
/*

  KLayout Layout Viewer
  Copyright (C) 2006-2026 Matthias Koefferlein

  This program is free software; 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 2 of the License, or
  (at your option) any later version.

  This program is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA

*/


#include "gsiDecl.h"
#include "gsiDeclDbPropertiesSupport.h"
#include "dbPoint.h"
#include "dbPolygon.h"
#include "dbPolygonTools.h"
#include "dbPolygonGenerators.h"
#include "dbHash.h"
#include "dbPLCTriangulation.h"
#include "dbPLCConvexDecomposition.h"
#include "dbBinarySerialize.h"

namespace gsi
{

const std::string hm_docstring =
  "The Hertel-Mehlhorn decomposition starts with a Delaunay triangulation of the polygons and recombines the "
  "triangles into convex polygons.\n"
  "\n"
  "The decomposition is controlled by two parameters: 'with_segments' and 'split_edges'.\n"
  "\n"
  "If 'with_segments' is true (the default), new segments are introduced perpendicular to the edges forming "
  "a concave corner. If false, only diagonals (edges connecting original vertexes) are used.\n"
  "\n"
  "If 'split_edges' is true, the algorithm is allowed to create collinear edges in the output. In this case, "
  "the resulting polygons may contain edges that are split into collinear partial edges. Such edges usually recombine "
  "into longer edges when processing the polygon further. When such a recombination happens, the edges no "
  "longer correspond to original edges or diagonals. When 'split_edges' is false (the default), the resulting "
  "polygons will not contain collinear edges, but the decomposition will be constrained to fewer cut lines."
  "\n"
  "'max_area' and 'min_b' are the corresponding parameters used for the triangulation (see \\delaunay).\n"
;

const std::string delaunay_docstring =
  "Refinement is implemented by Chew's second algorithm. A maximum area can be given. Triangles "
  "larger than this area will be split. In addition 'skinny' triangles will be resolved where "
  "possible. 'skinny' is defined in terms of shortest edge to circumcircle radius ratio (b). "
  "A minimum number for b can be given. A value of 1.0 corresponds to a minimum angle of 30 degree "
  "and is usually a good choice. The algorithm is stable up to roughly 1.2 which corresponds to "
  "a minimum angle of abouth 37 degree.\n"
  "\n"
  "The minimum angle of the resulting triangles relates to the 'b' parameter as: @t min_angle = arcsin(B/2) @/t.\n"
  "\n"
  "Picking a value of 0.0 for max_area and min_b will "
  "make the implementation skip the refinement step. In that case, the results are identical to "
  "the standard constrained Delaunay triangulation.\n"
;

const std::string dbu_docstring =
  "The 'dbu' parameter a numerical scaling parameter. It should be choosen in a way that the polygon dimensions "
  "are \"in the order of 1\" (very roughly) after multiplication with the dbu parameter. A value of 0.001 is suitable "
  "for polygons with typical dimensions in the order to 1000 DBU. Usually the default value is good enough.\n"
;

template <class T>
static db::Region region_from_graph (const db::plc::Graph &plc, const T &trans)
{
  db::Region result;
  result.set_merged_semantics (false);

  for (auto t = plc.begin (); t != plc.end (); ++t) {
    db::DPolygon dp = t->polygon ();
    db::SimplePolygon sp;
    sp.assign_hull (dp.hull ().begin (), dp.hull ().end (), trans, false);
    result.insert (sp);
  }

  return result;
}

template <class P, class T>
static std::vector<P> polygons_from_graph (const db::plc::Graph &plc, const T &trans)
{
  std::vector<P> result;
  result.reserve (plc.num_polygons ());

  for (auto t = plc.begin (); t != plc.end (); ++t) {
    db::DPolygon dp = t->polygon ();
    result.push_back (P ());
    result.back ().assign_hull (dp.hull ().begin (), dp.hull ().end (), trans, false);
  }

  return result;
}

template <class C>
static db::polygon<C> to_polygon (const db::simple_polygon<C> &sp)
{
  db::polygon<C> p;
  p.assign_hull (sp.begin_hull (), sp.end_hull ());
  return p;
}

template <class C>
static db::polygon<C> to_polygon (const db::polygon<C> &p)
{
  return p;
}

template <class P>
static db::Region hm_decompose_ipolygon (const P *p, bool with_segments, bool split_edges, double max_area, double min_b, double dbu)
{
  db::plc::Graph plc;
  db::plc::ConvexDecomposition decomp (&plc);
  db::plc::ConvexDecompositionParameters param;
  param.with_segments = with_segments;
  param.split_edges = split_edges;
  param.tri_param.max_area = max_area;
  param.tri_param.min_b = min_b;

  db::CplxTrans trans = db::CplxTrans (dbu) * db::ICplxTrans (db::Trans (db::Point () - p->box ().center ()));

  decomp.decompose (to_polygon (*p), param, trans);

  return region_from_graph (plc, trans.inverted ());
}

template <class P>
static std::vector<P> hm_decompose_dpolygon (const P *p, bool with_segments, bool split_edges, double max_area, double min_b)
{
  db::plc::Graph plc;
  db::plc::ConvexDecomposition decomp (&plc);
  db::plc::ConvexDecompositionParameters param;
  param.with_segments = with_segments;
  param.split_edges = split_edges;
  param.tri_param.max_area = max_area;
  param.tri_param.min_b = min_b;

  db::DCplxTrans trans = db::DCplxTrans (db::DTrans (db::DPoint () - p->box ().center ()));

  decomp.decompose (to_polygon (*p), param, trans);

  return polygons_from_graph<P, db::DCplxTrans> (plc, trans.inverted ());
}

template <class P>
static db::Region triangulate_ipolygon (const P *p, double max_area, double min_b, double dbu)
{
  db::plc::Graph tris;
  db::plc::Triangulation triangulation (&tris);
  db::plc::TriangulationParameters param;
  param.min_b = min_b;
  param.max_area = max_area * dbu * dbu;

  db::CplxTrans trans = db::CplxTrans (dbu) * db::ICplxTrans (db::Trans (db::Point () - p->box ().center ()));

  triangulation.triangulate (to_polygon (*p), param, trans);

  return region_from_graph (tris, trans.inverted ());
}

template <class P>
static db::Region triangulate_ipolygon_v (const P *p, const std::vector<db::Point> &vertexes, double max_area, double min_b, double dbu)
{
  db::plc::Graph tris;
  db::plc::Triangulation triangulation (&tris);
  db::plc::TriangulationParameters param;
  param.min_b = min_b;
  param.max_area = max_area * dbu * dbu;

  db::CplxTrans trans = db::CplxTrans (dbu) * db::ICplxTrans (db::Trans (db::Point () - p->box ().center ()));

  triangulation.triangulate (to_polygon (*p), vertexes, param, trans);

  return region_from_graph (tris, trans.inverted ());
}

template <class P>
static std::vector<P> triangulate_dpolygon (const P *p, double max_area = 0.0, double min_b = 0.0)
{
  db::plc::Graph tris;
  db::plc::Triangulation triangulation (&tris);
  db::plc::TriangulationParameters param;
  param.min_b = min_b;
  param.max_area = max_area;

  db::DCplxTrans trans = db::DCplxTrans (db::DTrans (db::DPoint () - p->box ().center ()));

  triangulation.triangulate (to_polygon (*p), param, trans);

  return polygons_from_graph<P, db::DCplxTrans> (tris, trans.inverted ());
}

template <class P>
static std::vector<P> triangulate_dpolygon_v (const P *p, const std::vector<db::DPoint> &vertexes, double max_area = 0.0, double min_b = 0.0)
{
  db::plc::Graph tris;
  db::plc::Triangulation triangulation (&tris);
  db::plc::TriangulationParameters param;
  param.min_b = min_b;
  param.max_area = max_area;

  db::DCplxTrans trans = db::DCplxTrans (db::DTrans (db::DPoint () - p->box ().center ()));

  triangulation.triangulate (to_polygon (*p), vertexes, param, trans);

  return polygons_from_graph<P, db::DCplxTrans> (tris, trans.inverted ());
}

template <class C>
static std::vector<C> split_poly (const C *p)
{
  std::vector<C> parts;
  db::split_polygon (*p, parts);
  return parts;
}

template <class C>
static void break_polygon (const C &poly, size_t max_vertex_count, double max_area_ratio, std::vector<C> &result)
{
  if (db::suggest_split_polygon (poly, max_vertex_count, max_area_ratio)) {

    std::vector<C> split_polygons;
    db::split_polygon (poly, split_polygons);
    for (auto p = split_polygons.begin (); p != split_polygons.end (); ++p) {
      break_polygon (*p, max_vertex_count, max_area_ratio, result);
    }

  } else {
    result.push_back (poly);
  }
}

template <class C>
static std::vector<C> break_poly (const C *p, size_t max_vertex_count, double max_area_ratio)
{
  std::vector<C> parts;
  break_polygon (*p, max_vertex_count, max_area_ratio, parts);
  return parts;
}

// ---------------------------------------------------------------
//  simple polygon binding

template <class C>
struct simple_polygon_defs
{
  typedef typename C::coord_type coord_type;
  typedef typename C::box_type box_type;
  typedef typename C::point_type point_type;
  typedef typename C::vector_type vector_type;
  typedef typename C::distance_type distance_type;
  typedef typename C::area_type area_type;
  typedef db::simple_trans<coord_type> simple_trans_type;
  typedef db::complex_trans<coord_type, double> complex_trans_type;
  typedef db::complex_trans<coord_type, coord_type> icomplex_trans_type;

  static void set_points1 (C *c, const std::vector<point_type> &pts)
  {
    c->assign_hull (pts.begin (), pts.end (), false);
  }

  static void set_points (C *c, const std::vector<point_type> &pts, bool raw)
  {
    if (raw) {
      c->assign_hull (pts.begin (), pts.end (), false);
    } else {
      c->assign_hull (pts.begin (), pts.end ());
    }
  }

  static point_type point (const C *c, size_t p)
  {
    if (c->hull ().size () > p) {
      return c->hull ()[p];
    } else {
      return point_type ();
    }
  }

  static size_t num_points (const C *c)
  {
    return c->hull ().size ();
  }

  static bool is_empty (const C *c)
  {
    return c->hull ().size () == 0;
  }

  static C *from_string (const char *s)
  {
    tl::Extractor ex (s);
    std::unique_ptr<C> c (new C ());
    ex.read (*c.get ());
    return c.release ();
  }

  static C *from_bytes (const std::vector<char> &s)
  {
    std::unique_ptr<C> c (new C ());
    db::from_bytes (s, *c);
    return c.release ();
  }

  static std::vector<char> to_bytes (const C *c)
  {
    return db::to_bytes (*c);
  }

  static C *new_v ()
  {
    return new C;
  }

  static C *new_p (const std::vector<point_type> &pts, bool raw)
  {
    C *c = new C;
    if (! raw) {
      c->assign_hull (pts.begin (), pts.end ());
    } else {
      c->assign_hull (pts.begin (), pts.end (), false);
    }
    return c;
  }

  static C *new_b (const box_type &box)
  {
    return new C (box);
  }

  static C *ellipse (const box_type &box, int npoints)
  {
    npoints = std::max (3, std::min (10000000, npoints));

    std::vector<point_type> pts;
    pts.reserve (npoints);

    double da = M_PI * 2.0 / npoints;
    for (int i = 0; i < npoints; ++i) {
      double x = box.center ().x () - box.width () * 0.5 * cos (da * i);
      double y = box.center ().y () + box.height () * 0.5 * sin (da * i);
      pts.push_back (point_type (x, y));
    }

