#include <Rcpp.h>
// Copyright (c) 2009  GeometryFactory (France)
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Kernel_23/include/CGAL/Kernel_23/internal/Projection_traits_base_3.h $
// $Id: include/CGAL/Kernel_23/internal/Projection_traits_base_3.h 50cfbde3b84 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Laurent Rineau


#ifndef CGAL_INTERNAL_PROJECTION_TRAITS_BASE_3_H
#define CGAL_INTERNAL_PROJECTION_TRAITS_BASE_3_H

#include <CGAL/Profile_timer.h>
#include <CGAL/intersections.h>
#include <CGAL/predicates/sign_of_determinant.h>

namespace CGAL {

namespace TriangulationProjectionTraitsCartesianFunctors {

template <class Traits>
class Projected_orientation_with_normal_3
{
  // private members
  typename Traits::Vector_3 normal;

  // private type aliases
  typedef typename Traits::K K;
  typedef typename Traits::Point_2 Point;
  typedef typename Traits::Vector_3 Vector_3;
public:
  typedef typename K::Orientation Orientation;
  typedef Orientation result_type;

  Projected_orientation_with_normal_3(const Vector_3& normal_)
    : normal(normal_)
  {
    CGAL_PROFILER("Construct Projected_orientation_with_normal_3.")
    CGAL_TIME_PROFILER("Construct Projected_orientation_with_normal_3")
  }

  Orientation operator()(const Point& p,
                         const Point& q,
                         const Point& r) const
  {
    CGAL_PROFILER("Projected_orientation_with_normal_3::operator()");
    CGAL_TIME_PROFILER("Projected_orientation_with_normal_3::operator()");
    return orientation(q-p, r-p, normal);
  }
}; // end class Projected_orientation_with_normal_3<Traits>

template <class Traits>
class Projected_side_of_oriented_circle_with_normal_3
{
  // private members
  typename Traits::Vector_3 normal;

  // private types aliases
  typedef typename Traits::K K;
  typedef typename Traits::Point_2 Point;
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::FT FT;

  typedef Projected_side_of_oriented_circle_with_normal_3<Traits> Self;

public:
  typedef typename K::Oriented_side Oriented_side;
  typedef Oriented_side result_type;

  Projected_side_of_oriented_circle_with_normal_3(const Vector_3& normal_)
    : normal(normal_)
  {
    CGAL_PROFILER("Construct Projected_side_of_oriented_circle_with_normal_3.")
    CGAL_TIME_PROFILER("Construct Projected_side_of_oriented_circle_with_normal_3.")
  }

  Oriented_side operator()(const Point& p,
                           const Point& q,
                           const Point& r,
                           const Point& t) const
  {
    CGAL_PROFILER("Projected_side_of_oriented_circle_with_normal_3::operator()")
    CGAL_TIME_PROFILER("Projected_side_of_oriented_circle_with_normal_3::operator()")
    const Vector_3& u = normal;

    const Vector_3 tp = p - t;
    const Vector_3 tq = q - t;
    const Vector_3 tr = r - t;

    const FT tp2 = tp * tp;
    const FT tq2 = tq * tq;
    const FT tr2 = tr * tr;
    const FT u2  =  u * u;

    const FT k_p = tp * u;
    const FT k_q = tq * u;
    const FT k_r = tr * u;

    return sign_of_determinant<FT>(
        tp.x(), tp.y(), tp.z(), (tp2 + k_p) * u2 - k_p * k_p,
        tr.x(), tr.y(), tr.z(), (tr2 + k_r) * u2 - k_r * k_r,
        tq.x(), tq.y(), tq.z(), (tq2 + k_q) * u2 - k_q * k_q,
         u.x(),  u.y(),  u.z(), u2 * u2);
    // Note that q and r have been swapped in the determinant above, to
    // inverse its sign.
  }
}; // end class Projected_side_of_oriented_circle_with_normal_3

template <class Traits>
class Projected_squared_distance_with_normal_3
{
  // private members
  typename Traits::Vector_3 normal;

