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[erickee <>]

I can construct nef polyhedra by converting my polygons to half-spaces and
performing complements and intersections.  Unfortunately this is awkward. 
For example, if a section of my polygonal boundary is concave, I must find
the section and treat it separately.  (Imagine defining something like a
crescent shape as a union of half-spaces.)

The various constructors for nef polyhedra build the very structure that I
already have: a polygonal boundary with some points at infinity.  Points on
the polygon are converted from type Homogenous to Extended_homogeneous (line
460, Nef_polyhedron_2.h).  So, it seems like I should be able to construct
my polygon from Homogeneous points, and pass it to the polygon-based
constructor for Nef_polyhedron_2.  

I have constructed my polygons and passed them to Nef_polyhedron_2, but
something doesn't work.  For example, I can convert a polygon of standard
homogeneous points into a Nef_polyhedron_2:
  Homogeneous points on a finite square: (0,0,1);  (1,0,1);  (1,1,1); 
(0,1,1)
  Give a Nef_polyhedron_2 with three faces.  The last face is the "marked"
face:
     Edge 1: (0,0,1) ---> (1,0,1)
     Edge 2: (1,0,1) ---> (1,1,1)
     Edge 3: (1,1,1) ---> (0,1,1)
     Edge 4: (0,1,1) ---> (0,0,1)

    (code example A, below)  

But it appears that I can't convert an infinite square into a
Nef_polyhedron_2:
  Homogeneous points around the first quadrant: (0,0,1);  (1,0,0);  (1,1,0); 
(0,1,0)
  Give a Nef_polyhedron_2 with *two* faces.  There is no "marked" face.  The
second face is:
    Edge: (-1,1,0) ---> (-1,-1,0)
    Edge: (-1,-1,0) ---> (1,-1,0)
    Edge: (1,-1,0) ---> (1,0,0)
    Edge: (1,0,0) ---> (0,0,1)
    Edge: (0,0,1) ---> (1,0,0)
    Edge: (1,0,0) ---> (1,1,0)
    Edge: (1,1,0) ---> (-1,1,0)
    
    (code example B, below)


The problem is that Nef_polyhedron_2 only accepts standard points---even
homogeneous points are required to represent standard points.  I need to
pass non-standard points (points at infinity) and pass them into
Nef_polyhedron_2 somehow.  Is there a way?  Do I need to write a new
constructor? 





Code example A
  typedef CGAL::Filtered_extended_homogeneous<int> Extended_kernel;
  typedef CGAL::Nef_polyhedron_2<Extended_kernel> Nef_polyhedron;
  typedef Nef_polyhedron::Point Point;

  Point r1[4] = { Point(0,0,1), Point(1,0,1), Point(1,1,1), Point(0,1,1) };
  std::list<std::pair&lt;Point*,Point*> > polylines;
  polylines.push_back(std::make_pair(r1+0, r1+4)); 
  Nef_polyhedron RST(polylines.begin(), polylines.end(),
Nef_polyhedron::POLYGONS);


Code example B
  // Same as example A, except this line changes:
  Point r1[4] = { Point(0,0,1), Point(1,0,0), Point(1,1,0), Point(0,1,0) };





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