/CGAL/Minkowski_sum_2/Exact_offset_base_2.h

// Copyright (c) 2006  Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s)     : Ron Wein   <wein@post.tau.ac.il>

#ifndef CGAL_EXACT_OFFSET_BASE_H
#define CGAL_EXACT_OFFSET_BASE_H

#include <CGAL/Polygon_2.h>
#include <CGAL/Polygon_with_holes_2.h>
#include <CGAL/Gps_traits_2.h>
#include <CGAL/Minkowski_sum_2/Labels.h>
#include <CGAL/Minkowski_sum_2/Arr_labeled_traits_2.h>
#include <CGAL/use.h>

namespace CGAL {

/*! \class
 * A base class for computing the offset of a given polygon by a given
 * radius in an exact manner.
 */
template <class Traits_, class Container_>
class Exact_offset_base_2
{
private:
  
  typedef Traits_                                        Traits_2;
  
  // Rational kernel types:
  typedef typename Traits_2::Rat_kernel                  Rat_kernel;
  typedef typename Rat_kernel::FT                        Rational;
  typedef typename Rat_kernel::Point_2                   Rat_point_2;
  typedef typename Rat_kernel::Line_2                    Rat_line_2;
  typedef typename Rat_kernel::Circle_2                  Rat_circle_2;

protected:

  typedef Rat_kernel                                     Basic_kernel;
  typedef Rational                                       Basic_NT;

private:

  // Algebraic kernel types:
  typedef typename Traits_2::Alg_kernel                  Alg_kernel;
  typedef typename Alg_kernel::FT                        Algebraic;
  typedef typename Alg_kernel::Point_2                   Alg_point_2;

  typedef typename Traits_2::Nt_traits                   Nt_traits;

  // Traits-class types:
  typedef typename Traits_2::Curve_2                     Curve_2;
  typedef typename Traits_2::X_monotone_curve_2          X_monotone_curve_2;

  typedef CGAL::Gps_traits_2<Traits_2>                   Gps_traits_2;
 
protected:

  typedef CGAL::Polygon_2<Rat_kernel, Container_>        Polygon_2;
  typedef CGAL::Polygon_with_holes_2<Rat_kernel,
                                     Container_>         Polygon_with_holes_2;
  typedef typename Gps_traits_2::Polygon_2               Offset_polygon_2;
  
private:

  // Polygon-related types:
  typedef typename Polygon_2::Vertex_circulator          Vertex_circulator;

protected:

  typedef Arr_labeled_traits_2<Traits_2>                 Labeled_traits_2; 

  typedef typename Labeled_traits_2::X_monotone_curve_2  Labeled_curve_2;

public:

  /*! Default constructor. */
  Exact_offset_base_2 ()
  {}    

protected:

  /*!
   * Compute the curves that constitute the offset of a simple polygon by a
   * given radius.
   * \param pgn The polygon.
   * \param orient The orientation to traverse the vertices.
   * \param r The offset radius.
   * \param cycle_id The index of the cycle.
   * \param oi An output iterator for the offset curves.
   * \pre The value type of the output iterator is Labeled_curve_2.
   * \return A past-the-end iterator for the holes container.
   */
  template <class OutputIterator>
  OutputIterator _offset_polygon (const Polygon_2& pgn,
                                  CGAL::Orientation orient,
                                  const Rational& r,
                                  unsigned int cycle_id,
                                  OutputIterator oi) const
  {
    // Prepare circulators over the polygon vertices.
    const bool            forward = (pgn.orientation() == orient);
    Vertex_circulator     first, curr, next;
    
    first = pgn.vertices_circulator();
    curr = first; 
    next = first;

    // Traverse the polygon vertices and edges and construct the arcs that
    // constitute the single convolution cycle.
    Alg_kernel                    alg_ker;
    typename Alg_kernel::Equal_2  f_equal = alg_ker.equal_2_object();

    Nt_traits       nt_traits;
    const Rational  sqr_r = CGAL::square (r);
    const Algebraic alg_r = nt_traits.convert (r);
    Rational        x1, y1;              // The source of the current edge.
    Rational        x2, y2;              // The target of the current edge.
    Rational        delta_x, delta_y;    // (x2 - x1) and (y2 - y1), resp.
    Algebraic       len;                 // The length of the current edge.
    Algebraic       trans_x, trans_y;    // The translation vector.
    Alg_point_2     op1, op2;            // The edge points of the offset edge.
    Alg_point_2     first_op;            // The first offset point.
    Algebraic       a, b, c;

    unsigned int                    curve_index = 0;
    Traits_2                        traits;
    std::list<Object>               xobjs;
    std::list<Object>::iterator     xobj_it;
    typename Traits_2::Make_x_monotone_2
                       f_make_x_monotone = traits.make_x_monotone_2_object();
    Curve_2                         arc;
    X_monotone_curve_2              xarc;
    bool                            assign_success;

    do
    {
      // Get a circulator for the next vertex (in the proper orientation).
      if (forward)
        ++next;
      else
        --next;

