Ftyjtk

I have xy coordinates that represents a subject over a given space. It is referenced from another point and is therefore off centre. As in the longitudinal axes is not aligned along the x-axis.

The randomly generated ellipse below provides an indication of this:

import numpy as np

from matplotlib.pyplot import scatter



xx = np.array([-0.51, 51.2])

yy = np.array([0.33, 51.6])

means = [xx.mean(), yy.mean()]  

stds = [xx.std() / 3, yy.std() / 3]

corr = 0.8         # correlation

covs = [[stds[0]**2          , stds[0]*stds[1]*corr], 

    [stds[0]*stds[1]*corr,           stds[1]**2]] 



m = np.random.multivariate_normal(means, covs, 1000).T

scatter(m[0], m[1])

To straighten the coordinates I was thinking of applying the vector to a rotation matrix.

Would something like this work?

angle = 65.

theta = (angle/180.) * np.pi



rotMatrix = np.array([[np.cos(theta), -np.sin(theta)], 

                     [np.sin(theta),  np.cos(theta)]])

This may also seem like a silly question but is there a way to determine if the resulting vector of xy coordinates is perpendicular? Or will you just have to play around with the rotation angle?

If the slope of the two lines multiplied together is equal to -1 than they are perpendicular.
The other case this is true, is when one slope is 0 and the other is undefined (a perfectly horizontal line and a perfectly vertical line).