  // private types aliases
  typedef typename Traits::K K;
  typedef typename Traits::Point_2 Point;
  typedef typename Traits::Line_2 Line;
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::FT FT;

public:
  Projected_squared_distance_with_normal_3(const Vector_3& normal_)
    : normal(normal_)
  {
    CGAL_PROFILER("Construct Projected_squared_distance_with_normal_3.")
    CGAL_TIME_PROFILER("Construct Projected_squared_distance_with_normal_3")
  }

  FT operator()(const Point& p, const Point& q)
  {
    return squared_distance(p, q);
  }

  FT operator()(const Line& line, const Point& p)
  {
    CGAL_PROFILER("Projected_squared_distance_with_normal_3::operator()")
    CGAL_TIME_PROFILER("Projected_squared_distance_with_normal_3::operator()")
    const Vector_3& vl = line.to_vector();
    const Point& pl = line.point();
    const Vector_3 v = cross_product(normal,
                                     vl);
    if(v == NULL_VECTOR) {
      // den == 0 if the line is vertical
      // In that case, the distance is the distance to the line
      const Vector_3 w = cross_product(pl - p,
                                       vl);
      return (w * w) / (vl * vl);
    }
    else {
      const FT det = determinant(normal,
                                 vl,
                                 pl - p);
      return (det * det) / ( v * v );
    }
  }
}; // end class Projected_squared_distance_with_normal_3

template <class Traits>
class Projected_intersect_3
{
  // private members
  typename Traits::Vector_3 normal;

  // private types aliases
  typedef typename Traits::K K;
  typedef typename Traits::Point_2 Point;
  typedef typename Traits::Line_2 Line;
  typedef typename Traits::Segment_2 Segment;
  typedef typename K::Plane_3 Plane_3;
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::FT FT;
public:
  Projected_intersect_3(const Vector_3& normal_)
    : normal(normal_)
  {
    CGAL_PROFILER("Construct Projected_intersect_3")
    CGAL_TIME_PROFILER("Construct Projected_intersect_3")
  }

  std::optional<std::variant<Point,Segment> >
  operator()(const Segment& s1, const Segment& s2)
  {
    CGAL_PROFILER("Projected_intersect_3::operator()")
    CGAL_TIME_PROFILER("Projected_intersect_3::operator()")
    typedef std::variant<Point, Segment> variant_type;
    const Vector_3 u1 = cross_product(s1.to_vector(), normal);
    if(u1 == NULL_VECTOR)
      return K().intersect_3_object()(s1.supporting_line(), s2);

    const Vector_3 u2 = cross_product(s2.to_vector(), normal);
    if(u2 == NULL_VECTOR)
      return K().intersect_3_object()(s1, s2.supporting_line());

    const Plane_3 plane_1(s1.source(), u1);
    const Plane_3 plane_2(s2.source(), u2);

    auto planes_intersection = intersection(plane_1, plane_2);
    if(! planes_intersection) {
#ifdef CGAL_T2_PTB_3_DEBUG
      Rcpp::Rcerr << "planes_intersection is empty\n";
#endif
      return std::nullopt;
    }
    if(const Line* line = std::get_if<Line>(&*planes_intersection))
    {
      // check if the intersection line intersects both segments by
      // checking if a point on the intersection line is between
      // the segments endpoints
      const Point& pi = line->point(0);
      if(  cross_product(normal, pi - s1.source())
         * cross_product(normal, pi - s1.target()) > FT(0)
         ||
           cross_product(normal, pi - s2.source())
         * cross_product(normal, pi - s2.target()) > FT(0) )
      {
        // the intersection of the supporting lines is not inside both segments
#ifdef CGAL_T2_PTB_3_DEBUG
        Rcpp::Rcerr << "intersection not inside\n";
#endif
        return std::nullopt;
      }
      else
      {
        // Let the plane passing through s1.source() and with normal
        // the cross product of s1.to_vector() and s2.to_vector(). That
        // plane should intersect *l, now.
        auto inter = intersection(*line, Plane_3(s1.source(),
                                                 cross_product(s1.to_vector(),
                                                               s2.to_vector())));
        if(! inter){
          return std::nullopt;
        }
        if(const Point* point = std::get_if<Point>(&*inter)){
          return std::make_optional(variant_type(*point));
        }
      }
    }
    if(std::get_if<Plane_3>(&*planes_intersection))
    {
#ifdef CGAL_T2_PTB_3_DEBUG
      Rcpp::Rcerr << "coplanar supporting lines\n";
#endif
      auto is_inside_segment = [](const Segment& s, const Point& q)
      {
        return Vector_3(q,s.source()) * Vector_3(q,s.target()) <=0;
      };

