/* -*- C++ -*- * * This file is a part of LEMON, a generic C++ optimization library * * Copyright (C) 2003-2008 * 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 namespace lemon { namespace dim2 { class BezierBase { public: typedef lemon::dim2::Point 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 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