cgal/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h

// Copyright (c) 2012
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s): Efi Fogel <efifogel@gmail.com>

#ifndef CGAL_DRAW_ARRANGEMENT_2_H
#define CGAL_DRAW_ARRANGEMENT_2_H

#include <CGAL/license/Arrangement_on_surface_2.h>


#include <CGAL/config.h>

#include <unordered_map>
#include <cstdlib>
#include <random>

#include <CGAL/Qt/Basic_viewer.h>
#include <CGAL/Graphics_scene.h>
#include <CGAL/Graphics_scene_options.h>
#include <CGAL/Random.h>

#include <type_traits>
#include <CGAL/Arrangement_on_surface_2.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>

namespace CGAL {

namespace draw_function_for_arrangement_2
{
  template<typename Arr, typename GSOptions>
  class Draw_arr_tool
  {
  public:
    using Halfedge_const_handle=typename Arr::Halfedge_const_handle;
    using Vertex_const_handle=typename Arr::Vertex_const_handle;
    using Face_const_handle=typename Arr::Face_const_handle;
    using Ccb_halfedge_const_circulator=typename Arr::Ccb_halfedge_const_circulator;
    using Inner_ccb_const_iterator=typename Arr::Inner_ccb_const_iterator;
    using Outer_ccb_const_iterator=typename Arr::Outer_ccb_const_iterator;
    using Gt=typename Arr::Geometry_traits_2;
    using Point=typename Arr::Point_2;
    using X_monotone_curve = typename Arr::X_monotone_curve_2;

    Draw_arr_tool(Arr& a_aos, CGAL::Graphics_scene& a_gs, const GSOptions& a_gso):
      m_aos(a_aos), m_gs(a_gs), m_gso(a_gso)
    {}

    /// Add a face.
    void add_face(Face_const_handle face)
    {
      // std::cout << "add_face()\n";
      for (Inner_ccb_const_iterator it = face->inner_ccbs_begin();
           it != face->inner_ccbs_end(); ++it)
      { add_ccb(*it); }

      for (Outer_ccb_const_iterator it = face->outer_ccbs_begin();
           it != face->outer_ccbs_end(); ++it)
      {
        add_ccb(*it);
        draw_region(*it);
      }
    }

    /// Add a Connected Component of the Boundary.
    void add_ccb(Ccb_halfedge_const_circulator circ)
    {
      // std::cout << "add_ccb()\n";
      auto curr = circ;
      do {
        auto new_face = curr->twin()->face();
        if (m_visited.find(new_face) != m_visited.end()) continue;
        m_visited[new_face] = true;
        add_face(new_face);
      } while (++curr != circ);
    }

    ///! Draw a region.
    void draw_region(Ccb_halfedge_const_circulator circ)
    {
    // std::cout << "draw_region()\n";
    /* Check whether the traits has a member function called
     * approximate_2_object() and if so check whether the return type, namely
     * `Approximate_2` has an appropriate operator.
     *
     * C++20 supports concepts and `requires` expression; see, e.g.,
     * https://en.cppreference.com/w/cpp/language/constraints; thus, the first
     * condition above can be elegantly verified as follows:
     * constexpr bool has_approximate_2_object =
     *   requires(const Gt& traits) { traits.approximate_2_object(); };
     *
     * C++17 has experimental constructs called is_detected and
     * is_detected_v that can be used to achieve the same goal.
     *
     * For now we use C++14 features.
     */
      if(m_gso.colored_face(m_aos, circ->face()))
      { m_gs.face_begin(m_gso.face_color(m_aos, circ->face())); }
      else
      { m_gs.face_begin(); }

      const auto* traits = this->m_aos.geometry_traits();
      auto ext = find_smallest(circ, *traits);
      auto curr = ext;

      do {
        // Skip halfedges that are "antenas":
        while (curr->face() == curr->twin()->face()) curr = curr->twin()->next();
        draw_region_impl1(curr, *traits, 0);
        curr = curr->next();
      } while (curr != ext);

      m_gs.face_end();
    }

  /// Compile time dispatching
#if 0
    template <typename T, typename I = void>
    void draw_region_impl2(Halfedge_const_handle curr, T const&, long)
    { draw_exact_region(curr); }

    template <typename T, typename I>
    auto draw_region_impl2(Halfedge_const_handle curr, T const& approx, int) ->
      decltype(approx.template operator()<I>(X_monotone_curve{}, double{}, I{},
                                             bool{}), void())
    { draw_approximate_region(curr, approx); }

