[128] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_BEZIER_H |
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| 20 | #define LEMON_BEZIER_H |
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| 21 | |
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| 22 | ///\ingroup misc |
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| 23 | ///\file |
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| 24 | ///\brief Classes to compute with Bezier curves. |
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| 25 | /// |
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| 26 | ///Up to now this file is used internally by \ref graph_to_eps.h |
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| 27 | |
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| 28 | #include<lemon/dim2.h> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | namespace dim2 { |
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| 32 | |
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| 33 | class BezierBase { |
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| 34 | public: |
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| 35 | typedef Point<double> Point; |
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| 36 | protected: |
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| 37 | static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;} |
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| 38 | }; |
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| 39 | |
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| 40 | class Bezier1 : public BezierBase |
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| 41 | { |
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| 42 | public: |
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| 43 | Point p1,p2; |
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| 44 | |
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| 45 | Bezier1() {} |
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| 46 | Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
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| 47 | |
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| 48 | Point operator()(double t) const |
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| 49 | { |
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| 50 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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| 51 | return conv(p1,p2,t); |
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| 52 | } |
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| 53 | Bezier1 before(double t) const |
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| 54 | { |
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| 55 | return Bezier1(p1,conv(p1,p2,t)); |
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| 56 | } |
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| 57 | |
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| 58 | Bezier1 after(double t) const |
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| 59 | { |
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| 60 | return Bezier1(conv(p1,p2,t),p2); |
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| 61 | } |
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| 62 | |
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| 63 | Bezier1 revert() const { return Bezier1(p2,p1);} |
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| 64 | Bezier1 operator()(double a,double b) const { return before(b).after(a/b); } |
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| 65 | Point grad() const { return p2-p1; } |
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| 66 | Point norm() const { return rot90(p2-p1); } |
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| 67 | Point grad(double) const { return grad(); } |
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| 68 | Point norm(double t) const { return rot90(grad(t)); } |
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| 69 | }; |
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| 70 | |
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| 71 | class Bezier2 : public BezierBase |
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| 72 | { |
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| 73 | public: |
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| 74 | Point p1,p2,p3; |
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| 75 | |
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| 76 | Bezier2() {} |
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| 77 | Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
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| 78 | Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
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| 79 | Point operator()(double t) const |
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| 80 | { |
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| 81 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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| 82 | return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
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| 83 | } |
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| 84 | Bezier2 before(double t) const |
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| 85 | { |
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| 86 | Point q(conv(p1,p2,t)); |
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| 87 | Point r(conv(p2,p3,t)); |
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| 88 | return Bezier2(p1,q,conv(q,r,t)); |
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| 89 | } |
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| 90 | |
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| 91 | Bezier2 after(double t) const |
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| 92 | { |
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| 93 | Point q(conv(p1,p2,t)); |
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| 94 | Point r(conv(p2,p3,t)); |
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| 95 | return Bezier2(conv(q,r,t),r,p3); |
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| 96 | } |
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| 97 | Bezier2 revert() const { return Bezier2(p3,p2,p1);} |
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| 98 | Bezier2 operator()(double a,double b) const { return before(b).after(a/b); } |
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| 99 | Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
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| 100 | Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); } |
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| 101 | Point grad(double t) const { return grad()(t); } |
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| 102 | Point norm(double t) const { return rot90(grad(t)); } |
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| 103 | }; |
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| 104 | |
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| 105 | class Bezier3 : public BezierBase |
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| 106 | { |
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| 107 | public: |
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| 108 | Point p1,p2,p3,p4; |
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| 109 | |
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| 110 | Bezier3() {} |
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| 111 | Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) |
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| 112 | : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
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| 113 | Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
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| 114 | p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
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| 115 | Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
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| 116 | p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
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| 117 | |
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| 118 | Point operator()(double t) const |
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| 119 | { |
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| 120 | // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
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| 121 | return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
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| 122 | (3*t*t*(1-t))*p3+(t*t*t)*p4; |
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| 123 | } |
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| 124 | Bezier3 before(double t) const |
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| 125 | { |
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| 126 | Point p(conv(p1,p2,t)); |
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| 127 | Point q(conv(p2,p3,t)); |
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| 128 | Point r(conv(p3,p4,t)); |
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| 129 | Point a(conv(p,q,t)); |
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| 130 | Point b(conv(q,r,t)); |
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| 131 | Point c(conv(a,b,t)); |
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| 132 | return Bezier3(p1,p,a,c); |
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| 133 | } |
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| 134 | |
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| 135 | Bezier3 after(double t) const |
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| 136 | { |
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| 137 | Point p(conv(p1,p2,t)); |
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| 138 | Point q(conv(p2,p3,t)); |
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| 139 | Point r(conv(p3,p4,t)); |
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| 140 | Point a(conv(p,q,t)); |
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| 141 | Point b(conv(q,r,t)); |
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| 142 | Point c(conv(a,b,t)); |
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| 143 | return Bezier3(c,b,r,p4); |
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| 144 | } |
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| 145 | Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
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| 146 | Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } |
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| 147 | Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
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| 148 | Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
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| 149 | 3.0*rot90(p3-p2), |
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| 150 | 3.0*rot90(p4-p3)); } |
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| 151 | Point grad(double t) const { return grad()(t); } |
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| 152 | Point norm(double t) const { return rot90(grad(t)); } |
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| 153 | |
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| 154 | template<class R,class F,class S,class D> |
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| 155 | R recSplit(F &_f,const S &_s,D _d) const |
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| 156 | { |
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| 157 | const Point a=(p1+p2)/2; |
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| 158 | const Point b=(p2+p3)/2; |
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| 159 | const Point c=(p3+p4)/2; |
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| 160 | const Point d=(a+b)/2; |
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| 161 | const Point e=(b+c)/2; |
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| 162 | const Point f=(d+e)/2; |
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| 163 | R f1=_f(Bezier3(p1,a,d,e),_d); |
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| 164 | R f2=_f(Bezier3(e,d,c,p4),_d); |
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| 165 | return _s(f1,f2); |
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| 166 | } |
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| 167 | |
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| 168 | }; |
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| 169 | |
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| 170 | |
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| 171 | } //END OF NAMESPACE dim2 |
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| 172 | } //END OF NAMESPACE lemon |
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| 173 | |
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| 174 | #endif // LEMON_BEZIER_H |
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