    C *c = new C;
    c->assign_hull (pts.begin (), pts.end (), false);
    return c;
  }

  static bool inside (const C *poly, point_type pt)
  {
    return db::inside_poly (poly->begin_edge (), pt) >= 0;
  }

  static void compress (C *poly, bool remove_reflected)
  {
    poly->compress (remove_reflected);
  }

  static C &move_xy (C *poly, coord_type dx, coord_type dy)
  {
    return poly->move (vector_type (dx, dy));
  }

  static C moved_xy (const C *poly, coord_type dx, coord_type dy)
  {
    return poly->moved (vector_type (dx, dy));
  }

  static C scale (const C *p, double s)
  {
    return C (p->transformed_ext (icomplex_trans_type (s), false /*don't compress*/));
  }

  static C *transform (C *poly, const simple_trans_type &t)
  {
    poly->transform (t, false /*don't compress*/);
    return poly;
  }

  static C transformed (const C *poly, const simple_trans_type &t)
  {
    return poly->transformed_ext (t, false /*don't compress*/);
  }

  static db::simple_polygon<double> transformed_cplx (const C *poly, const complex_trans_type &t)
  {
    return poly->transformed_ext (t, false /*don't compress*/);
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area (const C *poly)
#else
  static area_type area (const C *poly)
#endif
  { 
    return poly->area ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area2 (const C *poly)
#else
  static area_type area2 (const C *poly)
#endif
  {
    return poly->area2 ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area_upper_manhattan_bound (const C *poly)
#else
  static area_type area_upper_manhattan_bound (const C *poly)
#endif
  {
    return poly->area_upper_manhattan_bound ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area_upper_manhattan_bound2 (const C *poly)
#else
  static area_type area_upper_manhattan_bound2 (const C *poly)
#endif
  {
    return poly->area_upper_manhattan_bound2 ();
  }

  static std::vector<tl::Variant> extract_rad (const C *sp)
  {
    db::polygon<coord_type> p, pnew;
    p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
    double rinner = 0.0, router = 0.0;
    unsigned int n = 1;
    if (! db::extract_rad (p, rinner, router, n, &pnew) || pnew.holes () > 0) {
      return std::vector<tl::Variant> ();
    } else {
      std::vector<tl::Variant> res;
      C spnew;
      spnew.assign_hull (pnew.begin_hull (), pnew.end_hull ());
      res.push_back (tl::Variant (spnew));
      res.push_back (rinner);
      res.push_back (router);
      res.push_back (n);
      return res;
    }
  }

  static C round_corners (const C *sp, double rinner, double router, unsigned int n)
  {
    db::polygon<coord_type> p;
    p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
    p = db::compute_rounded (p, rinner, router, n);
    tl_assert (p.holes () == 0);
    C res;
    res.assign_hull (p.begin_hull (), p.end_hull ());
    return res;
  }

  static size_t hash_value (const C *p)
  {
    return tl::hfunc (*p);
  }

  static bool touches_box (const C *p, const db::box<coord_type> &box)
  {
    return db::interact (*p, box);
  }

  static bool touches_edge (const C *p, const db::edge<coord_type> &edge)
  {
    return db::interact (*p, edge);
  }

  static bool touches_poly (const C *p, const db::polygon<coord_type> &poly)
  {
    return db::interact (*p, poly);
  }

  static bool touches_spoly (const C *p, const db::simple_polygon<coord_type> &spoly)
  {
    return db::interact (*p, spoly);
  }

  static gsi::Methods methods ()
  {
    return
    constructor ("new", &new_v, 
      "@brief Default constructor: creates an empty (invalid) polygon"
    ) +
    constructor ("new", &new_p, gsi::arg ("pts"), gsi::arg ("raw", false),
      "@brief Constructor given the points of the simple polygon\n"
      "\n"
      "@param pts The points forming the simple polygon\n"
      "@param raw If true, the points are taken as they are (see below)\n"
      "\n"
      "If the 'raw' argument is set to true, the points are taken as they are. "
      "Specifically no removal of redundant points or joining of coincident edges will take place. "
      "In effect, polygons consisting of a single point or two points can be constructed as "
      "well as polygons with duplicate points. "
      "Note that such polygons may cause problems in some applications.\n"
      "\n"
      "Regardless of raw mode, the point list will be adjusted such that the first point "
      "is the lowest-leftmost one and the orientation is clockwise always.\n"
      "\n"
      "The 'raw' argument has been added in version 0.24.\n"
    ) +
    constructor ("new", &new_b, gsi::arg ("box"),
      "@brief Constructor converting a box to a polygon\n"
      "\n"
      "@param box The box to convert to a polygon\n"
    ) +
    constructor ("ellipse", &ellipse, gsi::arg ("box"), gsi::arg ("n"),
      "@brief Creates a simple polygon approximating an ellipse\n"
      "\n"
      "@param box The bounding box of the ellipse\n"
      "@param n The number of points that will be used to approximate the ellipse\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method ("<", &C::less, gsi::arg ("p"),
      "@brief Returns a value indicating whether self is less than p\n"
      "@param p The object to compare against\n"
      "This operator is provided to establish some, not necessarily a certain sorting order\n"
      "\n"
      "This method has been introduced in version 0.25."
    ) +
    method ("==", &C::equal, gsi::arg ("p"),
      "@brief Returns a value indicating whether self is equal to p\n"
      "@param p The object to compare against\n"
    ) +
    method ("!=", &C::not_equal, gsi::arg ("p"),
      "@brief Returns a value indicating whether self is not equal to p\n"
      "@param p The object to compare against\n"
    ) +
    method_ext ("hash", &hash_value,
      "@brief Computes a hash value\n"
      "Returns a hash value for the given polygon. This method enables polygons as hash keys.\n"
      "\n"
      "This method has been introduced in version 0.25.\n"
    ) +
    method_ext ("points=", &set_points1, gsi::arg ("pts"),
      "@brief Sets the points of the simple polygon\n"
      "\n"
      "@param pts An array of points to assign to the simple polygon\n"
      "\n"
      "See the constructor description for details about raw mode.\n"
    ) +
    method_ext ("set_points", &set_points, gsi::arg ("pts"), gsi::arg ("raw", false),
      "@brief Sets the points of the simple polygon\n"
      "\n"
      "@param pts An array of points to assign to the simple polygon\n"
      "@param raw If true, the points are taken as they are\n"
      "\n"
      "See the constructor description for details about raw mode.\n"
      "\n"
      "This method has been added in version 0.24.\n"
    ) +
    method_ext ("point", &point, gsi::arg ("p"),
      "@brief Gets a specific point of the contour"
      "@param p The index of the point to get\n"
      "If the index of the point is not a valid index, a default value is returned.\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method_ext ("num_points", &num_points,
      "@brief Gets the number of points"
    ) +
    iterator ("each_point", &C::begin_hull, &C::end_hull, 
      "@brief Iterates over the points that make up the simple polygon"
    ) +
    iterator ("each_edge", &C::begin_edge, 
      "@brief Iterates over the edges that make up the simple polygon"
    ) +
    method_ext ("is_empty?", &is_empty,
      "@brief Returns a value indicating whether the polygon is empty\n"
    ) +
    method ("is_rectilinear?", &C::is_rectilinear,
      "@brief Returns a value indicating whether the polygon is rectilinear\n"
    ) +
    method ("is_halfmanhattan?", &C::is_halfmanhattan,
      "@brief Returns a value indicating whether the polygon is half-manhattan\n"
      "Half-manhattan polygons have edges which are multiples of 45 degree. These polygons can be clipped at a rectangle without "
      "potential grid snapping.\n"
      "\n"
      "This predicate was introduced in version 0.27.\n"
    ) +
    method_ext ("inside?", &inside, gsi::arg ("p"),
      "@brief Gets a value indicating whether the given point is inside the polygon\n"
      "If the given point is inside or on the edge the polygon, true is returned. "
      "This tests works well only if the polygon is not self-overlapping and oriented clockwise. "
    ) +
    method_ext ("compress", &compress, gsi::arg ("remove_reflected"),
      "@brief Compressed the simple polygon.\n"
      "\n"
      "This method removes redundant points from the polygon, such as points being on a line formed by two other points.\n"
      "If remove_reflected is true, points are also removed if the two adjacent edges form a spike.\n"
      "\n"
      "@param remove_reflected See description of the functionality.\n"
      "\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method ("is_box?", &C::is_box,
      "@brief Returns a value indicating whether the polygon is a simple box.\n"
      "\n"
      "A polygon is a box if it is identical to its bounding box.\n"
      "\n"
      "@return True if the polygon is a box.\n"
      "\n"
      "This method was introduced in version 0.23.\n"
    ) +
    method_ext ("*", &scale, gsi::arg ("f"),
      "@brief Scales the polygon by some factor\n"
      "\n"
      "Returns the scaled object. All coordinates are multiplied with the given factor and if "
      "necessary rounded."
    ) +
    method ("move", &C::move, gsi::arg ("v"),
      "@brief Moves the simple polygon.\n"
      "\n"
      "Moves the simple polygon by the given offset and returns the \n"
      "moved simple polygon. The polygon is overwritten.\n"
      "\n"
      "@param v The distance to move the simple polygon.\n"
      "\n"
      "@return The moved simple polygon.\n"
    ) +
    method_ext ("move", &move_xy, gsi::arg ("dx", 0), gsi::arg ("dy", 0),
      "@brief Moves the polygon.\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is overwritten.\n"
      "\n"
      "@param dx The x distance to move the polygon.\n"
      "@param dy The y distance to move the polygon.\n"
      "\n"
      "@return The moved polygon (self).\n"
    ) +
    method ("moved", &C::moved, gsi::arg ("v"),
      "@brief Returns the moved simple polygon\n"
      "\n"
      "Moves the simple polygon by the given offset and returns the \n"
      "moved simple polygon. The polygon is not modified.\n"
      "\n"
      "@param v The distance to move the simple polygon.\n"
      "\n"
      "@return The moved simple polygon.\n"
    ) +
    method_ext ("moved", &moved_xy, gsi::arg ("dx", 0), gsi::arg ("dy", 0),
      "@brief Returns the moved polygon (does not modify self)\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is not modified.\n"
      "\n"
      "@param dx The x distance to move the polygon.\n"
      "@param dy The y distance to move the polygon.\n"
      "\n"
      "@return The moved polygon.\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("transform", &transform, gsi::arg ("t"),
      "@brief Transforms the simple polygon (in-place)\n"
      "\n"
      "Transforms the simple polygon with the given transformation.\n"
      "Modifies self and returns self. An out-of-place version which does not modify self is \\transformed.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "This method has been introduced in version 0.24.\n"
    ) +
    method_ext ("transformed", &transformed, gsi::arg ("t"),
      "@brief Transforms the simple polygon.\n"
      "\n"
      "Transforms the simple polygon with the given transformation.\n"
      "Does not modify the simple polygon but returns the transformed polygon.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "@return The transformed simple polygon.\n"
    ) +
    method_ext ("transformed|#transformed_cplx", &transformed_cplx, gsi::arg ("t"),
      "@brief Transforms the simple polygon.\n"
      "\n"
      "Transforms the simple polygon with the given complex transformation.\n"
      "Does not modify the simple polygon but returns the transformed polygon.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "@return The transformed simple polygon.\n"
      "\n"
      "With version 0.25, the original 'transformed_cplx' method is deprecated and "
      "'transformed' takes both simple and complex transformations."
    ) +
    constructor ("from_s", &from_string, gsi::arg ("s"),
      "@brief Creates an object from a string\n"
      "Creates the object from a string representation (as returned by \\to_s)\n"
      "\n"
      "This method has been added in version 0.23.\n"
    ) +
    method ("to_s", (std::string (C::*) () const) &C::to_string,
      "@brief Returns a string representing the polygon\n"
    ) +
    constructor ("from_bytes", &from_bytes, gsi::arg ("s"),
      "@brief Creates a polygon object from a binary serialization\n"
      "Creates the object from a binary representation (as returned by \\to_bytes)\n"
      "\n"
      "This method has been added in version 0.30.9.\n"
    ) +
    method_ext ("to_bytes", &to_bytes,
      "@brief Returns a binary string representing this polygon\n"
      "\n"
      "This string can be turned into a polygon again by using \\from_bytes\n. "
      "\n"
      "This method has been added in version 0.30.9.\n"
    ) +
    method_ext ("round_corners", &round_corners, gsi::arg ("rinner"), gsi::arg ("router"), gsi::arg ("n"),
      "@brief Rounds the corners of the polygon\n"
      "\n"
      "Replaces the corners of the polygon with circle segments.\n"
      "\n"
      "@param rinner The circle radius of inner corners (in database units).\n"
      "@param router The circle radius of outer corners (in database units).\n"
      "@param n The number of points per full circle.\n"
      "\n"
      "@return The new polygon.\n"
      "\n"
      "This method was introduced in version 0.22 for integer coordinates and in 0.25 for all coordinate types.\n"
    ) +
    method_ext ("extract_rad", &extract_rad,
      "@brief Extracts the corner radii from a rounded polygon\n"
      "\n"
      "Attempts to extract the radii of rounded corner polygon. This is essentially the inverse of "
      "the \\round_corners method. If this method succeeds, if will return an array of four elements: "
      "@ul\n"
      "@li The polygon with the rounded corners replaced by edgy ones @/li\n"
      "@li The radius of the inner corners @/li\n"
      "@li The radius of the outer corners @/li\n"
      "@li The number of points per full circle @/li\n"
      "@/ul\n"
      "\n"
      "This method is based on some assumptions and may fail. In this case, an empty array is returned.\n"
      "\n"
      "If successful, the following code will more or less render the original polygon and parameters\n"
      "\n"
      "@code\n"
      "p = ...   # some polygon\n"
      "p.round_corners(ri, ro, n)\n"
      "(p2, ri2, ro2, n2) = p.extract_rad\n"
      "# -> p2 == p, ro2 == ro, ri2 == ri, n2 == n (within some limits)\n"
      "@/code\n"
      "\n"
      "This method was introduced in version 0.25.\n"
    ) +
    method_ext ("split", &split_poly<C>,
      "@brief Splits the polygon into two or more parts\n"
      "This method will break the polygon into parts. The exact breaking algorithm is unspecified, the "
      "result are smaller polygons of roughly equal number of points and 'less concave' nature. "
      "Usually the returned polygon set consists of two polygons, but there can be more. "
      "The merged region of the resulting polygons equals the original polygon with the exception of "
      "small snapping effects at new vertexes.\n"
      "\n"
      "The intended use for this method is a iteratively split polygons until the satisfy some "
      "maximum number of points limit.\n"
      "\n"
      "This method has been introduced in version 0.25.3."
    ) +
    method_ext ("break", &break_poly<C>, gsi::arg ("max_vertex_count"), gsi::arg ("max_area_ratio"),
      "@brief Splits the polygon into parts with a maximum vertex count and area ratio\n"
      "The area ratio is the ratio between the bounding box area and the polygon area. Higher values "
      "mean more 'skinny' polygons.\n"
      "\n"
      "This method will split the input polygon into pieces having a maximum of 'max_vertex_count' vertices "
      "and an area ratio less than 'max_area_ratio'. 'max_vertex_count' can be zero. In this case the "
      "limit is ignored. Also 'max_area_ratio' can be zero, in which case it is ignored as well.\n"
      "\n"
      "The method of splitting is unspecified. The algorithm will apply 'split' recursively until the "
      "parts satisfy the limits.\n"
      "\n"
      "This method has been introduced in version 0.29."
    ) +
    method_ext ("area", &area,
      "@brief Gets the area of the polygon\n"
      "The area is correct only if the polygon is not self-overlapping and the polygon is oriented clockwise."
    ) +
    method_ext ("area2", &area2,
      "@brief Gets the double area of the polygon\n"
      "This method is provided because the area for an integer-type polygon is a multiple of 1/2. "
      "Hence the double area can be expresses precisely as an integer for these types.\n"
      "\n"
      "This method has been introduced in version 0.26.1\n"
    ) +
    method_ext ("area_upper_manhattan_bound", &area_upper_manhattan_bound,
      "@hide"  //  too special
    ) +
    method_ext ("area_upper_manhattan_bound2", &area_upper_manhattan_bound2,
      "@hide"  //  too special
    ) +
    method ("perimeter", &C::perimeter,
      "@brief Gets the perimeter of the polygon\n"
      "The perimeter is sum of the lengths of all edges making up the polygon."
    ) +
    method ("bbox", &C::box,
      "@brief Returns the bounding box of the simple polygon"
    ) +
    method_ext ("touches?", &touches_box, gsi::arg ("box"),
      "@brief Returns true, if the polygon touches the given box.\n"
      "The box and the polygon touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_edge, gsi::arg ("edge"),
      "@brief Returns true, if the polygon touches the given edge.\n"
      "The edge and the polygon touch if they overlap or the edge shares at least one point with the polygon's contour.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_poly, gsi::arg ("polygon"),
      "@brief Returns true, if the polygon touches the other polygon.\n"
      "The polygons touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_spoly, gsi::arg ("simple_polygon"),
      "@brief Returns true, if the polygon touches the other polygon.\n"
      "The polygons touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    )
    ;
  }
};

