/* -*- C++ -*-

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

  *

  * Copyright (C) 2005 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