// Copyright (c) 2000
// 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: https://github.com/CGAL/cgal/blob/v6.2-beta1/Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.h $
// $Id: include/CGAL/constructions/kernel_ftC2.h 431cfb5357d $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sven Schoenherr, Herve Bronnimann, Sylvain Pion

#ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC2_H
#define CGAL_CONSTRUCTIONS_KERNEL_FTC2_H

#include <CGAL/determinant.h>
#include <CGAL/number_utils.h>
#include <boost/type_traits/is_integral.hpp>

namespace CGAL {

template < class FT >
CGAL_KERNEL_INLINE
void
midpointC2( const FT &px, const FT &py,
            const FT &qx, const FT &qy,
            FT &x, FT &y )
{
  x = (px+qx) / 2;
  y = (py+qy) / 2;
}

template < class FT >
CGAL_KERNEL_LARGE_INLINE
void
determinants_for_circumcenterC2(const FT &px, const FT &py,
                                const FT &qx, const FT &qy,
                                const FT &rx, const FT &ry,
                                FT &num_x, FT &num_y, FT& den)
{
  FT dqx = qx - px;
  FT dqy = qy - py;
  FT drx = rx - px;
  FT dry = ry - py;
  FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
  FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
  den = determinant(dqx, dqy, drx, dry);
  num_x = determinant(dry, dqy, r2, q2);
  num_y = determinant(drx, dqx, r2, q2);
}

template < class FT >
CGAL_KERNEL_LARGE_INLINE
void
circumcenter_translateC2(const FT &dqx, const FT &dqy,
                         const FT &drx, const FT &dry,
                               FT &dcx,       FT &dcy)
{
  // Given 3 points P, Q, R, this function takes as input:
  // qx-px, qy-py, rx-px, ry-py.  And returns cx-px, cy-py,
  // where (cx, cy) are the coordinates of the circumcenter C.

  // What we do is intersect the bisectors.
  FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
  FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
  FT den = 2 * determinant(dqx, dqy, drx, dry);

  // The 3 points aren't collinear.
  // Hopefully, this is already checked at the upper level.
  CGAL_kernel_assertion ( ! CGAL_NTS is_zero(den) );

  // One possible optimization here is to precompute 1/den, to avoid one
  // division.  However, we lose precision, and it's maybe not worth it (?).
  dcx =   determinant (dry, dqy, r2, q2) / den;
  dcy = - determinant (drx, dqx, r2, q2) / den;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
circumcenterC2( const FT &px, const FT &py,
                const FT &qx, const FT &qy,
                const FT &rx, const FT &ry,
                FT &x, FT &y )
{
  circumcenter_translateC2<FT>(qx-px, qy-py, rx-px, ry-py, x, y);
  x += px;
  y += py;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y,
             FT &x, FT &y)
{
   FT w2 = 1 - w1;
   x = w1 * p1x + w2 * p2x;
   y = w1 * p1y + w2 * p2y;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y, const FT &w2,
             FT &x, FT &y)
{
   FT sum = w1 + w2;
   CGAL_kernel_assertion(sum != 0);
   x = (w1 * p1x + w2 * p2x) / sum;
   y = (w1 * p1y + w2 * p2y) / sum;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y, const FT &w2,
             const FT &p3x, const FT &p3y,
             FT &x, FT &y)
{
   FT w3 = 1 - w1 - w2;
   x = w1 * p1x + w2 * p2x + w3 * p3x;
   y = w1 * p1y + w2 * p2y + w3 * p3y;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y, const FT &w2,
             const FT &p3x, const FT &p3y, const FT &w3,
             FT &x, FT &y)
{
   FT sum = w1 + w2 + w3;
   CGAL_kernel_assertion(sum != 0);
   x = (w1 * p1x + w2 * p2x + w3 * p3x) / sum;
   y = (w1 * p1y + w2 * p2y + w3 * p3y) / sum;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y, const FT &w2,
             const FT &p3x, const FT &p3y, const FT &w3,
             const FT &p4x, const FT &p4y,
             FT &x, FT &y)
{
   FT w4 = 1 - w1 - w2 - w3;
   x = w1 * p1x + w2 * p2x + w3 * p3x + w4 * p4x;
   y = w1 * p1y + w2 * p2y + w3 * p3y + w4 * p4y;
}

