Generate Points On Sphere (not by vertices)

Hello!
Live: https://jsfiddle.net/mbowaurv/

The idea is to:

  1. Visualise the half of the sphere based on perpendicular (red arrow) to the plane-like 3DMesh (rotate sphere it to the correct side)
  2. Generate Million of points on this sphere (no need to visualise them if this is not possible due to performance issues)

The problem is:

  1. Can not rotate “visual sphere” to the correct direction (rotation.copy can not be used because 3DMesh is always with 0 rotation) and can not find how to build this red perpendicular as no face normal can be used (I guess?).
  2. Don’t have a glue how to generate points in other way as I’ve presented in Live example… Vertices of “Visual sphere” can not be used as there is a need to have millions of points (with angle 1 minute of arc at the sphere)

Please, if anyone know how to solve any of this questions - provide your help.

I am really appreciating your time.
Thank you.

Not a complete answer but you can use MeshSurfaceSampler to sample points on arbitrary mesh surfaces.

Thank you mr. Mugen87 for your answer,
will give it a try!