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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4CylindricalSurface.cc,v 1.8 2006/06/29 18:42:08 gunter Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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29 | // |
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30 | // ---------------------------------------------------------------------- |
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31 | // GEANT 4 class source file |
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32 | // |
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33 | // G4CylindricalSurface.cc |
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34 | // |
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35 | // ---------------------------------------------------------------------- |
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36 | |
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37 | #include "G4CylindricalSurface.hh" |
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38 | #include "G4Sort.hh" |
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39 | #include "G4Globals.hh" |
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40 | |
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41 | G4CylindricalSurface::G4CylindricalSurface() : G4Surface() |
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42 | { |
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43 | // default constructor |
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44 | // default axis is ( 1.0, 0.0, 0.0 ), default radius is 1.0 |
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45 | axis = G4Vector3D( 1.0, 0.0, 0.0 ); |
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46 | radius = 1.0; |
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47 | } |
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48 | |
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49 | |
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50 | G4CylindricalSurface::G4CylindricalSurface( const G4Vector3D& o, |
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51 | const G4Vector3D& a, |
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52 | G4double r ) //: G4Surface( o ) |
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53 | { |
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54 | // Normal constructor |
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55 | // require axis to be a unit vector |
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56 | G4double amag = a.mag(); |
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57 | if ( amag != 0.0 ) |
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58 | axis = a * (1/ amag); // this makes the axis a unit vector |
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59 | else |
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60 | { |
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61 | G4cerr << "Error in G4CylindricalSurface::G4CylindricalSurface--axis " |
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62 | <<"has zero length\n" |
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63 | << "\tDefault axis ( 1.0, 0.0, 0.0 ) is used.\n"; |
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64 | |
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65 | axis = G4Vector3D( 1.0, 0.0, 0.0 ); |
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66 | } |
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67 | |
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68 | // Require radius to be non-negative |
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69 | if ( r >= 0.0 ) |
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70 | radius = r; |
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71 | else |
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72 | { |
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73 | G4cerr << "Error in G4CylindricalSurface::G4CylindricalSurface" |
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74 | << "--asked for negative radius\n" |
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75 | << "\tDefault radius of 1.0 is used.\n"; |
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76 | |
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77 | radius = 1.0; |
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78 | } |
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79 | |
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80 | origin =o; |
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81 | } |
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82 | |
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83 | |
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84 | G4CylindricalSurface::~G4CylindricalSurface() |
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85 | { |
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86 | } |
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87 | |
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88 | /* |
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89 | G4CylindricalSurface::G4CylindricalSurface( const G4CylindricalSurface& c ) |
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90 | : G4Surface( c.origin ) |
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91 | { |
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92 | axis = c.axis; radius = c.radius; |
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93 | } |
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94 | */ |
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95 | |
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96 | const char* G4CylindricalSurface::NameOf() const |
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97 | { |
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98 | return "G4CylindricalSurface"; |
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99 | } |
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100 | |
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101 | void G4CylindricalSurface::PrintOn( std::ostream& os ) const |
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102 | { |