    template <typename T>
    void draw_region_impl1(Halfedge_const_handle curr, T const&, long)
    { draw_exact_region(curr); }

    template <typename T>
    auto draw_region_impl1(Halfedge_const_handle curr, T const& traits, int) ->
      decltype(traits.approximate_2_object(), void()) {
      using Approximate = typename Gt::Approximate_2;
      draw_region_impl2<Approximate, int>(curr, traits.approximate_2_object(), 0);
    }
#else
    template <typename T>
    void draw_region_impl1(Halfedge_const_handle curr, T const& traits, int)
    { draw_approximate_region(curr, traits.approximate_2_object()); }
#endif

    template <typename Kernel_, int AtanX, int AtanY>
    void draw_region_impl1
    (Halfedge_const_handle curr,
     Arr_geodesic_arc_on_sphere_traits_2<Kernel_, AtanX, AtanY> const& traits,
     int)
    {
      if(!m_gso.draw_edge(m_aos, curr))
      {  return; }

      // std::cout << "draw_region_impl1()\n";
      auto approx = traits.approximate_2_object();
      using Kernel = Kernel_;
      using Traits = Arr_geodesic_arc_on_sphere_traits_2<Kernel, AtanX, AtanY>;
      using Ak = typename Traits::Approximate_kernel;
      using Ap = typename Traits::Approximate_point_2;
      using Approx_point_3 = typename Ak::Point_3;

      std::vector<Ap> polyline;
      double error(0.01);
      bool l2r = curr->direction() == ARR_LEFT_TO_RIGHT;
      approx(curr->curve(), error, std::back_inserter(polyline), l2r);
      if (polyline.empty()) return;
      auto it = polyline.begin();
      auto x = it->dx();
      auto y = it->dy();
      auto z = it->dz();
      auto l = std::sqrt(x*x + y*y + z*z);
      Approx_point_3 prev(x/l, y/l, z/l);
      for (++it; it != polyline.end(); ++it) {
        auto x = it->dx();
        auto y = it->dy();
        auto z = it->dz();
        auto l = std::sqrt(x*x + y*y + z*z);
        Approx_point_3 next(x/l, y/l, z/l);

        if(m_gso.colored_edge(m_aos, curr))
        { m_gs.add_segment(prev, next, m_gso.edge_color(m_aos, curr)); }
        else
        { m_gs.add_segment(prev, next); }

        prev = next;
        // m_gs.add_point_in_face(*prev);
      }
    }

    /*! Draw a region using approximate coordinates.
     * Call this member function only if the geometry traits is equipped with
     * the coordinate-approximation functionality of a curve.
     * This function must be inlined (e.g., a template) to enable the
     * compiled-time dispatching in the function `draw_region()`.
     */
    template <typename Approximate>
    void draw_approximate_region(Halfedge_const_handle curr,
                                 const Approximate& approx)
    {
      // std::cout << "draw_approximate_region()\n";
      std::vector<typename Gt::Approximate_point_2> polyline;
      double error(0.01); // TODO? (this->pixel_ratio());
      bool l2r = curr->direction() == ARR_LEFT_TO_RIGHT;
      approx(curr->curve(), error, std::back_inserter(polyline), l2r);
      if (polyline.empty()) return;
      auto it = polyline.begin();
      auto prev = it++;
      for (; it != polyline.end(); prev = it++) {
        if(m_gso.draw_edge(m_aos, curr))
        {
          if(m_gso.colored_edge(m_aos, curr))
          { m_gs.add_segment(*prev, *it, m_gso.edge_color(m_aos, curr)); }
          else
          { m_gs.add_segment(*prev, *it); }
        }
        m_gs.add_point_in_face(*prev);
      }
    }

    /// Draw an exact curve.
    template <typename XMonotoneCurve>
    void draw_exact_curve(const XMonotoneCurve& curve)
    {
      const auto* traits = this->m_aos.geometry_traits();
      auto ctr_min = traits->construct_min_vertex_2_object();
      auto ctr_max = traits->construct_max_vertex_2_object();
      m_gs.add_segment(ctr_min(curve), ctr_max(curve));
    }

    /// Draw an exact region.
    void draw_exact_region(Halfedge_const_handle curr)
    {
      // this->add_point_in_face(curr->source()->point());
      draw_exact_curve(curr->curve());
    }

    /// Add all faces.
    template <typename Traits>
    void add_faces(const Traits&)
    {
      for (auto it=m_aos.unbounded_faces_begin(); it!=m_aos.unbounded_faces_end(); ++it)
      { add_face(it); }
    }

