# Documentation

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# ellipsoid

Generate ellipsoid

## Syntax

```[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr,n) [x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr) ellipsoid(axes_handle,...) ellipsoid(...) ```

## Description

`[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr,n)` generates a surface mesh described by three `n+1`-by-`n+1` matrices, enabling `surf(x,y,z)` to plot an ellipsoid with center `(xc,yc,zc)` and semi-axis lengths `(xr,yr,zr)`.

`[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr)` uses ```n = 20```.

`ellipsoid(axes_handle,...)` plots into the axes with handle `axes_handle` instead of the current axes (`gca`).

`ellipsoid(...)` with no output arguments plots the ellipsoid as a surface.

## Examples

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Generate data for an ellipsoid with a center at (0,0,0) and semi-axis lengths (5.9,3.25,3.25). Use `surf` to plot the ellipsoid.

```[x, y, z] = ellipsoid(0,0,0,5.9,3.25,3.25,30); figure surf(x, y, z) axis equal```

## Algorithms

`ellipsoid` generates the data using the following equation:

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

Note that `ellipsoid(0,0,0,.5,.5,.5)` is equivalent to a unit sphere.