1 | //STARTHEADER |
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2 | // $Id: ClusterSequenceVoronoiArea.cc 859 2012-11-28 01:49:23Z pavel $ |
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3 | // |
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4 | // Copyright (c) 2006-2007 Matteo Cacciari, Gavin Salam and Gregory Soyez |
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5 | // |
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6 | //---------------------------------------------------------------------- |
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7 | // This file is part of a simple command-line handling environment |
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8 | // |
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9 | // FastJet is free software; you can redistribute it and/or modify |
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10 | // it under the terms of the GNU General Public License as published by |
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11 | // the Free Software Foundation; either version 2 of the License, or |
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12 | // (at your option) any later version. |
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13 | // |
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14 | // The algorithms that underlie FastJet have required considerable |
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15 | // development and are described in hep-ph/0512210. If you use |
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16 | // FastJet as part of work towards a scientific publication, please |
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17 | // include a citation to the FastJet paper. |
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18 | // |
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19 | // FastJet is distributed in the hope that it will be useful, |
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20 | // but WITHOUT ANY WARRANTY; without even the implied warranty of |
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21 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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22 | // GNU General Public License for more details. |
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23 | // |
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24 | // You should have received a copy of the GNU General Public License |
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25 | // along with FastJet. If not, see <http://www.gnu.org/licenses/>. |
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26 | //---------------------------------------------------------------------- |
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27 | //ENDHEADER |
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28 | |
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29 | #include "fastjet/ClusterSequenceVoronoiArea.hh" |
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30 | #include "fastjet/internal/Voronoi.hh" |
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31 | #include <list> |
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32 | #include <cassert> |
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33 | #include <ostream> |
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34 | #include <fstream> |
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35 | #include <iterator> |
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36 | #include <cmath> |
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37 | #include <limits> |
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38 | |
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39 | using namespace std; |
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40 | |
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41 | FASTJET_BEGIN_NAMESPACE // defined in fastjet/internal/base.hh |
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42 | |
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43 | typedef ClusterSequenceVoronoiArea::VoronoiAreaCalc VAC; |
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44 | |
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45 | /// class for carrying out a voronoi area calculation on a set of |
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46 | /// initial vectors |
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47 | class ClusterSequenceVoronoiArea::VoronoiAreaCalc { |
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48 | public: |
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49 | /// constructor that takes a range of a vector together with the |
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50 | /// effective radius for the intersection of discs with voronoi |
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51 | /// cells |
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52 | VoronoiAreaCalc(const vector<PseudoJet>::const_iterator &, |
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53 | const vector<PseudoJet>::const_iterator &, |
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54 | double effective_R); |
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55 | |
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56 | /// return the area of the particle associated with the given |
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57 | /// index |
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58 | inline double area (int index) const {return _areas[index];}; |
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59 | |
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60 | private: |
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61 | std::vector<double> _areas; ///< areas, numbered as jets |
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62 | double _effective_R; ///< effective radius |
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63 | double _effective_R_squared; ///< effective radius squared |
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64 | |
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65 | /** |
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66 | * compute the intersection of one triangle with the circle |
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67 | * the area is returned |
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68 | */ |
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69 | double edge_circle_intersection(const VPoint &p0, |
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70 | const GraphEdge &edge); |
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71 | |
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72 | /// get the area of a circle of radius R centred on the point 0 with |
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73 | /// 1 and 2 on each "side" of the arc. dij is the distance between |
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74 | /// point i and point j and all distances are squared |
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75 | inline double circle_area(const double d12_2, double d01_2, double d02_2){ |
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76 | return 0.5*_effective_R_squared |
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77 | *acos(min(1.0,(d01_2+d02_2-d12_2)/(2*sqrt(d01_2*d02_2)))); |
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78 | } |
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79 | }; |
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80 | |
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81 | |
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82 | /** |
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83 | * compute the intersection of one triangle with the circle |
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84 | * the area is returned |
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85 | */ |
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86 | double VAC::edge_circle_intersection(const VPoint &p0, |
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87 | const GraphEdge &edge){ |
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88 | VPoint p1(edge.x1-p0.x, edge.y1-p0.y); |
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89 | VPoint p2(edge.x2-p0.x, edge.y2-p0.y); |
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90 | VPoint pdiff = p2-p1; |
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91 | |
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92 | //fprintf(stdout, "\tpt(%f,%f)\n", p0.x, p0.y); |
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93 | |
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94 | double cross = vector_product(p1, p2); |
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95 | double d12_2 = norm(pdiff); |
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96 | double d01_2 = norm(p1); |
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97 | double d02_2 = norm(p2); |
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98 | |
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99 | // compute intersections between edge line and circle |
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100 | double delta = d12_2*_effective_R_squared - cross*cross; |
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101 | |
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102 | // if no intersection, area=area_circle |
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103 | if (delta<=0){ |
