Inspired by [url=http://www.geogebra.org/forum/viewtopic.php?f=2&t=28489]this topic[/url], this construction demonstrates how, given a list of points [math]{v_1, \ldots, v_n}[/math] a polygon with those points as vertices can be constructed such that there are no self intersections (ie the line between two adjacent vertices does not intersect the interior of the polygon). The algorithm used here relies on the midpoint of the polygon and is not stable in the sense that the polygon is changed unnecessarily.
This is basically just a question of finding the right permutation of vertices, a problem which solution in GeoGebra is explained [url=http://wiki.geogebra.org/en/Tutorial:Advanced_List_Sorting]in this tutorial[/url].
