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# plot::hull

Compute the convex hull of a set of points

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```plot::hull(L)
```

## Description

plot::hull computes the convex hull of a list of points in any dimension, i.e., the smallest convex region containing all the points. Such a region is bounded by simplices (straight lines in the plane, triangles in 3D) and it is these simplices which plot::hull returns.

## Environment Interactions

Although plot::hull 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

We generate a list of random points and compute their convex hull:

```X := stats::uniformRandom(0, 20):
l := [[X(), X()] \$ i = 1..10]:
h := plot::hull(l):```

The convex hull is returned as lists of lists, as accepted by plot::Polygon2d:

`h[1]`

```plot(plot::PointList2d(l),
plot::Polygon2d(t) \$ t in h,
Closed, PointSize=2)```

### Example 2

The convex hull of a list of points in 3D is also easy to visualize:

```l := [[x, y, z] \$ y = z..x \$ z = -x..x \$ x = 0..10]:
h := plot::hull(l):
plot(plot::PointList3d(l, PointSize=1),
plot::Polygon3d(t) \$ t in h,
Closed, Filled, FillColor=RGB::LightOrange.[0.6])```

## Parameters

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

## Return Values

List of simplices of dimension one less than that of the points in L, given as lists of lists of floating-point values.

## Algorithms

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