How to implement arctan conversion angle in Python

Cartesian coordinate system

For the plane coordinate system, the range of the angle θ between any ray OP and the x-axis can be [0,2π) or (-&pi ;,π], unless otherwise specified, we use the latter.
Represent the point in the Cartesian space coordinate system Pc = ( x , y , z ) into the spherical coordinate system The form of Ps = ( θ , ϕ , r ).

where

According to the definition of spherical coordinates, it is required that θ∈[−π,π], ϕ∈[−π/2,π/2], r∈[0, ∞).

Forθ, the period of the tangent function is π, so the arctangent function arctan generally only takes one period, its domain is R, and its value range is (−π /2, π/2). To solve this problem, the Arctan function, also known as the arctan2 function, was introduced.

atan2 Function usage atan2(delta_y, delta_x)

import math
a = math.atan2(400,-692.820)
# 2.6179936760992044
angle = a/math.pi*180
# 149.99998843242386

atan Function usage atan(delta_y / delta_x)

import math
delta_y = 400
delta_x = -692.820

if delta_x == 0:
    b = math.pi / 2.0
    angle = b/math.pi*180
    if delta_y == 0:
        angle = 0.0
    elif delta_y < 0:
        angle -= 180
else:
    b =  math.atan(delta_y/delta_x) 
    angle = b/math.pi*180
    if delta_y > 0 and delta_x < 0:
        angle = angle + 180
    if delta_y < 0 and delta_x < 0:
        angle = angle - 180

b,angle
# (-0.5235989774905888, 149.99998843242386)

atan Similarities and differences with atan2

• The number of parameters is different

• The return value of both is radians

• If delta_x is equal to 0, atan2 can still be calculated, but atan needs to be judged in advance, otherwise it will cause a program error

• Quadrant processing

atan2(b,a) is the 4-quadrant arctangent. Its value depends not only on the tangent value b/a, but also on which quadrant the point (b,a) falls into:

• When point (b,a) falls into the first quadrant (b>0, a>0), the range of atan2(b,a) is 0 ~ pi /2

• ##When point (b,a) falls into the second quadrant (b>0, a<0), the range of atan2(b,a) is

  pi/2 ~ pi

• When point (b,a) falls into the third quadrant (b<0, a<0), atan2(b,a ) range is

  -pi~-pi/2

• When point (b, a) falls into the fourth quadrant (b<0, a>0) When, the range of atan2(b,a) is

  -pi/2～0

and atan(b/a) is a/b only based on the tangent value Find the corresponding angle (can be regarded as just the arc tangent of the two quadrants):

• When b/a > 0, the value range of atan(b/a) is

  0 ~ pi/2

• When b/a < 0, the value range of atan(b/a) is

  -pi/2~0

Value range

##Point(b ,a) When falling into
• the first quadrant (b>0, a>0)

  or the fourth quadrant (b<0, a>0), atan2(b ,a) = atan(b/a)

  ##Point (b,a) falls into
the second quadrant (b>0, a<0)
• , b/a<0, so the value range of atan(b/a) is always

  -pi/2~0, however, the range of atan2(b,a) is pi/2 ~ pi, so atan(b/a) needs to add 180 to calculate the angle value.

  Point (b,a) falls into the
third quadrant (b<0, a<0)
• , b/a>0, so atan(b/ a) The value range is

  0 ~ pi/2, and at this time the range of atan2(b,a) is -pi~-pi/2, so atan(b/a ) To calculate the angle value, subtract 180.

  Conclusion: atan and atan2 functions, it is recommended to use the atan2 function

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