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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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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) 2003-2013
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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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kpeter@314
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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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#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 lemon::dim2::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
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