// Copyright (c) 1997-2001
// ETH Zurich (Switzerland).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6/Bounding_volumes/include/CGAL/Min_ellipse_2/Optimisation_ellipse_2.h $
// $Id: Optimisation_ellipse_2.h 74e4d89 2022-09-27T10:42:05+01:00 Andreas Fabri
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sven Schoenherr <sven@inf.ethz.ch>, Bernd Gaertner

#ifndef CGAL_OPTIMISATION_ELLIPSE_2_H
#define CGAL_OPTIMISATION_ELLIPSE_2_H

#include <CGAL/license/Bounding_volumes.h>


#include <CGAL/Conic_2.h>
#include <CGAL/assertions.h>
#include <CGAL/Kernel/global_functions_2.h>


namespace CGAL {

// Class interface
// ===============
template < class K_ >
class Optimisation_ellipse_2 {
    /*
    friend  std::ostream&  operator << <> (
        std::ostream&, const Optimisation_ellipse_2<K_>&);
    friend  std::istream&  operator >> <> (
        std::istream&, Optimisation_ellipse_2<K_> &);
    */
  public:
    // types
    typedef           K_                K;
    typedef  typename K_::RT            RT;
    typedef  typename K_::FT            FT;
    typedef  typename K::Point_2        Point;
    typedef  typename K::Conic_2        Conic;

    /**************************************************************************
    WORKAROUND: Some compilers are unable to match member functions defined
    outside the class template. Therefore, all member functions are implemented
    in the class interface.

    // creation
    Optimisation_ellipse_2( );

    void  set( );
    void  set( const Point& p);
    void  set( const Point& p,  const Point& q);
    void  set( const Point& p1, const Point& p2, const Point& p3);
    void  set( const Point& p1, const Point& p2,
               const Point& p3, const Point& p4);
    void  set( const Point& p1, const Point& p2,
               const Point& p3, const Point& p4, const Point& p5);

    // access functions
    int  number_of_boundary_points()

    // equality tests
    bool  operator == ( const Optimisation_ellipse_2<K>& e) const;
    bool  operator != ( const Optimisation_ellipse_2<K>& e) const;

    // predicates
    CGAL::Bounded_side  bounded_side( const Point& p) const;
    bool  has_on_bounded_side      ( const Point& p) const;
    bool  has_on_boundary          ( const Point& p) const;
    bool  has_on_unbounded_side    ( const Point& p) const;

    bool  is_empty     ( ) const;
    bool  is_degenerate( ) const;
    **************************************************************************/

  /* private: */
    // private data members
    int    n_boundary_points;                   // number of boundary points
    Point  boundary_point1,
           boundary_point2,
           boundary_point3,
           boundary_point4,
           boundary_point5;                     // <= 5 support point
    Conic  conic1, conic2;                      // two conics

    // this gradient vector has dr=0 and is used in testing the
    // position of a point relative to an ellipse through 4 points
    mutable RT     dr, ds, dt, du, dv, dw;
    mutable bool   d_values_set;

    // this gradient vector is just conic2 - conic1 and is used in
    // obtaining an explicit conic representing an ellipse through 4 poinnts
    mutable RT     er, es, et, eu, ev, ew;
    mutable bool e_values_set;

    // needed in bounded-side predicate over ellipse with 4 support points
    mutable Conic helper_ellipse; // needed in bounded-side predicate over
    mutable bool helper_ellipse_set;

    mutable Conic helper_conic; // also needed in bounded-side test

// ============================================================================

// Class implementation
// ====================

  public:
    // Constructor
    // -----------
    inline
    Optimisation_ellipse_2( ) { }

    // Set functions
    // -------------
    void
    set( )
    {
        n_boundary_points = 0;
    }

    void
    set( const Point& p)
    {
        n_boundary_points = 1;
        boundary_point1   = p;
    }

    void
    set( const Point& p, const Point& q)
    {
        n_boundary_points = 2;
        CGAL_precondition(boundary_point1 == p); CGAL_USE(p);
        boundary_point2 = q;
    }

    void
    set( const Point& p1, const Point& p2, const Point& p3)
    {
        n_boundary_points = 3;
        CGAL_precondition(boundary_point1 == p1);
        CGAL_precondition(boundary_point2 == p2);
        boundary_point3 = p3;
        helper_conic.set_ellipse( p1, p2, p3);
        CGAL_assertion(helper_conic.is_ellipse());
    }

    void
    set( const Point& p1, const Point& p2, const Point& p3, const Point& p4)
    {
        n_boundary_points = 4;
        CGAL_precondition(boundary_point1 == p1);
        CGAL_precondition(boundary_point2 == p2);
        CGAL_precondition(boundary_point3 == p3);
        boundary_point4 = p4;
        Conic::set_two_linepairs( p1, p2, p3, p4, conic1, conic2);

