Thanks

2. ## "The" bisector

It is incorrect to talk about "The" bisector of an ellipsoid, unlike a sphere it doesn't have just one that is the same throughout. The bisectors would be ellipses, but I am not aware of any special names given to one of them.

4. Originally Posted by loollool
Do you mean that to bisect an ellipsoid, we need to use an ellipse?
Here is my question in other words: Is a bisector of an ellipsoid a reasonabley described curve? For instance, in the plane, it is a straight line halfway between the two points. How about in an ellipsoid?
1. In general a bisector is one dimension lower than the bisected object. For example:

the bisector of a circle (dim = 2) is a straight line (dim = 1)
the bisector of a solid (dim = 3) is a plane (dim = 2)

2. There are 2 different types of ellipsoids:
a) Elliptic ellipsoid: Then every bisector is an ellipse
b) Rotational ellipsoid: Then the bisector is either a circle (the axis of rotation is perpendicular to this circle) or an ellipse.

EDIT: After playing around a little bit I noticed that it must be possible to get a circular bisector with elliptic ellipsoids too!

5. Thanks! It makes sense.