// Copyright (c) 2014
// INRIA Saclay-Ile de France (France)
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.2/NewKernel_d/include/CGAL/NewKernel_d/Types/Weighted_point.h $
// $Id: Weighted_point.h 53ed991b5de 2020-08-27T15:39:08+02:00 Marc Glisse
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Marc Glisse

#ifndef CGAL_KD_TYPE_WP_H
#define CGAL_KD_TYPE_WP_H
#include <CGAL/NewKernel_d/store_kernel.h>
#include <CGAL/boost/iterator/counting_iterator.hpp>
namespace CGAL {
namespace KerD {
template <class R_> class Weighted_point {
        typedef typename Get_type<R_, FT_tag>::type FT_;
        typedef typename Get_type<R_, Point_tag>::type        Point_;
        Point_ c_;
        FT_ w_;

        public:
        Weighted_point(){}
        Weighted_point(Point_ const&p, FT_ const&w): c_(p), w_(w) {}
        // TODO: Add a piecewise constructor?

        Point_ const& point()const{return c_;}
        FT_ const& weight()const{return w_;}
};
}

namespace CartesianDKernelFunctors {
template <class R_> struct Construct_weighted_point : Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(Construct_weighted_point)
  typedef typename Get_type<R_, Weighted_point_tag>::type        result_type;
  typedef typename Get_type<R_, Point_tag>::type        Point;
  typedef typename Get_type<R_, FT_tag>::type FT;
  result_type operator()(Point const&a, FT const&b)const{
    return result_type(a,b);
  }
  // Not really needed
  result_type operator()()const{
    typename Get_functor<R_, Construct_ttag<Point_tag> >::type cp(this->kernel());
#if defined(BOOST_MSVC) && (BOOST_MSVC == 1900)
#  pragma warning(push)
#  pragma warning(disable: 4309)
#endif
    return result_type(cp(),0);
#if defined(BOOST_MSVC) && (BOOST_MSVC == 1900)
#  pragma warning(pop)
#endif
  }
};

template <class R_> struct Point_drop_weight {
  CGAL_FUNCTOR_INIT_IGNORE(Point_drop_weight)
  typedef typename Get_type<R_, Weighted_point_tag>::type        argument_type;
  typedef typename Get_type<R_, Point_tag>::type const&                result_type;
  // Returning a reference is fragile

  result_type operator()(argument_type const&s)const{
    return s.point();
  }
};

template <class R_> struct Point_weight {
  CGAL_FUNCTOR_INIT_IGNORE(Point_weight)
  typedef typename Get_type<R_, Weighted_point_tag>::type        argument_type;
  typedef typename Get_type<R_, FT_tag>::type                        result_type;

  result_type operator()(argument_type const&s)const{
    return s.weight();
  }
};

template <class R_> struct Power_distance : private Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(Power_distance)
  typedef typename Get_type<R_, Weighted_point_tag>::type        first_argument_type;
  typedef first_argument_type                                        second_argument_type;
  typedef typename Get_type<R_, FT_tag>::type                        result_type;

  result_type operator()(first_argument_type const&a, second_argument_type const&b)const{
    typename Get_functor<R_, Point_drop_weight_tag>::type pdw(this->kernel());
    typename Get_functor<R_, Point_weight_tag>::type pw(this->kernel());
    typename Get_functor<R_, Squared_distance_tag>::type sd(this->kernel());
    return sd(pdw(a),pdw(b))-pw(a)-pw(b);
  }
};
template <class R_> struct Power_distance_to_point : private Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(Power_distance_to_point)
  typedef typename Get_type<R_, Weighted_point_tag>::type        first_argument_type;
  typedef typename Get_type<R_, Point_tag>::type                second_argument_type;
  typedef typename Get_type<R_, FT_tag>::type                        result_type;

