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
- 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
- ##Point(b ,a) When falling into
- the first quadrant (b>0, a>0)
or
##Point (b,a) falls intothe fourth quadrant (b<0, a>0)
,atan2(b ,a) = atan(b/a)
the second quadrant (b>0, a<0) - , b/a<0, so the value range of atan(b/a) is always
-pi/2~0
Point (b,a) falls into the, however, the range of atan2(b,a) is
pi/2 ~ pi, so atan(b/a) needs to add 180 to calculate the angle value.
third quadrant (b<0, a<0) - , b/a>0, so atan(b/ a) The value range is
0 ~ pi/2
Conclusion: atan and atan2 functions, it is recommended to use the atan2 function, 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.
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