lemon/bits/bezier.h
author Akos Ladanyi <ladanyi@tmit.bme.hu>
Sun, 13 Apr 2008 13:22:52 +0200
changeset 141 96f81c791f0c
child 157 2ccc1afc2c52
permissions -rw-r--r--
CMake based build system
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/* -*- C++ -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library
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 *
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 * Copyright (C) 2003-2008
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_BEZIER_H
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#define LEMON_BEZIER_H
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///\ingroup misc
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///\file
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///\brief Classes to compute with Bezier curves.
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///
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///Up to now this file is used internally by \ref graph_to_eps.h
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///
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///\author Alpar Juttner
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#include<lemon/dim2.h>
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namespace lemon {
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  namespace dim2 {
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class BezierBase {
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public:
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  typedef Point<double> Point;
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protected:
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  static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;}
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};
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class Bezier1 : public BezierBase
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{
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public:
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  Point p1,p2;
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  Bezier1() {}
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  Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {}
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  Point operator()(double t) const
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  {
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    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
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    return conv(p1,p2,t);
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  }
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  Bezier1 before(double t) const
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  {
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    return Bezier1(p1,conv(p1,p2,t));
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  }
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  Bezier1 after(double t) const
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  {
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    return Bezier1(conv(p1,p2,t),p2);
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  }
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  Bezier1 revert() const { return Bezier1(p2,p1);}
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  Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
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  Point grad() const { return p2-p1; }
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  Point norm() const { return rot90(p2-p1); }
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  Point grad(double) const { return grad(); }
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  Point norm(double t) const { return rot90(grad(t)); }
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};
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class Bezier2 : public BezierBase
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{
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public:
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  Point p1,p2,p3;
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  Bezier2() {}
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  Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {}
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  Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
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  Point operator()(double t) const
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  {
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    //    return conv(conv(p1,p2,t),conv(p2,p3,t),t);
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    return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
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  }
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  Bezier2 before(double t) const
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  {
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    Point q(conv(p1,p2,t));
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    Point r(conv(p2,p3,t));
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    return Bezier2(p1,q,conv(q,r,t));
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  }
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  Bezier2 after(double t) const
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  {
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    Point q(conv(p1,p2,t));
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    Point r(conv(p2,p3,t));
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    return Bezier2(conv(q,r,t),r,p3);
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  }
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  Bezier2 revert() const { return Bezier2(p3,p2,p1);}
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  Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
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  Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
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  Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
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  Point grad(double t) const { return grad()(t); }
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  Point norm(double t) const { return rot90(grad(t)); }
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};
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class Bezier3 : public BezierBase
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{
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public:
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  Point p1,p2,p3,p4;
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  Bezier3() {}
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  Bezier3(Point _p1, Point _p2, Point _p3, Point _p4)
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    : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
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  Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), 
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			      p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
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  Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
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			      p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
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  Point operator()(double t) const 
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    {
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      //    return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
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      return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
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	(3*t*t*(1-t))*p3+(t*t*t)*p4;
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    }
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  Bezier3 before(double t) const
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    {
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      Point p(conv(p1,p2,t));
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      Point q(conv(p2,p3,t));
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      Point r(conv(p3,p4,t));
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      Point a(conv(p,q,t));
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      Point b(conv(q,r,t));
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      Point c(conv(a,b,t));
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      return Bezier3(p1,p,a,c);
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    }
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  Bezier3 after(double t) const
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    {
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      Point p(conv(p1,p2,t));
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      Point q(conv(p2,p3,t));
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      Point r(conv(p3,p4,t));
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      Point a(conv(p,q,t));
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      Point b(conv(q,r,t));
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      Point c(conv(a,b,t));
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      return Bezier3(c,b,r,p4);
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    }
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  Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
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  Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
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  Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
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  Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
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				  3.0*rot90(p3-p2),
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				  3.0*rot90(p4-p3)); }
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  Point grad(double t) const { return grad()(t); }
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  Point norm(double t) const { return rot90(grad(t)); }
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  template<class R,class F,class S,class D>
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  R recSplit(F &_f,const S &_s,D _d) const 
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  {
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    const Point a=(p1+p2)/2;
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    const Point b=(p2+p3)/2;
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    const Point c=(p3+p4)/2;
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    const Point d=(a+b)/2;
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    const Point e=(b+c)/2;
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    const Point f=(d+e)/2;
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    R f1=_f(Bezier3(p1,a,d,e),_d);
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    R f2=_f(Bezier3(e,d,c,p4),_d);
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    return _s(f1,f2);
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  }
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};
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} //END OF NAMESPACE dim2
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} //END OF NAMESPACE lemon
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#endif // LEMON_BEZIER_H