What is the external normal of an ellipsoid at a certain point (x,y,z)? How do I compute it?
Thanks,
Yuval
Let be your ellipsoid. Define the function .
Now use the property that is orthogonal to the ellipsoid .
Thus, is orthogonal to the ellipsoid.
It remains to put a in front of it if you want it to be internal or external.
Put the right sign and you have your outward normal vector.