    /// Add all faces.
    template <typename Kernel_, int AtanX, int AtanY>
    void add_faces(Arr_geodesic_arc_on_sphere_traits_2<Kernel_, AtanX, AtanY> const&)
    { add_face(m_aos.faces_begin()); }

    /// Compile time dispatching
#if 0
    template <typename T>
    void draw_point_impl2(const Point& p, T const&, long) { m_gs.add_point(p); }

    template <typename T>
    auto draw_point_impl2(const Point& p, T const& approx, int) ->
      decltype(approx.operator()(p), void())
    { m_gs.add_point(approx(p)); }

    template <typename T>
    void draw_point_impl1(const Point& p, T const&, long) { m_gs.add_point(p); }

    template <typename T>
    auto draw_point_impl1(const Point& p, T const& traits, int) ->
      decltype(traits.approximate_2_object(), void()) {
      using Approximate = typename Gt::Approximate_2;
      draw_point_impl2<Approximate>(p, traits.approximate_2_object(), true);
    }
#else
    template <typename T>
    void draw_point_impl1(const Point& p, T const& traits, int,
                          bool colored, const CGAL::IO::Color& color)
    {
      if(colored)
      { m_gs.add_point(traits.approximate_2_object()(p), color); }
      else
      { m_gs.add_point(traits.approximate_2_object()(p)); }
    }
#endif

    template <typename Kernel_, int AtanX, int AtanY>
    void draw_point_impl1
    (const Point& p,
     Arr_geodesic_arc_on_sphere_traits_2<Kernel_, AtanX, AtanY> const& traits,
     int,
     bool colored,
     const CGAL::IO::Color& color)
    {
      auto approx = traits.approximate_2_object();
      using Traits = Arr_geodesic_arc_on_sphere_traits_2<Kernel_, AtanX, AtanY>;
      using Ak = typename Traits::Approximate_kernel;
      using Approx_point_3 = typename Ak::Point_3;
      auto ap = approx(p);
      auto x = ap.dx();
      auto y = ap.dy();
      auto z = ap.dz();
      auto l = std::sqrt(x*x + y*y + z*z);
      Approx_point_3 p3(x/l, y/l, z/l);
      if(colored)
      { m_gs.add_point(p3, color); }
      else
      { m_gs.add_point(p3); }
    }

    /// Draw a point.
    void draw_point(Vertex_const_handle vh)
    {
      const auto* traits = m_aos.geometry_traits();
      if(m_gso.draw_vertex(m_aos, vh))
      {
        if(m_gso.colored_vertex(m_aos, vh))
        { draw_point_impl1(vh->point(), *traits, 0, true,
                           m_gso.vertex_color(m_aos, vh)); }
        else
        { draw_point_impl1(vh->point(), *traits, 0, false, CGAL::IO::Color()); } // color will be unused
      }
    }

    template <typename Kernel, int AtanX, int AtanY>
    Halfedge_const_handle
    find_smallest(Ccb_halfedge_const_circulator circ,
                  Arr_geodesic_arc_on_sphere_traits_2<Kernel, AtanX, AtanY> const&)
    { return circ; }

    /*! Find the halfedge incident to the lexicographically smallest vertex
     * along the CCB, such that there is no other halfedge underneath.
     */
    template <typename Traits>
    Halfedge_const_handle find_smallest(Ccb_halfedge_const_circulator circ,
                                        const Traits&)
    {
      // std::cout << "find_smallest()\n";
      const auto* traits = this->m_aos.geometry_traits();
      auto cmp_xy = traits->compare_xy_2_object();
      auto cmp_y = traits->compare_y_at_x_right_2_object();

      // Find the first halfedge directed from left to right
      auto curr = circ;
      do if (curr->direction() == CGAL::ARR_LEFT_TO_RIGHT) break;
      while (++curr != circ);
      Halfedge_const_handle ext = curr;

      // Find the halfedge incident to the lexicographically smallest vertex,
      //  such that there is no other halfedge underneath.
      do {
        // Discard edges not directed from left to right:
        if (curr->direction() != CGAL::ARR_LEFT_TO_RIGHT) continue;

        auto res = cmp_xy(curr->source()->point(), ext->source()->point());

        // Discard the edges inciden to a point strictly larger than the point
        // incident to the stored extreme halfedge:
        if (res == LARGER) continue;

        // Store the edge inciden to a point strictly smaller:
        if (res == SMALLER) {
          ext = curr;
          continue;
        }