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103 | // printing function using C++ std::ostream class |
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104 | os << "G4CylindricalSurface surface with origin: " << origin << "\t" |
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105 | << "radius: " << radius << "\tand axis " << axis << "\n"; |
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106 | } |
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107 | |
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108 | //G4int G4Surface::Intersect(const G4Ray& ry) |
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109 | G4int G4CylindricalSurface::Intersect(const G4Ray& ry) |
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110 | { |
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111 | |
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112 | // L. Broglia : copy of G4FCylindricalSurface::Intersect |
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113 | |
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114 | // Distance along a Ray (straight line with G4ThreeVec) to leave or enter |
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115 | // a G4CylindricalSurface. The input variable which_way should be set |
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116 | // to +1 to indicate leaving a G4CylindricalSurface, -1 to indicate |
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117 | // entering a G4CylindricalSurface. |
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118 | // p is the point of intersection of the Ray with the G4CylindricalSurface. |
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119 | // If the G4Vector3D of the Ray is opposite to that of the Normal to |
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120 | // the G4CylindricalSurface at the intersection point, it will not leave |
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121 | // the G4CylindricalSurface. |
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122 | // Similarly, if the G4Vector3D of the Ray is along that of the Normal |
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123 | // to the G4CylindricalSurface at the intersection point, it will not enter |
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124 | // the G4CylindricalSurface. |
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125 | // This method is called by all finite shapes sub-classed to |
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126 | // G4CylindricalSurface. |
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127 | // Use the virtual function table to check if the intersection point |
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128 | // is within the boundary of the finite shape. |
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129 | // A negative result means no intersection. |
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130 | // If no valid intersection point is found, set the distance |
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131 | // and intersection point to large numbers. |
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132 | |
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133 | // G4int which_way = -1; |
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134 | //Originally a parameter.Read explanation above. |
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135 | |
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136 | G4int which_way=1; |
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137 | |
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138 | if(!Inside(ry.GetStart())) |
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139 | which_way = -1; |
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140 | |
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141 | distance = FLT_MAXX; |
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142 | G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX ); |
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143 | |
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144 | closest_hit = lv; |
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145 | |
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146 | // Origin and G4Vector3D unit vector of Ray. |
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147 | G4Vector3D x = ry.GetStart(); |
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148 | G4Vector3D dhat = ry.GetDir(); |
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149 | |
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150 | // Axis unit vector of the G4CylindricalSurface. |
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151 | G4Vector3D ahat = GetAxis(); |
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152 | G4int isoln = 0, |
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153 | maxsoln = 2; |
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154 | |
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155 | // array of solutions in distance along the Ray |
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156 | G4double s[2]; |
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157 | s[0] = -1.0; |
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158 | s[1] = -1.0 ; |
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159 | |
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160 | // calculate the two solutions (quadratic equation) |
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161 | G4Vector3D d = x - GetOrigin(); |
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162 | G4double radiu = GetRadius(); |
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163 | |
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164 | //quit with no intersection if the radius of the G4CylindricalSurface is zero |
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165 | // if ( radiu <= 0.0 ) |
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166 | // return 0; |
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167 | |
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168 | G4double dsq = d * d; |
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169 | G4double da = d * ahat; |
