Plane

• 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.