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Ellipsoid—Wolfram Language Documentation

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• See Also
  • Disk
  • Ball
  • Sphere
  • ImplicitRegion
  • BoundingRegion
  • PositiveDefiniteMatrixQ
  • Formats
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  • PLY
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Ellipsoid[p,{r₁,…}]

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

Ellipsoid[p,Σ]

represents an ellipsoid centered at p and weight matrix Σ.

• 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 , r_i 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, p_i, and radii r_i can be Scaled and Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, Specularity, Opacity, and color.

An axis-aligned ellipsoid in 3D:

In 2D:

Measure and centroid:

An axis-aligned ellipsoid in 3D:

In 2D:

A general ellipsoid in 3D:

In 2D:

Balls with different specular exponents:

Black ball that glows red:

Opacity specifies the face opacity:

2D styling:

Specify coordinates by fractions of the plot range:

Specify scaled offsets from the ordinary coordinates:

Embedding dimension is the dimension of the space in which the ball lives:

Geometric dimension is the dimension of the shape itself:

Membership testing:

Get conditions for point membership:

Volume:

Centroid:

Distance from a point:

The distance to the nearest point for an ellipse:

Signed distance from a point:

Signed distance to an ellipse:

Nearest point in the region:

Nearest points to an enclosing sphere:

An ellipsoid is bounded:

Find its range:

Integrate over an ellipsoid region:

Optimize over an ellipsoid region:

Solve equations in an ellipsoid region:

A spheroid is an ellipsoid with two equal axes:

Compute its volume:

Total mass for an ellipsoid region with density given by :

Find the mass of methanol in an Ellipsoid:

Density of methanol:

Volume of ellipsoid:

Mass of methanol in the ellipsoid:

Find a bounding Ellipsoid to a region's bounding box:

Compute the bounding box:

Compute a bounding ellipsoid to the bounding box:

Compute the difference in Volume of the bounding solids:

Visualize bounding surfaces:

Random ellipsoid collections:

Sweep an ellipsoid around an axis:

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