Y5)) / ((Y4 - Y1) * (Y4 - Y2) * (Y4 - Y3) * (Y4 - Y5))
w_Y4 = ((Y - Y1) * (Y - Y2) * (Y - Y3) * (Y - Y4)) / ((Y5 - Y1) * (Y5 - Y2) * (Y5 - Y3) * (Y5 - Y4))
return (w_Y*L1) + (w_Y1*L2) + (w_Y2*L3) + (w_Y3*L4) + (w_Y4*L5)
x, y = np.arange(0, 883, 1), np.arange(0, 675, 1)
xL, yL = LX(x), LY(y)
# xL will contain Longitude Values as X pixels decide the Longitude
# yL will contain Latitude Values as Y pixels decide the Latitude
X = np.array([83, 620, 640, 80, 441])
Lx = np.array([23.211144, 23.211170, 23.209616, 23.209530, 23.209997])
Y = np.array([70, 61, 427, 444, 337])
Ly = np.array([72.6833273, 72.685835, 72.685929, 72.683318, 72.685008])
mx, cx = np.polyfit(X, Ly, 1)
my, cy = np.polyfit(Y, Lx, 1)
plt.plot(x, xL)
plt.plot(X, Ly, "o", color = "red")
plt.title("Lagrange 4th order Polynomial Long vs. X")
plt.show()
plt.plot(x, mx*x + cx)
plt.plot(X, Ly, "o", color = "red")
plt.title("Linear Polyfit Long vs. X")
plt.show()
plt.plot(y, yL)
plt.plot(Y, Lx, "o", color = "red")
plt.title("Lagrange 4th order Polynomial Lat vs. Y")
plt.show()
plt.plot(y, my*y + cy)
plt.plot(Y, Lx, "o", color = "red")
plt.title("Linear Polyfit Lat vs. Y")
plt.show()
# print(yL-23.211366)
def get_XY(L, Lo):
return (round((Lo - cx)/mx), round((L - cy)/my))
def get_XY_Alt(L, Lo):
Xi, Yi = find_nearest(xL, Lo), find_nearest(yL, L)
return Xi, Yi
def find_nearest(array, value):
idx = (np.abs(array - value)).argmin()
return idx
