Creating a parabola (?) shaped zone of interaction...

So I want a zone of interaction originating from a object, but i don’t want to use shapes with colliders that have simply been rendered invisible. I was thinking more pure maths?
E.g.

Say you have a Player, and just draw a parabola from the player as a origin, cant u use it to create a sort of half dome?

I don’t know if this makes sense, or maybe I’m way off as far as how this works. But I need the most performance efficient solution due to needing a lot of pawns present at the same time.

In your precise situation, I strongly recommend using a sphere collider with “filtering”. Indeed, the physics engine is optimized (space subdivision, …), and I don’t think you have the possibility to “include” your custom collision detection algorithm.

Since you have a basic shape (half sphere), I guess you can do the following using a Sphere collider (set to trigger)

private void OnTriggerEnter(Collider other)
{
    // Filter to keep half of the sphere
    Vector3 direction = (other.transform.position - transform.position).normalized;
    if( Vector3.Dot( direction, transform.forward ) > 0 )
    {
        // Do something
    }
}

Just solve an equation y=x^2 and see if your current position is higher or lower than the function’s response value.