Given a path of ((x1, y1), (x2, y2), ... (xn, yn)), finding the sum of the angle between consecutive line segments of the path in radians will give an idea of how variance a path has.
This helps to differentiate jagged and squiggly paths from lengthier and more leveled paths. This allows us to filter out noise or paths that we want to tailor to different use cases.
def get_total_angle(path):
total_angle = 0.0
for i in xrange(len(path)-2):
point1 = path[i]
point2 = path[i+1]
point3 = path[i+2]
angle = find_angle(point1, point2, point3)
total_angle += angle
return total_angle
In order to find the angle, I first went down the path of using the law of cosines and the in-built math library. Unfortunately, that didnt quite pan out since I kept running into issues of numeric instability. This is where the magic of scientific libraries in python like numpy, make our lives so much easier.
def find_angle(point_a, point_b, point_c):
"""
Expects arguments to be a list or tuple of length 2
Returns the angle made at point_b in radians
"""
# Any or all points are the same
if point_a == point_b or point_b == point_c or point_a == point_c:
return 0
angle = (numpy.arctan2(point_c[0] - point_b[0], point_c[1] - point_b[1]) -
numpy.arctan2(point_a[0] - point_b[0], point_a[1] - point_b[1]))
if angle > numpy.pi:
return numpy.absolute(2 * numpy.pi - angle)
if angle < -numpy.pi:
return numpy.absolute(2 * numpy.pi + angle)
return numpy.absolute(angle)