Also known as the ground in ancient flight simulators
Plane Equation: ax + by + cz = d.
If n = [a,b,c] : p·n = d.
n is perpendicular to the plane, the normal.
Distance a from plane to point q : a = q·n - d
Closest point q' on a plane to point q
Calculate distance between plane and closest point and then offset from q.
q' = q + (q·n - d ) n
Intersection of a plane and a sphere.
Get sphere center distance d from plane.
If d > radius then sphere in front of plane. If d < -radius then sphere behind plane. Otherwise it intersect the plane.