      bool src2_in_s1 = is_inside_segment(s1, s2.source());
      bool tgt2_in_s1 = is_inside_segment(s1, s2.target());
      bool src1_in_s2 = is_inside_segment(s2, s1.source());
      bool tgt1_in_s2 = is_inside_segment(s2, s1.target());

      if (src1_in_s2 && tgt1_in_s2) return std::make_optional(variant_type(s1));
      if (src2_in_s1 && tgt2_in_s1) return std::make_optional(variant_type(s2));

      if (src1_in_s2)
      {
        if (src2_in_s1)
        {
          if (cross_product(normal, Vector_3(s1.source(), s2.source())) != NULL_VECTOR)
            return std::make_optional(variant_type(Segment(s1.source(), s2.source())));
          else
            return std::make_optional(variant_type((s1.source())));
        }
        if (tgt2_in_s1)
        {
          if (cross_product(normal, Vector_3(s1.source(), s2.target())) != NULL_VECTOR)
            return std::make_optional(variant_type(Segment(s1.source(), s2.target())));
          else
            return std::make_optional(variant_type(s1.source()));
        }
        // should never get here with a Kernel with exact constructions
        return std::make_optional(variant_type(s1.source()));
      }
      if (tgt1_in_s2)
      {
        if (src2_in_s1)
        {
          if (cross_product(normal, Vector_3(s1.target(), s2.source())) != NULL_VECTOR)
            return std::make_optional(variant_type(Segment(s1.target(), s2.source())));
          else
            return std::make_optional(variant_type(s1.target()));
        }
        if (tgt2_in_s1)
        {
          if (cross_product(normal, Vector_3(s1.target(), s2.target())) != NULL_VECTOR)
            return std::make_optional(variant_type(Segment(s1.target(), s2.target())));
          else
            return std::make_optional(variant_type(s1.target()));
        }
        // should never get here with a Kernel with exact constructions
        return std::make_optional(variant_type(s1.target()));
      }
      return std::nullopt;
    }
    return std::nullopt;
  }
}; // end class Projected_intersect_3


template <class Traits>
class Less_along_axis
{
  // private members
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::Point_2 Point;
  Vector_3 base;
public:
  Less_along_axis(const Vector_3& base) : base(base)
  {
    CGAL_PROFILER("Construct Less_along_axis")
    CGAL_TIME_PROFILER("Construct Less_along_axis")
  }

  typedef bool result_type;

  bool operator() (const Point &p, const Point &q) const {
    return base * (p - q) < 0;
  }
}; // end class Less_along_axis

template <class Traits>
class Compare_along_axis
{
  // private members
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::Point_2 Point;
  Vector_3 base;
public:
  Compare_along_axis(const Vector_3& base) : base(base)
  {
    CGAL_PROFILER("Construct Compare_along_axis")
    CGAL_TIME_PROFILER("Construct Compare_along_axis")
  }

  typedef Comparison_result result_type;