        // The incident points are equal; compare the halfedges themselves:
        if (cmp_y(curr->curve(), ext->curve(), curr->source()->point()) ==
            SMALLER)
          ext = curr;
      } while (++curr != circ);

      return ext;
    }

  /// Add all elements to be drawn.
  void add_elements()
  {
    // std::cout << "add_elements()\n";
    // std::cout << "ratio: " << this->pixel_ratio() << std::endl;
    m_visited.clear();

    if (m_aos.is_empty()) return;

    if(m_gso.are_faces_enabled())
    { add_faces(*(this->m_aos.geometry_traits())); }

    // Add edges that do not separate faces.
    if(m_gso.are_edges_enabled())
    {
      for (auto it = m_aos.edges_begin(); it != m_aos.edges_end(); ++it)
      { if (it->face()==it->twin()->face())
        {
          if(m_gso.draw_edge(m_aos, it))
          {
            if(m_gso.colored_edge(m_aos, it))
            { draw_curve(it->curve(), true, m_gso.edge_color(m_aos, it)); }
            else
            { draw_curve(it->curve(), false, CGAL::IO::Color()); }
          }
        }
      }
    }

    // Add all points
    if(m_gso.are_vertices_enabled())
    {
      for (auto it = m_aos.vertices_begin(); it != m_aos.vertices_end(); ++it)
      { draw_point(it); }
    }

    m_visited.clear();
  }

  /*! Draw a curve using approximate coordinates.
   * Call this member function only of the geometry traits is equipped with
   * the coordinate-aproximation functionality of a curve.
   * This function must be inlined (e.g., a template) to enable the
   * compiled-time dispatching in the function `draw_curve()`.
   */
  template <typename XMonotoneCurve, typename Approximate>
  void draw_approximate_curve(const XMonotoneCurve& curve,
                              const Approximate& approx,
                               bool colored, const CGAL::IO::Color& c)
    {
    std::vector<typename Gt::Approximate_point_2> polyline;
    double error(0.01); // TODO? (this->pixel_ratio());
    approx(curve, error, std::back_inserter(polyline));
    if (polyline.empty()) return;
    auto it = polyline.begin();
    auto prev = it++;
    for (; it != polyline.end(); prev = it++)
    {
      if(colored)
      { m_gs.add_segment(*prev, *it, c); }
      else
      { m_gs.add_segment(*prev, *it); }
    }

  }

  /*! Compile time dispatching
   */
#if 0
    template <typename T, typename I = void>
    void draw_curve_impl2(const X_monotone_curve& xcv, T const&, long)
    { draw_exact_curve(xcv); }

    template <typename T, typename I>
    auto draw_curve_impl2(const X_monotone_curve& xcv, T const& approx, int) ->
      decltype(approx.template operator()<I>(X_monotone_curve{}, double{}, I{},
                                             bool{}), void())
    { draw_approximate_curve(xcv, approx); }

    template <typename T>
    void draw_curve_impl1(const X_monotone_curve& xcv, T const&, long)
    { draw_exact_curve(xcv); }

    template <typename T>
    auto draw_curve_impl1(const X_monotone_curve& xcv, T const& traits, int) ->
      decltype(traits.approximate_2_object(), void()) {
      using Approximate = typename Gt::Approximate_2;
      draw_curve_impl2<Approximate, int>(xcv, traits.approximate_2_object(), 0);
    }
#else
    template <typename T>
    void draw_curve_impl1(const X_monotone_curve& xcv, T const& traits, int,
                          bool colored, const CGAL::IO::Color& c)
    { draw_approximate_curve(xcv, traits.approximate_2_object(), colored, c); }
#endif

    template <typename Kernel_, int AtanX, int AtanY>
    void draw_curve_impl1
    (const X_monotone_curve& xcv,
     Arr_geodesic_arc_on_sphere_traits_2<Kernel_, AtanX, AtanY> const& traits,
     int,
     bool colored, const CGAL::IO::Color& c)
    {
      auto approx = traits.approximate_2_object();
      using Kernel = Kernel_;
      using Traits = Arr_geodesic_arc_on_sphere_traits_2<Kernel, AtanX, AtanY>;
      using Ak = typename Traits::Approximate_kernel;
      using Ap = typename Traits::Approximate_point_2;
      using Approx_point_3 = typename Ak::Point_3;
      std::vector<Ap> apoints;
      double error(0.01);
      approx(xcv, error, std::back_inserter(apoints));
      auto it = apoints.begin();
      auto x = it->dx();
      auto y = it->dy();
      auto z = it->dz();
      auto l = std::sqrt(x*x + y*y + z*z);
      Approx_point_3 prev(x/l, y/l, z/l);
      for (++it; it != apoints.end(); ++it) {
        auto x = it->dx();
        auto y = it->dy();
        auto z = it->dz();
        auto l = std::sqrt(x*x + y*y + z*z);
        Approx_point_3 next(x/l, y/l, z/l);
        if(colored)
        { m_gs.add_segment(prev, next, c); }
        else
        { m_gs.add_segment(prev, next); }
        prev = next;
      }
    }