  result_type operator()(first_argument_type const&a, second_argument_type const&b)const{
    typename Get_functor<R_, Point_drop_weight_tag>::type pdw(this->kernel());
    typename Get_functor<R_, Point_weight_tag>::type pw(this->kernel());
    typename Get_functor<R_, Squared_distance_tag>::type sd(this->kernel());
    return sd(pdw(a),b)-pw(a);
  }
};

template<class R_> struct Power_side_of_power_sphere : private Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(Power_side_of_power_sphere)
  typedef R_ R;
  typedef typename Get_type<R, Oriented_side_tag>::type result_type;

  template<class Iter, class Pt>
    result_type operator()(Iter const& f, Iter const& e, Pt const& p0) const {
      typename Get_functor<R, Power_side_of_power_sphere_raw_tag>::type ptr(this->kernel());
      typename Get_functor<R, Point_drop_weight_tag>::type pdw(this->kernel());
      typename Get_functor<R, Point_weight_tag>::type pw(this->kernel());
      return ptr (
          make_transforming_iterator (f, pdw),
          make_transforming_iterator (e, pdw),
          make_transforming_iterator (f, pw),
          make_transforming_iterator (e, pw),
          pdw (p0),
          pw (p0));
    }
};

template<class R_> struct In_flat_power_side_of_power_sphere : private Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(In_flat_power_side_of_power_sphere)
  typedef R_ R;
  typedef typename Get_type<R, Oriented_side_tag>::type result_type;

  template<class Fo, class Iter, class Pt>
    result_type operator()(Fo const& fo, Iter const& f, Iter const& e, Pt const& p0) const {
      typename Get_functor<R, In_flat_power_side_of_power_sphere_raw_tag>::type ptr(this->kernel());
      typename Get_functor<R, Point_drop_weight_tag>::type pdw(this->kernel());
      typename Get_functor<R, Point_weight_tag>::type pw(this->kernel());
      return ptr (
          fo,
          make_transforming_iterator (f, pdw),
          make_transforming_iterator (e, pdw),
          make_transforming_iterator (f, pw),
          make_transforming_iterator (e, pw),
          pdw (p0),
          pw (p0));
    }
};

// Construct a point at (weighted) distance 0 from all the input
template <class R_> struct Power_center : Store_kernel<R_> {
  CGAL_FUNCTOR_INIT_STORE(Power_center)
  typedef typename Get_type<R_, Weighted_point_tag>::type        WPoint;
  typedef WPoint result_type;
  typedef typename Get_type<R_, Point_tag>::type        Point;
  typedef typename Get_type<R_, Vector_tag>::type       Vector;
  typedef typename Get_type<R_, FT_tag>::type FT;
  template <class Iter>
  result_type operator()(Iter f, Iter e)const{
    // 2*(x-y).c == (x^2-wx^2)-(y^2-wy^2)
    typedef typename R_::LA LA;
    typedef typename LA::Square_matrix Matrix;
    typedef typename LA::Vector Vec;
    typedef typename LA::Construct_vector CVec;
    typename Get_functor<R_, Compute_point_cartesian_coordinate_tag>::type c(this->kernel());
    typename Get_functor<R_, Construct_ttag<Point_tag> >::type cp(this->kernel());
    typename Get_functor<R_, Point_dimension_tag>::type pd(this->kernel());
    typename Get_functor<R_, Squared_distance_to_origin_tag>::type sdo(this->kernel());
    typename Get_functor<R_, Power_distance_to_point_tag>::type pdp(this->kernel());
    typename Get_functor<R_, Point_drop_weight_tag>::type pdw(this->kernel());
    typename Get_functor<R_, Point_weight_tag>::type pw(this->kernel());
    typename Get_functor<R_, Construct_ttag<Weighted_point_tag> >::type cwp(this->kernel());