        d_values_set = false;
        e_values_set = false;
        helper_ellipse_set = false;
    }

    void
    set_d_values() const
    {
      if (!d_values_set) {
        dr = RT( 0);
        ds = conic1.r() * conic2.s() - conic2.r() * conic1.s(),
        dt = conic1.r() * conic2.t() - conic2.r() * conic1.t(),
        du = conic1.r() * conic2.u() - conic2.r() * conic1.u(),
        dv = conic1.r() * conic2.v() - conic2.r() * conic1.v(),
        dw = conic1.r() * conic2.w() - conic2.r() * conic1.w();
        d_values_set = true;
      }
    }

    void
    set_e_values() const
    {
      if (!e_values_set) {
               er = conic2.r() - conic1.r();
        es = conic2.s() - conic1.s();
        et = conic2.t() - conic1.t();
        eu = conic2.u() - conic1.u();
        ev = conic2.v() - conic1.v();
        ew = conic2.w() - conic1.w();
        e_values_set = true;
      }
    }

    void
    set_helper_ellipse () const
    {
      if (!helper_ellipse_set) {
        helper_ellipse.set_ellipse( conic1, conic2);
        helper_ellipse.analyse();
        CGAL_assertion (helper_ellipse.is_ellipse());
        helper_ellipse_set= true;
      }
    }

    void
    set( const Point& p1, const Point& p2,
         const Point& p3, const Point& p4, const Point& p5)
    {
        helper_conic.set(conic1, conic2, p5);
        helper_conic.analyse();
        // an optimization is possible if this set-call arose from
        // a successful violation test of ME(p1,p2,p3,p4) and p5.
        // In that case, helper_conic is already correct,
        // but in general, this optimization is NOT valid.
        n_boundary_points = 5;
        CGAL_assertion(helper_conic.is_ellipse());
        // the following assertion is too strict if we run under
        // double (which is sometimes the case, e.g. in demos)
        // CGAL_assertion(helper_conic.has_on_boundary(p5));
        CGAL_precondition(boundary_point1 == p1);
        CGAL_precondition(boundary_point2 == p2);
        CGAL_precondition(boundary_point3 == p3);
        CGAL_precondition(boundary_point4 == p4);
        CGAL_USE(p1); CGAL_USE(p2); CGAL_USE(p3); CGAL_USE(p4);
        boundary_point5 = p5;
    }

    // Access functions
    // ----------------
    inline
    int
    number_of_boundary_points( ) const
    {
        return( n_boundary_points);
    }

    template <typename DoubleConic_2>
    void
    double_conic(DoubleConic_2& e) const
    {
        double r,s,t,u,v,w;
        double_coefficients(r,s,t,u,v,w);
        e.set(r,s,t,u,v,w);
        // NOTE: the set method calls analyze, so the conic is clean
    }

    void
    double_coefficients (double &r, double &s,double &t,
                         double &u, double &v, double &w) const
    {
      // just like double_conic, but we only get the coefficients
      CGAL_precondition( ! is_degenerate());

      if ( n_boundary_points == 4) {
        set_e_values();
        double tau = conic1.vol_minimum( er, es, et, eu, ev, ew);
        r = CGAL::to_double( conic1.r()) + tau*CGAL::to_double( er);
        s = CGAL::to_double( conic1.s()) + tau*CGAL::to_double( es);
        t = CGAL::to_double( conic1.t()) + tau*CGAL::to_double( et);
        u = CGAL::to_double( conic1.u()) + tau*CGAL::to_double( eu);
        v = CGAL::to_double( conic1.v()) + tau*CGAL::to_double( ev);
        w = CGAL::to_double( conic1.w()) + tau*CGAL::to_double( ew);
      } else {
        // it's the helper_conic
        r = CGAL::to_double(helper_conic.r());
        s = CGAL::to_double(helper_conic.s());
        t = CGAL::to_double(helper_conic.t());
        u = CGAL::to_double(helper_conic.u());
        v = CGAL::to_double(helper_conic.v());
        w = CGAL::to_double(helper_conic.w());
      }
    }