template < class FT >
void
barycenterC2(const FT &p1x, const FT &p1y, const FT &w1,
             const FT &p2x, const FT &p2y, const FT &w2,
             const FT &p3x, const FT &p3y, const FT &w3,
             const FT &p4x, const FT &p4y, const FT &w4,
             FT &x, FT &y)
{
   FT sum = w1 + w2 + w3 + w4;
   CGAL_kernel_assertion(sum != 0);
   x = (w1 * p1x + w2 * p2x + w3 * p3x + w4 * p4x) / sum;
   y = (w1 * p1y + w2 * p2y + w3 * p3y + w4 * p4y) / sum;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
centroidC2( const FT &px, const FT &py,
            const FT &qx, const FT &qy,
            const FT &rx, const FT &ry,
            FT &x, FT &y)
{
   x = (px + qx + rx) / 3;
   y = (py + qy + ry) / 3;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
centroidC2( const FT &px, const FT &py,
            const FT &qx, const FT &qy,
            const FT &rx, const FT &ry,
            const FT &sx, const FT &sy,
            FT &x, FT &y)
{
   x = (px + qx + rx + sx) / 4;
   y = (py + qy + ry + sy) / 4;
}

template < class FT >
inline
void
line_from_pointsC2(const FT &px, const FT &py,
                   const FT &qx, const FT &qy,
                   FT &a, FT &b, FT &c)
{
  // The horizontal and vertical line get a special treatment
  // in order to make the intersection code robust for doubles
  if(py == qy){
    a = 0 ;
    if(qx > px){
      b = 1;
      c = -py;
    } else if(qx == px){
      b = 0;
      c = 0;
    }else{
      b = -1;
      c = py;
    }
  } else if(qx == px){
    b = 0;
    if(qy > py){
      a = -1;
      c = px;
    } else if (qy == py){
      a = 0;
      c = 0;
    } else {
      a = 1;
      c = -px;
    }
  } else {
    a = py - qy;
    b = qx - px;
    c = -px*a - py*b;
  }
}

template < class FT >
inline
void
line_from_point_directionC2(const FT &px, const FT &py,
                            const FT &dx, const FT &dy,
                            FT &a, FT &b, FT &c)
{
  a = - dy;
  b = dx;
  c = px*dy - py*dx;
}

template < class FT >
CGAL_KERNEL_INLINE
void
bisector_of_pointsC2(const FT &px, const FT &py,
                     const FT &qx, const FT &qy,
                     FT &a, FT &b, FT& c )
{
  a = 2 * (px - qx);
  b = 2 * (py - qy);
  c = CGAL_NTS square(qx) + CGAL_NTS square(qy) -
      CGAL_NTS square(px) - CGAL_NTS square(py);
}

template < class FT >
CGAL_KERNEL_INLINE
void
bisector_of_linesC2(const FT &pa, const FT &pb, const FT &pc,
                    const FT &qa, const FT &qb, const FT &qc,
                    FT &a, FT &b, FT &c)
{
  // We normalize the equations of the 2 lines, and we then add them.
  FT n1 = CGAL_NTS approximate_sqrt( FT(CGAL_NTS square(pa) + CGAL_NTS square(pb)) );
  FT n2 = CGAL_NTS approximate_sqrt( FT(CGAL_NTS square(qa) + CGAL_NTS square(qb)) );
  a = n2 * pa + n1 * qa;
  b = n2 * pb + n1 * qb;
  c = n2 * pc + n1 * qc;

  // Care must be taken for the case when this produces a degenerate line.
  if (a == 0 && b == 0) {
    a = n2 * pa - n1 * qa;
    b = n2 * pb - n1 * qb;
    c = n2 * pc - n1 * qc;
  }
}

template < class FT >
inline
FT
line_y_at_xC2(const FT &a, const FT &b, const FT &c, const FT &x)
{
  return (-a*x-c) / b;
}

