@ \subsection{Affine transformation of a map}

TODOS:
\begin{itemize}
\item sorting vertices not possible with inplace lists
\item reset minimal outedges
\item inserting and removing frame cornerns.
\end{itemize}

<<PM transformer implementation>>=
template <typename PMDEC, typename GEOM>
void PM_transformer<PMDEC,GEOM>::
  transform(const Aff_transformation& t) const
{
  TRACEN("transforming"); 
  <<determine and store infimaximal frame corners>>
  <<invert map if transformation is odd>>
  <<transform vertices and reduce representation>>
  <<recreate infimaximal frame>>
  <<reset minimal outedges>>
}

<<protected members>>=
Vertex_handle Corner[4];
bool is_corner(Vertex_handle v) const
{ for (int i=0; i<4; ++i) if ( v == Corner[i] ) return true; }

<<determine and store infimaximal frame corners>>=
CGAL_assertion( point(vertices_begin())==K.SW() );
CGAL_assertion( point(--vertices_end())==K.NE() );
Vertex_iterator v = vertices_begin(); Corner[0] = v;
while ( point(v) != K.NW() ) ++v; Corner[1] = v;
while ( point(v) != K.SE() ) ++v; Corner[2] = v;
while ( point(v) != K.NE() ) ++v; Corner[3] = v;

<<invert map if transformation is odd>>=
if ( t.is_odd() ) reflecting_inversion();

<<transform vertices and reduce representation>>=
Vertex_iterator v;
for(v = vertices_begin(); v != vertices_end(); ++v)
  K.transform(point(v),t);

<<recreate infimaximal frame>>=
<<sort vertices by points>>
v = vertices_begin();
if ( point(v) != K.SW() )   
  <<insert SW in frame edge>>
while ( K.on_left_box_segment(point(v)) ) ++v;
if ( point(--v) != K.NW() ) 
  <<insert NW in frame edge>>
v = --vertices_end();
if ( point(v) != K.NE() ) 
  <<insert NE in frame edge>>
while ( K.on_right_box_segment(point(v)) ) --v;
if ( point(++v) != K.SW() )
  <<insert SW in frame edge>>


<<reset minimal outedges>>=
for(v = vertices_begin(); v != vertices_end(); ++v)
  reset_minimal_outedge(v);

<<PM transformer>>=
template <typename PMDEC, typename GEOM>
class PM_transformer : public PMDEC {
  typedef PM_transformer<PMDEC,GEOM>  Self;
  typedef PMDEC                       Base;
  const GEOM& K; // geometry reference

public:
  typedef PMDEC                     PM_decorator;
  typedef typename PMDEC::Plane_map Plane_map;
  typedef GEOM                      Geometry;
  typedef typename GEOM::Point_2    Point;
  typedef typename GEOM::sAff_transformation_2 Aff_transformation;

  <<handles, iterators, and circulators from PMDEC>>
protected:
  <<protected members>>

PM_transformer(Plane_map& P, const Geometry& g = Geometry()) : 
void transform(const Aff_transformation& t) const;

}; // PM_transformer<PMDEC,GEOM>


<<handles, iterators, and circulators from PMDEC>>=
#define CGAL_USING(t) typedef typename PMDEC::t t
CGAL_USING(Halfedge_handle);
CGAL_USING(Vertex_handle);
CGAL_USING(Face_handle);
CGAL_USING(Vertex_iterator);
CGAL_USING(Halfedge_iterator);
CGAL_USING(Face_iterator);
#undef CGAL_USING

<<PM_transformer.h>>=
<<CGAL Header>>
#ifndef CGAL_PM_TRANSFORMER_H
#define CGAL_PM_TRANSFORMER_H

#undef _DEBUG
#define _DEBUG 13
#include <CGAL/Nef_2/debug.h>

CGAL_BEGIN_NAMESPACE

<<PM transformer>>
<<PM transformer implementation>>

CGAL_END_NAMESPACE
#endif // CGAL_PM_TRANSFORMER_H

<<CGAL Header>>=
// ============================================================================
//
// Copyright (c) 1997-2000 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------------
//
// release       : $CGAL_Revision$
// release_date  : $CGAL_Date$
//
// file          : include/CGAL/Nef_2/PM_transformer.h
// package       : Nef_2 
// chapter       : Nef Polyhedra
//
// source        : nef_2d/PM_transformer.lw
// revision      : $Id$
// revision_date : $Date$
//
// author(s)     : Michael Seel <seel@mpi-sb.mpg.de>
// maintainer    : Michael Seel <seel@mpi-sb.mpg.de>
// coordinator   : Michael Seel <seel@mpi-sb.mpg.de>
//
// implementation: Transformation module for plane maps
// ============================================================================