1. Is it possible to find the minimal bounding ellipse called the "Steiner ellipse" for the 3 that actually exist for a triangle? What is a quick way of deciding which of the 3 is the one that we want?
2. Suppose a collection of points >3 exists in R3 space. We can determine the Steiner ellipses for any 3 non-linear points, but how does one determine the minimal 3d ellipsoid from these collections of Steiner ellipses?
In particular how does one find the minimal othogonal basis for the minimal ellipsoid?
In a collection n>4 of either 2d or 3d points, it is always possible to locate the "outermost" 3 non-linear points for 2d, or the 4 nonlinear non-planar points for the ellipsoid. However a method of quickly finding those points would save much computer time for an algorithm.