static db::Polygon sp_minkowski_sum_pe (const db::SimplePolygon *sp, const db::Edge &e, bool rh)
{
  db::Polygon p;
  p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
  return db::minkowski_sum (p, e, rh);
}

static db::Polygon sp_minkowski_sum_pp (const db::SimplePolygon *sp, const db::SimplePolygon &spp, bool rh)
{
  db::Polygon p;
  p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
  db::Polygon pp;
  pp.assign_hull (spp.begin_hull (), spp.end_hull (), false);
  return db::minkowski_sum (p, pp, rh);
}

static db::Polygon sp_minkowski_sum_pb (const db::SimplePolygon *sp, const db::Box &b, bool rh)
{
  db::Polygon p;
  p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
  return db::minkowski_sum (p, b, rh);
}

static db::Polygon sp_minkowski_sum_pc (const db::SimplePolygon *sp, const std::vector<db::Point> &c, bool rh)
{
  db::Polygon p;
  p.assign_hull (sp->begin_hull (), sp->end_hull (), false);
  return db::minkowski_sum (p, c, rh);
}

static db::DSimplePolygon *transform_cplx_sp (db::DSimplePolygon *p, const db::DCplxTrans &t)
{
  p->transform (t, false /*no compression*/);
  return p;
}

static db::SimplePolygon *transform_icplx_sp (db::SimplePolygon *p, const db::ICplxTrans &t)
{
  p->transform (t, false /*no compression*/);
  return p;
}

static db::SimplePolygon transformed_icplx_sp (const db::SimplePolygon *p, const db::ICplxTrans &t)
{
  return p->transformed_ext (t, false /*no compression*/);
}

static db::SimplePolygon *spolygon_from_dspolygon (const db::DSimplePolygon &p)
{
  return new db::SimplePolygon (p, false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::DSimplePolygon spolygon_to_dspolygon (const db::SimplePolygon *p, double dbu)
{
  return db::DSimplePolygon (*p, db::CplxTrans (dbu), false, false /*don't remove reflected*/, false /*no normalize*/);
}

Class<db::SimplePolygon> decl_SimplePolygon ("db", "SimplePolygon",
  constructor ("new|#from_dpoly", &spolygon_from_dspolygon, gsi::arg ("dpolygon"),
    "@brief Creates an integer coordinate polygon from a floating-point coordinate polygon\n"
    "\n"
    "This constructor has been introduced in version 0.25 and replaces the previous static method 'from_dpoly'."
  ) +
  method_ext ("to_dtype", &spolygon_to_dspolygon, gsi::arg ("dbu", 1.0),
    "@brief Converts the polygon to a floating-point coordinate polygon\n"
    "\n"
    "The database unit can be specified to translate the integer-coordinate polygon into a floating-point coordinate "
    "polygon in micron units. The database unit is basically a scaling factor.\n"
    "\n"
    "This method has been introduced in version 0.25."
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &sp_minkowski_sum_pe, gsi::arg ("e"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of a polygon and an edge\n"
    "\n"
    "@param e The edge.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and e.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &sp_minkowski_sum_pp, gsi::arg ("p"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of a polygon and a polygon\n"
    "\n"
    "@param p The other polygon.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and p.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &sp_minkowski_sum_pb, gsi::arg ("b"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of a polygon and a box\n"
    "\n"
    "@param b The box.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and b.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &sp_minkowski_sum_pc, gsi::arg ("c"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of a polygon and a contour of points (a trace)\n"
    "\n"
    "@param c The contour (a series of points forming the trace).\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and c.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("transform", &transform_icplx_sp, gsi::arg ("t"),
    "@brief Transforms the simple polygon with a complex transformation (in-place)\n"
    "\n"
    "Transforms the simple polygon with the given complex transformation.\n"
    "Modifies self and returns self. An out-of-place version which does not modify self is \\transformed.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "This method has been introduced in version 0.24.\n"
  ) +
  method_ext ("transformed", &transformed_icplx_sp, gsi::arg ("t"),
    "@brief Transforms the simple polygon.\n"
    "\n"
    "Transforms the simple polygon with the given complex transformation.\n"
    "Does not modify the simple polygon but returns the transformed polygon.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "@return The transformed simple polygon (in this case an integer coordinate object).\n"
    "\n"
    "This method has been introduced in version 0.18.\n"
  ) +
  method_ext ("hm_decomposition", &hm_decompose_ipolygon<db::SimplePolygon>,
              gsi::arg ("with_segments", true), gsi::arg ("split_edges", false),
              gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
              gsi::arg ("dbu", 0.001),
    "@brief Performs a Hertel-Mehlhorn convex decomposition.\n"
    "\n"
    "@return A \\Region holding the polygons of the decomposition.\n"
    "The resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the polygons during following operations.\n"
    "\n" + hm_docstring + "\n" + dbu_docstring + "\n"
    "This method has been introduced in version 0.30.1."
  ) +
  method_ext ("delaunay", &triangulate_ipolygon<db::SimplePolygon>, gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0), gsi::arg ("dbu", 0.001),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "@return A \\Region holding the triangles of the refined, constrained Delaunay triangulation.\n"
    "\n" + delaunay_docstring + "\n"
    "The area value is given in terms of DBU units.\n"
    "\n" + dbu_docstring + "\n"
    "This method has been introduced in version 0.30. Since version 0.30.1, the resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the triangles during following operations."
  ) +
  method_ext ("delaunay", &triangulate_ipolygon_v<db::SimplePolygon>, gsi::arg ("vertexes"), gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0), gsi::arg ("dbu", 0.001),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "This variant of the triangulation function accepts an array of additional vertexes for the triangulation.\n"
    "\n"
    "This method has been introduced in version 0.30. Since version 0.30.1, the resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the triangles during following operations."
  ) +
  simple_polygon_defs<db::SimplePolygon>::methods (),
  "@brief A simple polygon class\n"
  "\n"
  "A simple polygon consists of an outer hull only. To support polygons with holes, use \\Polygon.\n"
  "The hull contour consists of several points. The point\n"
  "list is normalized such that the leftmost, lowest point is \n"
  "the first one. The orientation is normalized such that\n"
  "the orientation of the hull contour is clockwise.\n"
  "\n"
  "It is in no way checked that the contours are not overlapping\n"
  "This must be ensured by the user of the object\n"
  "when filling the contours.\n"
  "\n"
  "The \\SimplePolygon class stores coordinates in integer format. "
  "A class that stores floating-point coordinates is \\DSimplePolygon.\n"
  "\n"
  "See @<a href=\"/programming/database_api.xml\">The Database API@</a> for more details about the "
  "database objects."
);

static db::SimplePolygonWithProperties *new_simple_polygon_with_properties (const db::SimplePolygon &poly, db::properties_id_type pid)
{
  return new db::SimplePolygonWithProperties (poly, pid);
}

static db::SimplePolygonWithProperties *new_simple_polygon_with_properties2 (const db::SimplePolygon &poly, const std::map<tl::Variant, tl::Variant> &properties)
{
  return new db::SimplePolygonWithProperties (poly, db::properties_id (db::PropertiesSet (properties.begin (), properties.end ())));
}

