[831] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // |
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[850] | 27 | // $Id: G4IntersectingCone.cc,v 1.12 2008/04/28 08:59:47 gcosmo Exp $ |
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| 28 | // GEANT4 tag $Name: HEAD $ |
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[831] | 29 | // |
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| 30 | // |
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| 31 | // -------------------------------------------------------------------- |
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| 32 | // GEANT 4 class source file |
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| 33 | // |
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| 34 | // |
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| 35 | // G4IntersectingCone.cc |
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| 36 | // |
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| 37 | // Implementation of a utility class which calculates the intersection |
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| 38 | // of an arbitrary line with a fixed cone |
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| 39 | // -------------------------------------------------------------------- |
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| 40 | |
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| 41 | #include "G4IntersectingCone.hh" |
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| 42 | #include "G4GeometryTolerance.hh" |
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| 43 | |
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| 44 | // |
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| 45 | // Constructor |
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| 46 | // |
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| 47 | G4IntersectingCone::G4IntersectingCone( const G4double r[2], |
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| 48 | const G4double z[2] ) |
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| 49 | { |
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| 50 | |
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| 51 | |
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| 52 | half_kCarTolerance = 0.5 * G4GeometryTolerance::GetInstance() |
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| 53 | ->GetSurfaceTolerance(); |
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| 54 | // |
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| 55 | // What type of cone are we? |
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| 56 | // |
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| 57 | type1 = (std::fabs(z[1]-z[0]) > std::fabs(r[1]-r[0])); |
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| 58 | |
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| 59 | if (type1) |
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| 60 | { |
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| 61 | B = (r[1]-r[0])/(z[1]-z[0]); // tube like |
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| 62 | A = 0.5*( r[1]+r[0] - B*(z[1]+z[0]) ); |
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| 63 | } |
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| 64 | else |
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| 65 | { |
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| 66 | B = (z[1]-z[0])/(r[1]-r[0]); // disk like |
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| 67 | A = 0.5*( z[1]+z[0] - B*(r[1]+r[0]) ); |
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| 68 | } |
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| 69 | // |
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| 70 | // Calculate extent |
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| 71 | // |
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| 72 | if (r[0] < r[1]) |
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| 73 | { |
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| 74 | rLo = r[0]-half_kCarTolerance; rHi = r[1]+half_kCarTolerance; |
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| 75 | } |
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| 76 | else |
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| 77 | { |
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| 78 | rLo = r[1]-half_kCarTolerance; rHi = r[0]+half_kCarTolerance; |
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| 79 | } |
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| 80 | |
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| 81 | if (z[0] < z[1]) |
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| 82 | { |
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| 83 | zLo = z[0]-half_kCarTolerance; zHi = z[1]+half_kCarTolerance; |
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| 84 | } |
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| 85 | else |
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| 86 | { |
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| 87 | zLo = z[1]-half_kCarTolerance; zHi = z[0]+half_kCarTolerance; |
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| 88 | } |
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| 89 | } |
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| 90 | |
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| 91 | |
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| 92 | // |
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| 93 | // Fake default constructor - sets only member data and allocates memory |
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| 94 | // for usage restricted to object persistency. |
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| 95 | // |
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| 96 | G4IntersectingCone::G4IntersectingCone( __void__& ) |
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| 97 | { |
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| 98 | } |
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| 99 | |
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| 100 | |
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| 101 | // |
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| 102 | // Destructor |
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| 103 | // |
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| 104 | G4IntersectingCone::~G4IntersectingCone() |
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| 105 | { |
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| 106 | } |
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| 107 | |
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| 108 | |
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| 109 | // |
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| 110 | // HitOn |
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| 111 | // |
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| 112 | // Check r or z extent, as appropriate, to see if the point is possibly |
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| 113 | // on the cone. |
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| 114 | // |
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| 115 | G4bool G4IntersectingCone::HitOn( const G4double r, |
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| 116 | const G4double z ) |
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| 117 | { |
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| 118 | // |
