Random Points on a Sphere
Random Points on a Sphere
There are several ways to pick random points on a sphere. Using points of the form , where and , gives an evenly distributed set of points. Using spherical coordinates, , causes too many points to cluster at the poles. Picking points at random in a cube around the sphere and normalizing, ++,++,++, creates too many points that come from the corners of the cube.
cos(θ)
1-
,sin(θ)2
u
1-
,u2
u
0≤θ≤2π
-1≤u≤1
(cos(θ)sin(ϕ),sin(θ)sin(ϕ),cos(ϕ))
x
2
x
2
y
2
z
y
2
x
2
y
2
z
z
2
x
2
y
2
z