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D.13.2.9 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