# Singular

#### D.13.2.12 findOrientedBoundary

Procedure from library polymake.lib (see polymake_lib).

Usage:
findOrientedBoundary(polygon); polygon list

Assume:
polygon is a list of integer vectors defining integer lattice points in the plane

Return:
list l with the following interpretation
l[1] = list of integer vectors such that the polygonal path defined by these is the boundary of the convex hull of the lattice points in polygon
l[2] = list, the redundant points in l[1] have been removed

Example:
 LIB "polymake.lib"; ==> Welcome to polymake version ==> Copyright (c) 1997-2015 ==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt) ==> http://www.polymake.org // the following lattice points in the plane define a polygon list polygon=intvec(0,0),intvec(3,1),intvec(1,0),intvec(2,0), intvec(1,1),intvec(3,2),intvec(1,2),intvec(2,3), intvec(2,4); // we compute its boundary list boundarypolygon=findOrientedBoundary(polygon); // the points on the boundary ordered clockwise are boundarypolygon[1] boundarypolygon[1]; ==> [1]: ==> 0,0 ==> [2]: ==> 1,2 ==> [3]: ==> 2,4 ==> [4]: ==> 3,2 ==> [5]: ==> 3,1 ==> [6]: ==> 2,0 ==> [7]: ==> 1,0 // the vertices of the boundary are boundarypolygon[2] boundarypolygon[2]; ==> [1]: ==> 0,0 ==> [2]: ==> 2,4 ==> [3]: ==> 3,2 ==> [4]: ==> 3,1 ==> [5]: ==> 2,0