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Question

I would like to work in polar coordinates with a meshgrid. First I have to determine theta angle with an origin situated in the middle of the meshgrid, it s not a problem, I have splitted the meshgrid in 4 parts in order to determine the angle as you can see below.

And now I would like to apply a rotation of the landmark of an angle which be chosen , so I try to change the "landmark" with "XAprim" and "YAprim" but working with the 4 parts is not easy..I think it s not the easiest way...

import numpy as np
import matplotlib.pyplot as plt

Lx=1345.
Ly=1428.
x0 = Lx/2.
y0 = Ly/2.

YA, XA = np.mgrid[0:Ly, 0:Lx]
Theta1 = np.arctan((YA-y0)/(XA-x0))
Theta2 = np.pi/2*np.ones((YAp.shape[0], YA.shape[1]))
Theta3 = 3*np.pi/2*np.ones((YA.shape[0], YA.shape[1]))

mask = np.fromfunction(lambda i, j: (i >= y0) * (j > (x0)), (XA.shape[0], XA.shape[1]), dtype=int)
test = np.invert(mask)
V1_test1 = np.ma.array(-Theta1, mask=test)
mask2 = np.fromfunction(lambda i, j: (i >= y0) * (j < (x0)), (XA.shape[0], XA.shape[1]), dtype=int)
test2 = np.invert(mask2)
V1_test2 = np.ma.array(-Theta1 - np.pi, mask=test2) #Entaille
mask3 = np.fromfunction(lambda i, j: (i < y0) * (j > (x0)), (XA.shape[0], XA.shape[1]), dtype=int)
test3 = np.invert(mask3)
V1_test3 = np.ma.array(-Theta1, mask=test3)
mask4 = np.fromfunction(lambda i, j: (i < y0) * (j <(x0)), (XA.shape[0], XA.shape[1]), dtype=int)
test4 = np.invert(mask4)
V1_test4 = np.ma.array((-Theta1 + np.pi), mask=test4) #Entaille
mask5 = np.fromfunction(lambda i, j: (i > y0) * (j==x0), (XA.shape[0], XA.shape[1]), dtype=int)
test5 = np.invert(mask5)
Theta2 = np.pi/2*np.ones((YA.shape[0], YA.shape[1]))
V1_test5 = np.ma.array(Theta2, mask=test5)
mask6 = np.fromfunction(lambda i, j: (i < y0) * (j==x0), (XA.shape[0], XA.shape[1]), dtype=int)
test6 = np.invert(mask6)
Theta3 = -np.pi/2*np.ones((YA.shape[0], YA.shape[1]))
V1_test6 = np.ma.array(Theta3, mask=test6)

a = np.ma.filled(V1_test1, 0)
b = np.ma.filled(V1_test2, 0)
c = np.ma.filled(V1_test3, 0)
d = np.ma.filled(V1_test4, 0)
e = np.ma.filled(V1_test5, 0)
f = np.ma.filled(V1_test6, 0)
theta = (a + b + c + d + e + f)

plt.imshow(theta,aspect='auto',cmap=plt.cm.hot)
plt.colorbar()
plt.show()

So I got this meshgrid which is expected :

And now, I would like to apply a rotation since the origin of the landmark As example with a 23 degrees angle, I calculate the new coordinates to do the change, but doing the same as over it because of the 4 parts of the angle...So I would like to know if there are not a more efficient way to deal this problem?

ang_rot = 23*np.pi/180.
XAprim = XA*np.cos(ang_rot)+YA*np.sin(ang_rot)
YAprim = -XA*np.sin(ang_rot)+YA*np.cos(ang_rot)
Theta1 = np.arctan((YAprim-y0)/(XAprim-x0))

plt.imshow(Theta1,aspect='auto',cmap=plt.cm.hot)
plt.colorbar()
plt.show()

Answer 1

So the solution is :

import numpy as np
import matplotlib.pyplot as plt

Lx=1345.
Ly=1428.
x0 = Lx/2.
y0 = Ly/2.
YA, XA = np.mgrid[0:Ly, 0:Lx]
XA = XA - x0
YA = YA - y0
ang_rot = 23*np.pi/180.
XAprim = XA*np.cos(ang_rot) - YA*np.sin(ang_rot) 
YAprim = XA*np.sin(ang_rot) + YA*np.cos(ang_rot)
Theta1 = np.arctan2((YAprim),(XAprim))*-180./np.pi

plt.imshow(Theta1,aspect='auto',cmap=plt.cm.hot)
plt.colorbar()
plt.show()