      // Compute the vector v = (delta_x, delta_y) of the current edge,
      // and compute the edge length ||v||.
      x1 = curr->x();
      y1 = curr->y();
      x2 = next->x();
      y2 = next->y();

      delta_x = x2 - x1;
      delta_y = y2 - y1;
      len = nt_traits.sqrt (nt_traits.convert (CGAL::square (delta_x) + 
                                               CGAL::square (delta_y)));

      // The angle theta between the vector v and the x-axis is given by:
      //
      //                 y2 - y1                        x2 - x1
      //   sin(alpha) = ---------         cos(alpha) = ---------
      //                  ||v||                          ||v||
      //
      // To offset the endpoints of the current edge we compute a vector
      // (trans_x, trans_y) perpendicular to v. Since we traverse the polygon
      // in a counterclockwise manner, the angle this vector forms with the
      // x-axis is (alpha - PI/2), and we have:
      //
      //   trans_x = r*cos(alpha - PI/2) = r*sin(alpha)
      //   trans_y = r*sin(alpha - PI/2) = -r*cos(alpha)
      trans_x = nt_traits.convert (r * delta_y) / len;
      trans_y = nt_traits.convert (-r * delta_x) / len;

      // Construct the first offset vertex, which corresponds to the
      // source vertex of the current polygon edge.
      op1 = Alg_point_2 (nt_traits.convert (x1) + trans_x, 
                         nt_traits.convert (y1) + trans_y);

      if (curr == first)
      {
        // This is the first edge we visit -- store op1 for future use.
        first_op = op1;
      }
      else
      {
        if (! f_equal (op2, op1))
        {
          // Connect op2 (from the previous iteration) and op1 with a circular
          // arc, whose supporting circle is (x1, x2) with radius r.
          arc = Curve_2 (Rat_circle_2 (*curr, sqr_r),
                         CGAL::COUNTERCLOCKWISE,
                         op2, op1);
          
          // Subdivide the arc into x-monotone subarcs and append them to the
          // convolution cycle.
          xobjs.clear();
          f_make_x_monotone (arc, std::back_inserter(xobjs));
          
          for (xobj_it = xobjs.begin(); xobj_it != xobjs.end(); ++xobj_it)
          {
            assign_success = CGAL::assign (xarc, *xobj_it);
            CGAL_assertion (assign_success);
            CGAL_USE(assign_success);

            *oi = Labeled_curve_2 (xarc,
                                   X_curve_label (xarc.is_directed_right(),
                                                  cycle_id,
                                                  curve_index));
            ++oi;
            curve_index++;
          }
        }
      }

      // Construct the second offset vertex, which corresponds to the
      // target vertex of the current polygon edge.
      op2 = Alg_point_2 (nt_traits.convert (x2) + trans_x, 
                         nt_traits.convert (y2) + trans_y);

      // The equation of the line connecting op1 and op2 is given by:
      //
      //   (y1 - y2)*x + (x2 - x1)*y + (r*len - y1*x2 - x1*y2) = 0
      //
      a = nt_traits.convert (-delta_y);
      b = nt_traits.convert (delta_x);
      c = alg_r*len - nt_traits.convert (y1*x2 - x1*y2);

      xarc = X_monotone_curve_2 (a, b, c,
                                 op1, op2);

      *oi = Labeled_curve_2 (xarc,
                             X_curve_label (xarc.is_directed_right(),
                                            cycle_id,
                                            curve_index));
      ++oi;
      curve_index++;

      // Proceed to the next polygon vertex.
      curr = next;
    
    } while (curr != first);

    if (! f_equal (op2, first_op))
    {
      // Close the convolution cycle by creating the final circular arc,
      // centered at the first vertex.
      arc = Curve_2 (Rat_circle_2 (*first, sqr_r),
                     CGAL::COUNTERCLOCKWISE,
                     op2, first_op);
      
      // Subdivide the arc into x-monotone subarcs and append them to the
      // convolution cycle.
      bool           is_last;
      
      xobjs.clear();
      f_make_x_monotone (arc, std::back_inserter(xobjs));
      
      xobj_it = xobjs.begin();
      while (xobj_it != xobjs.end())
      {
        assign_success = CGAL::assign (xarc, *xobj_it);
        CGAL_assertion (assign_success);
        CGAL_USE(assign_success);
        
        ++xobj_it;
        is_last = (xobj_it == xobjs.end());

        *oi = Labeled_curve_2 (xarc,
                               X_curve_label (xarc.is_directed_right(),
                                              cycle_id,
                                              curve_index,
                                              is_last));
        ++oi;
        curve_index++;
      }
    }

    return (oi);
  }

};


} //namespace CGAL

#endif