// Silence a warning for MSVC 2017
// > include\cgal\constructions\kernel_ftc2.h(287) :
// >   warning C4723: potential divide by 0
#if defined(BOOST_MSVC)
#pragma warning(push)
#pragma warning(disable:4723)
#endif
template < class FT >
inline
void
line_get_pointC2(const FT &a, const FT &b, const FT &c, const FT &i,
                 FT &x, FT &y)
{
  if (CGAL_NTS is_zero(b))
    {

      x = -c/a;
      y = 1 - i * a;
    }
  else
    {
      x = 1 + i * b;
      y = -(a+c)/b - i * a;
    }
}
#if defined(BOOST_MSVC)
#pragma warning(pop)
#endif

template < class FT >
inline
void
perpendicular_through_pointC2(const FT &la, const FT &lb,
                              const FT &px, const FT &py,
                              FT &a, FT &b, FT &c)
{
  a = -lb;
  b = la;
  c = lb * px - la * py;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
line_project_pointC2(const FT &la, const FT &lb, const FT &lc,
                     const FT &px, const FT &py,
                     FT &x, FT &y)
{
  if (certainly(is_zero(la))) // horizontal line
  {
    x = px;
    y = -lc/lb;
  }
  else if (certainly(is_zero(lb))) // vertical line
  {
    x = -lc/la;
    y = py;
  }
  else
  {
    FT a2 = CGAL_NTS square(la);
    FT b2 = CGAL_NTS square(lb);
    FT d = a2 + b2;
    x = (b2*px - la*lb*py  - la*lc) / d;
    y = (-la*lb*px + a2*py - lb*lc) / d;
  }
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
void
squared_radiusC2(const FT &px, const FT &py,
                 const FT &qx, const FT &qy,
                 const FT &rx, const FT &ry,
                 FT &num, FT &den)
{
  // Translate r to origin to simplify the expression.
  FT prx = px - rx;
  FT pry = py - ry;
  FT pr2 = CGAL_NTS square(prx) + CGAL_NTS square(pry);
  FT qrx = qx - rx;
  FT qry = qy - ry;
  FT qr2 = CGAL_NTS square(qrx) + CGAL_NTS square(qry);

  FT num_x = determinant(qry, qr2,
                         pry, pr2);
  FT num_y = determinant(qrx, qr2,
                         prx, pr2);
  FT dden = determinant(qrx, qry,
                        prx, pry);

  num = CGAL_NTS square(num_x) + CGAL_NTS square(num_y);
  den = CGAL_NTS square(2 * dden);
}

template < class FT >
inline
FT
squared_distanceC2(const FT &px, const FT &py,
                   const FT &qx, const FT &qy)
{
  return CGAL_NTS square(px-qx) + CGAL_NTS square(py-qy);
}

template < class FT >
inline
void
squared_radiusC2(const FT &px, const FT &py,
                 const FT &qx, const FT &qy,
                 FT &num, FT &den)
{
  num = squared_distanceC2(px, py,qx, qy);
  den = 4;
}

template < class FT >
CGAL_KERNEL_INLINE
FT
scaled_distance_to_lineC2( const FT &la, const FT &lb, const FT &lc,
                           const FT &px, const FT &py)
{
  // for comparisons, use distance_to_directionsC2 instead
  // since lc is irrelevant
  return la*px + lb*py + lc;
}

template < class FT >
CGAL_KERNEL_INLINE
FT
scaled_distance_to_directionC2( const FT &la, const FT &lb,
                                const FT &px, const FT &py)
{
  // scalar product with direction
  return la*px + lb*py;
}

template < class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
scaled_distance_to_lineC2( const FT &px, const FT &py,
                           const FT &qx, const FT &qy,
                           const FT &rx, const FT &ry)
{
  return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
}

template < class RT >
void
determinants_for_weighted_circumcenterC2(const RT &px, const RT &py, const RT &pw,
                                         const RT &qx, const RT &qy, const RT &qw,
                                         const RT &rx, const RT &ry, const RT &rw,
                                         RT &num_x, RT &num_y, RT& den)
{
  RT dqx = qx - px;
  RT dqy = qy - py;
  RT dqw = qw - pw;
  RT drx = rx - px;
  RT dry = ry - py;
  RT drw = rw - pw;
  RT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry) - drw;
  RT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - dqw;
  den = determinant(dqx, dqy, drx, dry);
  num_x = determinant(dry, dqy, r2, q2);
  num_y = determinant(drx, dqx, r2, q2);
}

template < class RT >
void
weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
                                  const RT &drx, const RT &dry, const RT &drw,
                                  RT &dcx, RT &dcy)
{
  // Given 3 points P, Q, R, this function takes as input:
  // qx-px, qy-py,qw-pw,  rx-px, ry-py, rw-pw.  And returns cx-px, cy-py,
  // where (cx, cy) are the coordinates of the circumcenter C.