    // Equality tests
    // --------------
    bool
    operator == ( const Optimisation_ellipse_2<K>& e) const
    {
        if ( n_boundary_points != e.n_boundary_points)
            return( false);

        switch ( n_boundary_points) {
          case 0:
            return( true);
          case 1:
            return( boundary_point1 == e.boundary_point1);
          case 2:
            return(    (    ( boundary_point1 == e.boundary_point1)
                         && ( boundary_point2 == e.boundary_point2))
                    || (    ( boundary_point1 == e.boundary_point2)
                         && ( boundary_point2 == e.boundary_point1)));
          case 3:
          case 5:
            return( helper_conic == e.helper_conic);
          case 4:
            return(    (    ( conic1 == e.conic1)
                         && ( conic2 == e.conic2))
                    || (    ( conic1 == e.conic2)
                         && ( conic2 == e.conic1)));
          default:
            CGAL_assertion(    ( n_boundary_points >= 0)
                                         && ( n_boundary_points <= 5)); }
        // keeps g++ happy
        return( false);
    }

    inline
    bool
    operator != ( const Optimisation_ellipse_2<K>& e) const
    {
        return( ! operator == ( e));
    }

    // Predicates
    // ----------
    inline
    CGAL::Bounded_side
    bounded_side( const Point& p) const
    {
        switch ( n_boundary_points) {
          case 0:
            return( CGAL::ON_UNBOUNDED_SIDE);
          case 1:
            return( ( p == boundary_point1) ?
                           CGAL::ON_BOUNDARY : CGAL::ON_UNBOUNDED_SIDE);
          case 2:
            return(    ( p == boundary_point1)
                    || ( p == boundary_point2)
                    || ( CGAL::are_ordered_along_line(
                             boundary_point1, p, boundary_point2)) ?
                         CGAL::ON_BOUNDARY : CGAL::ON_UNBOUNDED_SIDE);
          case 3:
          case 5:
            return(helper_conic.convex_side( p));
          case 4: {
            helper_conic.set( conic1, conic2, p);
            helper_conic.analyse();
            if ( !helper_conic.is_ellipse()) {
                set_helper_ellipse();
                return( helper_ellipse.convex_side( p)); }
            else {
                set_d_values();
                int tau_star =
                  helper_conic.vol_derivative( dr, ds, dt, du, dv, dw);
                return( CGAL::Bounded_side( CGAL_NTS sign( tau_star))); } }
          default:
            CGAL_assertion( ( n_boundary_points >= 0) &&
                                         ( n_boundary_points <= 5) ); }
        // keeps g++ happy
        return( CGAL::Bounded_side( 0));
    }

    inline
    bool
    has_on_bounded_side( const Point& p) const
    {
        return( bounded_side( p) == CGAL::ON_BOUNDED_SIDE);
    }

    inline
    bool
    has_on_boundary( const Point& p) const
    {
        return( bounded_side( p) == CGAL::ON_BOUNDARY);
    }

    inline
    bool
    has_on_unbounded_side( const Point& p) const
    {
        return( bounded_side( p) == CGAL::ON_UNBOUNDED_SIDE);
    }

    inline
    bool
    is_empty( ) const
    {
        return( n_boundary_points == 0);
    }

    inline
    bool
    is_degenerate( ) const
    {
        return( n_boundary_points < 3);
    }

    bool
    is_circle( ) const
    {
       switch ( n_boundary_points) {
       case 0:
         return false; // the empty set is not a circle
       case 1:
         return true;
       case 2:
         return false; // a segment is not a circle
       case 3:
       case 5:
         return helper_conic.is_circle();
       case 4:
         // the smallest ellipse through four points is
         // a circle only if the four points are cocircular;
         // if so, compute this circle (as a conic) and check
         // its volume derivative
         if (CGAL::ON_BOUNDARY !=  CGAL::side_of_bounded_circle
                   (boundary_point1,
                    boundary_point2,
                    boundary_point3,
                    boundary_point4)) {
           return false;
         } else {
           // ok, they are cocircular, now get the circle and check it
           Conic c;
           c.set_circle(boundary_point1, boundary_point2, boundary_point3);
           set_d_values();
           return (CGAL::ZERO ==  (c.vol_derivative(dr, ds, dt, du, dv, dw)));
         }
       default:
         CGAL_assertion( ( n_boundary_points >= 0) &&
                                      ( n_boundary_points <= 5) );
         return false;
       }
    }
};

// Function declarations
// =====================
// I/O
// ---
template < class K_ >
std::ostream&
operator << ( std::ostream&, const CGAL::Optimisation_ellipse_2<K_>&);

template < class K_ >
std::istream&
operator >> ( std::istream&, CGAL::Optimisation_ellipse_2<K_>&);

} //namespace CGAL

#include <CGAL/Min_ellipse_2/Optimisation_ellipse_2_impl.h>

#endif // CGAL_OPTIMISATION_ELLIPSE_2_H

// ===== EOF ==================================================================