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170 | G4double dasq = da * da; |
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171 | G4double rsq = radiu * radiu; |
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172 | G4double qsq = dsq - dasq; |
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173 | G4double dira = dhat * ahat; |
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174 | G4double a = 1.0 - dira * dira; |
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175 | |
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176 | if ( a <= 0.0 ) |
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177 | return 0; |
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178 | |
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179 | G4double b = 2. * ( d * dhat - da * dira ); |
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180 | G4double c = rsq - qsq; |
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181 | G4double radical = b * b + 4. * a * c; |
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182 | |
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183 | if ( radical < 0.0 ) |
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184 | return 0; |
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185 | |
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186 | G4double root = std::sqrt( radical ); |
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187 | s[0] = ( - b + root ) / ( 2. * a ); |
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188 | s[1] = ( - b - root ) / ( 2. * a ); |
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189 | |
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190 | // order the possible solutions by increasing distance along the Ray |
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191 | // (G4Sorting routines are in support/G4Sort.h) |
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192 | sort_double( s, isoln, maxsoln-1 ); |
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193 | |
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194 | // now loop over each positive solution, keeping the first one (smallest |
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195 | // distance along the Ray) which is within the boundary of the sub-shape |
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196 | // and which also has the correct G4Vector3D with respect to the Normal to |
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197 | // the G4CylindricalSurface at the intersection point |
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198 | for ( isoln = 0; isoln < maxsoln; isoln++ ) |
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199 | { |
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200 | if ( s[isoln] >= kCarTolerance*0.5 ) |
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201 | { |
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202 | if ( s[isoln] >= FLT_MAXX ) // quit if too large |
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203 | return 0; |
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204 | |
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205 | distance = s[isoln]; |
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206 | closest_hit = ry.GetPoint( distance ); |
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207 | G4double tmp = dhat * (Normal( closest_hit )); |
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208 | |
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209 | if ((tmp * which_way) >= 0.0 ) |
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210 | if ( WithinBoundary( closest_hit ) == 1 ) |
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211 | distance = distance*distance; |
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212 | |
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213 | return 1; |
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214 | } |
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215 | } |
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216 | |
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217 | // get here only if there was no solution within the boundary, Reset |
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218 | // distance and intersection point to large numbers |
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219 | distance = FLT_MAXX; |
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220 | closest_hit = lv; |
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221 | |
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222 | |
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223 | return 0; |
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224 | } |
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225 | |
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226 | |
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227 | |
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228 | |
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229 | G4double G4CylindricalSurface::HowNear( const G4Vector3D& x ) const |
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230 | { |
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231 | // Distance from the point x to the infinite G4CylindricalSurface. |
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232 | // The distance will be positive if the point is Inside the |
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233 | // G4CylindricalSurface, negative if the point is outside. |
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234 | // Note that this may not be correct for a bounded cylindrical object |
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235 | // subclassed to G4CylindricalSurface. |
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236 | G4Vector3D d = x - origin; |
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237 | G4double dA = d * axis; |
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238 | G4double rad = std::sqrt( d.mag2() - dA*dA ); |
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239 | G4double hownear = std::fabs( radius - rad ); |
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240 | |