  Comparison_result operator() (const Point &p, const Point &q) const {
    return compare(base * (p - q), 0);
  }
}; // end class Compare_along_axis

template <class Traits>
class Less_xy_along_axis
{
  // private members
  typedef typename Traits::Vector_3 Vector_3;
  typedef typename Traits::Point_2 Point;
  Vector_3 base1, base2;
public:
  Less_xy_along_axis(const Vector_3& base1, const Vector_3& base2) : base1(base1), base2(base2)
  {
    CGAL_PROFILER("Construct Less_xy_along_axis")
    CGAL_TIME_PROFILER("Construct Less_xy_along_axis")
  }

  typedef bool result_type;

  bool operator() (const Point &p, const Point &q) const {

    Compare_along_axis<Traits> cx(base1);
    Comparison_result crx = cx(p, q);
    if (crx == SMALLER) { return true; }
    if (crx == LARGER) { return false; }
    Less_along_axis<Traits> ly(base2);
    return ly(p, q);
  }
}; // end class Less_xy_along_axis

} // end namespace TriangulationProjectionTraitsCartesianFunctors


template < class Kernel >
class Projection_traits_base_3
{
  typedef Projection_traits_base_3<Kernel> Self;

  typename Kernel::Vector_3 n, b1, b2;

public:
  typedef typename Kernel::Vector_3 Vector_3;


  explicit Projection_traits_base_3(const Vector_3& n_)
    : n(n_)
  {
    typedef typename Kernel::FT FT;
    typedef typename Kernel::Vector_3 Vector_3;

    const FT& nx = n.x();
    const FT& ny = n.y();
    const FT& nz = n.z();
    if(CGAL::abs(nz) >= CGAL::abs(ny)) {
      b1 = Vector_3(nz, 0, -nx);
    }
    else {
      b1 = Vector_3(ny, -nx, 0);
    }
    b2 = cross_product(n, b1);
  }

  const Vector_3& normal() const
  {
    return n;
  }

  const Vector_3& base1() const{
    return b1;
  }

  const Vector_3& base2() const{
    return b2;
  }

  typedef Kernel K;
  typedef typename K::FT          FT;
  typedef typename K::Point_3     Point_2;
  typedef typename K::Segment_3   Segment_2;
  typedef typename K::Vector_3    Vector_2;
  typedef typename K::Triangle_3  Triangle_2;
  typedef typename K::Line_3      Line_2;

  typedef typename K::Angle_3                                Angle_2;
  typedef typename K::Compare_xyz_3                          Compare_xy_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
    Compare_along_axis<Self>                                 Compare_x_2;
  typedef TriangulationProjectionTraitsCartesianFunctors::
    Compare_along_axis<Self>                                 Compare_y_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
    Less_along_axis<Self>                                    Less_x_2;
  typedef TriangulationProjectionTraitsCartesianFunctors::
    Less_along_axis<Self>                                    Less_y_2;
  typedef TriangulationProjectionTraitsCartesianFunctors::
    Less_xy_along_axis<Self>                                 Less_xy_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
    Projected_orientation_with_normal_3<Self>                Orientation_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
    Projected_side_of_oriented_circle_with_normal_3<Self>    Side_of_oriented_circle_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
  Projected_squared_distance_with_normal_3<Self>             Compute_squared_distance_2;

  typedef TriangulationProjectionTraitsCartesianFunctors::
  Projected_intersect_3<Self>                                Intersect_2;

  typedef typename K::Construct_point_3   Construct_point_2;
  typedef typename K::Construct_weighted_point_3  Construct_weighted_point_2;
  typedef typename K::Construct_segment_3  Construct_segment_2;
  typedef typename K::Construct_vector_3   Construct_vector_2;
  typedef typename K::Construct_line_3     Construct_line_2;
  typedef typename K::Construct_triangle_3 Construct_triangle_2;

  typedef typename K::Construct_scaled_vector_3     Construct_scaled_vector_2;
  typedef typename K::Construct_translated_point_3  Construct_translated_point_2;
  typedef typename K::Construct_midpoint_3          Construct_midpoint_2;
  typedef typename K::Construct_circumcenter_3      Construct_circumcenter_2;
  typedef typename K::Construct_barycenter_3        Construct_barycenter_2;

  typedef typename K::Compute_area_3                Compute_area_2;
  typedef typename K::Construct_bbox_3              Construct_bbox_2;

