I have a 2x32 numpy array of x,y coordinates "A", and I want to rotate it by 45 degrees, around the centre.
x = np.tile([1,2,3,4],8)y = np.repeat([1,2,3,4,5,6,7,8],4)A = np.vstack((x,y)) # just a quick exampleIs there a quick and easy way to do this?
Best Answer
Steps:
- Center your data on the origin using a translation
- Rotate the data about the origin (45 degrees clockwise = -pi/4 radians)
- Translate your data back to the original center
Using some linear algebra:
import numpy as npx = np.tile([1,2,3,4],8)y = np.repeat([1,2,3,4,5,6,7,8],4)A = np.vstack((x,y)) # just a quick example# Rotation matrix as in e.g. https://en.wikipedia.org/wiki/Rotation_matrixtheta = -np.pi / 4rotate = np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta), np.cos(theta)]])# Translation vector is the mean of all xs and ys. translate = A.mean(axis=1, keepdims=True)Apply transformations:
out = A - translate # Step 1out = rotate @ out # Step 2out = out + translate # Step 3