The convex hull of a set ps of points is the smallest convex polygon P for which each point in ps is either on the boundary of P or in its interior.

The result is returned as a list of points (vertices) of the convex polygon P in counter-clockwise order.

The routine uses an $n\log \left(n\right)$ algorithm computing tangents of pairs of points.

For an equivalent command with a few more options, see simplex[convexhull].  Input and output are simple points rather than geometric points, and the output can be the area enclosed in the polygon, the points defining the vertices, or a plot of the polygon.

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

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

$\mathrm{point}\left(A\,\left[0\,0\right]\right),\mathrm{point}\left(B\,\left[1\,1\right]\right),\mathrm{point}\left(C\,\left[2\,0\right]\right),\mathrm{point}\left(F\,\left[1\,0\right]\right),\mathrm{point}\left(\mathrm{E1}\,\left[1\,\frac{1}{2}\right]\right)\:$

$\mathrm{hullname}≔\mathrm{convexhull}\left(\left\{A\,B\,C\,\mathrm{E1}\,F\right\}\right)$

$\mathrm{hullname}≔\left[A\,C\,B\right]$

$\mathrm{triangle}\left(T\,\mathrm{hullname}\right)\:$

$\mathrm{draw}\left(\left\{A\,B\,C\,\mathrm{E1}\,F\,T\right\}\,\mathrm{printtext}=\mathrm{true}\,\mathrm{axes}=\mathrm{NONE}\right)$