Find which two angles an angle is between in Python-CodePudding

I have a list of angles (in radians) in the range [-pi, pi]. The angles can be assumed to ordered as follows:

every increasing index in the list will be counter-clockwise to the previous
there are no duplicates in the list
the values in the list will never surpass a full 2*pi rotation from the first value in the list

Now given a random angle in the [-pi, pi] range, I want to determine which two of the angles in the list the random angle is between. Example usage of this is_between function would be like so:

# doesn't work for angle == pi!
def is_between(angle, angles):
    for i in range(len(angles)):
        min = angles[i]
        max = angles[(i   1) % len(angles)]
        if min <= angle <= max:
            return min, max
 

angles = [-pi/6, pi/4, 5*pi/6, -2*pi/3]
bounds = is_between(pi, angles)
print(bounds) # should print (5*pi/6, -2*pi/3)

My initial though would be to just iterate through the list, picking two adjacent angles, and check if the provided angle is between the two values, but this doesn't work in cases near pi. I've seen a solution similar to this in degrees, but I would like a solution that doesn't involve converting the units for the entire angles list as a prerequisite step.

CodePudding user response：

each to angles create two arcs on the circle, if we assume the shortest arc is the distance between two angles, and all the angles are in [-pi, pi], then we can solve this problem like this:

from cmath import pi

eps = 0.00001

def arc_vector(a1, a2):
    result = a2 - a1
    if result > pi   : result -= 2*pi
    elif result <-pi : result  = 2*pi
    return result

def is_between(angle, angles):
    for i in range(len(angles)):
        min = angles[i]
        max = angles[(i   1) % len(angles)]
        arc1 = arc_vector(min, angle)
        arc2 = arc_vector(angle, max)
        arct = arc_vector(min, max)
        if abs(arc1   arc2 - arct) < eps and arc1 * arc2 > 0: # means they are on the same arc and the angle is between them
            return min, max
 

angles = [-pi/6, pi/4, 5*pi/6, -2*pi/3]
bounds = is_between(pi, angles)
print(bounds) # should print (5*pi/6, -2*pi/3)

CodePudding user response：

As described in a comment by the OP, the first element gives the starting point for the angle generation process. If we see an angle with a radian value that is smaller than the first element, we can normalize it by adding 2 * pi to it, and then we can perform our comparison operation as normal

For example, when given the bounds 5*pi/6 and -2*pi/3, we turn these inputs into 5*pi/6 and 4*pi/3, so that the lower bound is strictly less than the upper bound.

This implementation uses math.pi rather than np.pi. They're all the same constant, so this shouldn't affect correctness..

from math import pi

def is_between(angle, angles):
    if angle < angles[0]:
        angle  = 2 * pi
        
    for i in range(len(angles)):
        if angles[0] < angles[i]:
            lower_bound = angles[i]
        else:
            lower_bound = angles[i]   2 * pi
        
        if angles[0] < angles[(i   1) % len(angles)]:
            upper_bound = angles[(i   1) % len(angles)]
        else:
            upper_bound = angles[(i   1) % len(angles)]   2 * pi
        if lower_bound <= angle <= upper_bound:
            return angles[i], angles[(i   1) % len(angles)]
            
    raise ValueError("Could not find bounds")

angles = [-pi/6, pi/4, 5*pi/6, -2*pi/3]
bounds = is_between(pi, angles)

This outputs:

(2.6179938779914944, -2.0943951023931953)