How to Rotate Points from a Meshgrid and Preserve Orthogonality

When I use a rotation matrix to rotate points from a meshgrid, the points are no longer orthogonal. Using NumPy, how do I keep the gridlines perpendicular when rotating?

Here's the Python code that I'm using:

import numpy as np
import matplotlib.pyplot as plt

# Input
rot_degrees = 10
x = np.linspace(200, 600, 4)
y = np.linspace(200, 700, 5)
xv, yv = np.meshgrid(x, y)
pts = np.column_stack( (xv.flatten(), yv.flatten()) )

# Rotate points
radians = np.radians(rot_degrees)
rot_mat = np.array([[np.cos(radians),-np.sin(radians)],
                    [np.sin(radians), np.cos(radians)]])
einsum = np.einsum('ji, mni -> jmn', rot_mat, [pts])
pts_rotated = np.squeeze(einsum).T

# Output
plt.scatter(pts[:,0], pts[:,1], c='r')
plt.scatter(pts_rotated[:,0], pts_rotated[:,1], c='b')
plt.show()

Solution

How did you checked that the points are not orthogonal?

If you just look at the plot, and it doesn't looks like, try setting the aspect ratio equal for both axis with

plt.gca().set_aspect('equal')