Class<db::SimplePolygonWithProperties> decl_SimplePolygonWithProperties (decl_SimplePolygon, "db", "SimplePolygonWithProperties",
  gsi::properties_support_methods<db::SimplePolygonWithProperties> () +
  constructor ("new", &new_simple_polygon_with_properties, gsi::arg ("polygon"), gsi::arg ("properties_id", db::properties_id_type (0)),
    "@brief Creates a new object from a property-less object and a properties ID."
  ) +
  constructor ("new", &new_simple_polygon_with_properties2, gsi::arg ("polygon"), gsi::arg ("properties"),
    "@brief Creates a new object from a property-less object and a properties hash."
  )
  ,
  "@brief A SimplePolygon object with properties attached.\n"
  "This class represents a combination of a SimplePolygon object an user properties. User properties are "
  "stored in form of a properties ID. Convenience methods are provided to manipulate or retrieve "
  "user properties directly.\n"
  "\n"
  "This class has been introduced in version 0.30."
);

static db::DSimplePolygon *dspolygon_from_ispolygon (const db::SimplePolygon &p)
{
  return new db::DSimplePolygon (p, false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::SimplePolygon dspolygon_to_spolygon (const db::DSimplePolygon *p, double dbu)
{
  return db::SimplePolygon (*p, db::VCplxTrans (1.0 / dbu), false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::SimplePolygon transformed_vplx_sp (const db::DSimplePolygon *p, const db::VCplxTrans &t)
{
  return p->transformed_ext (t, false /*no compression*/);
}

Class<db::DSimplePolygon> decl_DSimplePolygon ("db", "DSimplePolygon",
  constructor ("new|#from_ipoly", &dspolygon_from_ispolygon, gsi::arg ("polygon"),
    "@brief Creates a floating-point coordinate polygon from an integer coordinate polygon"
    "\n"
    "This constructor has been introduced in version 0.25 and replaces the previous static method 'from_ipoly'."
  ) +
  method_ext ("to_itype", &dspolygon_to_spolygon, gsi::arg ("dbu", 1.0),
    "@brief Converts the polygon to an integer coordinate polygon"
    "\n"
    "The database unit can be specified to translate the floating-point coordinate "
    "polygon in micron units to an integer-coordinate polygon in database units. The polygon's' "
    "coordinates will be divided by the database unit.\n"
    "\n"
    "This method has been introduced in version 0.25."
  ) +
  method_ext ("transform", &transform_cplx_sp, gsi::arg ("t"),
    "@brief Transforms the simple polygon with a complex transformation (in-place)\n"
    "\n"
    "Transforms the simple polygon with the given complex transformation.\n"
    "Modifies self and returns self. An out-of-place version which does not modify self is \\transformed.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "This method has been introduced in version 0.24.\n"
  ) +
  method_ext ("transformed", &transformed_vplx_sp, gsi::arg ("t"),
    "@brief Transforms the polygon with the given complex transformation\n"
    "\n"
    "@param t The magnifying transformation to apply\n"
    "@return The transformed polygon (in this case an integer coordinate polygon)\n"
    "\n"
    "This method has been introduced in version 0.25.\n"
  ) +
  method_ext ("hm_decomposition", &hm_decompose_dpolygon<db::DSimplePolygon>,
              gsi::arg ("with_segments", true), gsi::arg ("split_edges", false),
              gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Hertel-Mehlhorn convex decomposition.\n"
    "\n"
    "@return An array holding the polygons of the decomposition.\n"
    "\n" + hm_docstring + "\n"
    "This method has been introduced in version 0.30.1."
  ) +
  method_ext ("delaunay", &triangulate_dpolygon<db::DSimplePolygon>, gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "@return An array of triangular polygons of the refined, constrained Delaunay triangulation.\n"
    "\n" + delaunay_docstring + "\n"
    "This method has been introduced in version 0.30."
  ) +
  method_ext ("delaunay", &triangulate_dpolygon_v<db::DSimplePolygon>, gsi::arg ("vertexes"), gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "This variant of the triangulation function accepts an array of additional vertexes for the triangulation.\n"
    "\n"
    "This method has been introduced in version 0.30."
  ) +
  simple_polygon_defs<db::DSimplePolygon>::methods (),
  "@brief A simple polygon class\n"
  "\n"
  "A simple polygon consists of an outer hull only. To support polygons with holes, use \\DPolygon.\n"
  "The contour consists of several points. The point\n"
  "list is normalized such that the leftmost, lowest point is \n"
  "the first one. The orientation is normalized such that\n"
  "the orientation of the hull contour is clockwise.\n"
  "\n"
  "It is in no way checked that the contours are not over-\n"
  "lapping. This must be ensured by the user of the object\n"
  "when filling the contours.\n"
  "\n"
  "The \\DSimplePolygon class stores coordinates in floating-point format which gives a higher precision "
  "for some operations. A class that stores integer coordinates is \\SimplePolygon.\n"
  "\n"
  "See @<a href=\"/programming/database_api.xml\">The Database API@</a> for more details about the "
  "database objects."
);

static db::DSimplePolygonWithProperties *new_dsimple_polygon_with_properties (const db::DSimplePolygon &poly, db::properties_id_type pid)
{
  return new db::DSimplePolygonWithProperties (poly, pid);
}

static db::DSimplePolygonWithProperties *new_dsimple_polygon_with_properties2 (const db::DSimplePolygon &poly, const std::map<tl::Variant, tl::Variant> &properties)
{
  return new db::DSimplePolygonWithProperties (poly, db::properties_id (db::PropertiesSet (properties.begin (), properties.end ())));
}

Class<db::DSimplePolygonWithProperties> decl_DSimplePolygonWithProperties (decl_DSimplePolygon, "db", "DSimplePolygonWithProperties",
  gsi::properties_support_methods<db::DSimplePolygonWithProperties> () +
  constructor ("new", &new_dsimple_polygon_with_properties, gsi::arg ("polygon"), gsi::arg ("properties_id", db::properties_id_type (0)),
    "@brief Creates a new object from a property-less object and a properties ID."
  ) +
  constructor ("new", &new_dsimple_polygon_with_properties2, gsi::arg ("polygon"), gsi::arg ("properties"),
    "@brief Creates a new object from a property-less object and a properties hash."
  )
  ,
  "@brief A DSimplePolygon object with properties attached.\n"
  "This class represents a combination of a DSimplePolygon object an user properties. User properties are "
  "stored in form of a properties ID. Convenience methods are provided to manipulate or retrieve "
  "user properties directly.\n"
  "\n"
  "This class has been introduced in version 0.30."
);

// ---------------------------------------------------------------
//  polygon binding

template <class C>
struct polygon_defs
{
  typedef typename C::coord_type coord_type;
  typedef typename C::box_type box_type;
  typedef typename C::point_type point_type;
  typedef typename C::vector_type vector_type;
  typedef typename C::distance_type distance_type;
  typedef typename C::area_type area_type;
  typedef db::simple_trans<coord_type> simple_trans_type;
  typedef db::complex_trans<coord_type, double> complex_trans_type;
  typedef db::complex_trans<coord_type, coord_type> icomplex_trans_type;

  static C *p_from_sp (const db::simple_polygon<coord_type> &sp)
  {
    C *p = new C ();
    p->assign_hull (sp.begin_hull (), sp.end_hull (), false);
    return p;
  }

  static C *ellipse (const box_type &box, int npoints)
  {
    npoints = std::max (3, std::min (10000000, npoints));

    std::vector<point_type> pts;
    pts.reserve (npoints);

    double da = M_PI * 2.0 / npoints;
    for (int i = 0; i < npoints; ++i) {
      double x = box.center ().x () - box.width () * 0.5 * cos (da * i);
      double y = box.center ().y () + box.height () * 0.5 * sin (da * i);
      pts.push_back (point_type (x, y));
    }

    C *c = new C;
    c->assign_hull (pts.begin (), pts.end (), false);
    return c;
  }

  static void set_hull1 (C *c, const std::vector<point_type> &pts)
  {
    c->assign_hull (pts.begin (), pts.end (), false);
  }

  static void set_hull (C *c, const std::vector<point_type> &pts, bool raw)
  {
    if (raw) {
      c->assign_hull (pts.begin (), pts.end (), false);
    } else {
      c->assign_hull (pts.begin (), pts.end ());
    }
  }

  static void set_hole_box (C *c, unsigned int n, const box_type &box)
  {
    if (c->holes () > n) {
      point_type pts[4] = {
        point_type (box.left (), box.bottom ()),
        point_type (box.left (), box.top ()),
        point_type (box.right (), box.top ()),
        point_type (box.right (), box.bottom ())
      };
      c->assign_hole (n, &pts[0], &pts[0] + sizeof (pts) / sizeof (pts[0]));
    }
  }

  static void set_hole (C *c, unsigned int n, const std::vector<point_type> &pts, bool raw)
  {
    if (c->holes () > n) {
      if (raw) {
        c->assign_hole (n, pts.begin (), pts.end (), false);
      } else {
        c->assign_hole (n, pts.begin (), pts.end ());
      }
    }
  }

  static size_t num_points (const C *c)
  {
    return c->vertices ();
  }

  static bool is_empty (const C *c)
  {
    return c->vertices () == 0;
  }

  static point_type point_hull (const C *c, size_t p)
  {
    if (c->hull ().size () > p) {
      return c->hull ()[p];
    } else {
      return point_type ();
    }
  }

  static point_type point_hole (const C *c, unsigned int n, size_t p)
  {
    if (c->holes () > n && c->contour (n + 1).size () > p) {
      return c->contour (n + 1)[p];
    } else {
      return point_type ();
    }
  }

  static size_t num_points_hull (const C *c)
  {
    return c->hull ().size ();
  }

  static size_t num_points_hole (const C *c, unsigned int n)
  {
    return c->contour (n + 1).size ();
  }

  static void insert_hole (C *c, const std::vector<point_type> &pts, bool raw)
  {
    if (raw) {
      return c->insert_hole (pts.begin (), pts.end (), false);
    } else {
      return c->insert_hole (pts.begin (), pts.end ());
    }
  }

  static void insert_hole_box (C *c, const box_type &box)
  {
    point_type pts[4] = {
      point_type (box.left (), box.bottom ()),
      point_type (box.left (), box.top ()),
      point_type (box.right (), box.top ()),
      point_type (box.right (), box.bottom ())
    };
    return c->insert_hole (&pts[0], &pts[0] + sizeof (pts) / sizeof (pts[0]));
  }

  static void sort_holes (C *c)
  {
    c->sort_holes ();
  }

  static C *from_string (const char *s)
  {
    tl::Extractor ex (s);
    std::unique_ptr<C> c (new C ());
    ex.read (*c.get ());
    return c.release ();
  }

  static C *from_bytes (const std::vector<char> &s)
  {
    std::unique_ptr<C> c (new C ());
    db::from_bytes (s, *c);
    return c.release ();
  }

  static std::vector<char> to_bytes (const C *c)
  {
    return db::to_bytes (*c);
  }

  static C *new_v ()
  {
    return new C;
  }

  static C *new_p (const std::vector<point_type> &pts, bool raw)
  {
    C *c = new C;
    if (raw) {
      c->assign_hull (pts.begin (), pts.end (), false);
    } else {
      c->assign_hull (pts.begin (), pts.end ());
    }
    return c;
  }

  static C *new_b (const box_type &box)
  {
    return new C (box);
  }

  static void size_xy (C *poly, coord_type dx, coord_type dy, unsigned int mode)
  {
    poly->size (dx, dy, mode);
  }

  static void size_dm (C *poly, coord_type d, unsigned int mode)
  {
    poly->size (d, d, mode);
  }

  static void size_dvm (C *poly, const db::Vector &dv, unsigned int mode)
  {
    poly->size (dv.x (), dv.y (), mode);
  }

  static C sized_xy (const C *poly, coord_type dx, coord_type dy, unsigned int mode)
  {
    return poly->sized (dx, dy, mode);
  }

  static C sized_dm (const C *poly, coord_type d, unsigned int mode)
  {
    return poly->sized (d, d, mode);
  }

  static C sized_dvm (const C *poly, const db::Vector &dv, unsigned int mode)
  {
    return poly->sized (dv.x (), dv.y (), mode);
  }

  static bool inside (const C *poly, point_type pt)
  {
    return db::inside_poly (poly->begin_edge (), pt) >= 0;
  }

  static C &move_xy (C *poly, coord_type dx, coord_type dy)
  {
    return poly->move (vector_type (dx, dy));
  }

  static C moved_xy (const C *poly, coord_type dx, coord_type dy)
  {
    return poly->moved (vector_type (dx, dy));
  }

  static C scale (const C *p, double s)
  {
    return C (p->transformed_ext (icomplex_trans_type (s), false /*no compression*/));
  }

  static void compress (C *poly, bool remove_reflected)
  {
    poly->compress (remove_reflected);
  }

  static C *transform (C *poly, const simple_trans_type &t)
  {
    poly->transform (t, false /*no compression*/);
    return poly;
  }

  static C transformed (const C *poly, const simple_trans_type &t)
  {
    return poly->transformed_ext (t, false /*no compression*/);
  }

  static db::polygon<double> transformed_cplx (const C *poly, const complex_trans_type &t)
  {
    return poly->transformed_ext (t, false /*no compression*/);
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area (const C *poly)
#else
  static area_type area (const C *poly)
#endif
  { 
    return poly->area ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area2 (const C *poly)
#else
  static area_type area2 (const C *poly)
#endif
  {
    return poly->area2 ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area_upper_manhattan_bound (const C *poly)
#else
  static area_type area_upper_manhattan_bound (const C *poly)
#endif
  {
    return poly->area_upper_manhattan_bound ();
  }