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241 | return hownear; |
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242 | } |
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243 | |
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244 | |
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245 | /* |
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246 | G4double G4CylindricalSurface::distanceAlongRay( G4int which_way, const G4Ray* ry, |
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247 | G4Vector3D& p ) const |
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248 | { // Distance along a Ray (straight line with G4Vector3D) to leave or enter |
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249 | // a G4CylindricalSurface. The input variable which_way should be set to +1 |
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250 | // to indicate leaving a G4CylindricalSurface, -1 to indicate entering a |
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251 | // G4CylindricalSurface. |
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252 | // p is the point of intersection of the Ray with the G4CylindricalSurface. |
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253 | // If the G4Vector3D of the Ray is opposite to that of the Normal to |
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254 | // the G4CylindricalSurface at the intersection point, it will not leave the |
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255 | // G4CylindricalSurface. |
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256 | // Similarly, if the G4Vector3D of the Ray is along that of the Normal |
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257 | // to the G4CylindricalSurface at the intersection point, it will not enter |
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258 | // the G4CylindricalSurface. |
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259 | // This method is called by all finite shapes sub-classed to |
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260 | // G4CylindricalSurface. |
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261 | // Use the virtual function table to check if the intersection point |
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262 | // is within the boundary of the finite shape. |
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263 | // A negative result means no intersection. |
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264 | // If no valid intersection point is found, set the distance |
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265 | // and intersection point to large numbers. |
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266 | G4double Dist = FLT_MAXX; |
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267 | G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX ); |
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268 | p = lv; |
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269 | // Origin and G4Vector3D unit vector of Ray. |
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270 | G4Vector3D x = ry->Position(); |
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271 | G4Vector3D dhat = ry->Direction( 0.0 ); |
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272 | // Axis unit vector of the G4CylindricalSurface. |
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273 | G4Vector3D ahat = GetAxis(); |
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274 | G4int isoln = 0, maxsoln = 2; |
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275 | // array of solutions in distance along the Ray |
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276 | // G4double s[2] = { -1.0, -1.0 }; |
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277 | G4double s[2];s[0] = -1.0; s[1]= -1.0 ; |
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278 | // calculate the two solutions (quadratic equation) |
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279 | G4Vector3D d = x - GetOrigin(); |
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280 | G4double radius = GetRadius(); |
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281 | // quit with no intersection if the radius of the G4CylindricalSurface is zero |
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282 | if ( radius <= 0.0 ) |
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283 | return Dist; |
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284 | G4double dsq = d * d; |
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285 | G4double da = d * ahat; |
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286 | G4double dasq = da * da; |
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287 | G4double rsq = radius * radius; |
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288 | G4double qsq = dsq - dasq; |
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289 | G4double dira = dhat * ahat; |
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290 | G4double a = 1.0 - dira * dira; |
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291 | if ( a <= 0.0 ) |
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292 | return Dist; |
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293 | G4double b = 2. * ( d * dhat - da * dira ); |
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294 | G4double c = rsq - qsq; |
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295 | G4double radical = b * b + 4. * a * c; |
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296 | if ( radical < 0.0 ) |
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297 | return Dist; |
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298 | G4double root = std::sqrt( radical ); |
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299 | s[0] = ( - b + root ) / ( 2. * a ); |
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300 | s[1] = ( - b - root ) / ( 2. * a ); |
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301 | // order the possible solutions by increasing distance along the Ray |
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302 | // (G4Sorting routines are in support/G4Sort.h) |
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303 | G4Sort_double( s, isoln, maxsoln-1 ); |
