/* -*- C++ -*-

 * lemon/bezier.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_BEZIER_H

#define LEMON_BEZIER_H

///\ingroup misc

///\file

///\brief Classes to compute with Bezier curves.

///

///Up to now this file is used internally by \ref graph_to_eps.h

///

///\author Alpar Juttner

#include<lemon/xy.h>

namespace lemon {

class BezierBase {

public:

  typedef xy<double> xy;

protected:

  static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}

};

class Bezier1 : public BezierBase

{

public:

  xy p1,p2;

  Bezier1() {}

  Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}

  xy operator()(double t) const

  {

    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);

    return conv(p1,p2,t);

  }

  Bezier1 before(double t) const

  {

    return Bezier1(p1,conv(p1,p2,t));

  }

  Bezier1 after(double t) const

  {

    return Bezier1(conv(p1,p2,t),p2);

  }

  Bezier1 revert() const { return Bezier1(p2,p1);}

  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }

  xy grad() const { return p2-p1; }

  xy norm() const { return rot90(p2-p1); }

  xy grad(double) const { return grad(); }

  xy norm(double t) const { return rot90(grad(t)); }

};

class Bezier2 : public BezierBase

{

public:

  xy p1,p2,p3;

  Bezier2() {}

  Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}

  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}

  xy operator()(double t) const

  {

    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);

    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;

  }

  Bezier2 before(double t) const

  {

    xy q(conv(p1,p2,t));

    xy r(conv(p2,p3,t));

    return Bezier2(p1,q,conv(q,r,t));

  }

  Bezier2 after(double t) const

  {

    xy q(conv(p1,p2,t));

    xy r(conv(p2,p3,t));

    return Bezier2(conv(q,r,t),r,p3);

  }

  Bezier2 revert() const { return Bezier2(p3,p2,p1);}

  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }

  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }

  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }

  xy grad(double t) const { return grad()(t); }

  xy norm(double t) const { return rot90(grad(t)); }

};

class Bezier3 : public BezierBase

{

public:

  xy p1,p2,p3,p4;

  Bezier3() {}

  Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}

  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 

			      p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}

  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),

			      p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}

  xy operator()(double t) const 

    {

      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);

      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+

	(3*t*t*(1-t))*p3+(t*t*t)*p4;

    }

  Bezier3 before(double t) const

    {

      xy p(conv(p1,p2,t));

      xy q(conv(p2,p3,t));

      xy r(conv(p3,p4,t));

      xy a(conv(p,q,t));

      xy b(conv(q,r,t));

      xy c(conv(a,b,t));

      return Bezier3(p1,p,a,c);

    }

  Bezier3 after(double t) const

    {

      xy p(conv(p1,p2,t));

      xy q(conv(p2,p3,t));

      xy r(conv(p3,p4,t));

      xy a(conv(p,q,t));

      xy b(conv(q,r,t));

      xy c(conv(a,b,t));

      return Bezier3(c,b,r,p4);

    }

  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}

  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }

  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }

  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),

				  3.0*rot90(p3-p2),

				  3.0*rot90(p4-p3)); }

  xy grad(double t) const { return grad()(t); }

  xy norm(double t) const { return rot90(grad(t)); }

  template<class R,class F,class S,class D>

  R recSplit(F &_f,const S &_s,D _d) const 

  {

    const xy a=(p1+p2)/2;

    const xy b=(p2+p3)/2;

    const xy c=(p3+p4)/2;

    const xy d=(a+b)/2;

    const xy e=(b+c)/2;

    const xy f=(d+e)/2;

    R f1=_f(Bezier3(p1,a,d,e),_d);

    R f2=_f(Bezier3(e,d,c,p4),_d);

    return _s(f1,f2);

  }

};

} //END OF NAMESPACE LEMON

#endif // LEMON_BEZIER_H