    WPoint const& wp0 = *f;
    Point const& p0 = pdw(wp0);
    FT const& w0 = pw(wp0);
    int d = pd(p0);
    int k = static_cast<int>(std::distance(f,e));
    if (k == 1) return cwp(p0, -w0);
    // TODO: check for degenerate cases?
    if (k == 2) {
      typename Get_functor<R_, Difference_of_points_tag>::type dp(this->kernel());
      typename Get_functor<R_, Squared_length_tag>::type sl(this->kernel());
      typename Get_functor<R_, Translated_point_tag>::type tp(this->kernel());
      typename Get_functor<R_, Scaled_vector_tag>::type sv(this->kernel());
      WPoint const& wp1 = *++f;
      Point const& p1 = pdw(wp1);
      FT const& w1 = pw(wp1);
      Vector v01 = dp(p1, p0);
      FT l01 = sl(v01);
      FT coef = ((w0 - w1) / l01 + 1) / 2;
      return cwp(tp(p0, sv(v01, coef)), CGAL::square(coef) * l01 - w0);
    }
    if (d+1 == k) {
      FT const& n0 = sdo(p0) - w0;
      Matrix m(d,d);
      Vec b = typename CVec::Dimension()(d);
      // Write the point coordinates in lines.
      int i;
      for(i=0; ++f!=e; ++i) {
        WPoint const& wp=*f;
        Point const& p=pdw(wp);
        for(int j=0;j<d;++j) {
          m(i,j)=2*(c(p,j)-c(p0,j));
        }
        b[i] = sdo(p) - pw(wp) - n0;
      }
      CGAL_assertion (i == d);
      Vec res = typename CVec::Dimension()(d);;
      //std::cout << "Mat: " << m << "\n Vec: " << one << std::endl;
      LA::solve(res, std::move(m), std::move(b));
      //std::cout << "Sol: " << res << std::endl;
      Point center = cp(d,LA::vector_begin(res),LA::vector_end(res));
      FT const& r2 = pdp (wp0, center);
      return cwp(std::move(center), r2);
    }

    {
      // The general case. ui=p(i+1)-p0, center-p0=c=sum ai*ui, c.2ui=ui²+w-w, M*a=b with M symmetric
      typedef typename Increment_dimension<typename R_::Max_ambient_dimension>::type D2;
      typedef typename R_::LA::template Rebind_dimension<Dynamic_dimension_tag,D2>::Other LA;
      typedef typename LA::Square_matrix Matrix;
      typedef typename LA::Vector Vec;
      typedef typename LA::Construct_vector CVec;
      typename Get_functor<R_, Translated_point_tag>::type tp(this->kernel());
      typename Get_functor<R_, Scaled_vector_tag>::type sv(this->kernel());
      typename Get_functor<R_, Difference_of_points_tag>::type dp(this->kernel());
      typename Get_functor<R_, Scalar_product_tag>::type sp(this->kernel());
      typename Get_functor<R_, Sum_of_vectors_tag>::type pv(this->kernel());
      typename Get_functor<R_, Squared_length_tag>::type sl(this->kernel());

      Matrix m(k-1,k-1);
      Vec b = typename CVec::Dimension()(k-1);
      std::vector<Vector> vecs; vecs.reserve(k-1);
      for(int i=0; ++f!=e; ++i) {
        WPoint const& wp = *f;
        Point const& p = pdw(wp);
        vecs.emplace_back(dp(p, p0));
        b[i] = w0 - pw(wp);
      }
      // Only need to fill the lower half
      for(int i = 0; i < k-1; ++i){
        for(int j = i; j < k-1; ++j){
          m(j, i) = sp(vecs[i], vecs[j]);
#if ! EIGEN_VERSION_AT_LEAST(3, 3, 5)
          m(i, j) = m(j, i);
#endif
        }
        b[i] += m(i, i);
        b[i] /= 2;
      }
      // Assumes Eigen...
#if EIGEN_VERSION_AT_LEAST(3, 3, 5)
      Vec res = m.ldlt().solve(b);
#else
      // Older versions of Eigen use 1/highest as tolerance,
      // which we have no way to set to 0 for exact types.
      // Use something slow but that should work.
      Vec res = m.fullPivLu().solve(b);
#endif
      Vector to_center = sv(vecs[0], res[0]);
      for(int i=1;i<k-1;++i)
        to_center = pv(to_center, sv(vecs[i],res[i]));
      return cwp(tp(p0, to_center), sl(to_center) - w0);
    }
  }
};
template<class R_> struct Power_side_of_bounded_power_circumsphere : private Store_kernel<R_> {
        CGAL_FUNCTOR_INIT_STORE(Power_side_of_bounded_power_circumsphere)
        typedef typename Get_type<R_, Bounded_side_tag>::type result_type;