#if defined(HAVE_64BIT_COORD)
  //  workaround for missing 128bit binding of GSI
  static double area_upper_manhattan_bound2 (const C *poly)
#else
  static area_type area_upper_manhattan_bound2 (const C *poly)
#endif
  {
    return poly->area_upper_manhattan_bound2 ();
  }

  static std::vector<tl::Variant> extract_rad (const C *p)
  {
    C pnew;
    double rinner = 0.0, router = 0.0;
    unsigned int n = 1;
    if (! db::extract_rad (*p, rinner, router, n, &pnew)) {
      return std::vector<tl::Variant> ();
    } else {
      std::vector<tl::Variant> res;
      res.push_back (tl::Variant (pnew));
      res.push_back (rinner);
      res.push_back (router);
      res.push_back (n);
      return res;
    }
  }

  static C round_corners (const C *p, double rinner, double router, unsigned int n)
  {
    return db::compute_rounded (*p, rinner, router, n);
  }

  static size_t hash_value (const C *p)
  {
    return tl::hfunc (*p);
  }

  static bool touches_box (const C *p, const db::box<coord_type> &box)
  {
    return db::interact (*p, box);
  }

  static bool touches_edge (const C *p, const db::edge<coord_type> &edge)
  {
    return db::interact (*p, edge);
  }

  static bool touches_poly (const C *p, const db::polygon<coord_type> &poly)
  {
    return db::interact (*p, poly);
  }

  static bool touches_spoly (const C *p, const db::simple_polygon<coord_type> &spoly)
  {
    return db::interact (*p, spoly);
  }

