Function Repository Resource:

# MinimumVolumeEllipsoid

Find the minimum-volume enclosing ellipsoid of a set of points

Contributed by: Jan Mangaldan
 ResourceFunction["MinimumVolumeEllipsoid"][{p1,p2,…}] gives the minimum-volume enclosing ellipsoid of the points p1,p2,….

## Details and Options

The minimum-volume enclosing ellipsoid is also known as the Löwner ellipsoid or Löwner–John ellipsoid.
The minimum-volume enclosing ellipsoid is the smallest ellipsoid that includes the points pi.
The result is returned as an Ellipsoid.
ResourceFunction["MinimumVolumeEllipsoid"] takes the following options:
 MaxIterations 100 maximum number of iterations to use Tolerance Automatic tolerance for accepting an enclosing ellipsoid

## Examples

### Basic Examples (2)

A minimum volume ellipse:

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The region is the smallest ellipse that includes the points:

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A minimum volume ellipsoid:

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The region is the smallest ellipsoid that includes the points:

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### Options (2)

#### MaxIterations (1)

Limit or increase the number of steps taken:

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#### Tolerance (1)

Increase or decrease the Tolerance:

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### Applications (1)

Find the minimum-volume enclosing ellipsoid for a 3D graphics object:

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### Properties and Relations (2)

Compare the result of MinimumVolumeEllipsoid with the bounding ellipse returned by BoundingRegion[pts,"FastEllipse"]:

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Compare the result of MinimumVolumeEllipsoid with the bounding ellipsoid returned by BoundingRegion[pts,"FastEllipsoid"]:

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## Version History

• 1.0.0 – 31 December 2020