alpar@1073: /* -*- C++ -*-
ladanyi@1435: * lemon/bezier.h - Part of LEMON, a generic C++ optimization library
alpar@1073: *
alpar@1164: * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359: * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@1073: *
alpar@1073: * Permission to use, modify and distribute this software is granted
alpar@1073: * provided that this copyright notice appears in all copies. For
alpar@1073: * precise terms see the accompanying LICENSE file.
alpar@1073: *
alpar@1073: * This software is provided "AS IS" with no warranty of any kind,
alpar@1073: * express or implied, and with no claim as to its suitability for any
alpar@1073: * purpose.
alpar@1073: *
alpar@1073: */
alpar@1073:
alpar@1073: #ifndef LEMON_BEZIER_H
alpar@1073: #define LEMON_BEZIER_H
alpar@1073:
alpar@1073: ///\ingroup misc
alpar@1073: ///\file
alpar@1073: ///\brief Classes to compute with Bezier curves.
alpar@1073: ///
alpar@1084: ///Up to now this file is used internally by \ref graph_to_eps.h
alpar@1073: ///
alpar@1073: ///\author Alpar Juttner
alpar@1073:
alpar@1073: #include<lemon/xy.h>
alpar@1073:
alpar@1073: namespace lemon {
alpar@1073:
alpar@1073: class BezierBase {
alpar@1073: public:
alpar@1073: typedef xy<double> xy;
alpar@1073: protected:
alpar@1073: static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
alpar@1073: };
alpar@1073:
alpar@1073: class Bezier1 : public BezierBase
alpar@1073: {
alpar@1073: public:
alpar@1073: xy p1,p2;
alpar@1073:
alpar@1073: Bezier1() {}
alpar@1073: Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
alpar@1073:
alpar@1073: xy operator()(double t) const
alpar@1073: {
alpar@1073: // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
alpar@1073: return conv(p1,p2,t);
alpar@1073: }
alpar@1073: Bezier1 before(double t) const
alpar@1073: {
alpar@1073: return Bezier1(p1,conv(p1,p2,t));
alpar@1073: }
alpar@1073:
alpar@1073: Bezier1 after(double t) const
alpar@1073: {
alpar@1073: return Bezier1(conv(p1,p2,t),p2);
alpar@1073: }
alpar@1084:
alpar@1548: Bezier1 revert() const { return Bezier1(p2,p1);}
alpar@1548: Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@1548: xy grad() const { return p2-p1; }
alpar@1548: xy norm() const { return rot90(p2-p1); }
alpar@1548: xy grad(double) const { return grad(); }
alpar@1548: xy norm(double t) const { return rot90(grad(t)); }
alpar@1073: };
alpar@1073:
alpar@1073: class Bezier2 : public BezierBase
alpar@1073: {
alpar@1073: public:
alpar@1073: xy p1,p2,p3;
alpar@1073:
alpar@1073: Bezier2() {}
alpar@1073: Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
alpar@1073: Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
alpar@1073: xy operator()(double t) const
alpar@1073: {
alpar@1073: // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
alpar@1073: return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
alpar@1073: }
alpar@1073: Bezier2 before(double t) const
alpar@1073: {
alpar@1073: xy q(conv(p1,p2,t));
alpar@1073: xy r(conv(p2,p3,t));
alpar@1073: return Bezier2(p1,q,conv(q,r,t));
alpar@1073: }
alpar@1073:
alpar@1073: Bezier2 after(double t) const
alpar@1073: {
alpar@1073: xy q(conv(p1,p2,t));
alpar@1073: xy r(conv(p2,p3,t));
alpar@1073: return Bezier2(conv(q,r,t),r,p3);
alpar@1073: }
alpar@1548: Bezier2 revert() const { return Bezier2(p3,p2,p1);}
alpar@1548: Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@1548: Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
alpar@1548: Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
alpar@1548: xy grad(double t) const { return grad()(t); }
alpar@1548: xy norm(double t) const { return rot90(grad(t)); }
alpar@1073: };
alpar@1073:
alpar@1073: class Bezier3 : public BezierBase
alpar@1073: {
alpar@1073: public:
alpar@1073: xy p1,p2,p3,p4;
alpar@1073:
alpar@1073: Bezier3() {}
alpar@1073: Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
alpar@1073: Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
alpar@1073: p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
alpar@1073: Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
alpar@1073: p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
alpar@1073:
alpar@1073: xy operator()(double t) const
alpar@1073: {
alpar@1073: // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
alpar@1073: return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
alpar@1073: (3*t*t*(1-t))*p3+(t*t*t)*p4;
alpar@1073: }
alpar@1073: Bezier3 before(double t) const
alpar@1073: {
alpar@1073: xy p(conv(p1,p2,t));
alpar@1073: xy q(conv(p2,p3,t));
alpar@1073: xy r(conv(p3,p4,t));
alpar@1073: xy a(conv(p,q,t));
alpar@1073: xy b(conv(q,r,t));
alpar@1073: xy c(conv(a,b,t));
alpar@1073: return Bezier3(p1,p,a,c);
alpar@1073: }
alpar@1073:
alpar@1073: Bezier3 after(double t) const
alpar@1073: {
alpar@1073: xy p(conv(p1,p2,t));
alpar@1073: xy q(conv(p2,p3,t));
alpar@1073: xy r(conv(p3,p4,t));
alpar@1073: xy a(conv(p,q,t));
alpar@1073: xy b(conv(q,r,t));
alpar@1073: xy c(conv(a,b,t));
alpar@1073: return Bezier3(c,b,r,p4);
alpar@1073: }
alpar@1548: Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
alpar@1548: Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
alpar@1548: Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
alpar@1548: Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
alpar@1548: 3.0*rot90(p3-p2),
alpar@1548: 3.0*rot90(p4-p3)); }
alpar@1548: xy grad(double t) const { return grad()(t); }
alpar@1548: xy norm(double t) const { return rot90(grad(t)); }
alpar@1548:
alpar@1548: template<class R,class F,class S,class D>
alpar@1548: R recSplit(F &_f,const S &_s,D _d) const
alpar@1548: {
alpar@1548: const xy a=(p1+p2)/2;
alpar@1548: const xy b=(p2+p3)/2;
alpar@1548: const xy c=(p3+p4)/2;
alpar@1548: const xy d=(a+b)/2;
alpar@1548: const xy e=(b+c)/2;
alpar@1548: const xy f=(d+e)/2;
alpar@1548: R f1=_f(Bezier3(p1,a,d,e),_d);
alpar@1548: R f2=_f(Bezier3(e,d,c,p4),_d);
alpar@1548: return _s(f1,f2);
alpar@1548: }
alpar@1548:
alpar@1073: };
alpar@1073:
alpar@1073: } //END OF NAMESPACE LEMON
alpar@1073:
alpar@1073: #endif // LEMON_BEZIER_H