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# ellipsoid

Create ellipsoid

## Syntax

``[X,Y,Z] = ellipsoid(xc,yc,zc,xr,yr,zr)``
``[X,Y,Z] = ellipsoid(xc,yc,zc,xr,yr,zr,n)``
``ellipsoid(___)``
``ellipsoid(ax,___)``

## Description

example

````[X,Y,Z] = ellipsoid(xc,yc,zc,xr,yr,zr)` returns the x-, y-, and z-coordinates of an ellipsoid without drawing it. The returned ellipsoid has center coordinates at `(xc,yc,zc)`, semiaxis lengths `(xr,yr,zr)`, and consists of 20-by-20 faces.The function returns the x-, y-, and z- coordinates as three `21`-by-`21` matrices.To draw the ellipsoid using the returned coordinates, use the `surf` or `mesh` functions.```

example

````[X,Y,Z] = ellipsoid(xc,yc,zc,xr,yr,zr,n)` returns the x-, y-, and z-coordinates of an ellipsoid with `n`-by-`n` faces. The function returns the x-, y-, and z-coordinates as three `(n+1)`-by-`(n+1)` matrices.```

example

````ellipsoid(___)` plots the ellipsoid without returning the coordinates. Use this syntax with any of the previous input arguments in previous syntaxes.```

example

````ellipsoid(ax,___)` plots into the axes specified by `ax` instead of the current axes. Specify the axes as the first input argument.```

## Examples

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Create and plot an ellipsoid with a center at (0, –0.5, 0) and semiaxis lengths (6, 3.25, 3.25). Use `axis equal` to use equal data units along each coordinate direction.

```ellipsoid(0,-0.5,0,6,3.25,3.25) axis equal```

Generate coordinates of an ellipsoid with a center at (0, 0, 0) and semiaxis lengths (1.5, 1.5, 3).

`[X,Y,Z] = ellipsoid(0,0,0,1.5,1.5,3);`

Create a surface plot of the ellipsoid.

```surf(X,Y,Z); axis equal```

Plot a second ellipsoid with its center translated by (3, 0, 5) from the first ellipsoid. To be able to rotate the second ellipsoid in the next step, return the surface object as `s`.

```hold on s = surf(X+3,Y,Z+5);```

Rotate the second ellipsoid by 45 degrees around its $x$-axis. The new coordinates of the translated and rotated ellipsoid are stored in `s.Xdata`, `s.Ydata`, and `s.Zdata`.

```direction = [1 0 0]; rotate(s,direction,45)```

Display ellipsoids with center coordinates (0, 0, 0) and semiaxis lengths (2, 1, 1) with different number of faces.

Call the `tiledlayout` function to create a 2-by-2 tiled chart layout. Call the `nexttile` function to create the axes. Then, use the `ellipsoid` function to plot three ellipsoids with different numbers of faces. Plot the ellipsoids in different tiles of the chart by specifying the axes.

```tiledlayout(2,2); ax1 = nexttile; ellipsoid(ax1,0,0,0,2,1,1) axis equal title('20-by-20 faces (Default)') ax2 = nexttile; ellipsoid(ax2,0,0,0,2,1,1,50) axis equal title('50-by-50 faces') ax3 = nexttile; ellipsoid(ax3,0,0,0,2,1,1,80) axis equal title('80-by-80 faces')```

## Input Arguments

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Coordinates of ellipsoid center, specified as three comma-separated scalar numbers.

Data Types: `single` | `double`

Principal semiaxes along the x-, y-, and z-axes, specified as three comma-separated scalar numbers.

Data Types: `single` | `double`

Number of faces, specified as a positive scalar integer.

Target axes, specified as an `Axes` object. If you do not specify the axes, then `ellipsoid` plots into the current axes.

## Algorithms

`ellipsoid` generates the data using this equation:

`$\frac{{\left(x-xc\right)}^{2}}{x{r}^{2}}+\frac{{\left(y-yc\right)}^{2}}{y{r}^{2}}+\frac{{\left(z-zc\right)}^{2}}{z{r}^{2}}=1.$`

`ellipsoid(0,0,0,1,1,1)` is equivalent to a unit sphere.

## Version History

Introduced before R2006a