    /// Draw a curve.
    template <typename XMonotoneCurve>
    void draw_curve(const XMonotoneCurve& curve,
                    bool colored, const CGAL::IO::Color& c)
    {
      /* Check whether the traits has a member function called
       * approximate_2_object() and if so check whether the return type, namely
       * `Approximate_2` has an appropriate operator.
       *
       * C++20 supports concepts and `requires` expression; see, e.g.,
       * https://en.cppreference.com/w/cpp/language/constraints; thus, the first
       * condition above can be elegantly verified as follows:
       * constexpr bool has_approximate_2_object =
       *   requires(const Gt& traits) { traits.approximate_2_object(); };
       *
       * C++17 has experimental constructs called is_detected and
       * is_detected_v that can be used to achieve the same goal.
       *
       * For now we use C++14 features.
       */
#if 0
      if constexpr (std::experimental::is_detected_v<approximate_2_object_t, Gt>)
      {
        const auto* traits = this->m_aos.geometry_traits();
        auto approx = traits->approximate_2_object();
        draw_approximate_curve(curve, approx);
        return;
      }
      draw_exact_curve(curve);
#else
      const auto* traits = this->m_aos.geometry_traits();
      draw_curve_impl1(curve, *traits, 0, colored, c);
#endif
    }

  protected:
    Arr& m_aos;
    CGAL::Graphics_scene& m_gs;
    const GSOptions& m_gso;
    std::unordered_map<Face_const_handle, bool> m_visited;
  };

} // namespace draw_function_for_arrangement_2

#define CGAL_ARR_TYPE CGAL::Arrangement_on_surface_2<GeometryTraits_2, TopologyTraits>

template <typename GeometryTraits_2, typename TopologyTraits, class GSOptions>
void add_to_graphics_scene(const CGAL_ARR_TYPE& aos,
                           CGAL::Graphics_scene& graphics_scene,
                           const GSOptions& gso)
{
  draw_function_for_arrangement_2::Draw_arr_tool dar(aos, graphics_scene, gso);
  dar.add_elements();
}

template <typename GeometryTraits_2, typename TopologyTraits>
void add_to_graphics_scene(const CGAL_ARR_TYPE& aos,
                           CGAL::Graphics_scene& graphics_scene)
{
  CGAL::Graphics_scene_options<CGAL_ARR_TYPE,
                               typename CGAL_ARR_TYPE::Vertex_const_handle,
                               typename CGAL_ARR_TYPE::Halfedge_const_handle,
                               typename CGAL_ARR_TYPE::Face_const_handle>
    gso;
  gso.colored_face=[](const CGAL_ARR_TYPE&,
                      typename CGAL_ARR_TYPE::Face_const_handle) -> bool
  { return true; };

  gso.face_color=[](const CGAL_ARR_TYPE&,
                    typename CGAL_ARR_TYPE::Face_const_handle fh) -> CGAL::IO::Color
  {
    CGAL::Random random((unsigned int)(std::size_t)(&*fh));
    return get_random_color(random);
  };

  add_to_graphics_scene(aos, graphics_scene, gso);
}

#ifdef CGAL_USE_BASIC_VIEWER

/// Draw an arrangement on surface.
template <typename GeometryTraits_2, typename TopologyTraits, class GSOptions>
void draw(const CGAL_ARR_TYPE& aos, const GSOptions& gso,
          const char* title = "2D Arrangement on Surface Basic Viewer")
{
  CGAL::Graphics_scene graphics_scene;
  add_to_graphics_scene(aos, graphics_scene, gso);
  draw_graphics_scene(graphics_scene, title);

}

template <typename GeometryTraits_2, typename TopologyTraits>
void draw(const CGAL_ARR_TYPE& aos,
          const char* title = "2D Arrangement on Surface Basic Viewer")
{
  CGAL::Graphics_scene graphics_scene;
  add_to_graphics_scene(aos, graphics_scene);
  draw_graphics_scene(graphics_scene, title);
}

#endif // CGAL_USE_BASIC_VIEWER

#undef CGAL_ARR_TYPE

} // namespace CGAL

#endif