# 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