# plot::delaunay

Compute the Delaunay triangulation of a set of points

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```plot::delaunay(`L`)
```

## Description

`plot::delaunay` computes the Delaunay triangulation of a list of points in arbitrary dimension.

The Delaunay triangulation of a list of points is a triangulation of their convex hull such that for each edge of the triangulation, there is a circle containing the two endpoints of this edge but no other point of the list.

## Environment Interactions

Although `plot::delaunay` accepts and returns floating-point values, the actual computations take place in hardware floating-points and are therefore not affected by the value of `DIGITS`.

## Examples

### Example 1

Delaunay triangulation does not introduce new points:

```n0 := 10: l := [[Re, Im](exp(float(2*I*PI*n)/n0)) \$ n = 1.. n0]: d := plot::delaunay(l): plot(plot::PointList2d(l, PointSize=3), plot::Polygon2d(t, Closed) \$ t in d)```

## Parameters

 `L` A list of points, which are given as lists of real values

## Return Values

List of simplices in the dimension of the points in `L`, given as lists of lists of floating-point values.

## Algorithms

`plot::delaunay` uses qhull from the Geometry Center of the University of Minnesota, see www.qhull.org.

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