The command convexhull(P) returns a list of points defining the convex hull of the points in P in counter-clockwise order.

Every point in P must be a list of an x and y coordinate, both of which must be numbers (of type numeric).

If the option output=area is specified, the area of the convex hull of the points is returned.

If the option output=hull is specified, the convex hull is is returned as a list of points.  This is the default return value.

If the option output=plot is specified, a plot of the points and the convex hull is returned.

Multiple outputs can be specified, for example, output=[hull,area] returns a sequence of two values.

An $n\log \left(n\right)$ algorithm computing tangents of pairs of points is used.

For a slightly more geometrical interpretation of the same command, see geometry[convexhull].  The points input and output are geometric points, and the output is considered to be a convex polygon.

The command with(simplex,convexhull) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{simplex}\right)\:$

$P≔\left\{\left[0\,0\right]\,\left[1\,0\right]\,\left[1\,1\right]\,\left[1\,\frac{1}{2}\right]\,\left[2\,0\right]\,\left[\frac{1}{2}\,\frac{1}{2}\right]\right\}$

$P≔\left\{\left[0\,0\right]\,\left[1\,0\right]\,\left[1\,1\right]\,\left[1\,\frac{1}{2}\right]\,\left[2\,0\right]\,\left[\frac{1}{2}\,\frac{1}{2}\right]\right\}$

$\mathrm{convexhull}\left(P\right)$

$\left[\left[0\,0\right]\,\left[2\,0\right]\,\left[1\,1\right]\right]$

$\mathrm{convexhull}\left(P\,\mathrm{output}=\mathrm{area}\right)$

$1$

$H,A≔\mathrm{convexhull}\left(P\,\mathrm{output}=\left[\mathrm{hull}\,\mathrm{area}\right]\right)$

$H,A≔\left[\left[0\,0\right]\,\left[2\,0\right]\,\left[1\,1\right]\right],1$

$\mathrm{convexhull}\left(P\,\mathrm{output}=\mathrm{plot}\right)$

$R≔\mathrm{rand}\left({10}^{10}\right)\:$

U01 := proc() Float( R(), -10 ) end proc:

$P≔\left\{\mathrm{seq}\left(\left[\mathrm{U01}\left(\right)\,\mathrm{U01}\left(\right)\right]\,i=1..50\right)\right\}\:$

$\mathrm{convexhull}\left(P\,\mathrm{output}=\mathrm{area}\right)$

$0.7570693924$

$\mathrm{convexhull}\left(P\,\mathrm{output}=\mathrm{plot}\right)$