        template<class Iter, class P>
        result_type operator()(Iter f, Iter const& e, P const& p0) const {
          // TODO: Special case when the dimension is full.
          typename Get_functor<R_, Power_center_tag>::type pc(this->kernel());
          typename Get_functor<R_, Power_distance_tag>::type pd(this->kernel());

          // ON_UNBOUNDED_SIDE = -1
          return enum_cast<Bounded_side>(-CGAL::sign(pd(pc(f, e), p0)));
        }
};

}
CGAL_KD_DEFAULT_TYPE(Weighted_point_tag,(CGAL::KerD::Weighted_point<K>),(Point_tag),());
CGAL_KD_DEFAULT_FUNCTOR(Construct_ttag<Weighted_point_tag>,(CartesianDKernelFunctors::Construct_weighted_point<K>),(Weighted_point_tag,Point_tag),());
CGAL_KD_DEFAULT_FUNCTOR(Point_drop_weight_tag,(CartesianDKernelFunctors::Point_drop_weight<K>),(Weighted_point_tag,Point_tag),());
CGAL_KD_DEFAULT_FUNCTOR(Point_weight_tag,(CartesianDKernelFunctors::Point_weight<K>),(Weighted_point_tag,Point_tag),());
CGAL_KD_DEFAULT_FUNCTOR(Power_side_of_power_sphere_tag,(CartesianDKernelFunctors::Power_side_of_power_sphere<K>),(Weighted_point_tag),(Power_side_of_power_sphere_raw_tag,Point_drop_weight_tag,Point_weight_tag));
CGAL_KD_DEFAULT_FUNCTOR(In_flat_power_side_of_power_sphere_tag,(CartesianDKernelFunctors::In_flat_power_side_of_power_sphere<K>),(Weighted_point_tag),(In_flat_power_side_of_power_sphere_raw_tag,Point_drop_weight_tag,Point_weight_tag));
CGAL_KD_DEFAULT_FUNCTOR(Power_distance_tag,(CartesianDKernelFunctors::Power_distance<K>),(Weighted_point_tag,Point_tag),(Squared_distance_tag,Point_drop_weight_tag,Point_weight_tag));
CGAL_KD_DEFAULT_FUNCTOR(Power_distance_to_point_tag,(CartesianDKernelFunctors::Power_distance_to_point<K>),(Weighted_point_tag,Point_tag),(Squared_distance_tag,Point_drop_weight_tag,Point_weight_tag));
CGAL_KD_DEFAULT_FUNCTOR(Power_center_tag,(CartesianDKernelFunctors::Power_center<K>),(Weighted_point_tag,Point_tag,Vector_tag),(Compute_point_cartesian_coordinate_tag,Construct_ttag<Point_tag>,Construct_ttag<Weighted_point_tag>,Point_dimension_tag,Squared_distance_to_origin_tag,Point_drop_weight_tag,Point_weight_tag,Power_distance_to_point_tag,Translated_point_tag,Scaled_vector_tag,Difference_of_points_tag,Scalar_product_tag,Sum_of_vectors_tag,Squared_length_tag));
CGAL_KD_DEFAULT_FUNCTOR(Power_side_of_bounded_power_circumsphere_tag,(CartesianDKernelFunctors::Power_side_of_bounded_power_circumsphere<K>),(Weighted_point_tag),(Power_distance_tag,Power_center_tag));
} // namespace CGAL
#endif
