[1] | 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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