1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/bits/bezier.h Mon Aug 14 15:15:57 2006 +0000
1.3 @@ -0,0 +1,172 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2006
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_BEZIER_H
1.23 +#define LEMON_BEZIER_H
1.24 +
1.25 +///\ingroup misc
1.26 +///\file
1.27 +///\brief Classes to compute with Bezier curves.
1.28 +///
1.29 +///Up to now this file is used internally by \ref graph_to_eps.h
1.30 +///
1.31 +///\author Alpar Juttner
1.32 +
1.33 +#include<lemon/xy.h>
1.34 +
1.35 +namespace lemon {
1.36 +
1.37 +class BezierBase {
1.38 +public:
1.39 + typedef xy<double> xy;
1.40 +protected:
1.41 + static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;}
1.42 +};
1.43 +
1.44 +class Bezier1 : public BezierBase
1.45 +{
1.46 +public:
1.47 + xy p1,p2;
1.48 +
1.49 + Bezier1() {}
1.50 + Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {}
1.51 +
1.52 + xy operator()(double t) const
1.53 + {
1.54 + // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
1.55 + return conv(p1,p2,t);
1.56 + }
1.57 + Bezier1 before(double t) const
1.58 + {
1.59 + return Bezier1(p1,conv(p1,p2,t));
1.60 + }
1.61 +
1.62 + Bezier1 after(double t) const
1.63 + {
1.64 + return Bezier1(conv(p1,p2,t),p2);
1.65 + }
1.66 +
1.67 + Bezier1 revert() const { return Bezier1(p2,p1);}
1.68 + Bezier1 operator()(double a,double b) const { return before(b).after(a/b); }
1.69 + xy grad() const { return p2-p1; }
1.70 + xy norm() const { return rot90(p2-p1); }
1.71 + xy grad(double) const { return grad(); }
1.72 + xy norm(double t) const { return rot90(grad(t)); }
1.73 +};
1.74 +
1.75 +class Bezier2 : public BezierBase
1.76 +{
1.77 +public:
1.78 + xy p1,p2,p3;
1.79 +
1.80 + Bezier2() {}
1.81 + Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {}
1.82 + Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {}
1.83 + xy operator()(double t) const
1.84 + {
1.85 + // return conv(conv(p1,p2,t),conv(p2,p3,t),t);
1.86 + return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3;
1.87 + }
1.88 + Bezier2 before(double t) const
1.89 + {
1.90 + xy q(conv(p1,p2,t));
1.91 + xy r(conv(p2,p3,t));
1.92 + return Bezier2(p1,q,conv(q,r,t));
1.93 + }
1.94 +
1.95 + Bezier2 after(double t) const
1.96 + {
1.97 + xy q(conv(p1,p2,t));
1.98 + xy r(conv(p2,p3,t));
1.99 + return Bezier2(conv(q,r,t),r,p3);
1.100 + }
1.101 + Bezier2 revert() const { return Bezier2(p3,p2,p1);}
1.102 + Bezier2 operator()(double a,double b) const { return before(b).after(a/b); }
1.103 + Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); }
1.104 + Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); }
1.105 + xy grad(double t) const { return grad()(t); }
1.106 + xy norm(double t) const { return rot90(grad(t)); }
1.107 +};
1.108 +
1.109 +class Bezier3 : public BezierBase
1.110 +{
1.111 +public:
1.112 + xy p1,p2,p3,p4;
1.113 +
1.114 + Bezier3() {}
1.115 + Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {}
1.116 + Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)),
1.117 + p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {}
1.118 + Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)),
1.119 + p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {}
1.120 +
1.121 + xy operator()(double t) const
1.122 + {
1.123 + // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t);
1.124 + return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+
1.125 + (3*t*t*(1-t))*p3+(t*t*t)*p4;
1.126 + }
1.127 + Bezier3 before(double t) const
1.128 + {
1.129 + xy p(conv(p1,p2,t));
1.130 + xy q(conv(p2,p3,t));
1.131 + xy r(conv(p3,p4,t));
1.132 + xy a(conv(p,q,t));
1.133 + xy b(conv(q,r,t));
1.134 + xy c(conv(a,b,t));
1.135 + return Bezier3(p1,p,a,c);
1.136 + }
1.137 +
1.138 + Bezier3 after(double t) const
1.139 + {
1.140 + xy p(conv(p1,p2,t));
1.141 + xy q(conv(p2,p3,t));
1.142 + xy r(conv(p3,p4,t));
1.143 + xy a(conv(p,q,t));
1.144 + xy b(conv(q,r,t));
1.145 + xy c(conv(a,b,t));
1.146 + return Bezier3(c,b,r,p4);
1.147 + }
1.148 + Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);}
1.149 + Bezier3 operator()(double a,double b) const { return before(b).after(a/b); }
1.150 + Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); }
1.151 + Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1),
1.152 + 3.0*rot90(p3-p2),
1.153 + 3.0*rot90(p4-p3)); }
1.154 + xy grad(double t) const { return grad()(t); }
1.155 + xy norm(double t) const { return rot90(grad(t)); }
1.156 +
1.157 + template<class R,class F,class S,class D>
1.158 + R recSplit(F &_f,const S &_s,D _d) const
1.159 + {
1.160 + const xy a=(p1+p2)/2;
1.161 + const xy b=(p2+p3)/2;
1.162 + const xy c=(p3+p4)/2;
1.163 + const xy d=(a+b)/2;
1.164 + const xy e=(b+c)/2;
1.165 + const xy f=(d+e)/2;
1.166 + R f1=_f(Bezier3(p1,a,d,e),_d);
1.167 + R f2=_f(Bezier3(e,d,c,p4),_d);
1.168 + return _s(f1,f2);
1.169 + }
1.170 +
1.171 +};
1.172 +
1.173 +} //END OF NAMESPACE LEMON
1.174 +
1.175 +#endif // LEMON_BEZIER_H