  static gsi::Methods methods ()
  {
    return
    constructor ("new", &new_v, 
      "@brief Creates an empty (invalid) polygon"
    ) +
    constructor ("new", &p_from_sp, gsi::arg ("sp"),
      "@brief Creates a polygon from a simple polygon\n"
      "@param sp The simple polygon that is converted into the polygon\n"
      "This method was introduced in version 0.22.\n"
    ) +
    constructor ("new", &new_p, gsi::arg ("pts"), gsi::arg ("raw", false),
      "@brief Creates a polygon from a point array for the hull\n"
      "\n"
      "@param pts The points forming the polygon hull\n"
      "@param raw If true, the point list won't be modified (see \\assign_hull)\n"
      "\n"
      "The 'raw' argument was added in version 0.24.\n"
    ) +
    constructor ("new", &new_b, gsi::arg ("box"),
      "@brief Creates a polygon from a box\n"
      "\n"
      "@param box The box to convert to a polygon\n"
    ) +
    constructor ("ellipse", &ellipse, gsi::arg ("box"), gsi::arg ("n"),
      "@brief Creates a simple polygon approximating an ellipse\n"
      "\n"
      "@param box The bounding box of the ellipse\n"
      "@param n The number of points that will be used to approximate the ellipse\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method ("<", &C::less, gsi::arg ("p"),
      "@brief Returns a value indicating whether self is less than p\n"
      "@param p The object to compare against\n"
      "This operator is provided to establish some, not necessarily a certain sorting order\n"
    ) +
    method ("==", &C::equal, gsi::arg ("p"),
      "@brief Returns a value indicating whether the polygons are equal\n"
      "@param p The object to compare against\n"
    ) +
    method ("!=", &C::not_equal, gsi::arg ("p"),
      "@brief Returns a value indicating whether the polygons are not equal\n"
      "@param p The object to compare against\n"
    ) +
    method_ext ("is_empty?", &is_empty,
      "@brief Returns a value indicating whether the polygon is empty\n"
    ) +
    method ("is_rectilinear?", &C::is_rectilinear,
      "@brief Returns a value indicating whether the polygon is rectilinear\n"
    ) +
    method ("is_halfmanhattan?", &C::is_halfmanhattan,
      "@brief Returns a value indicating whether the polygon is half-manhattan\n"
      "Half-manhattan polygons have edges which are multiples of 45 degree. These polygons can be clipped at a rectangle without "
      "potential grid snapping.\n"
      "\n"
      "This predicate was introduced in version 0.27.\n"
    ) +
    method_ext ("hash", &hash_value,
      "@brief Computes a hash value\n"
      "Returns a hash value for the given polygon. This method enables polygons as hash keys.\n"
      "\n"
      "This method has been introduced in version 0.25.\n"
    ) +
    method_ext ("hull=", &set_hull1, gsi::arg ("p"),
      "@brief Sets the points of the hull of polygon\n"
      "@param p An array of points to assign to the polygon's hull"
      "\n"
      "The 'assign_hull' variant is provided in analogy to 'assign_hole'.\n"
    ) +
    method_ext ("assign_hull", &set_hull, gsi::arg ("p"), gsi::arg ("raw", false),
      "@brief Sets the points of the hull of polygon\n"
      "@param p An array of points to assign to the polygon's hull\n"
      "@param raw If true, the points won't be compressed\n"
      "\n"
      "If the 'raw' argument is set to true, the points are taken as they are. "
      "Specifically no removal of redundant points or joining of coincident edges will take place. "
      "In effect, polygons consisting of a single point or two points can be constructed as "
      "well as polygons with duplicate points. "
      "Note that such polygons may cause problems in some applications.\n"
      "\n"
      "Regardless of raw mode, the point list will be adjusted such that the first point "
      "is the lowest-leftmost one and the orientation is clockwise always.\n"
      "\n"
      "The 'assign_hull' variant is provided in analogy to 'assign_hole'.\n"
      "\n"
      "The 'raw' argument was added in version 0.24.\n"
    ) +
    method_ext ("assign_hole", &set_hole, gsi::arg ("n"), gsi::arg ("p"), gsi::arg ("raw", false),
      "@brief Sets the points of the given hole of the polygon\n"
      "@param n The index of the hole to which the points should be assigned\n"
      "@param p An array of points to assign to the polygon's hole\n"
      "@param raw If true, the points won't be compressed (see \\assign_hull)\n"
      "If the hole index is not valid, this method does nothing.\n"
      "\n"
      "This method was introduced in version 0.18.\n"
      "The 'raw' argument was added in version 0.24.\n"
    ) +
    method_ext ("assign_hole", &set_hole_box, gsi::arg ("n"), gsi::arg ("b"),
      "@brief Sets the box as the given hole of the polygon\n"
      "@param n The index of the hole to which the points should be assigned\n"
      "@param b The box to assign to the polygon's hole\n"
      "If the hole index is not valid, this method does nothing.\n"
      "This method was introduced in version 0.23.\n"
    ) +
    method_ext ("num_points", &num_points,
      "@brief Gets the total number of points (hull plus holes)\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method_ext ("point_hull", &point_hull, gsi::arg ("p"),
      "@brief Gets a specific point of the hull\n"
      "@param p The index of the point to get\n"
      "If the index of the point is not a valid index, a default value is returned.\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method_ext ("point_hole", &point_hole, gsi::arg ("n"), gsi::arg ("p"),
      "@brief Gets a specific point of a hole\n"
      "@param n The index of the hole to which the points should be assigned\n"
      "@param p The index of the point to get\n"
      "If the index of the point or of the hole is not valid, a default value is returned.\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method_ext ("num_points_hull", &num_points_hull,
      "@brief Gets the number of points of the hull\n"
    ) +
    method_ext ("num_points_hole", &num_points_hole, gsi::arg ("n"),
      "@brief Gets the number of points of the given hole\n"
      "The argument gives the index of the hole of which the number of points "
      "are requested. The index must be less than the number of holes (see \\holes). "
    ) +
    method_ext ("insert_hole", &insert_hole, gsi::arg ("p"), gsi::arg ("raw", false),
      "@brief Inserts a hole with the given points\n"
      "@param p An array of points to insert as a new hole\n"
      "@param raw If true, the points won't be compressed (see \\assign_hull)\n"
      "\n"
      "The 'raw' argument was added in version 0.24.\n"
    ) +
    method_ext ("insert_hole", &insert_hole_box, gsi::arg ("b"),
      "@brief Inserts a hole from the given box\n"
      "@param b The box to insert as a new hole\n"
      "This method was introduced in version 0.23.\n"
    ) +
    iterator ("each_point_hull", &C::begin_hull, &C::end_hull, 
      "@brief Iterates over the points that make up the hull"
    ) +
    iterator ("each_point_hole", &C::begin_hole, &C::end_hole, gsi::arg ("n"),
      "@brief Iterates over the points that make up the nth hole\n"
      "The hole number must be less than the number of holes (see \\holes)"
    ) +
    method_ext ("sort_holes", &sort_holes,
      "@brief Brings the holes in a specific order\n"
      "This function is normalize the hole order so the comparison of two "
      "polygons does not depend on the order the holes were inserted. "
      "Polygons generated by KLayout's alorithms have their holes sorted.\n"
      "\n"
      "This method has been introduced in version 0.28.8."
    ) +
    method_ext ("size", &size_xy, gsi::arg ("dx"), gsi::arg ("dy"), gsi::arg ("mode"),
      "@brief Sizes the polygon (biasing)\n"
      "\n"
      "Shifts the contour outwards (dx,dy>0) or inwards (dx,dy<0).\n"
      "dx is the sizing in x-direction and dy is the sizing in y-direction. The sign of dx and dy should be identical.\n"
      "The sizing operation create invalid (self-overlapping, reverse oriented) contours. \n"
      "\n"
      "The mode defines at which bending angle cutoff occurs \n"
      "(0:>0, 1:>45, 2:>90, 3:>135, 4:>approx. 168, other:>approx. 179)\n"
      "\n"
      "In order to obtain a proper polygon in the general case, the\n"
      "sized polygon must be merged in 'greater than zero' wrap count mode. This is necessary since in the general case,\n"
      "sizing can be complicated operation which lets a single polygon fall apart into disjoint pieces for example.\n"
      "This can be achieved using the \\EdgeProcessor class for example:\n"
      "\n"
      "@code\n"
      "poly = ... # a RBA::Polygon\n"
      "poly.size(-50, 2)\n"
      "ep = RBA::EdgeProcessor::new\n"
      "# result is an array of RBA::Polygon objects\n"
      "result = ep.simple_merge_p2p([ poly ], false, false, 1)\n"
      "@/code\n"
    ) +
    method_ext ("size", &size_dvm, gsi::arg ("dv"), gsi::arg ("mode", (unsigned int) 2),
      "@brief Sizes the polygon (biasing)\n"
      "\n"
      "This method is equivalent to\n"
      "@code\n"
      "size(dv.x, dv.y, mode)\n"
      "@/code\n"
      "\n"
      "See \\size for a detailed description.\n"
      "\n"
      "This version has been introduced in version 0.28.\n"
    ) +
    method_ext ("size", &size_dm, gsi::arg ("d"), gsi::arg ("mode", (unsigned int) 2),
      "@brief Sizes the polygon (biasing)\n"
      "\n"
      "Shifts the contour outwards (d>0) or inwards (d<0).\n"
      "This method is equivalent to\n"
      "@code\n"
      "size(d, d, mode)\n"
      "@/code\n"
      "\n"
      "See \\size for a detailed description.\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("sized", &sized_xy, gsi::arg ("dx"), gsi::arg ("dy"), gsi::arg ("mode"),
      "@brief Sizes the polygon (biasing) without modifying self\n"
      "\n"
      "This method applies sizing to the polygon but does not modify self. Instead a sized copy "
      "is returned.\n"
      "See \\size for a description of the operation.\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("sized", &sized_dvm, gsi::arg ("dv"), gsi::arg ("mode", (unsigned int) 2),
      "@brief Sizes the polygon (biasing) without modifying self\n"
      "\n"
      "This method is equivalent to\n"
      "@code\n"
      "sized(dv.x, dv.y, mode)\n"
      "@/code\n"
      "\n"
      "See \\size and \\sized for a detailed description.\n"
      "\n"
      "This version has been introduced in version 0.28.\n"
    ) +
    method_ext ("sized", &sized_dm, gsi::arg ("d"), gsi::arg ("mode", (unsigned int) 2),
      "@brief Sizes the polygon (biasing) without modifying self\n"
      "\n"
      "Shifts the contour outwards (d>0) or inwards (d<0).\n"
      "This method is equivalent to\n"
      "@code\n"
      "sized(d, d, mode)\n"
      "@/code\n"
      "\n"
      "See \\size and \\sized for a detailed description.\n"
    ) +
    method ("holes", &C::holes,
      "@brief Returns the number of holes"
    ) +
    iterator ("each_edge", (typename C::polygon_edge_iterator (C::*)() const) (&C::begin_edge), 
      "@brief Iterates over the edges that make up the polygon\n"
      "\n"
      "This iterator will deliver all edges, including those of the holes. "
      "Hole edges are oriented counterclockwise while hull edges are oriented clockwise.\n"
    ) +
    iterator ("each_edge", (typename C::polygon_edge_iterator (C::*)(unsigned int) const) (&C::begin_edge), gsi::arg ("contour"),
      "@brief Iterates over the edges of one contour of the polygon\n"
      "\n"
      "@param contour The contour number (0 for hull, 1 for first hole ...)\n"
      "\n"
      "This iterator will deliver all edges of the contour specified by the contour parameter. "
      "The hull has contour number 0, the first hole has contour 1 etc.\n"
      "Hole edges are oriented counterclockwise while hull edges are oriented clockwise.\n"
      "\n"
      "This method was introduced in version 0.24."
    ) +
    method_ext ("inside?", &inside, gsi::arg ("p"),
      "@brief Tests, if the given point is inside the polygon\n"
      "If the given point is inside or on the edge of the polygon, true is returned. "
      "This tests works well only if the polygon is not self-overlapping and oriented clockwise. "
    ) +
    method_ext ("compress", &compress, gsi::arg ("remove_reflected"),
      "@brief Compresses the polygon.\n"
      "\n"
      "This method removes redundant points from the polygon, such as points being on a line formed by two other points.\n"
      "If remove_reflected is true, points are also removed if the two adjacent edges form a spike.\n"
      "\n"
      "@param remove_reflected See description of the functionality.\n"
      "\n"
      "This method was introduced in version 0.18.\n"
    ) +
    method ("is_box?", &C::is_box,
      "@brief Returns true, if the polygon is a simple box.\n"
      "\n"
      "A polygon is a box if it is identical to its bounding box.\n"
      "\n"
      "@return True if the polygon is a box.\n"
      "\n"
      "This method was introduced in version 0.23.\n"
    ) +
    method_ext ("*", &scale, gsi::arg ("f"),
      "@brief Scales the polygon by some factor\n"
      "\n"
      "Returns the scaled object. All coordinates are multiplied with the given factor and if "
      "necessary rounded."
    ) +
    method ("move", &C::move, gsi::arg ("v"),
      "@brief Moves the polygon.\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is overwritten.\n"
      "\n"
      "@param v The distance to move the polygon.\n"
      "\n"
      "@return The moved polygon (self).\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("move", &move_xy, gsi::arg ("dx", 0), gsi::arg ("dy", 0),
      "@brief Moves the polygon.\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is overwritten.\n"
      "\n"
      "@param dx The x distance to move the polygon.\n"
      "@param dy The y distance to move the polygon.\n"
      "\n"
      "@return The moved polygon (self).\n"
    ) +
    method ("moved", &C::moved, gsi::arg ("v"),
      "@brief Returns the moved polygon (does not modify self)\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is not modified.\n"
      "\n"
      "@param p The distance to move the polygon.\n"
      "\n"
      "@return The moved polygon.\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("moved", &moved_xy, gsi::arg ("dx", 0), gsi::arg ("dy", 0),
      "@brief Returns the moved polygon (does not modify self)\n"
      "\n"
      "Moves the polygon by the given offset and returns the \n"
      "moved polygon. The polygon is not modified.\n"
      "\n"
      "@param dx The x distance to move the polygon.\n"
      "@param dy The y distance to move the polygon.\n"
      "\n"
      "@return The moved polygon.\n"
      "\n"
      "This method has been introduced in version 0.23.\n"
    ) +
    method_ext ("transform", &transform, gsi::arg ("t"),
      "@brief Transforms the polygon (in-place)\n"
      "\n"
      "Transforms the polygon with the given transformation.\n"
      "Modifies self and returns self. An out-of-place version which does not modify self is \\transformed.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "This method has been introduced in version 0.24.\n"
    ) +
    method_ext ("transformed", &transformed, gsi::arg ("t"),
      "@brief Transforms the polygon\n"
      "\n"
      "Transforms the polygon with the given transformation.\n"
      "Does not modify the polygon but returns the transformed polygon.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "@return The transformed polygon.\n"
    ) +
    method_ext ("transformed|#transformed_cplx", &transformed_cplx, gsi::arg ("t"),
      "@brief Transforms the polygon with a complex transformation\n"
      "\n"
      "Transforms the polygon with the given complex transformation.\n"
      "Does not modify the polygon but returns the transformed polygon.\n"
      "\n"
      "@param t The transformation to apply.\n"
      "\n"
      "@return The transformed polygon.\n"
      "\n"
      "With version 0.25, the original 'transformed_cplx' method is deprecated and "
      "'transformed' takes both simple and complex transformations."
    ) +
    constructor ("from_s", &from_string, gsi::arg ("s"),
      "@brief Creates a polygon from a string\n"
      "Creates the object from a string representation (as returned by \\to_s)\n"
      "\n"
      "This method has been added in version 0.23.\n"
    ) +
    method ("to_s", (std::string (C::*) () const) &C::to_string,
      "@brief Returns a string representing the polygon\n"
    ) +
    constructor ("from_bytes", &from_bytes, gsi::arg ("s"),
      "@brief Creates a polygon object from a binary serialization\n"
      "Creates the object from a binary representation (as returned by \\to_bytes)\n"
      "\n"
      "This method has been added in version 0.30.9.\n"
    ) +
    method_ext ("to_bytes", &to_bytes,
      "@brief Returns a binary string representing this polygon\n"
      "\n"
      "This string can be turned into a polygon again by using \\from_bytes\n. "
      "\n"
      "This method has been added in version 0.30.9.\n"
    ) +
    method_ext ("round_corners", &round_corners, gsi::arg ("rinner"), gsi::arg ("router"), gsi::arg ("n"),
      "@brief Rounds the corners of the polygon\n"
      "\n"
      "Replaces the corners of the polygon with circle segments.\n"
      "\n"
      "@param rinner The circle radius of inner corners (in database units).\n"
      "@param router The circle radius of outer corners (in database units).\n"
      "@param n The number of points per full circle.\n"
      "\n"
      "@return The new polygon.\n"
      "\n"
      "This method was introduced in version 0.20 for integer coordinates and in 0.25 for all coordinate types.\n"
    ) +
    method_ext ("extract_rad", &extract_rad,
      "@brief Extracts the corner radii from a rounded polygon\n"
      "\n"
      "Attempts to extract the radii of rounded corner polygon. This is essentially the inverse of "
      "the \\round_corners method. If this method succeeds, if will return an array of four elements: "
      "@ul\n"
      "@li The polygon with the rounded corners replaced by edgy ones @/li\n"
      "@li The radius of the inner corners @/li\n"
      "@li The radius of the outer corners @/li\n"
      "@li The number of points per full circle @/li\n"
      "@/ul\n"
      "\n"
      "This method is based on some assumptions and may fail. In this case, an empty array is returned.\n"
      "\n"
      "If successful, the following code will more or less render the original polygon and parameters\n"
      "\n"
      "@code\n"
      "p = ...   # some polygon\n"
      "p.round_corners(ri, ro, n)\n"
      "(p2, ri2, ro2, n2) = p.extract_rad\n"
      "# -> p2 == p, ro2 == ro, ri2 == ri, n2 == n (within some limits)\n"
      "@/code\n"
      "\n"
      "This method was introduced in version 0.25.\n"
    ) +
    method_ext ("split", &split_poly<C>,
      "@brief Splits the polygon into two or more parts\n"
      "This method will break the polygon into parts. The exact breaking algorithm is unspecified, the "
      "result are smaller polygons of roughly equal number of points and 'less concave' nature. "
      "Usually the returned polygon set consists of two polygons, but there can be more. "
      "The merged region of the resulting polygons equals the original polygon with the exception of "
      "small snapping effects at new vertexes.\n"
      "\n"
      "The intended use for this method is a iteratively split polygons until the satisfy some "
      "maximum number of points limit.\n"
      "\n"
      "This method has been introduced in version 0.25.3."
    ) +
    method_ext ("break", &break_poly<C>, gsi::arg ("max_vertex_count"), gsi::arg ("max_area_ratio"),
      "@brief Splits the polygon into parts with a maximum vertex count and area ratio\n"
      "The area ratio is the ratio between the bounding box area and the polygon area. Higher values "
      "mean more 'skinny' polygons.\n"
      "\n"
      "This method will split the input polygon into pieces having a maximum of 'max_vertex_count' vertices "
      "and an area ratio less than 'max_area_ratio'. 'max_vertex_count' can be zero. In this case the "
      "limit is ignored. Also 'max_area_ratio' can be zero, in which case it is ignored as well.\n"
      "\n"
      "The method of splitting is unspecified. The algorithm will apply 'split' recursively until the "
      "parts satisfy the limits.\n"
      "\n"
      "This method has been introduced in version 0.29."
    ) +
    method_ext ("area", &area,
      "@brief Gets the area of the polygon\n"
      "The area is correct only if the polygon is not self-overlapping and the polygon is oriented clockwise."
      "Orientation is ensured automatically in most cases.\n"
    ) +
    method_ext ("area2", &area2,
      "@brief Gets the double area of the polygon\n"
      "This method is provided because the area for an integer-type polygon is a multiple of 1/2. "
      "Hence the double area can be expresses precisely as an integer for these types.\n"
      "\n"
      "This method has been introduced in version 0.26.1\n"
    ) +
    method_ext ("area_upper_manhattan_bound", &area_upper_manhattan_bound,
      "@hide"  //  too special
    ) +
    method_ext ("area_upper_manhattan_bound2", &area_upper_manhattan_bound2,
      "@hide"  //  too special
    ) +
    method ("perimeter", &C::perimeter,
      "@brief Gets the perimeter of the polygon\n"
      "The perimeter is sum of the lengths of all edges making up the polygon.\n"
      "\n"
      "This method has been introduce in version 0.23.\n"
    ) +
    method ("bbox", &C::box,
      "@brief Returns the bounding box of the polygon\n"
      "The bounding box is the box enclosing all points of the polygon.\n"
    ) +
    method_ext ("touches?", &touches_box, gsi::arg ("box"),
      "@brief Returns true, if the polygon touches the given box.\n"
      "The box and the polygon touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_edge, gsi::arg ("edge"),
      "@brief Returns true, if the polygon touches the given edge.\n"
      "The edge and the polygon touch if they overlap or the edge shares at least one point with the polygon's contour.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_poly, gsi::arg ("polygon"),
      "@brief Returns true, if the polygon touches the other polygon.\n"
      "The polygons touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    ) +
    method_ext ("touches?", &touches_spoly, gsi::arg ("simple_polygon"),
      "@brief Returns true, if the polygon touches the other polygon.\n"
      "The polygons touch if they overlap or their contours share at least one point.\n"
      "\n"
      "This method was introduced in version 0.25.1.\n"
    )
    ;
  }
};

