ellipsoid

Calculates a <code>qmesh3d</code> object representing a 3D ellipsoid
with given <code>center</code> and <code>shape</code> matrix. The function allows for
degenerate ellipsoids where the <code>shape</code> matrix has rank &lt; 3 and plots
as an ellipse or a line.

dplot

Represents generalized geometric ellipsoids with the "(U,D)" representation. It allows degenerate
and/or unbounded ellipsoids, together with methods for linear and duality transformations, and for plotting.
Thus ellipsoids are naturally extended to include lines, hyperplanes, points, cylinders, etc.
This permits exploration of a variety to statistical issues that can be visualized using ellipsoids
as discussed by Friendly, Fox & Monette (2013), Elliptical Insights: Understanding Statistical Methods
Through Elliptical Geometry <doi:10.1214/12-STS402>.

Michael Friendly

gellipsoid

Generalized Ellipsoids

ellipsoid function

<dl><dt>center</dt>
<dd>A vector of length 3 giving the center of the 3D ellipsoid,
typically the mean vector of a data matrix.</dd>
<dt>shape</dt>
<dd>A 3 x 3 matrix giving the shape of the 3D ellipsoid, typical a
covariance matrix of a data matrix.</dd>
<dt>radius</dt>
<dd>radius of the ellipsoid, with default <code>radius=1</code>, giving
a standard ellipsoid. For a multivariate sample with <code>dfe</code> degrees of
freedom associated with <code>shape</code>, an ellipsoid of <code>level</code> coverage
can be calculated using <code>radius=sqrt(3 * qf(level, 3, dfe))</code>.</dd>
<dt>segments</dt>
<dd>number of line segments to use in each direction in the
wire-frame representation of the ellipsoid</dd>
<dt>warn.rank</dt>
<dd>warn if the <code>shape</code> matrix is of rank &lt; 3?</dd></dl>

Arguments

Michael Friendly and John Fox, extending Duncan Murdoch

Author

Calculate an ellipsoid in 3D — ellipsoid

<dl>

<dt>center</dt>
<dd>A vector of length 3 giving the center of the 3D ellipsoid,
typically the mean vector of a data matrix.</dd>


<dt>shape</dt>
<dd>A 3 x 3 matrix giving the shape of the 3D ellipsoid, typical a
covariance matrix of a data matrix.</dd>


<dt>radius</dt>
<dd>radius of the ellipsoid, with default <code>radius=1</code>, giving
a standard ellipsoid. For a multivariate sample with <code>dfe</code> degrees of
freedom associated with <code>shape</code>, an ellipsoid of <code>level</code> coverage
can be calculated using <code>radius=sqrt(3 * qf(level, 3, dfe))</code>.</dd>


<dt>segments</dt>
<dd>number of line segments to use in each direction in the
wire-frame representation of the ellipsoid</dd>


<dt>warn.rank</dt>
<dd>warn if the <code>shape</code> matrix is of rank &lt; 3?</dd>

</dl>

ellipsoid: Calculate an ellipsoid in 3D

Description

Usage

Value

Arguments

Author

Details

Examples