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| 119 | // Be careful! The inequalities cannot be "<=" and ">=" here without |
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| 120 | // punching a tiny hole in our shape! |
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| 121 | // |
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| 122 | if (type1) |
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| 123 | { |
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| 124 | if (z < zLo || z > zHi) return false; |
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| 125 | } |
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| 126 | else |
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| 127 | { |
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| 128 | if (r < rLo || r > rHi) return false; |
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| 129 | } |
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| 130 | |
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| 131 | return true; |
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| 132 | } |
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| 133 | |
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| 134 | |
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| 135 | // |
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| 136 | // LineHitsCone |
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| 137 | // |
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| 138 | // Calculate the intersection of a line with our conical surface, ignoring |
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| 139 | // any phi division |
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| 140 | // |
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| 141 | G4int G4IntersectingCone::LineHitsCone( const G4ThreeVector &p, |
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| 142 | const G4ThreeVector &v, |
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| 143 | G4double *s1, G4double *s2 ) |
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| 144 | { |
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| 145 | if (type1) |
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| 146 | { |
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| 147 | return LineHitsCone1( p, v, s1, s2 ); |
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| 148 | } |
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| 149 | else |
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| 150 | { |
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| 151 | return LineHitsCone2( p, v, s1, s2 ); |
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| 152 | } |
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| 153 | } |
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| 154 | |
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| 155 | |
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| 156 | // |
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| 157 | // LineHitsCone1 |
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| 158 | // |
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| 159 | // Calculate the intersections of a line with a conical surface. Only |
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| 160 | // suitable if zPlane[0] != zPlane[1]. |
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| 161 | // |
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| 162 | // Equation of a line: |
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| 163 | // |
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| 164 | // x = x0 + s*tx y = y0 + s*ty z = z0 + s*tz |
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| 165 | // |
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| 166 | // Equation of a conical surface: |
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| 167 | // |
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| 168 | // x**2 + y**2 = (A + B*z)**2 |
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| 169 | // |
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| 170 | // Solution is quadratic: |
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| 171 | // |
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| 172 | // a*s**2 + b*s + c = 0 |
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| 173 | // |
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| 174 | // where: |
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| 175 | // |
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| 176 | // a = x0**2 + y0**2 - (A + B*z0)**2 |
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| 177 | // |
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| 178 | // b = 2*( x0*tx + y0*ty - (A*B - B*B*z0)*tz) |
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| 179 | // |
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| 180 | // c = tx**2 + ty**2 - (B*tz)**2 |
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| 181 | // |
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| 182 | // Notice, that if a < 0, this indicates that the two solutions (assuming |
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| 183 | // they exist) are in opposite cones (that is, given z0 = -A/B, one z < z0 |
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| 184 | // and the other z > z0). For our shapes, the invalid solution is one |
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| 185 | // which produces A + Bz < 0, or the one where Bz is smallest (most negative). |
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| 186 | // Since Bz = B*s*tz, if B*tz > 0, we want the largest s, otherwise, |
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| 187 | // the smaller. |
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| 188 | // |
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| 189 | // If there are two solutions on one side of the cone, we want to make |
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| 190 | // sure that they are on the "correct" side, that is A + B*z0 + s*B*tz >= 0. |
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| 191 | // |
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| 192 | // If a = 0, we have a linear problem: s = c/b, which again gives one solution. |
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| 193 | // This should be rare. |
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| 194 | // |
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| 195 | // For b*b - 4*a*c = 0, we also have one solution, which is almost always |
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| 196 | // a line just grazing the surface of a the cone, which we want to ignore. |
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| 197 | // However, there are two other, very rare, possibilities: |
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| 198 | // a line intersecting the z axis and either: |
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| 199 | // 1. At the same angle std::atan(B) to just miss one side of the cone, or |
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| 200 | // 2. Intersecting the cone apex (0,0,-A/B) |
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| 201 | // We *don't* want to miss these! How do we identify them? Well, since |
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| 202 | // this case is rare, we can at least swallow a little more CPU than we would |