static db::Polygon resolved_holes (const db::Polygon *p)
{
  return db::resolve_holes (*p);
}

static void resolve_holes (db::Polygon *p)
{
  if (p->holes () > 0) {
    *p = db::resolve_holes (*p);
  }
}

static db::SimplePolygon to_simple_polygon (const db::Polygon *p)
{
  return db::polygon_to_simple_polygon (*p);
}

static db::DPolygon *transform_cplx_dp (db::DPolygon *p, const db::DCplxTrans &t)
{
  p->transform (t, false /*don't compress*/);
  return p;
}

static db::Polygon *transform_icplx_dp (db::Polygon *p, const db::ICplxTrans &t)
{
  p->transform (t, false /*don't compress*/);
  return p;
}

static db::Polygon transformed_icplx_dp (const db::Polygon *p, const db::ICplxTrans &t)
{
  return p->transformed_ext (t, false /*don't compress*/);
}

static db::Polygon smooth (const db::Polygon *p, db::Coord d, bool keep_hv)
{
  return db::smooth (*p, d, keep_hv);
}

static db::Polygon minkowski_sum_pe (const db::Polygon *p, const db::Edge &e, bool rh)
{
  return db::minkowski_sum (*p, e, rh);
}

static db::Polygon minkowski_sum_pp (const db::Polygon *p, const db::Polygon &pp, bool rh)
{
  return db::minkowski_sum (*p, pp, rh);
}

static db::Polygon minkowski_sum_pb (const db::Polygon *p, const db::Box &b, bool rh)
{
  return db::minkowski_sum (*p, b, rh);
}

static db::Polygon minkowski_sum_pc (const db::Polygon *p, const std::vector<db::Point> &c, bool rh)
{
  return db::minkowski_sum (*p, c, rh);
}

static db::Polygon *polygon_from_dpolygon (const db::DPolygon &p)
{
  return new db::Polygon (p, false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::DPolygon polygon_to_dpolygon (const db::Polygon *p, double dbu)
{
  return db::DPolygon (*p, db::CplxTrans (dbu), false, false /*don't remove reflected*/, false /*no normalize*/);
}

static bool is_convex (const db::Polygon *p)
{
  return db::is_convex (*p);
}

static std::vector<db::SimplePolygon> decompose_convex (const db::Polygon *p, int po)
{
  db::SimplePolygonContainer sc;
  db::decompose_convex (*p, db::PreferredOrientation (po), sc);
  return sc.polygons ();
}

static std::vector<db::SimplePolygon> decompose_trapezoids (const db::Polygon *p, int td_mode)
{
  db::SimplePolygonContainer sc;
  db::decompose_trapezoids (*p, db::TrapezoidDecompositionMode (td_mode), sc);
  return sc.polygons ();
}

int po_any () { return db::PO_any; }
int po_horizontal () { return db::PO_horizontal; }
int po_vertical () { return db::PO_vertical; }
int po_htrapezoids () { return db::PO_htrapezoids; }
int po_vtrapezoids () { return db::PO_vtrapezoids; }

static gsi::Methods make_po_constants ()
{
  return
    constant ("PO_any", po_any,
      "@brief A value for the preferred orientation parameter of \\decompose_convex\n"
      "This value indicates that there is not cut preference\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("PO_horizontal", po_horizontal,
      "@brief A value for the preferred orientation parameter of \\decompose_convex\n"
      "This value indicates that there only horizontal cuts are allowed\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("PO_vertical", po_vertical,
      "@brief A value for the preferred orientation parameter of \\decompose_convex\n"
      "This value indicates that there only vertical cuts are allowed\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("PO_htrapezoids", po_htrapezoids,
      "@brief A value for the preferred orientation parameter of \\decompose_convex\n"
      "This value indicates that cuts shall favor decomposition into horizontal trapezoids\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("PO_vtrapezoids", po_vtrapezoids,
      "@brief A value for the preferred orientation parameter of \\decompose_convex\n"
      "This value indicates that cuts shall favor decomposition into vertical trapezoids\n"
      "This constant has been introduced in version 0.25."
    );
}

int td_simple () { return db::TD_simple; }
int td_htrapezoids () { return db::TD_htrapezoids; }
int td_vtrapezoids () { return db::TD_vtrapezoids; }

static gsi::Methods make_td_constants ()
{
  return
    constant ("TD_simple", td_simple,
      "@brief A value for the mode parameter of \\decompose_trapezoids\n"
      "This value indicates simple decomposition mode. This mode is fast but does not make any attempts to "
      "produce less trapezoids.\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("TD_htrapezoids", td_htrapezoids,
      "@brief A value for the mode parameter of \\decompose_trapezoids\n"
      "This value indicates simple decomposition mode. This mode produces horizontal trapezoids and tries to "
      "minimize the number of trapezoids.\n"
      "This constant has been introduced in version 0.25."
    ) +
    constant ("TD_vtrapezoids", td_vtrapezoids,
      "@brief A value for the mode parameter of \\decompose_trapezoids\n"
      "This value indicates simple decomposition mode. This mode produces vertical trapezoids and tries to "
      "minimize the number of trapezoids.\n"
    );
}

Class<db::Polygon> decl_Polygon ("db", "Polygon",
  constructor ("new|#from_dpoly", &polygon_from_dpolygon, gsi::arg ("dpolygon"),
    "@brief Creates an integer coordinate polygon from a floating-point coordinate polygon\n"
    "\n"
    "This constructor has been introduced in version 0.25 and replaces the previous static method 'from_dpolygon'."
  ) +
  method_ext ("to_dtype", &polygon_to_dpolygon, gsi::arg ("dbu", 1.0),
    "@brief Converts the polygon to a floating-point coordinate polygon\n"
    "\n"
    "The database unit can be specified to translate the integer-coordinate polygon into a floating-point coordinate "
    "polygon in micron units. The database unit is basically a scaling factor.\n"
    "\n"
    "This method has been introduced in version 0.25."
  ) +
  make_po_constants () +
  method_ext ("decompose_convex", &decompose_convex, gsi::arg ("preferred_orientation", po_any (), "\\PO_any"),
    "@brief Decomposes the polygon into convex pieces\n"
    "\n"
    "This method returns a decomposition of the polygon that contains convex pieces only.\n"
    "If the polygon was convex already, the list returned has a single element which is the\n"
    "original polygon.\n"
    "\n"
    "@param preferred_orientation One of the PO_... constants\n"
    "\n"
    "This method was introduced in version 0.25.\n"
  ) +
  make_td_constants () +
  method_ext ("decompose_trapezoids", &decompose_trapezoids, gsi::arg ("mode", td_simple (), "\\TD_simple"),
    "@brief Decomposes the polygon into trapezoids\n"
    "\n"
    "This method returns a decomposition of the polygon into trapezoid pieces.\n"
    "It supports different modes for various applications. See the TD_... constants for details.\n"
    "\n"
    "@param mode One of the TD_... constants\n"
    "\n"
    "This method was introduced in version 0.25.\n"
  ) +
  method_ext ("is_convex?", &is_convex,
    "@brief Returns a value indicating whether the polygon is convex\n"
    "\n"
    "This method will return true, if the polygon is convex.\n"
    "\n"
    "This method was introduced in version 0.25.\n"
  ) +
  method_ext ("resolve_holes", &resolve_holes,
    "@brief Resolve holes by inserting cut lines and joining the holes with the hull\n"
    "\n"
    "This method modifies the polygon. The out-of-place version is \\resolved_holes.\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("resolved_holes", &resolved_holes,
    "@brief Returns a polygon without holes\n"
    "\n"
    "@return The new polygon without holes.\n"
    "\n"
    "This method does not modify the polygon but return a new polygon.\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("to_simple_polygon", &to_simple_polygon,
    "@brief Converts a polygon to a simple polygon\n"
    "\n"
    "@return The simple polygon.\n"
    "\n"
    "If the polygon contains holes, these will be resolved.\n"
    "This operation requires a well-formed polygon. Reflecting edges, self-intersections and "
    "coincident points will be removed.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("smooth", &smooth, gsi::arg ("d"), gsi::arg ("keep_hv", false),
    "@brief Smooths a polygon\n"
    "\n"
    "Remove vertices that deviate by more than the distance d from the average contour.\n"
    "The value d is basically the roughness which is removed.\n"
    "\n"
    "@param d The smoothing \"roughness\".\n"
    "@param keep_hv If true, horizontal and vertical edges will be preserved always.\n"
    "\n"
    "@return The smoothed polygon.\n"
    "\n"
    "This method was introduced in version 0.23. The 'keep_hv' optional parameter was added in version 0.27.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &minkowski_sum_pe, gsi::arg ("e"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of the polygon and an edge\n"
    "\n"
    "@param e The edge.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum with the edge e.\n"
    "\n"
    "The Minkowski sum of a polygon and an edge basically results in the area covered when "
    "\"dragging\" the polygon along the line given by the edge. The effect is similar to drawing the line "
    "with a pencil that has the shape of the given polygon.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &minkowski_sum_pp, gsi::arg ("b"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of the polygon and a polygon\n"
    "\n"
    "@param p The first argument.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and p.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &minkowski_sum_pb, gsi::arg ("b"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of the polygon and a box\n"
    "\n"
    "@param b The box.\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and the box.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("minkowski_sum|#minkowsky_sum", &minkowski_sum_pc, gsi::arg ("b"), gsi::arg ("resolve_holes"),
    "@brief Computes the Minkowski sum of the polygon and a contour of points (a trace)\n"
    "\n"
    "@param b The contour (a series of points forming the trace).\n"
    "@param resolve_holes If true, the output polygon will not contain holes, but holes are resolved by joining the holes with the hull.\n"
    "\n"
    "@return The new polygon representing the Minkowski sum of self and the contour.\n"
    "\n"
    "This method was introduced in version 0.22.\n"
  ) +
  method_ext ("transform", &transform_icplx_dp, gsi::arg ("t"),
    "@brief Transforms the polygon with a complex transformation (in-place)\n"
    "\n"
    "Transforms the polygon with the given complex transformation.\n"
    "This version modifies self and will return self as the modified polygon. An out-of-place version "
    "which does not modify self is \\transformed.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "This method was introduced in version 0.24.\n"
  ) +
  method_ext ("#transformed", &transformed_icplx_dp, gsi::arg ("t"),
    "@brief Transforms the polygon with a complex transformation\n"
    "\n"
    "Transforms the polygon with the given complex transformation.\n"
    "Does not modify the polygon but returns the transformed polygon.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "@return The transformed polygon (in this case an integer coordinate polygon).\n"
    "\n"
    "This method was introduced in version 0.18.\n"
  ) +
  method_ext ("hm_decomposition", &hm_decompose_ipolygon<db::Polygon>,
              gsi::arg ("with_segments", true), gsi::arg ("split_edges", false),
              gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
              gsi::arg ("dbu", 0.001),
    "@brief Performs a Hertel-Mehlhorn convex decomposition.\n"
    "\n"
    "@return A \\Region holding the polygons of the decomposition.\n"
    "\n"
    "The resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the polygons during following operations.\n"
    "\n" + hm_docstring + "\n" + dbu_docstring + "\n"
    "This method has been introduced in version 0.30.1."
  ) +
  method_ext ("delaunay", &triangulate_ipolygon<db::Polygon>, gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0), gsi::arg ("dbu", 0.001),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "@return A \\Region holding the triangles of the refined, constrained Delaunay triangulation.\n"
    "\n" + delaunay_docstring + "\n"
    "The area value is given in terms of DBU units.\n"
    "\n" + dbu_docstring + "\n"
    "This method has been introduced in version 0.30. Since version 0.30.1, the resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the triangles during following operations."
  ) +
  method_ext ("delaunay", &triangulate_ipolygon_v<db::Polygon>, gsi::arg ("vertexes"), gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0), gsi::arg ("dbu", 0.001),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "This variant of the triangulation function accepts an array of additional vertexes for the triangulation.\n"
    "\n"
    "This method has been introduced in version 0.30. Since version 0.30.1, the resulting region is in 'no merged semantics' mode, "
    "to avoid re-merging of the triangles during following operations."
  ) +
  polygon_defs<db::Polygon>::methods (),
  "@brief A polygon class\n"
  "\n"
  "A polygon consists of an outer hull and zero to many\n"
  "holes. Each contour consists of several points. The point\n"
  "list is normalized such that the leftmost, lowest point is \n"
  "the first one. The orientation is normalized such that\n"
  "the orientation of the hull contour is clockwise, while\n"
  "the orientation of the holes is counterclockwise.\n"
  "\n"
  "It is in no way checked that the contours are not overlapping.\n"
  "This must be ensured by the user of the object\n"
  "when filling the contours.\n"
  "\n"
  "A polygon can be asked for the number of holes using the \\holes method. "
  "\\each_point_hull delivers the points of the hull contour. \\each_point_hole delivers the points "
  "of a specific hole. \\each_edge delivers the edges (point-to-point connections) of both hull and holes. "
  "\\bbox delivers the bounding box, \\area the area and \\perimeter the perimeter of the polygon.\n"
  "\n"
  "Here's an example of how to create a polygon:\n"
  "\n"
  "@code\n"
  "hull =  [ RBA::Point::new(0, 0),       RBA::Point::new(6000, 0), \n"
  "          RBA::Point::new(6000, 3000), RBA::Point::new(0, 3000) ]\n"
  "hole1 = [ RBA::Point::new(1000, 1000), RBA::Point::new(2000, 1000), \n"
  "          RBA::Point::new(2000, 2000), RBA::Point::new(1000, 2000) ]\n"
  "hole2 = [ RBA::Point::new(3000, 1000), RBA::Point::new(4000, 1000), \n"
  "          RBA::Point::new(4000, 2000), RBA::Point::new(3000, 2000) ]\n"
  "poly = RBA::Polygon::new(hull)\n"
  "poly.insert_hole(hole1)\n"
  "poly.insert_hole(hole2)\n"
  "\n"
  "# ask the polygon for some properties\n"
  "poly.holes      # -> 2\n"
  "poly.area       # -> 16000000\n"
  "poly.perimeter  # -> 26000\n"
  "poly.bbox       # -> (0,0;6000,3000)\n"
  "@/code\n"
  "\n"
  "The \\Polygon class stores coordinates in integer format. "
  "A class that stores floating-point coordinates is \\DPolygon.\n"
  "\n"
  "See @<a href=\"/programming/database_api.xml\">The Database API@</a> for more details about the "
  "database objects."
);

