Ellipsoid

Ellipsoid[p,{r1,}]

represents an axis-aligned ellipsoid centered at the point p and with semiaxes lengths ri.

Ellipsoid[p,Σ]

represents an ellipsoid centered at p and weight matrix Σ.

Details

  • Ellipsoid is also known as center interval, ellipse, and hyperellipsoid.
  • Ellipsoid can be used as a geometric region and a graphics primitive.
  • Ellipsoid represents the axis-aligned filled ellipsoid or general ellipsoid .
  • Ellipsoid allows p to be any point in , ri any positive real numbers, and Σ any real symmetric positive definite matrix.
  • Ellipsoid can be used in Graphics and Graphics3D.
  • In graphics, the points p, pi, and radii ri can be Scaled and Dynamic expressions.
  • Graphics rendering is affected by directives such as FaceForm, Specularity, Opacity, and color.

Examples

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Basic Examples  (2)

An axis-aligned ellipsoid in 3D:

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In 2D:

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Measure and centroid:

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Scope  (20)

Applications  (4)

Properties & Relations  (4)

Neat Examples  (2)

See Also

Disk  Ball  Sphere  ImplicitRegion  BoundingRegion  PositiveDefiniteMatrixQ

Introduced in 2014
(10.0)