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| 203 | // normally be comfortable with. Intersection with the z axis means |
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| 204 | // x0*ty - y0*tx = 0. Case (1) means a==0, and we've already dealt with that |
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| 205 | // above. Case (2) means a < 0. |
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| 206 | // |
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| 207 | // Now: x0*tx + y0*ty = 0 in terms of roundoff error. We can write: |
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| 208 | // Delta = x0*tx + y0*ty |
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| 209 | // b = 2*( Delta - (A*B + B*B*z0)*tz ) |
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| 210 | // For: |
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| 211 | // b*b - 4*a*c = epsilon |
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| 212 | // where epsilon is small, then: |
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| 213 | // Delta = epsilon/2/B |
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| 214 | // |
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| 215 | G4int G4IntersectingCone::LineHitsCone1( const G4ThreeVector &p, |
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| 216 | const G4ThreeVector &v, |
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| 217 | G4double *s1, G4double *s2 ) |
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| 218 | { |
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| 219 | G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); |
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| 220 | G4double tx = v.x(), ty = v.y(), tz = v.z(); |
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| 221 | |
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| 222 | G4double a = tx*tx + ty*ty - sqr(B*tz); |
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| 223 | G4double b = 2*( x0*tx + y0*ty - (A*B + B*B*z0)*tz); |
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| 224 | G4double c = x0*x0 + y0*y0 - sqr(A + B*z0); |
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| 225 | |
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| 226 | G4double radical = b*b - 4*a*c; |
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| 227 | |
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| 228 | if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution |
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| 229 | |
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| 230 | if (radical < 1E-6*std::fabs(b)) |
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| 231 | { |
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| 232 | // |
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| 233 | // The radical is roughly zero: check for special, very rare, cases |
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| 234 | // |
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| 235 | if (std::fabs(a) > 1/kInfinity) |
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| 236 | { |
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| 237 | if(B==0.) { return 0; } |
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| 238 | if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) ) |
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| 239 | { |
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| 240 | *s1 = -0.5*b/a; |
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| 241 | return 1; |
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| 242 | } |
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| 243 | return 0; |
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| 244 | } |
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| 245 | } |
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| 246 | else |
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| 247 | { |
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| 248 | radical = std::sqrt(radical); |
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| 249 | } |
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| 250 | |
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| 251 | if (a > 1/kInfinity) |
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| 252 | { |
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| 253 | G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) ); |
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| 254 | sa = q/a; |
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| 255 | sb = c/q; |
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| 256 | if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; } |
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| 257 | if (A + B*(z0+(*s1)*tz) < 0) { return 0; } |
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| 258 | return 2; |
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| 259 | } |
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| 260 | else if (a < -1/kInfinity) |
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| 261 | { |
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| 262 | G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) ); |
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| 263 | sa = q/a; |
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| 264 | sb = c/q; |
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| 265 | *s1 = (B*tz > 0)^(sa > sb) ? sb : sa; |
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| 266 | return 1; |
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| 267 | } |
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| 268 | else if (std::fabs(b) < 1/kInfinity) |
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| 269 | { |
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| 270 | return 0; |
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| 271 | } |
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| 272 | else |
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| 273 | { |
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| 274 | *s1 = -c/b; |
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| 275 | if (A + B*(z0+(*s1)*tz) < 0) { return 0; } |
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| 276 | return 1; |
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| 277 | } |
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| 278 | } |
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| 279 | |
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| 280 | |
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| 281 | // |
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| 282 | // LineHitsCone2 |
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| 283 | // |
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| 284 | // See comments under LineHitsCone1. In this routine, case2, we have: |
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| 285 | // |
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| 286 | // Z = A + B*R |
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| 287 | // |
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| 288 | // The solution is still quadratic: |
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| 289 | // |
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| 290 | // a = tz**2 - B*B*(tx**2 + ty**2) |
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| 291 | // |
