Plotting a point on the edge of a sphere

Question

So coming from a flash background I have an OK understanding of some simple 2D trig. In 2d with I circle, I know the math to place an item on the edge given an angle and a

Answer 1

Your position in 3d is given by two angles (+ radius, which in your case is constant)

x = r * cos(s) * sin(t)
y = r * sin(s) * sin(t)
z = r * cos(t)

here, s is the angle around the z-axis, and t is the height angle, measured 'down' from the z-axis.

The picture below shows what the angles represent, s=theta in the range 0 to 2*PI in the xy-plane, and t=phi in the range 0 to PI.

Answer 2

The accepted answer did not seem to support negative x values (possibly I did something wrong), but just in case, using notation from ISO convention on coordinate systems defined in this Wikipedia entry, this system of equations should work:

import math

x = radius * sin(theta) * cos(phi)
y = radius * sin(theta) * sin(phi)
z = radius * cos(theta)

radius = math.sqrt(math.pow(x, 2) + math.pow(y, 2) + math.pow(z, 2))

phi = math.atan2(y, x)
theta = math.acos((z / radius))