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304 | // now loop over each positive solution, keeping the first one (smallest |
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305 | // distance along the Ray) which is within the boundary of the sub-shape |
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306 | // and which also has the correct G4Vector3D with respect to the Normal to |
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307 | // the G4CylindricalSurface at the intersection point |
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308 | for ( isoln = 0; isoln < maxsoln; isoln++ ) { |
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309 | if ( s[isoln] >= 0.0 ) { |
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310 | if ( s[isoln] >= FLT_MAXX ) // quit if too large |
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311 | return Dist; |
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312 | Dist = s[isoln]; |
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313 | p = ry->Position( Dist ); |
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314 | if ( ( ( dhat * Normal( p ) * which_way ) >= 0.0 ) |
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315 | && ( WithinBoundary( p ) == 1 ) ) |
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316 | return Dist; |
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317 | } |
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318 | } |
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319 | // get here only if there was no solution within the boundary, Reset |
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320 | // distance and intersection point to large numbers |
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321 | p = lv; |
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322 | return FLT_MAXX; |
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323 | } |
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324 | |
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325 | */ |
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326 | |
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327 | |
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328 | /* |
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329 | |
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330 | |
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331 | G4double G4CylindricalSurface::distanceAlongHelix( G4int which_way, |
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332 | const Helix* hx, |
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333 | G4Vector3D& p ) const |
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334 | { // Distance along a Helix to leave or enter a G4CylindricalSurface. |
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335 | // The input variable which_way should be set to +1 to |
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336 | // indicate leaving a G4CylindricalSurface, -1 to indicate entering a |
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337 | // G4CylindricalSurface. |
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338 | // p is the point of intersection of the Helix with the G4CylindricalSurface. |
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339 | // If the G4Vector3D of the Helix is opposite to that of the Normal to |
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340 | // the G4CylindricalSurface at the intersection point, it will not leave the |
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341 | // G4CylindricalSurface. |
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342 | // Similarly, if the G4Vector3D of the Helix is along that of the Normal |
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343 | // to the G4CylindricalSurface at the intersection point, it will not enter |
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344 | // the G4CylindricalSurface. |
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345 | // This method is called by all finite shapes sub-classed to |
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346 | // G4CylindricalSurface. |
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347 | // Use the virtual function table to check if the intersection point |
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348 | // is within the boundary of the finite shape. |
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349 | // If no valid intersection point is found, set the distance |
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350 | // and intersection point to large numbers. |
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351 | // Possible negative distance solutions are discarded. |
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352 | G4double Dist = FLT_MAXX; |
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353 | G4Vector3D lv ( FLT_MAXX, FLT_MAXX, FLT_MAXX ); |
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354 | G4Vector3D zerovec; // zero G4Vector3D |
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355 | p = lv; |
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356 | G4int isoln = 0, maxsoln = 4; |
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357 | // Array of solutions in turning angle |
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358 | // G4double s[4] = { -1.0, -1.0, -1.0, -1.0 }; |
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359 | G4double s[4];s[0]=-1.0;s[1]= -1.0;s[2]= -1.0;s[3]= -1.0; |
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360 | |
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361 | |
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362 | // Flag set to 1 if exact solution is found |
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363 | G4int exact = 0; |
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364 | // Helix parameters |
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365 | G4double rh = hx->GetRadius(); // radius of Helix |
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366 | G4Vector3D ah = hx->GetAxis(); // axis of Helix |
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367 | G4Vector3D oh = hx->position(); // origin of Helix |