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104 | return circle_area(d12_2, d01_2, d02_2); |
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105 | } |
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106 | |
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107 | // we'll only need delta's sqrt now |
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108 | delta = sqrt(delta); |
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109 | |
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110 | // b is the projection of 01 onto 12 |
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111 | double b = scalar_product(pdiff, p1); |
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112 | |
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113 | // intersections with the circle: |
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114 | // we compute the "coordinate along the line" of the intersection |
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115 | // with t=0 (1) corresponding to p1 (p2) |
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116 | // points with 0<t<1 are within the circle others are outside |
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117 | |
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118 | // positive intersection |
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119 | double tp = (delta-b)/d12_2; |
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120 | |
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121 | // if tp is negative, tm also => inters = circle |
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122 | if (tp<0) |
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123 | return circle_area(d12_2, d01_2, d02_2); |
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124 | |
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125 | // we need the second intersection |
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126 | double tm = -(delta+b)/d12_2; |
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127 | |
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128 | // if tp<1, it lies in the circle |
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129 | if (tp<1){ |
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130 | // if tm<0, the segment has one intersection |
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131 | // with the circle at p (t=tp) |
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132 | // the area is a triangle from 1 to p |
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133 | // then a circle from p to 2 |
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134 | // several tricks can be used: |
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135 | // - the area of the triangle is tp*area triangle |
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136 | // - the lenght for the circle are easily obtained |
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137 | if (tm<0) |
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138 | return tp*0.5*fabs(cross) |
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139 | +circle_area((1-tp)*(1-tp)*d12_2, _effective_R_squared, d02_2); |
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140 | |
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141 | // now, 0 < tm < tp < 1 |
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142 | // the segment intersects twice the circle |
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143 | // area = 2 cirles at ends + a triangle in the middle |
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144 | // again, simplifications are staightforward |
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145 | return (tp-tm)*0.5*fabs(cross) |
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146 | + circle_area(tm*tm*d12_2, d01_2, _effective_R_squared) |
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147 | + circle_area((1-tp)*(1-tp)*d12_2, _effective_R_squared, d02_2); |
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148 | } |
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149 | |
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150 | // now, we have tp>1 |
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151 | |
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152 | // if in addition tm>1, intersectino is a circle |
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153 | if (tm>1) |
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154 | return circle_area(d12_2, d01_2, d02_2); |
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155 | |
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156 | // if tm<0, the triangle is inside the circle |
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157 | if (tm<0) |
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158 | return 0.5*fabs(cross); |
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159 | |
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160 | // otherwise, only the "tm point" is on the segment |
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161 | // area = circle from 1 to m and triangle from m to 2 |
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162 | |
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163 | return (1-tm)*0.5*fabs(cross) |
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164 | +circle_area(tm*tm*d12_2, d01_2, _effective_R_squared); |
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165 | } |
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166 | |
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167 | |
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168 | // the constructor... |
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169 | //---------------------------------------------------------------------- |
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170 | VAC::VoronoiAreaCalc(const vector<PseudoJet>::const_iterator &jet_begin, |
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171 | const vector<PseudoJet>::const_iterator &jet_end, |
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172 | double effective_R) { |
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173 | |
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174 | assert(effective_R < 0.5*pi); |
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175 | |
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176 | vector<VPoint> voronoi_particles; |
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177 | vector<int> voronoi_indices; |
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178 | |
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179 | _effective_R = effective_R; |
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180 | _effective_R_squared = effective_R*effective_R; |
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181 | |
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182 | double minrap = numeric_limits<double>::max(); |
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183 | double maxrap = -minrap; |
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184 | |
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185 | unsigned int n_tot = 0, n_added = 0; |
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186 | |
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187 | // loop over jets and create the triangulation, as well as cross-referencing |
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188 | // info |
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189 | for (vector<PseudoJet>::const_iterator jet_it = jet_begin; |
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190 | jet_it != jet_end; jet_it++) { |
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191 | _areas.push_back(0.0); |
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192 | if ((jet_it->perp2()) != 0.0 || (jet_it->E() != jet_it->pz())){ |
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193 | // generate the corresponding point |
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194 | double rap = jet_it->rap(), phi = jet_it->phi(); |
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195 | voronoi_particles.push_back(VPoint(rap, phi)); |
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196 | voronoi_indices.push_back(n_tot); |
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197 | n_added++; |
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198 | |
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199 | // insert a copy of the point if it falls within 2*_R_effective |
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200 | // of the 0,2pi borders (because we are interested in any |
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201 | // voronoi edge within _R_effective of the other border) |
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202 | if (phi < 2*_effective_R) { |
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203 | voronoi_particles.push_back(VPoint(rap,phi+twopi)); |
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204 | voronoi_indices.push_back(-1); |
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205 | n_added++; |
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206 | } else if (twopi-phi < 2*_effective_R) { |
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207 | voronoi_particles.push_back(VPoint(rap,phi-twopi)); |
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208 | voronoi_indices.push_back(-1); |
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209 | n_added++; |
