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) 2003-2006 |
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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 | ///\author Alpar Juttner |
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29 | |
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30 | #include<lemon/dim2.h> |
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31 | |
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32 | namespace lemon { |
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33 | namespace dim2 { |
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34 | |
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35 | class BezierBase { |
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36 | public: |
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37 | typedef Point<double> Point; |
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38 | protected: |
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39 | static Point conv(Point x,Point y,double t) {return (1-t)*x+t*y;} |
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40 | }; |
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41 | |
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42 | class Bezier1 : public BezierBase |
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43 | { |
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44 | public: |
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45 | Point p1,p2; |
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46 | |
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47 | Bezier1() {} |
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48 | Bezier1(Point _p1, Point _p2) :p1(_p1), p2(_p2) {} |
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49 | |
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50 | Point operator()(double t) const |
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51 | { |
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52 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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53 | return conv(p1,p2,t); |
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54 | } |
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55 | Bezier1 before(double t) const |
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56 | { |
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57 | return Bezier1(p1,conv(p1,p2,t)); |
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58 | } |
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59 | |
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60 | Bezier1 after(double t) const |
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61 | { |
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62 | return Bezier1(conv(p1,p2,t),p2); |
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63 | } |
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64 | |
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65 | Bezier1 revert() const { return Bezier1(p2,p1);} |
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66 | Bezier1 operator()(double a,double b) const { return before(b).after(a/b); } |
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67 | Point grad() const { return p2-p1; } |
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68 | Point norm() const { return rot90(p2-p1); } |
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69 | Point grad(double) const { return grad(); } |
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70 | Point norm(double t) const { return rot90(grad(t)); } |
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71 | }; |
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72 | |
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73 | class Bezier2 : public BezierBase |
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74 | { |
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75 | public: |
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76 | Point p1,p2,p3; |
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77 | |
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78 | Bezier2() {} |
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79 | Bezier2(Point _p1, Point _p2, Point _p3) :p1(_p1), p2(_p2), p3(_p3) {} |
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80 | Bezier2(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,.5)), p3(b.p2) {} |
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81 | Point operator()(double t) const |
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82 | { |
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83 | // return conv(conv(p1,p2,t),conv(p2,p3,t),t); |
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84 | return ((1-t)*(1-t))*p1+(2*(1-t)*t)*p2+(t*t)*p3; |
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85 | } |
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86 | Bezier2 before(double t) const |
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87 | { |
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88 | Point q(conv(p1,p2,t)); |
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89 | Point r(conv(p2,p3,t)); |
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90 | return Bezier2(p1,q,conv(q,r,t)); |
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91 | } |
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92 | |
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93 | Bezier2 after(double t) const |
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94 | { |
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95 | Point q(conv(p1,p2,t)); |
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96 | Point r(conv(p2,p3,t)); |
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97 | return Bezier2(conv(q,r,t),r,p3); |
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98 | } |
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99 | Bezier2 revert() const { return Bezier2(p3,p2,p1);} |
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100 | Bezier2 operator()(double a,double b) const { return before(b).after(a/b); } |
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101 | Bezier1 grad() const { return Bezier1(2.0*(p2-p1),2.0*(p3-p2)); } |
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102 | Bezier1 norm() const { return Bezier1(2.0*rot90(p2-p1),2.0*rot90(p3-p2)); } |
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103 | Point grad(double t) const { return grad()(t); } |
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104 | Point norm(double t) const { return rot90(grad(t)); } |
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105 | }; |
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106 | |
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107 | class Bezier3 : public BezierBase |
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108 | { |
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109 | public: |
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110 | Point p1,p2,p3,p4; |
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111 | |
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112 | Bezier3() {} |
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113 | Bezier3(Point _p1, Point _p2, Point _p3, Point _p4) |
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114 | : p1(_p1), p2(_p2), p3(_p3), p4(_p4) {} |
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115 | Bezier3(const Bezier1 &b) : p1(b.p1), p2(conv(b.p1,b.p2,1.0/3.0)), |
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116 | p3(conv(b.p1,b.p2,2.0/3.0)), p4(b.p2) {} |
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117 | Bezier3(const Bezier2 &b) : p1(b.p1), p2(conv(b.p1,b.p2,2.0/3.0)), |
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118 | p3(conv(b.p2,b.p3,1.0/3.0)), p4(b.p3) {} |
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119 | |
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120 | Point operator()(double t) const |
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121 | { |
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122 | // return Bezier2(conv(p1,p2,t),conv(p2,p3,t),conv(p3,p4,t))(t); |
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123 | return ((1-t)*(1-t)*(1-t))*p1+(3*t*(1-t)*(1-t))*p2+ |
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124 | (3*t*t*(1-t))*p3+(t*t*t)*p4; |
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125 | } |
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126 | Bezier3 before(double t) const |
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127 | { |
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128 | Point p(conv(p1,p2,t)); |
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129 | Point q(conv(p2,p3,t)); |
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130 | Point r(conv(p3,p4,t)); |
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131 | Point a(conv(p,q,t)); |
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132 | Point b(conv(q,r,t)); |
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133 | Point c(conv(a,b,t)); |
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134 | return Bezier3(p1,p,a,c); |
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135 | } |
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136 | |
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137 | Bezier3 after(double t) const |
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138 | { |
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139 | Point p(conv(p1,p2,t)); |
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140 | Point q(conv(p2,p3,t)); |
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141 | Point r(conv(p3,p4,t)); |
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142 | Point a(conv(p,q,t)); |
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143 | Point b(conv(q,r,t)); |
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144 | Point c(conv(a,b,t)); |
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145 | return Bezier3(c,b,r,p4); |
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146 | } |
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147 | Bezier3 revert() const { return Bezier3(p4,p3,p2,p1);} |
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148 | Bezier3 operator()(double a,double b) const { return before(b).after(a/b); } |
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149 | Bezier2 grad() const { return Bezier2(3.0*(p2-p1),3.0*(p3-p2),3.0*(p4-p3)); } |
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150 | Bezier2 norm() const { return Bezier2(3.0*rot90(p2-p1), |
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151 | 3.0*rot90(p3-p2), |
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152 | 3.0*rot90(p4-p3)); } |
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153 | Point grad(double t) const { return grad()(t); } |
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154 | Point norm(double t) const { return rot90(grad(t)); } |
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155 | |
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156 | template<class R,class F,class S,class D> |
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157 | R recSplit(F &_f,const S &_s,D _d) const |
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158 | { |
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159 | const Point a=(p1+p2)/2; |
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160 | const Point b=(p2+p3)/2; |
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161 | const Point c=(p3+p4)/2; |
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162 | const Point d=(a+b)/2; |
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163 | const Point e=(b+c)/2; |
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164 | const Point f=(d+e)/2; |
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165 | R f1=_f(Bezier3(p1,a,d,e),_d); |
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166 | R f2=_f(Bezier3(e,d,c,p4),_d); |
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167 | return _s(f1,f2); |
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168 | } |
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169 | |
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170 | }; |
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171 | |
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172 | |
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173 | } //END OF NAMESPACE dim2 |
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174 | } //END OF NAMESPACE lemon |
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175 | |
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176 | #endif // LEMON_BEZIER_H |
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