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368 | G4Vector3D dh = hx->direction( 0.0 ); // initial G4Vector3D of Helix |
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369 | G4Vector3D prp = hx->getPerp(); // perpendicular vector |
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370 | G4double prpmag = prp.Magnitude(); |
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371 | G4double rhp = rh / prpmag; |
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372 | // G4CylindricalSurface parameters |
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373 | G4double rc = GetRadius(); // radius of G4CylindricalSurface |
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374 | if ( rc == 0.0 ) // quit if zero radius |
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375 | return Dist; |
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376 | G4Vector3D oc = GetOrigin(); // origin of G4CylindricalSurface |
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377 | G4Vector3D ac = GetAxis(); // axis of G4CylindricalSurface |
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378 | // |
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379 | // Calculate quantities of use later on. |
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380 | G4Vector3D alpha = rhp * prp; |
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381 | G4Vector3D beta = rhp * dh; |
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382 | G4Vector3D gamma = oh - oc; |
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383 | // Declare variables used later on in several places. |
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384 | G4double rcd2 = 0.0, alpha2 = 0.0; |
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385 | G4double A = 0.0, B = 0.0, C = 0.0, F = 0.0, G = 0.0, H = 0.0; |
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386 | G4double CoverB = 0.0, radical = 0.0, root = 0.0, s1 = 0.0, s2 = 0.0; |
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387 | G4Vector3D ghat; |
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388 | // |
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389 | // Set flag for special cases |
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390 | G4int special_case = 0; // 0 means general case |
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391 | // |
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392 | // Test to see if axes of Helix and G4CylindricalSurface are parallel, in which |
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393 | // case there are exact solutions. |
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394 | if ( ( std::fabs( ah.AngleBetween(ac) ) < FLT_EPSILO ) |
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395 | || ( std::fabs( ah.AngleBetween(ac) - pi ) < FLT_EPSILO ) ) { |
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396 | special_case = 1; |
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397 | // If, in addition, gamma is a zero vector or is parallel to the |
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398 | // G4CylindricalSurface axis, this simplifies the previous case. |
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399 | if ( gamma == zerovec ) { |
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400 | special_case = 3; |
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401 | ghat = gamma; |
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402 | } |
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403 | else { |
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404 | ghat = gamma / gamma.Magnitude(); |
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405 | if ( ( std::fabs( ghat.AngleBetween(ac) ) < FLT_EPSILO ) |
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406 | || ( std::fabs( ghat.AngleBetween(ac) - pi ) < |
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407 | FLT_EPSILO ) ) |
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408 | special_case = 3; |
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409 | } |
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410 | // Test to see if, in addition to the axes of the Helix and G4CylindricalSurface |
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411 | // being parallel, the axis of the G4CylindricalSurface is perpendicular to the |
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412 | // initial G4Vector3D of the Helix. |
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413 | if ( std::fabs( ( ac * dh ) ) < FLT_EPSILO ) { |
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414 | // And, if, in addition to all this, the difference in origins of the Helix |
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415 | // and G4CylindricalSurface is perpendicular to the initial G4Vector3D of the |
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416 | // Helix, there is a separate special case. |
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417 | if ( std::fabs( ( ghat * dh ) ) < FLT_EPSILO ) |
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418 | special_case = 4; |
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419 | } |
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420 | } // end of section with axes of Helix and G4CylindricalSurface parallel |
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421 | // |
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422 | // Another peculiar case occurs if the axis of the G4CylindricalSurface and the |
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423 | // initial G4Vector3D of the Helix line up and their origins are the same. |
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424 | // This will require a higher order approximation than the general case. |
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425 | if ( ( ( std::fabs( dh.AngleBetween(ac) ) < FLT_EPSILO ) |
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426 | || ( std::fabs( dh.AngleBetween(ac) - pi ) < FLT_EPSILO ) ) |
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427 | && ( gamma == zerovec ) ) |
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428 | special_case = 2; |
