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D.13.4.9 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
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