I have to say that I'm terrified and surprised how little I know about basic math. Essentially what I have is an origin point (0,0,0), I know the radius of the circle (10), and I know both angles (theta and phi). Given this assumptions I want to calculate the projected point on the sphere. I've came up with the bottom code through reading the answers of https://stackoverflow.com/a/969880/1230358, https://stackoverflow.com/a/36369852/1230358, http://tutorial.math.lamar.edu/Classes/CalcII/SphericalCoords.aspx and https://en.wikipedia.org/wiki/Spherical_coordinate_system.
My current code:
#!/usr/bin/env python3
import math
PI = math.pi
PI_2 = PI / 2
def calc_sphere_coordinates(radius, phi, theta):
# see: https://stackoverflow.com/a/969880/1230358
# see: https://stackoverflow.com/q/19673067/1230358
# see: http://mathinsight.org/spherical_coordinates
# see: https://en.wikipedia.org/wiki/Spherical_coordinate_system
# see: http://tutorial.math.lamar.edu/Classes/CalcII/SphericalCoords.aspx
# φ phi is the polar angle, rotated down from the positive z-axis (slope)
# θ theta is azimuthal angle, the angle of the rotation around the z-axis (aspect)
# z
# | x
# | /
# |/
# +-------- y
# both angles need to be in radians, not degrees!
theta = theta * PI / 180
phi = phi * PI / 180
x = radius * math.sin(phi) * math.cos(theta)
y = radius * math.sin(phi) * math.sin(theta)
z = radius * math.cos(phi)
return (x, y, z)
if __name__ == "__main__":
# calculate point position in hemisphere by rotating down from positive z-axis
for i in (10, 20, 30, 40, 50, 60, 70 , 80, 90):
print(calc_sphere_coordinates(10, i, 0))
print("-"*10)
# calculate point position in hemisphere by rotating around the z axis
for i in (10, 20, 30, 40, 50, 60, 70 , 80, 90):
print(calc_sphere_coordinates(10, 0, i))
print("-"*10)
# calculate point position by rotating in both directions
for i in (10, 20, 30, 40, 50, 60, 70 , 80, 90):
print(calc_sphere_coordinates(10, i, 90-i))
The output of the code is as follows:
(1.7364817766693033, 0.0, 9.84807753012208)
(3.420201433256687, 0.0, 9.396926207859085)
(4.999999999999999, 0.0, 8.660254037844387)
(6.4278760968653925, 0.0, 7.660444431189781)
(7.66044443118978, 0.0, 6.427876096865393)
(8.660254037844386, 0.0, 5.000000000000001)
(9.396926207859083, 0.0, 3.4202014332566884)
(9.84807753012208, 0.0, 1.7364817766693041)
(10.0, 0.0, 6.123233995736766e-16)
----------
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
(0.0, 0.0, 10.0)
----------
(0.30153689607045814, 1.7101007166283433, 9.84807753012208)
(1.16977778440511, 3.2139380484326963, 9.396926207859085)
(2.5, 4.330127018922192, 8.660254037844387)
(4.131759111665348, 4.92403876506104, 7.660444431189781)
(5.868240888334652, 4.92403876506104, 6.427876096865393)
(7.5, 4.330127018922192, 5.000000000000001)
(8.83022221559489, 3.2139380484326963, 3.4202014332566884)
(9.69846310392954, 1.7101007166283433, 1.7364817766693041)
(10.0, 0.0, 6.123233995736766e-16)
Shouldn't the line with (10.0, 0.0, 6.123233995736766e-16) have a z-coordinate of 0 and not 6.123233995736766e-16? Also rotating around the z-axis gives always the same result, no matter what angle is used (0.0, 0.0, 10.0).
