[1073] | 1 | /* -*- C++ -*- |
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[1435] | 2 | * lemon/bezier.h - Part of LEMON, a generic C++ optimization library |
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[1073] | 3 | * |
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[1164] | 4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[1073] | 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | #ifndef LEMON_BEZIER_H |
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| 18 | #define LEMON_BEZIER_H |
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| 19 | |
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| 20 | ///\ingroup misc |
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| 21 | ///\file |
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| 22 | ///\brief Classes to compute with Bezier curves. |
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| 23 | /// |
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[1084] | 24 | ///Up to now this file is used internally by \ref graph_to_eps.h |
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[1073] | 25 | /// |
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| 26 | ///\author Alpar Juttner |
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| 27 | |
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| 28 | #include<lemon/xy.h> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | class BezierBase { |
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| 33 | public: |
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| 34 | typedef xy<double> xy; |
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| 35 | protected: |
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| 36 | static xy conv(xy x,xy y,double t) {return (1-t)*x+t*y;} |
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| 37 | }; |
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| 38 | |
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| 39 | class Bezier1 : public BezierBase |
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| 40 | { |
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| 41 | public: |
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| 42 | xy p1,p2; |
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| 43 | |
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| 44 | Bezier1() {} |
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| 45 | Bezier1(xy _p1, xy _p2) :p1(_p1), p2(_p2) {} |
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| 46 | |
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| 47 | xy operator()(double t) const |
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| 48 | { |
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| 49 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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| 50 | return conv(p1,p2,t); |
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| 51 | } |
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| 52 | Bezier1 before(double t) const |
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| 53 | { |
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| 54 | return Bezier1(p1,conv(p1,p2,t)); |
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| 55 | } |
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| 56 | |
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| 57 | Bezier1 after(double t) const |
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| 58 | { |
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| 59 | return Bezier1(conv(p1,p2,t),p2); |
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| 60 | } |
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[1084] | 61 | Bezier1 revert() { return Bezier1(p2,p1);} |
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| 62 | Bezier1 operator()(double a,double b) { return before(b).after(a/b); } |
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| 63 | xy grad() { return p2-p1; } |
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| 64 | xy grad(double t) { return grad(); } |
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| 65 | |
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[1073] | 66 | }; |
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| 67 | |
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| 68 | class Bezier2 : public BezierBase |
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| 69 | { |
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| 70 | public: |
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| 71 | xy p1,p2,p3; |
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| 72 | |
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| 73 | Bezier2() {} |
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| 74 | Bezier2(xy _p1, xy _p2, xy _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
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| 75 | Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
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| 76 | xy operator()(double t) const |
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| 77 | { |
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| 78 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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| 79 | return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
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| 80 | } |
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| 81 | Bezier2 before(double t) const |
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| 82 | { |
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| 83 | xy q(conv(p1,p2,t)); |
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| 84 | xy r(conv(p2,p3,t)); |
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| 85 | return Bezier2(p1,q,conv(q,r,t)); |
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| 86 | } |
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| 87 | |
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| 88 | Bezier2 after(double t) const |
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| 89 | { |
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| 90 | xy q(conv(p1,p2,t)); |
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| 91 | xy r(conv(p2,p3,t)); |
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| 92 | return Bezier2(conv(q,r,t),r,p3); |
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| 93 | } |
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[1084] | 94 | Bezier2 revert() { return Bezier2(p3,p2,p1);} |
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[1073] | 95 | Bezier2 operator()(double a,double b) { return before(b).after(a/b); } |
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[1084] | 96 | Bezier1 grad() { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
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| 97 | xy grad(double t) { return grad()(t); } |
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[1073] | 98 | }; |
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| 99 | |
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| 100 | class Bezier3 : public BezierBase |
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| 101 | { |
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| 102 | public: |
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| 103 | xy p1,p2,p3,p4; |
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| 104 | |
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| 105 | Bezier3() {} |
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| 106 | Bezier3(xy _p1, xy _p2, xy _p3, xy _p4) :p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
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| 107 | Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
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| 108 | p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
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| 109 | Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
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| 110 | p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
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| 111 | |
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| 112 | xy operator()(double t) const |
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| 113 | { |
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| 114 | // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
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| 115 | return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
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| 116 | (3*t*t*(1-t))*p3+(t*t*t)*p4; |
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| 117 | } |
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| 118 | Bezier3 before(double t) const |
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| 119 | { |
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| 120 | xy p(conv(p1,p2,t)); |
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| 121 | xy q(conv(p2,p3,t)); |
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| 122 | xy r(conv(p3,p4,t)); |
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| 123 | xy a(conv(p,q,t)); |
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| 124 | xy b(conv(q,r,t)); |
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| 125 | xy c(conv(a,b,t)); |
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| 126 | return Bezier3(p1,p,a,c); |
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| 127 | } |
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| 128 | |
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| 129 | Bezier3 after(double t) const |
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| 130 | { |
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| 131 | xy p(conv(p1,p2,t)); |
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| 132 | xy q(conv(p2,p3,t)); |
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| 133 | xy r(conv(p3,p4,t)); |
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| 134 | xy a(conv(p,q,t)); |
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| 135 | xy b(conv(q,r,t)); |
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| 136 | xy c(conv(a,b,t)); |
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| 137 | return Bezier3(c,b,r,p4); |
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| 138 | } |
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[1084] | 139 | Bezier3 revert() { return Bezier3(p4,p3,p2,p1);} |
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[1073] | 140 | Bezier3 operator()(double a,double b) { return before(b).after(a/b); } |
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[1084] | 141 | Bezier2 grad() { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
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| 142 | xy grad(double t) { return grad()(t); } |
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[1073] | 143 | }; |
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| 144 | |
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| 145 | } //END OF NAMESPACE LEMON |
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| 146 | |
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| 147 | #endif // LEMON_BEZIER_H |
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