Find intersection point of three planes in C# for Unity

DoPlanesIntersectAtSinglePoint.cs

private bool planesIntersectAtSinglePoint( Plane p0, Plane p1, Plane p2, out Vector3 intersectionPoint )
{
	const float EPSILON = 1e-4f;

	var det = Vector3.Dot( Vector3.Cross( p0.normal, p1.normal ), p2.normal );
	if( det < EPSILON )
	{
		intersectionPoint = Vector3.zero;
		return false;
	}

	intersectionPoint = 
		( -( p0.distance * Vector3.Cross( p1.normal, p2.normal ) ) -
		( p1.distance * Vector3.Cross( p2.normal, p0.normal ) ) -
		( p2.distance * Vector3.Cross( p0.normal, p1.normal ) ) ) / det;

	return true;
}

Hmmm... That sounds interesting, I think I'll give it a try.

It seems likely that to me that if that's correct, I missed it because the specific project I'm currently using this in is pretty narrowly scoped (always a convex hull, with plane normals always pointing in towards the center of a symmetric enclosed volume so det is always positive for a valid solution, strict minimum size, etc).

Thanks for the heads-up 👍

Hmm... Or it might be that the code above really only works for such situations, and will fall in cases where there's a greater than 90° angle between the plane normals, even if they do indeed all meet at a single point.

Checking the absolute value of det would really only be checking if the planes were nearly coplanar, right?

In my project, it works very well if I use Mathf.Abs(det). I haven't figured out the intersectionPoint formula, but it seems to be applicable to all situations.