static db::PolygonWithProperties *new_polygon_with_properties (const db::Polygon &poly, db::properties_id_type pid)
{
  return new db::PolygonWithProperties (poly, pid);
}

static db::PolygonWithProperties *new_polygon_with_properties2 (const db::Polygon &poly, const std::map<tl::Variant, tl::Variant> &properties)
{
  return new db::PolygonWithProperties (poly, db::properties_id (db::PropertiesSet (properties.begin (), properties.end ())));
}

Class<db::PolygonWithProperties> decl_PolygonWithProperties (decl_Polygon, "db", "PolygonWithProperties",
  gsi::properties_support_methods<db::PolygonWithProperties> () +
  constructor ("new", &new_polygon_with_properties, gsi::arg ("polygon"), gsi::arg ("properties_id", db::properties_id_type (0)),
    "@brief Creates a new object from a property-less object and a properties ID."
  ) +
  constructor ("new", &new_polygon_with_properties2, gsi::arg ("polygon"), gsi::arg ("properties"),
    "@brief Creates a new object from a property-less object and a properties hash."
  )
  ,
  "@brief A Polygon object with properties attached.\n"
  "This class represents a combination of a Polygon object an user properties. User properties are "
  "stored in form of a properties ID. Convenience methods are provided to manipulate or retrieve "
  "user properties directly.\n"
  "\n"
  "This class has been introduced in version 0.30."
);

static db::DPolygon *dpolygon_from_ipolygon (const db::Polygon &p)
{
  return new db::DPolygon (p, false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::Polygon dpolygon_to_polygon (const db::DPolygon *p, double dbu)
{
  return db::Polygon (*p, db::VCplxTrans (1.0 / dbu), false, false /*don't remove reflected*/, false /*no normalize*/);
}

static db::Polygon transformed_vcplx_dp (const db::DPolygon *p, const db::VCplxTrans &t)
{
  return p->transformed_ext (t, false /*don't compress*/);
}

Class<db::DPolygon> decl_DPolygon ("db", "DPolygon",
  constructor ("new|#from_ipoly", &dpolygon_from_ipolygon, gsi::arg ("polygon"),
    "@brief Creates a floating-point coordinate polygon from an integer coordinate polygon\n"
    "\n"
    "This constructor has been introduced in version 0.25 and replaces the previous static method 'from_ipolygon'."
  ) +
  method_ext ("to_itype", &dpolygon_to_polygon, gsi::arg ("dbu", 1.0),
    "@brief Converts the polygon to an integer coordinate polygon\n"
    "\n"
    "The database unit can be specified to translate the floating-point coordinate "
    "polygon in micron units to an integer-coordinate polygon in database units. The polygons "
    "coordinates will be divided by the database unit.\n"
    "\n"
    "This method has been introduced in version 0.25."
  ) +
  method_ext ("transform", &transform_cplx_dp, gsi::arg ("t"),
    "@brief Transforms the polygon with a complex transformation (in-place)\n"
    "\n"
    "Transforms the polygon with the given complex transformation.\n"
    "Modifies self and returns self. An out-of-place version which does not modify self is \\transformed.\n"
    "\n"
    "@param t The transformation to apply.\n"
    "\n"
    "This method has been introduced in version 0.24.\n"
  ) +
  method_ext ("transformed", &transformed_vcplx_dp, gsi::arg ("t"),
    "@brief Transforms the polygon with the given complex transformation\n"
    "\n"
    "\n"
    "@param t The magnifying transformation to apply\n"
    "@return The transformed polygon (in this case an integer coordinate polygon)\n"
    "\n"
    "This method has been introduced in version 0.25.\n"
  ) +
  method_ext ("hm_decomposition", &hm_decompose_dpolygon<db::DPolygon>,
              gsi::arg ("with_segments", true), gsi::arg ("split_edges", false),
              gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Hertel-Mehlhorn convex decomposition.\n"
    "\n"
    "@return An array holding the polygons of the decomposition.\n"
    "\n" + hm_docstring + "\n"
    "This method has been introduced in version 0.30.1."
  ) +
  method_ext ("delaunay", &triangulate_dpolygon<db::DPolygon>, gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "@return An array of triangular polygons of the refined, constrained Delaunay triangulation.\n"
    "\n" + delaunay_docstring + "\n"
    "This method has been introduced in version 0.30."
  ) +
  method_ext ("delaunay", &triangulate_dpolygon_v<db::DPolygon>, gsi::arg ("vertexes"), gsi::arg ("max_area", 0.0), gsi::arg ("min_b", 0.0),
    "@brief Performs a Delaunay triangulation of the polygon.\n"
    "\n"
    "This variant of the triangulation function accepts an array of additional vertexes for the triangulation.\n"
    "\n"
    "This method has been introduced in version 0.30."
  ) +
  polygon_defs<db::DPolygon>::methods (),
  "@brief A polygon class\n"
  "\n"
  "A polygon consists of an outer hull and zero to many\n"
  "holes. Each contour consists of several points. The point\n"
  "list is normalized such that the leftmost, lowest point is \n"
  "the first one. The orientation is normalized such that\n"
  "the orientation of the hull contour is clockwise, while\n"
  "the orientation of the holes is counterclockwise.\n"
  "\n"
  "It is in no way checked that the contours are not overlapping.\n"
  "This must be ensured by the user of the object\n"
  "when filling the contours.\n"
  "\n"
  "A polygon can be asked for the number of holes using the \\holes method. "
  "\\each_point_hull delivers the points of the hull contour. \\each_point_hole delivers the points "
  "of a specific hole. \\each_edge delivers the edges (point-to-point connections) of both hull and holes. "
  "\\bbox delivers the bounding box, \\area the area and \\perimeter the perimeter of the polygon.\n"
  "\n"
  "Here's an example of how to create a polygon:\n"
  "\n"
  "@code\n"
  "hull =  [ RBA::DPoint::new(0, 0),       RBA::DPoint::new(6000, 0), \n"
  "          RBA::DPoint::new(6000, 3000), RBA::DPoint::new(0, 3000) ]\n"
  "hole1 = [ RBA::DPoint::new(1000, 1000), RBA::DPoint::new(2000, 1000), \n"
  "          RBA::DPoint::new(2000, 2000), RBA::DPoint::new(1000, 2000) ]\n"
  "hole2 = [ RBA::DPoint::new(3000, 1000), RBA::DPoint::new(4000, 1000), \n"
  "          RBA::DPoint::new(4000, 2000), RBA::DPoint::new(3000, 2000) ]\n"
  "poly = RBA::DPolygon::new(hull)\n"
  "poly.insert_hole(hole1)\n"
  "poly.insert_hole(hole2)\n"
  "\n"
  "# ask the polygon for some properties\n"
  "poly.holes      # -> 2\n"
  "poly.area       # -> 16000000.0\n"
  "poly.perimeter  # -> 26000.0\n"
  "poly.bbox       # -> (0,0;6000,3000)\n"
  "@/code\n"
  "\n"
  "The \\DPolygon class stores coordinates in floating-point format which gives a higher precision "
  "for some operations. A class that stores integer coordinates is \\Polygon.\n"
  "\n"
  "See @<a href=\"/programming/database_api.xml\">The Database API@</a> for more details about the "
  "database objects."
);

static db::DPolygonWithProperties *new_dpolygon_with_properties (const db::DPolygon &poly, db::properties_id_type pid)
{
  return new db::DPolygonWithProperties (poly, pid);
}

static db::DPolygonWithProperties *new_dpolygon_with_properties2 (const db::DPolygon &poly, const std::map<tl::Variant, tl::Variant> &properties)
{
  return new db::DPolygonWithProperties (poly, db::properties_id (db::PropertiesSet (properties.begin (), properties.end ())));
}

Class<db::DPolygonWithProperties> decl_DPolygonWithProperties (decl_DPolygon, "db", "DPolygonWithProperties",
  gsi::properties_support_methods<db::DPolygonWithProperties> () +
  constructor ("new", &new_dpolygon_with_properties, gsi::arg ("polygon"), gsi::arg ("properties_id", db::properties_id_type (0)),
    "@brief Creates a new object from a property-less object and a properties ID."
  ) +
  constructor ("new", &new_dpolygon_with_properties2, gsi::arg ("polygon"), gsi::arg ("properties"),
    "@brief Creates a new object from a property-less object and a properties hash."
  )
  ,
  "@brief A DPolygon object with properties attached.\n"
  "This class represents a combination of a DPolygon object an user properties. User properties are "
  "stored in form of a properties ID. Convenience methods are provided to manipulate or retrieve "
  "user properties directly.\n"
  "\n"
  "This class has been introduced in version 0.30."
);

}