  Less_x_2
  less_x_2_object() const
  {
    return Less_x_2(this->base1());
  }

  Less_y_2
  less_y_2_object() const
  {
    return Less_y_2(this->base2());
  }

  Less_xy_2
  less_xy_2_object() const
  {
    return Less_xy_2(this->base1(), this->base2());
  }

  Compare_x_2
  compare_x_2_object() const
  {
    return Compare_x_2(this->base1());
  }

  Compare_y_2
  compare_y_2_object() const
  {
    return Compare_y_2(this->base2());
  }

  Orientation_2
  orientation_2_object() const
  {
    return Orientation_2(this->normal());
  }

  Side_of_oriented_circle_2
  side_of_oriented_circle_2_object() const
  {
    return Side_of_oriented_circle_2(this->normal());
  }

  Compute_squared_distance_2
  compute_squared_distance_2_object() const
  {
    return Compute_squared_distance_2(this->normal());
  }

  Intersect_2
  intersect_2_object () const
  {
    return Intersect_2(this->normal());
  }

  Angle_2  angle_2_object() const
    {return Angle_2();}

  Compare_xy_2  compare_xy_2_object() const
    {return Compare_xy_2();}

  Construct_point_2  construct_point_2_object() const
    {return Construct_point_2();}

  Construct_weighted_point_2  construct_weighted_point_2_object() const
    {return Construct_weighted_point_2();}

  Construct_segment_2  construct_segment_2_object() const
    {return Construct_segment_2();}

  Construct_vector_2  construct_vector_2_object() const
    {return Construct_vector_2();}

  Construct_scaled_vector_2  construct_scaled_vector_2_object() const
    {return Construct_scaled_vector_2();}

  Construct_midpoint_2  construct_midpoint_2_object() const
    {return Construct_midpoint_2();}

  Construct_circumcenter_2  construct_circumcenter_2_object() const
    {return Construct_circumcenter_2();}

  Construct_barycenter_2  construct_barycenter_2_object() const
    {return Construct_barycenter_2();}

  Construct_translated_point_2  construct_translated_point_2_object() const
    {return Construct_translated_point_2();}

  Construct_line_2  construct_line_2_object() const
    {return Construct_line_2();}

  Construct_triangle_2  construct_triangle_2_object() const
    {return Construct_triangle_2();}

  Compute_area_2 compute_area_2_object() const
  {return Compute_area_2();}


  Construct_bbox_2  construct_bbox_2_object() const
    {return Construct_bbox_2();}


  // Special functor, not in the Kernel concept
  class Projection_to_plan {
    // Remember: Point_2 is K::Point_3
    const Point_2& plane_point;
    const Vector_3& normal;
  public:
    // Return the projection of a point to a plane passing through
    // the point 'plane_point' and with orthogonal vector normal().
    Projection_to_plan(const Point_2& plane_point_, const Self& self)
      : plane_point(plane_point_),
        normal(self.normal())
    {}

    Point_2 operator()(const Point_2& point) const
    {
      return point +
        ( ( (plane_point - point) * normal ) / (normal * normal) ) * normal;
    }
  }; // end Projection_to_plan

  Projection_to_plan projection_to_plan_object(const Point_2& plane_point) const
  {
    return Projection_to_plan(plane_point, *this);
  }

}; // end class Projection_traits_base_3<Kernel>

} // end namespace CGAL

#endif // CGAL_INTERNAL_PROJECTION_TRAITS_BASE_3_H