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210 | } |
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211 | |
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212 | // track the rapidity range |
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213 | maxrap = max(maxrap,rap); |
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214 | minrap = min(minrap,rap); |
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215 | } |
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216 | n_tot++; |
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217 | } |
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218 | |
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219 | // allow for 0-particle case in graceful way |
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220 | if (n_added == 0) return; |
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221 | // assert(n_added > 0); // old (pre 2.4) non-graceful exit |
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222 | |
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223 | // add extreme cases (corner particles): |
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224 | double max_extend = 2*max(maxrap-minrap+4*_effective_R, twopi+8*_effective_R); |
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225 | voronoi_particles.push_back(VPoint(0.5*(minrap+maxrap)-max_extend, pi)); |
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226 | voronoi_particles.push_back(VPoint(0.5*(minrap+maxrap)+max_extend, pi)); |
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227 | voronoi_particles.push_back(VPoint(0.5*(minrap+maxrap), pi-max_extend)); |
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228 | voronoi_particles.push_back(VPoint(0.5*(minrap+maxrap), pi+max_extend)); |
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229 | |
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230 | // Build the VD |
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231 | VoronoiDiagramGenerator vdg; |
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232 | vdg.generateVoronoi(&voronoi_particles, |
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233 | 0.5*(minrap+maxrap)-max_extend, 0.5*(minrap+maxrap)+max_extend, |
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234 | pi-max_extend, pi+max_extend); |
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235 | |
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236 | vdg.resetIterator(); |
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237 | GraphEdge *e=NULL; |
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238 | unsigned int v_index; |
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239 | int p_index; |
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240 | vector<PseudoJet>::const_iterator jet; |
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241 | |
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242 | while(vdg.getNext(&e)){ |
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243 | v_index = e->point1; |
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244 | if (v_index<n_added){ // this removes the corner particles |
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245 | p_index = voronoi_indices[v_index]; |
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246 | if (p_index!=-1){ // this removes the copies |
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247 | jet = jet_begin+voronoi_indices[v_index]; |
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248 | _areas[p_index]+= |
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249 | edge_circle_intersection(voronoi_particles[v_index], *e); |
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250 | } |
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251 | } |
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252 | v_index = e->point2; |
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253 | if (v_index<n_added){ // this removes the corner particles |
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254 | p_index = voronoi_indices[v_index]; |
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255 | if (p_index!=-1){ // this removes the copies |
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256 | jet = jet_begin+voronoi_indices[v_index]; |
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257 | _areas[p_index]+= |
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258 | edge_circle_intersection(voronoi_particles[v_index], *e); |
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259 | } |
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260 | } |
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261 | } |
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262 | |
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263 | |
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264 | } |
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265 | |
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266 | |
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267 | //---------------------------------------------------------------------- |
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268 | /// |
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269 | void ClusterSequenceVoronoiArea::_initializeVA () { |
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270 | // run the VAC on our original particles |
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271 | _pa_calc = new VAC(_jets.begin(), |
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272 | _jets.begin()+n_particles(), |
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273 | _effective_Rfact*_jet_def.R()); |
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274 | |
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275 | // transfer the areas to our local structure |
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276 | // -- first the initial ones |
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277 | _voronoi_area.reserve(2*n_particles()); |
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278 | for (unsigned int i=0; i<n_particles(); i++) { |
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279 | _voronoi_area.push_back(_pa_calc->area(i)); |
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280 | // make a stab at a 4-vector area |
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281 | if (_jets[i].perp2() > 0) { |
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282 | _voronoi_area_4vector.push_back((_pa_calc->area(i)/_jets[i].perp()) |
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283 | * _jets[i]); |
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284 | } else { |
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285 | // not sure what to do here -- just put zero (it won't be meaningful |
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286 | // anyway) |
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287 | _voronoi_area_4vector.push_back(PseudoJet(0.0,0.0,0.0,0.0)); |
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288 | } |
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289 | } |
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290 | |
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291 | // -- then the combined areas that arise from the clustering |
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292 | for (unsigned int i = n_particles(); i < _history.size(); i++) { |
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293 | double area_local; |
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294 | PseudoJet area_4vect; |
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295 | if (_history[i].parent2 >= 0) { |
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296 | area_local = _voronoi_area[_history[i].parent1] + |
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297 | _voronoi_area[_history[i].parent2]; |
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298 | area_4vect = _voronoi_area_4vector[_history[i].parent1] + |
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299 | _voronoi_area_4vector[_history[i].parent2]; |
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300 | } else { |
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301 | area_local = _voronoi_area[_history[i].parent1]; |
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302 | area_4vect = _voronoi_area_4vector[_history[i].parent1]; |
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303 | } |
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304 | _voronoi_area.push_back(area_local); |
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305 | _voronoi_area_4vector.push_back(area_4vect); |
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306 | } |
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307 | |
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308 | } |
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309 | |
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310 | //---------------------------------------------------------------------- |
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311 | ClusterSequenceVoronoiArea::~ClusterSequenceVoronoiArea() { |
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312 | delete _pa_calc; |
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313 | } |
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314 | |
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315 | FASTJET_END_NAMESPACE |
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