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| 292 | // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) ) |
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| 293 | // |
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| 294 | // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) ) |
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| 295 | // |
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| 296 | // The rest is much the same, except some details. |
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| 297 | // |
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| 298 | // a > 0 now means we intersect only once in the correct hemisphere. |
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| 299 | // |
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| 300 | // a > 0 ? We only want solution which produces R > 0. |
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| 301 | // since R = (z0+s*tz-A)/B, for tz/B > 0, this is the largest s |
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| 302 | // for tz/B < 0, this is the smallest s |
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| 303 | // thus, same as in case 1 ( since sign(tz/B) = sign(tz*B) ) |
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| 304 | // |
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| 305 | G4int G4IntersectingCone::LineHitsCone2( const G4ThreeVector &p, |
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| 306 | const G4ThreeVector &v, |
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| 307 | G4double *s1, G4double *s2 ) |
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| 308 | { |
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| 309 | G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); |
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| 310 | G4double tx = v.x(), ty = v.y(), tz = v.z(); |
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| 311 | |
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| 312 | |
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| 313 | // Special case which might not be so rare: B = 0 (precisely) |
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| 314 | // |
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| 315 | if (B==0) |
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| 316 | { |
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| 317 | if (std::fabs(tz) < 1/kInfinity) { return 0; } |
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| 318 | |
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| 319 | *s1 = (A-z0)/tz; |
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| 320 | return 1; |
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| 321 | } |
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| 322 | |
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| 323 | G4double B2 = B*B; |
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| 324 | |
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| 325 | G4double a = tz*tz - B2*(tx*tx + ty*ty); |
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| 326 | G4double b = 2*( (z0-A)*tz - B2*(x0*tx + y0*ty) ); |
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| 327 | G4double c = sqr(z0-A) - B2*( x0*x0 + y0*y0 ); |
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| 328 | |
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| 329 | G4double radical = b*b - 4*a*c; |
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| 330 | |
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| 331 | if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution |
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| 332 | |
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| 333 | if (radical < 1E-6*std::fabs(b)) |
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| 334 | { |
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| 335 | // |
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| 336 | // The radical is roughly zero: check for special, very rare, cases |
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| 337 | // |
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| 338 | if (std::fabs(a) > 1/kInfinity) |
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| 339 | { |
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| 340 | if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) ) |
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| 341 | { |
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| 342 | *s1 = -0.5*b/a; |
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| 343 | return 1; |
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| 344 | } |
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| 345 | return 0; |
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| 346 | } |
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| 347 | } |
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| 348 | else |
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| 349 | { |
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| 350 | radical = std::sqrt(radical); |
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| 351 | } |
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| 352 | |
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| 353 | if (a < -1/kInfinity) |
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| 354 | { |
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| 355 | G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) ); |
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| 356 | sa = q/a; |
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| 357 | sb = c/q; |
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| 358 | if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; } |
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| 359 | if ((z0 + (*s1)*tz - A)/B < 0) { return 0; } |
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| 360 | return 2; |
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| 361 | } |
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| 362 | else if (a > 1/kInfinity) |
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| 363 | { |
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| 364 | G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) ); |
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| 365 | sa = q/a; |
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| 366 | sb = c/q; |
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| 367 | *s1 = (tz*B > 0)^(sa > sb) ? sb : sa; |
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| 368 | return 1; |
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| 369 | } |
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| 370 | else if (std::fabs(b) < 1/kInfinity) |
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| 371 | { |
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| 372 | return 0; |
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| 373 | } |
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| 374 | else |
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| 375 | { |
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| 376 | *s1 = -c/b; |
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| 377 | if ((z0 + (*s1)*tz - A)/B < 0) { return 0; } |
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| 378 | return 1; |
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| 379 | } |
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| 380 | } |
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