Convex hull of a simple polygon

In <a href="/facts/Discrete_geometry/Ixnl3GBc">discrete geometry</a> and <a href="/facts/Computational_geometry/eeaotQtl">computational geometry</a>, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given <a href="/facts/Simple_polygon/C5CfrPWf">simple polygon</a>. It is a special case of the more general concept of a <a href="/facts/Convex_hull/D4Id3JDS">convex hull</a>. It can be computed in <a href="/facts/Linear_time/77T62gmf">linear time</a>, faster than <a href="/facts/Convex_hull_algorithms/Wr70A2AI">algorithms for convex hulls of point sets</a>.
The convex hull of a simple polygon can be subdivided into the given polygon itself and into polygonal pockets bounded by a <a href="/facts/Polygonal_chain/GRQ6BMQS">polygonal chain</a> of the polygon together with a single convex hull edge. Repeatedly reflecting an arbitrarily chosen pocket across this convex hull edge produces a sequence of larger simple polygons; according to the <a href="/facts/Erd%C5%91s%E2%80%93Nagy_theorem/ENPXLKzV">Erdős–Nagy theorem</a>, this process eventually terminates with a convex polygon.

Convex hull of a simple polygon open-in-new

Convex hull of a simple polygon