Calculate angle (clockwise) between two points

Question

I have been not using math for a long time and this should be a simple problem to solve.

Suppose I have two points A: (1, 0) and B: (1, -1).

I want to use a program (Python or whatever programming language) to calculate the clockwise angle between A, origin (0, 0) and B. It will be something like this:

angle_clockwise(point1, point2)

Note that the order of the parameters matters. Since the angle calculation will be clockwise:

• If I call angle_clockwise(A, B), it returns 45.
• If I call angle_clockwise(B, A), it returns 315.

In other words, the algorithm is like this:

1. Draw a line (line 1) between the first point param with (0, 0).
2. Draw a line (line 2) between the second point param with (0, 0).
3. Revolve line 1 around (0, 0) clockwise until it overlaps line 2.
4. The angular distance line 1 traveled will be the returned angle.

Is there any way to code this problem?

Answer 1

Use the inner product and the determinant of the two vectors. This is really what you should understand if you want to understand how this works. You'll need to know/read about vector math to understand.

See: https://en.wikipedia.org/wiki/Dot_product and https://en.wikipedia.org/wiki/Determinant

from math import acos
from math import sqrt
from math import pi

def length(v):
    return sqrt(v[0]**2+v[1]**2)
def dot_product(v,w):
   return v[0]*w[0]+v[1]*w[1]
def determinant(v,w):
   return v[0]*w[1]-v[1]*w[0]
def inner_angle(v,w):
   cosx=dot_product(v,w)/(length(v)*length(w))
   rad=acos(cosx) # in radians
   return rad*180/pi # returns degrees
def angle_clockwise(A, B):
    inner=inner_angle(A,B)
    det = determinant(A,B)
    if det<0: #this is a property of the det. If the det < 0 then B is clockwise of A
        return inner
    else: # if the det > 0 then A is immediately clockwise of B
        return 360-inner

In the determinant computation, you're concatenating the two vectors to form a 2 x 2 matrix, for which you're computing the determinant.