Please do not put your all your questions in the same thread.
Moderator Note: Thread was split.
Yes, normal is different to normalized/unit
I've got a somewhat related question about ellipsoids..
If I'm trying to find a point on its surface that is in a direction v what do I need to do?
For a sphere centred at p with radius r it is just:
Perhaps you misunderstood what I was asking or I am misunderstanding your response. I'm not trying to find a normal to the surface but a point on the surface in a specific direction.
For instance the point on a sphere in a given direction can be found with:
where p is the center and v is the direction vector.
In this case it is simple since the sphere has uniform dimensions in all directions.
I need to know how to go about solving this problem for an ellipsoid which can have different dimensions in all axes.
Write Since the center of the ellipsoid is at the origin, you're looking for the intersection of the ellipsoid and the line defined by So solve for which yieldsOriginally Posted by scorpion007
and is your point on the surface. You can verify this formula gives your same solution for a sphere centered at the origin where