CODEWITHSUNDEEP
pythonnumpyangle
CreekGeek
CreekGeek

Reputation: 2329

more pythonic way to calculate angle from three x,y points return 0-360 degrees with "up" as 0?

I am working with a cartesian system with all positive values. I need to calculate the planimetric deflection between two points (x,y,z). I am mainly interested in returning a 0-360 value clockwise relative to a "north" reference vector, though I have written the function (I think) so I can assign the reference vector to any direction. The following code seems to return what I want, but the if statement seems like a bit of a hack. Is there a cleaner way to handle it purely within the calculations?

I tried arctan2 with similar results.

    import numpy as np

    # define 'origin' point where coords are X,Y,Z
    p1 = [10000,10000,0] 

    # create function to compute angle
    def ang(p1,p2):
        """
        p1 is [x,y,z] 'from'
        p2 is [x,y,z] 'to'
        """
        # set reference point relative to p1
        p0 = [p1[0],p1[1]+1000,0] # 1000 unit offset is arbitrary

        # assign X,Y points to variables as arrays
        a = np.array(p0[0:2])
        b = np.array(p1[0:2]) # the origin
        c = np.array(p2[0:2])

        # create vectors
        ba: ndarray = a - b # subtract the origin
        bc: ndarray = c - b # subtract the origin

        # calculate angle
        cosine_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
        angle = np.arccos(cosine_angle)

        # adjust for hemisphere
        if bc[0] < 0:
            return(360 - np.degrees(angle))
        else:
            return(np.degrees(angle))

    test_lst = [[10000, 20000,0],[20000, 20000,0],[20000,10000,0],[20000,0,0],[10000,0,0],[0,0,0],[0,10000,0],[0,20000,0]]

    for i in test_lst:
        a = ang(p1,i)
        print(a)

with the if statement (this is what I want):

expected      |     returned
  0.0         |        0.0
 45.0         |       45.0
 90.0         |       90.0
135.0         |      135.0
180.0         |      180.0
225.0         |      225.0
270.0         |      270.0
315.0         |      315.0

without the if statement:

expected      |     returned
  0.0         |        0.0
 45.0         |       45.0
 90.0         |       90.0
135.0         |      135.0
180.0         |      180.0
225.0         |      135.0
270.0         |       90.0
315.0         |       45.0

Upvotes: 0

Views: 1769

Answers (1)

trolley813
trolley813

Reputation: 932

This is not about Python, but about how the math works. The arccos (also arcsin, etc.) functions return a non-unique value, since the [-1, 1] range of possible sine/cosine values maps to an interval which is 180 degrees wide. The arctan2, which returns the angle in the range of -180 to 180 degrees, was introduced (into C, as atan2) to fight the very same issue. Fortunately, it's an easy way to convert [-180, 180] to [0, 360] in Python:

angle = np.arctan2(...)
return np.degrees(angle) % 360.0  # the modulo operator does this job well

Upvotes: 1

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