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Topic: Steiner Ellipses and Bounding Ellipsoid Questions
Replies: 3   Last Post: Jan 6, 2003 8:36 PM

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Randall Rathbun

Posts: 79
Registered: 12/6/04
Steiner Ellipses and Bounding Ellipsoid Questions
Posted: Feb 27, 2002 1:36 AM
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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.

Any ideas?

- Randall





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