# How to rotate the plot and find minimum point?

I want to rotate the below curve to 45 degree and then find the minimum point. For this, I have tried with below code:

def rotate_vector(data, angle):
co = np.cos(theta)
si = np.sin(theta)
rotation_matrix = np.array(((co,-si), (si, co)))
return np.matmul(rotation_matrix, data)

rotated_vector = rotate_vector(data, -45)
elbow = rotated_vector.min()


But what I get is this curve: • Sorry but... Why?? – Erwan Aug 8 '19 at 16:46
• @Erwan I want to get the point where the curve starts changing so as to find threshold. – Sajjadmanal Aug 9 '19 at 5:28
• @Sajjadmanal based on the code from my answer in the original post, I created a python package called kneebow which provides all the functionality plus some convenience methods and axis scaling. – georg-un Aug 9 '19 at 22:59
• @georg-un Wow. You made a whole library out of this question. Amazing..! – Sajjadmanal Aug 10 '19 at 18:51

Please refer to the original post.

The problem was the np.radians(angle). I corrected that.

Edit: The problem was not the radian conversion but the different scales of the x- and y-axis. 45 degrees rotation was simply not enough.

Let's use a modified version of the code you posted:

def rotate_vector(data, angle):
# make rotation matrix
co = np.cos(theta)
si = np.sin(theta)
rotation_matrix = np.array(((co, -si), (si, co)))
# rotate data vector
rotated_vector = data.dot(rotation_matrix)
# return index of elbow
return rotated_vector


Now, we define a square as test-data:

data = np.array([
[1, 0], [2, 0], [3, 0], [4, 0], [5, 0],
[0, 0], [0, 1], [0, 2], [0, 3], [0, 4],
[5, 1], [5, 2], [5, 3], [5, 4], [5, 5],
[0, 5], [1, 5], [2, 5], [3, 5], [4, 5],
])

plt.scatter(data[:, 0], data[:, 1])


Plotting the data gives us the following figure: Now, we rotate that vector using the function from above:

rotated_data = rotate_vector(data, 45)

plt.scatter(rotated_data[:, 0], rotated_data[:, 1])


If we plot the rotated data, we get the following figure: So it does work. However, if we want to rotate the graph that you posted to find the minimum, we need to remember that the scales of the two axes are different. That means the graph may look like a 45° rotation would be enough while actually, it is not.

I corrected the original post again. Also, I added a method to find an approximate rotation angle to account for the different axis scales.