Precision lost calling cv2.cartToPolar with angleInDegrees set to False

Question

I am using opencv 4.0.0 in python.

When calling the function cv2.cartToPolar with x value to -12 and y value to 0, with parameter angleInDegrees set to False, I'm getting a wrong answer. It should be pi instead I get 3.14159274, which is greater than pi.

x = np.asarray([[-12]], dtype = "float64")
y = np.asarray([[0]], dtype = "float64")

mag, angle = cv2.cartToPolar(x, y, angleInDegrees=True)
print('mag', mag)
print('angle', angle)

>>> mag [[12.]]
>>> angle [[180.]]

x = np.asarray([[-12]], dtype = "float64")
y = np.asarray([[0]], dtype = "float64")

mag, angle = cv2.cartToPolar(x, y, angleInDegrees=False)
print('mag', mag)
print('angle', angle)

>>> mag [[12.]]
>>> angle [[3.14159274]]

I expect the output of 3.14159265.

Answer 1

It's an interesting observation. This must have to do with the precision of floating point arithmetic as pointed out by @Sushi. As per the documentation here, the output of cv2.cartToPolar function is given by

x = np.asarray([[-12]], dtype = "float32")
y = np.asarray([[0]], dtype = "float32")

print(cv2.cartToPolar(x, y, angleInDegrees=False)[1])
print(np.radians(np.arctan2(y, x) * 180 / np.pi))

x = np.asarray([[-12]], dtype = "float64")
y = np.asarray([[0]], dtype = "float64")

print(cv2.cartToPolar(x, y, angleInDegrees=False)[1])
print(np.radians(np.arctan2(y, x) * 180 / np.pi))  

output:

[[3.1415927]]
[[3.1415927]]
[[3.14159274]]
[[3.14159265]]  # check this result

Answer 2

Please look at the documentation: "The angles are calculated with accuracy about 0.3 degrees". So this is expected behavior. Also your value differs from PI on the 7th decimal place so that may be caused by the precision of floating point arithmetic.