Calculate angle from slope in inverted Y axis-CodePudding

I currently have a series of lines drawn in a football pitch, each one formed by an X and Y point. These lines are the passes of a player and I want to see if it is a backward pass, forward pass, lateral pass depending on the angle of the slope with the X axis.

Axis Y is inverted(Positive values going down)

I have tried several ideas like arctan from numpy, from math, several calculations but I can't get the angle correctly. Results are not making any sense.

At the moment, the only certainty is the correct calculation of the slope of each line.

df['Slope'] = np.where(df['X'] == df['X2'], 0,   
                 np.where((df['Y'] == df['Y2']), 0,
                  -df['Y2']   df['Y'])/ (df['X2'] - df['X']))          
df['Radians'] = np.arctan(df['Slope'].astype(float))
df['Degrees'] = np.degrees(df['Radians']) 60

Some numbers and possibly angle expected:

A(40,48) and B(27,70): 210-230ª  Actual result: 60º 
A(27,74) and B(9,52) : 130-140º  Actual result: 310º
A(9,64) and B(11,45) : 75-80º  Actual result: 84º seems OK

CodePudding user response：

Here is a standard-library solution which seems to work. The same principle can be used with numpy.

Key points:

Use atan2 to get an answer in the right quadrant
Since Y axis points "down", negate Y values
Use % 360 to "fold" result to [0, 360] range.

(I have to write something here to get the formatting right... why?)

from math import degrees, atan2

def angle(x1, y1, x2, y2):
    # (-a)-(-b) = -a b
    return degrees(atan2(-y2 y1, x2-x1)) % 360

print(angle(40, 48, 27, 70)) # 239
print(angle(27, 74, 9, 52))  # 129
print(angle(9, 64, 11, 45))  # 84