  // What we do is intersect the radical axis
  RT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry) - drw;
  RT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - dqw;

  RT den = RT(2) * determinant(dqx, dqy, drx, dry);

  // The 3 points aren't collinear.
  // Hopefully, this is already checked at the upper level.
  CGAL_assertion ( den != RT(0) );

  // One possible optimization here is to precompute 1/den, to avoid one
  // division.  However, we lose precision, and it's maybe not worth it (?).
  dcx =   determinant (dry, dqy, r2, q2) / den;
  dcy = - determinant (drx, dqx, r2, q2) / den;
}

template < class RT, class We>
void
weighted_circumcenterC2( const RT &px, const RT &py, const We &pw,
                         const RT &qx, const RT &qy, const We &qw,
                         const RT &rx, const RT &ry, const We &rw,
                         RT &x, RT &y )
{
  RT dqw = RT(qw-pw);
  RT drw = RT(rw-pw);

  weighted_circumcenter_translateC2<RT>(qx-px, qy-py, dqw,rx-px, ry-py,drw,x, y);
  x += px;
  y += py;
}

template < class RT >
void
weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
                                  RT &dcx, RT &dcy)
{
  // Given 2 points P, Q, this function takes as input:
  // qx-px, qy-py,qw-pw.  And returns cx-px, cy-py,
  // where (cx, cy) are the coordinates of the circumcenter C.

  // What we do is intersect the radical axis
  RT dqx2 = CGAL_NTS square(dqx);
  RT dqy2 = CGAL_NTS square(dqy);
  RT q2 = dqx2 + dqy2 - dqw;

  RT den = RT(2) * dqx2 + RT(2) * dqy2;
  CGAL_assertion ( den != RT(0) );

  dcx =   determinant (dqy, q2, dqw) / den;
  dcy = - determinant (dqx, q2, dqw) / den;
}

template < class RT, class We>
void
weighted_circumcenterC2(const RT &px, const RT &py, const We &pw,
                        const RT &qx, const RT &qy, const We &qw,
                        RT &x, RT &y)
{
  RT dqw = RT(qw-pw);

  weighted_circumcenter_translateC2<RT>(qx-px, qy-py, dqw, x, y);
  x += px;
  y += py;
}

template< class FT >
FT
power_productC2(const FT &px, const FT &py, const FT &pw,
                const FT &qx, const FT &qy, const FT &qw)
{
  // computes the power product of two weighted points
  FT qpx = qx - px;
  FT qpy = qy - py;
  FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy);
  return qp2 - pw - qw;
}

template < class RT , class We>
void
radical_axisC2(const RT &px, const RT &py, const We &pw,
               const RT &qx, const RT &qy, const We &qw,
               RT &a, RT &b, RT& c )
{
  a =  RT(2)*(px - qx);
  b =  RT(2)*(py - qy);
  c = - CGAL_NTS square(px) - CGAL_NTS square(py)
      + CGAL_NTS square(qx) + CGAL_NTS square(qy)
      + RT(pw) - RT(qw);
}

template< class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
squared_radius_orthogonal_circleC2(const FT &px, const FT &py, const FT &pw,
                                   const FT &qx, const FT &qy, const FT &qw,
                                   const FT &rx, const FT &ry, const FT &rw)
{
  FT FT4(4);
  FT dpx = px - rx;
  FT dpy = py - ry;
  FT dqx = qx - rx;
  FT dqy = qy - ry;
  FT dpp = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pw + rw;
  FT dqq = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qw + rw;

  FT det0 = determinant(dpx, dpy, dqx, dqy);
  FT det1 = determinant(dpp, dpy, dqq, dqy);
  FT det2 = determinant(dpx, dpp, dqx, dqq);

  return (CGAL_NTS square(det1) + CGAL_NTS square(det2)) /
                                  (FT4 * CGAL_NTS square(det0)) - rw;
}

template< class FT >
CGAL_KERNEL_MEDIUM_INLINE
FT
squared_radius_smallest_orthogonal_circleC2(const FT &px, const FT &py, const FT &pw,
                                            const FT &qx, const FT &qy, const FT &qw)
{
  FT FT4(4);
  FT dpz = CGAL_NTS square(px - qx) + CGAL_NTS square(py - qy);
  return (CGAL_NTS square(dpz - pw + qw) / (FT4 * dpz) - qw);
}

} //namespace CGAL

#endif // CGAL_CONSTRUCTIONS_KERNEL_FTC2_H
