Ellipsoid normal vector

An ellipsoid is a fancy name for a three-dimensional shape that looks like a stretched out ball. Imagine holding a balloon and squishing it a bit so it becomes long and thin. That's what an ellipsoid looks like.

Now, imagine placing a little arrow at any point on the surface of the ellipsoid, pointing straight out from the surface. This arrow is called the normal vector. The normal vector is like a special garden gnome that always knows which way is up on the ellipsoid.

This normal vector can help us do lots of cool things, like finding out how bumpy or smooth the surface of the ellipsoid is at any given point. It also helps us figure out how light would bounce off the surface of the ellipsoid if we were shining a flashlight at it.

Basically, the ellipsoid normal vector is just a fancy way of describing the little arrow that points out from the surface at a specific point on the ellipsoid.