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Diffstat (limited to 'lemon/lemon/bits/bezier.h')
| -rw-r--r-- | lemon/lemon/bits/bezier.h | 174 |
1 files changed, 174 insertions, 0 deletions
diff --git a/lemon/lemon/bits/bezier.h b/lemon/lemon/bits/bezier.h new file mode 100644 index 0000000..cdec206 --- /dev/null +++ b/lemon/lemon/bits/bezier.h @@ -0,0 +1,174 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_BEZIER_H +#define LEMON_BEZIER_H + +//\ingroup misc +//\file +//\brief Classes to compute with Bezier curves. +// +//Up to now this file is used internally by \ref graph_to_eps.h + +#include<lemon/dim2.h> + +namespace lemon { + namespace dim2 { + +class BezierBase { +public: + typedef lemon::dim2::Point<double> Point; +protected: + static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;} +}; + +class Bezier1 : public BezierBase +{ +public: + Point p1,p2; + + Bezier1() {} + Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} + + Point operator()(double t) const + { + // return conv(conv(p1,p2,t),conv(p2,p3,t),t); + return conv(p1,p2,t); + } + Bezier1 before(double t) const + { + return Bezier1(p1,conv(p1,p2,t)); + } + + Bezier1 after(double t) const + { + return Bezier1(conv(p1,p2,t),p2); + } + + Bezier1 revert() const { return Bezier1(p2,p1);} + Bezier1 operator()(double a,double b) const { return before(b).after(a/b); } + Point grad() const { return p2-p1; } + Point norm() const { return rot90(p2-p1); } + Point grad(double) const { return grad(); } + Point norm(double t) const { return rot90(grad(t)); } +}; + +class Bezier2 : public BezierBase +{ +public: + Point p1,p2,p3; + + Bezier2() {} + Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {} + Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} + Point operator()(double t) const + { + // return conv(conv(p1,p2,t),conv(p2,p3,t),t); + return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; + } + Bezier2 before(double t) const + { + Point q(conv(p1,p2,t)); + Point r(conv(p2,p3,t)); + return Bezier2(p1,q,conv(q,r,t)); + } + + Bezier2 after(double t) const + { + Point q(conv(p1,p2,t)); + Point r(conv(p2,p3,t)); + return Bezier2(conv(q,r,t),r,p3); + } + Bezier2 revert() const { return Bezier2(p3,p2,p1);} + Bezier2 operator()(double a,double b) const { return before(b).after(a/b); } + Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } + Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); } + Point grad(double t) const { return grad()(t); } + Point norm(double t) const { return rot90(grad(t)); } +}; + +class Bezier3 : public BezierBase +{ +public: + Point p1,p2,p3,p4; + + Bezier3() {} + Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) + : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} + Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), + p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} + Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), + p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} + + Point operator()(double t) const + { + // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); + return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ + (3*t*t*(1-t))*p3+(t*t*t)*p4; + } + Bezier3 before(double t) const + { + Point p(conv(p1,p2,t)); + Point q(conv(p2,p3,t)); + Point r(conv(p3,p4,t)); + Point a(conv(p,q,t)); + Point b(conv(q,r,t)); + Point c(conv(a,b,t)); + return Bezier3(p1,p,a,c); + } + + Bezier3 after(double t) const + { + Point p(conv(p1,p2,t)); + Point q(conv(p2,p3,t)); + Point r(conv(p3,p4,t)); + Point a(conv(p,q,t)); + Point b(conv(q,r,t)); + Point c(conv(a,b,t)); + return Bezier3(c,b,r,p4); + } + Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} + Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } + Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } + Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), + 3.0*rot90(p3-p2), + 3.0*rot90(p4-p3)); } + Point grad(double t) const { return grad()(t); } + Point norm(double t) const { return rot90(grad(t)); } + + template<class R,class F,class S,class D> + R recSplit(F &_f,const S &_s,D _d) const + { + const Point a=(p1+p2)/2; + const Point b=(p2+p3)/2; + const Point c=(p3+p4)/2; + const Point d=(a+b)/2; + const Point e=(b+c)/2; + const Point f=(d+e)/2; + R f1=_f(Bezier3(p1,a,d,e),_d); + R f2=_f(Bezier3(e,d,c,p4),_d); + return _s(f1,f2); + } + +}; + + +} //END OF NAMESPACE dim2 +} //END OF NAMESPACE lemon + +#endif // LEMON_BEZIER_H |