From sphere collider contact point to quarter hemispheres...

I have a sphere collider around an object and incoming other objects from all directions. I can get the point of contact easy, but I would like to calculate from that Vector3 point from which “quarter hemisphere” of the collider sphere the collision was triggered from. Imagine dividing the 2 hemispheres 2 more times, gives you 8 “quarter hemispheres”...not sure what they are really called on a sphere. The result would a be an event like “an intrusion happened in quarter hemispheres nr 7” or so. Now I am sure that can be calculated, but I am a trigonometry nob and just tried for a few hours. Anyone out there who knows how to do that? Any help would be much appreciated and make my day;-)

 

Given these vectors:

- Position of the sphere (transform.position)
- Up, Right and Forward vectors of the sphere (transform.up, transform.right, transform.forward)
- Position of the contact point

Then:

- Compute the vector from the center of the sphere to the contact point, this is contact point - transform.position. Let's name it R.
- Compute the dot product between R and Up, R and Right, R and Forward (Vector3.Dot). Let's name them d1, d2 and d3 respectively.
- The sign combination of d1, d2, and d3 gives you the number quarter hemisphere of the contact point.

For example:

- - - => quarter 0
- - + => quarter 1
- + - => quarter 2
- + + => quarter 3
...

and so on. Note that the number of possible combinations is exactly 8 (2^3).