1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/lemon/bezier.h Tue Jan 11 09:15:25 2005 +0000
1.3 @@ -0,0 +1,139 @@
1.4 +/* -*- C++ -*-
1.5 + * src/lemon/bezier.h - Part of LEMON, a generic C++ optimization library
1.6 + *
1.7 + * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 + * (Egervary Combinatorial Optimization Research Group, EGRES).
1.9 + *
1.10 + * Permission to use, modify and distribute this software is granted
1.11 + * provided that this copyright notice appears in all copies. For
1.12 + * precise terms see the accompanying LICENSE file.
1.13 + *
1.14 + * This software is provided "AS IS" with no warranty of any kind,
1.15 + * express or implied, and with no claim as to its suitability for any
1.16 + * purpose.
1.17 + *
1.18 + */
1.19 +
1.20 +#ifndef LEMON_BEZIER_H
1.21 +#define LEMON_BEZIER_H
1.22 +
1.23 +///\ingroup misc
1.24 +///\file
1.25 +///\brief Classes to compute with Bezier curves.
1.26 +///
1.27 +///Up to now this file is internally used by \ref graph_to_eps.h
1.28 +///
1.29 +///\author Alpar Juttner
1.30 +
1.31 +#include<lemon/xy.h>
1.32 +
1.33 +namespace lemon {
1.34 +
1.35 +class BezierBase {
1.36 +public:
1.37 + typedef xy<double> xy;
1.38 +protected:
1.39 + static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
1.40 +};
1.41 +
1.42 +class Bezier1 : public BezierBase
1.43 +{
1.44 +public:
1.45 + xy p1,p2;
1.46 +
1.47 + Bezier1() {}
1.48 + Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
1.49 +
1.50 + xy operator()(double t) const
1.51 + {
1.52 + // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
1.53 + return conv(p1,p2,t);
1.54 + }
1.55 + Bezier1 before(double t) const
1.56 + {
1.57 + return Bezier1(p1,conv(p1,p2,t));
1.58 + }
1.59 +
1.60 + Bezier1 after(double t) const
1.61 + {
1.62 + return Bezier1(conv(p1,p2,t),p2);
1.63 + }
1.64 + Bezier1 operator()(double a,double b) { return before(b).after(a/b); }
1.65 +};
1.66 +
1.67 +class Bezier2 : public BezierBase
1.68 +{
1.69 +public:
1.70 + xy p1,p2,p3;
1.71 +
1.72 + Bezier2() {}
1.73 + Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
1.74 + Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
1.75 + xy operator()(double t) const
1.76 + {
1.77 + // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
1.78 + return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
1.79 + }
1.80 + Bezier2 before(double t) const
1.81 + {
1.82 + xy q(conv(p1,p2,t));
1.83 + xy r(conv(p2,p3,t));
1.84 + return Bezier2(p1,q,conv(q,r,t));
1.85 + }
1.86 +
1.87 + Bezier2 after(double t) const
1.88 + {
1.89 + xy q(conv(p1,p2,t));
1.90 + xy r(conv(p2,p3,t));
1.91 + return Bezier2(conv(q,r,t),r,p3);
1.92 + }
1.93 + Bezier2 operator()(double a,double b) { return before(b).after(a/b); }
1.94 +
1.95 +};
1.96 +
1.97 +class Bezier3 : public BezierBase
1.98 +{
1.99 +public:
1.100 + xy p1,p2,p3,p4;
1.101 +
1.102 + Bezier3() {}
1.103 + Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
1.104 + Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
1.105 + p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
1.106 + Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
1.107 + p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
1.108 +
1.109 + xy operator()(double t) const
1.110 + {
1.111 + // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
1.112 + return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
1.113 + (3*t*t*(1-t))*p3+(t*t*t)*p4;
1.114 + }
1.115 + Bezier3 before(double t) const
1.116 + {
1.117 + xy p(conv(p1,p2,t));
1.118 + xy q(conv(p2,p3,t));
1.119 + xy r(conv(p3,p4,t));
1.120 + xy a(conv(p,q,t));
1.121 + xy b(conv(q,r,t));
1.122 + xy c(conv(a,b,t));
1.123 + return Bezier3(p1,p,a,c);
1.124 + }
1.125 +
1.126 + Bezier3 after(double t) const
1.127 + {
1.128 + xy p(conv(p1,p2,t));
1.129 + xy q(conv(p2,p3,t));
1.130 + xy r(conv(p3,p4,t));
1.131 + xy a(conv(p,q,t));
1.132 + xy b(conv(q,r,t));
1.133 + xy c(conv(a,b,t));
1.134 + return Bezier3(c,b,r,p4);
1.135 + }
1.136 + Bezier3 operator()(double a,double b) { return before(b).after(a/b); }
1.137 +
1.138 +};
1.139 +
1.140 +} //END OF NAMESPACE LEMON
1.141 +
1.142 +#endif // LEMON_BEZIER_H