# Convex hull of a set of points

## Convex hull in a plane

This examples shows how to find the convex hull in the context of a plane. First we have to create an object representing the vertices. We have multiple ways of doing this

```
using Polyhedra
v = convexhull([0, 0], [0, 1], [1, 0], [0.1, 0.1]) # list of points
v = vrep([[0, 0], [0, 1], [1, 0], [0.1, 0.1]]) # vector of points
```

```
V-representation Polyhedra.PointsHull{Float64, Vector{Float64}, Int64}:
4-element iterator of Vector{Float64}:
[0.0, 0.0]
[0.0, 1.0]
[1.0, 0.0]
[0.1, 0.1]
```

number of points × dimension matrix

```
x = [0,0,1,0.1]
y = [0,1,0,0.1]
v = vrep([x y])
```

```
V-representation MixedMatVRep{Float64, Matrix{Float64}}:
4-element iterator of Vector{Float64}:
[0.0, 0.0]
[0.0, 1.0]
[1.0, 0.0]
[0.1, 0.1]
```

Then we can compute the hull of these points using the planar_hull function

`Polyhedra.planar_hull(v)`

```
V-representation Polyhedra.Hull{Float64, Vector{Float64}, Int64}:
3-element iterator of Vector{Float64}:
[0.0, 0.0]
[0.0, 1.0]
[1.0, 0.0]
```

## Convex hull in higher dimension

In higher dimension, we can do it with a linear programming solver implementing the MathOptInterface, e.g.,

```
import GLPK
removevredundancy(v, GLPK.Optimizer)
```

```
V-representation Polyhedra.Hull{Float64, Vector{Float64}, Int64}:
3-element iterator of Vector{Float64}:
[0.0, 0.0]
[0.0, 1.0]
[1.0, 0.0]
```

We can also use any Polyhedral library implementing the interface of this package. If we don't specify any library, it falls back to a default one implementing on this package which will use the `planar_hull`

if the dimension is 2 (so it's equivalent to the first approach shown above):

```
p = polyhedron(v)
removevredundancy!(p)
p
```

```
Polyhedron DefaultPolyhedron{Float64, MixedMatHRep{Float64, Matrix{Float64}}, MixedMatVRep{Float64, Matrix{Float64}}}:
3-element iterator of Vector{Float64}:
[0.0, 0.0]
[0.0, 1.0]
[1.0, 0.0]
```

We can also specify a library. For instance, to use `CDDLib`

, write `using CDDLib`

and then `p = polyhedron(v, CDDLib.Library())`

.

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