How can I find an angle of rotated geometry?

Urvesh 0
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I have 2d geometry and corresponding X and Y coordinates. How can find the rotation angle (in degree) of geometry with respect to X or Y axis? Suggestions will always be welcomed.

X = [0.71, 1.41, 2.12, 2.83, 2.12, 2.83, 3.54, 4.24, 4.95, 5.66, 4.95, 4.24, 3.54, 2.83, 2.12, 1.41]

Y = [-0.71, 0.0, 0.71, 1.41, 2.12, 2.83, 2.12, 1.41, 0.71, 0.0, -0.71, 0.0, 0.71, 0.0, -0.71, -1.41]

I have mentioned coordinates as above. My aim is to align the geometry's principal axis to the X or Y coordinates.

2d rotation computational-geometry pca python-3.x
1 Answers

In order to find a principal axis, I have applied Principal Componenet Analysis (PCA).

I created a dataframe of X and Y coordinate. Then,

First I centered the geometry considering the mean of X and Y coordinate.

data_centered1 = df_1.apply(lambda x: x-x.mean())     
data_centered1

Then I separated a list of X and Y coordinate (after centering) to two different list.

Then to apply PCA, I followed these steps,

(1) compute covariance matrix

def create_covariance_matrix(data_matrix):
    n = data_matrix.shape[0]
    cov_matrix = (1 / (n - 1)) * np.dot(data_matrix.T, data_matrix)
    return cov_matrix

cov_matrix = create_covariance_matrix(first_coord)

(2) Compute eigenvalues and eigenvectors from covariance matrix

eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)

(3) find the angle of first principal component

alpha = np.degrees(np.arctan(eigenvectors[1][1]/eigenvectors[0][1]))
beta = 90-alpha

(4) visulize a plot with original geometry with principal component

plt.scatter(X1_coordinate, Y1_coordinate)
plt.plot([0, eigenvectors[0][1]], [0, eigenvectors[1][1]], marker = 'o')
plt.show()

(5) Rotate all points of geometry with the angle obtained from eigenvectors (either alpha or beta). It will rotate the geometry such that geometry's principal axis aligned with global reference system axis.

I followed these steps and it works fine!!

Urvesh0
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