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429 | // |
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430 | // Now all the special cases have been tagged, so solutions are found |
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431 | // for each case. Exact solutions are indicated by setting exact = 1. |
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432 | // [For some reason switch doesn't work here, so do series of if's.] |
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433 | if ( special_case == 0 ) { // approximate quadratic solutions |
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434 | A = beta * beta - ( beta * ac ) * ( beta * ac ) |
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435 | + gamma * alpha - ( gamma * ac ) * ( alpha * ac ); |
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436 | B = 2.0 * gamma * beta |
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437 | - 2.0 * ( gamma * ac ) * ( beta * ac ); |
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438 | C = gamma * gamma |
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439 | - ( gamma * ac ) * ( gamma * ac ) - rc * rc; |
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440 | if ( std::fabs( A ) < FLT_EPSILO ) { // no quadratic term |
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441 | if ( B == 0.0 ) // no intersection, quit |
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442 | return Dist; |
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443 | else // B != 0 |
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444 | s[0] = -C / B; |
---|
445 | } |
---|
446 | else { // A != 0, general quadratic solution |
---|
447 | radical = B * B - 4.0 * A * C; |
---|
448 | if ( radical < 0.0 ) // no solution, quit |
---|
449 | return Dist; |
---|
450 | root = std::sqrt( radical ); |
---|
451 | s[0] = ( -B + root ) / ( 2.0 * A ); |
---|
452 | s[1] = ( -B - root ) / ( 2.0 * A ); |
---|
453 | if ( rh < 0.0 ) { |
---|
454 | s[0] = -s[0]; |
---|
455 | s[1] = -s[1]; |
---|
456 | } |
---|
457 | s[2] = s[0] + 2.0 * pi; |
---|
458 | s[3] = s[1] + 2.0 * pi; |
---|
459 | } |
---|
460 | } |
---|
461 | // |
---|
462 | else if ( special_case == 1 ) { // exact solutions |
---|
463 | exact = 1; |
---|
464 | H = 2.0 * ( alpha * alpha + gamma * alpha ); |
---|
465 | F = gamma * gamma |
---|
466 | - ( ( gamma * ac ) * ( gamma * ac ) ) |
---|
467 | - rc * rc + H; |
---|
468 | G = 2.0 * rhp * |
---|
469 | ( gamma * dh - ( gamma * ac ) * ( ac * dh ) ); |
---|
470 | A = G * G + H * H; |
---|
471 | B = -2.0 * F * H; |
---|
472 | C = F * F - G * G; |
---|
473 | if ( std::fabs( A ) < FLT_EPSILO ) { // no quadratic term |
---|
474 | if ( B == 0.0 ) // no intersection, quit |
---|
475 | return Dist; |
---|
476 | else { // B != 0 |
---|
477 | CoverB = -C / B; |
---|
478 | if ( std::fabs( CoverB ) > 1.0 ) |
---|
479 | return Dist; |
---|
480 | s[0] = std::acos( CoverB ); |
---|
481 | } |
---|
482 | } |
---|
483 | else { // A != 0, general quadratic solution |
---|
484 | // Try a different method of calculation using F, G, and H to avoid |
---|
485 | // precision problems. |
---|
486 | // radical = B * B - 4.0 * A * C; |
---|
487 | // if ( radical < 0.0 ) { |
---|
488 | if ( std::fabs( H ) > FLT_EPSILO ) { |
---|
489 | G4double r1 = G / H; |
---|
490 | G4double r2 = F / H; |
---|
491 | G4double radsq = 1.0 + r1*r1 - r2*r2; |
---|
492 | if ( radsq < 0.0 ) |
---|
493 | return Dist; |
---|
494 | root = G * std::sqrt( radsq ); |
---|
495 | G4double denominator = H * ( 1.0 + r1*r1 ); |
---|
496 | s1 = ( F + root ) / denominator; |
---|
497 | s2 = ( F - root ) / denominator; |
---|
498 | } |
---|
499 | else |
---|
500 | return Dist; |
---|
501 | // } // end radical < 0 condition |
---|
502 | // else { |
---|
503 | // root = std::sqrt( radical ); |
---|
504 | // s1 = ( -B + root ) / ( 2.0 * A ); |
---|
505 | // s2 = ( -B - root ) / ( 2.0 * A ); |
---|
506 | // } |
---|
507 | if ( std::fabs( s1 ) <= 1.0 ) { |
---|
508 | s[0] = std::acos( s1 ); |
---|
509 | s[2] = 2.0 * pi - s[0]; |
---|
510 | } |
---|
511 | if ( std::fabs( s2 ) <= 1.0 ) { |
---|
512 | s[1] = std::acos( s2 ); |
---|
513 | s[3] = 2.0 * pi - s[1]; |
---|
514 | } |
---|
515 | // Must take only solutions which satisfy original unsquared equation: |
---|
516 | // Gsin(s) - Hcos(s) + F = 0. Take best solution of pair and set false |
---|
517 | // solutions to -1. Only do this if the result is significantly different |
---|
518 | // from zero. |
---|
519 | G4double temp1 = 0.0, temp2 = 0.0; |
---|
520 | G4double rsign = 1.0; |
---|
521 | if ( rh < 0.0 ) rsign = -1.0; |
---|
522 | if ( s[0] > 0.0 ) { |
---|
523 | temp1 = G * rsign * std::sin( s[0] ) |
---|
524 | - H * std::cos( s[0] ) + F; |
---|
525 | temp2 = G * rsign * std::sin( s[2] ) |
---|
526 | - H * std::cos( s[2] ) + F; |
---|
527 | if ( std::fabs( temp1 ) > std::fabs( temp2 ) ) |
---|
528 | if ( std::fabs( temp1 ) > FLT_EPSILO ) |
---|
529 | s[0] = -1.0; |
---|
530 | else |
---|
531 | if ( std::fabs( temp2 ) > FLT_EPSILO ) |
---|
532 | s[2] = -1.0; |
---|
533 | } |
---|
534 | if ( s[1] > 0.0 ) { |
---|
535 | temp1 = G * rsign * std::sin( s[1] ) |
---|
536 | - H * std::cos( s[1] ) + F; |
---|
537 | temp2 = G * rsign * std::sin( s[3] ) |
---|
538 | - H * std::cos( s[3] ) + F; |
---|
539 | if ( std::fabs( temp1 ) > std::fabs( temp2 ) ) |
---|
540 | if ( std::fabs( temp1 ) > FLT_EPSILO ) |
---|
541 | s[1] = -1.0; |
---|
542 | else |
---|
543 | if ( std::fabs( temp2 ) > FLT_EPSILO ) |
---|
544 | s[3] = -1.0; |
---|
545 | } |
---|
546 | } |
---|
547 | } |
---|
548 | // |
---|
549 | else if ( special_case == 2 ) { // approximate solution |
---|
550 | G4Vector3D e = ah.cross( ac ); |
---|
551 | G4double re = std::fabs( rhp ) * e.Magnitude(); |
---|
552 | s[0] = std::sqrt( 2.0 * rc / re ); |
---|
553 | } |
---|
554 | // |
---|
555 | else if ( special_case == 3 ) { // exact solutions |
---|
556 | exact = 1; |
---|
557 | alpha2 = alpha * alpha; |
---|
558 | rcd2 = rhp * rhp * ( 1.0 - ( (ac*dh) * (ac*dh) ) ); |
---|
559 | A = alpha2 - rcd2; |
---|
560 | B = - 2.0 * alpha2; |
---|
561 | C = alpha2 + rcd2 - rc*rc; |
---|
562 | if ( std::fabs( A ) < FLT_EPSILO ) { // no quadratic term |
---|
563 | if ( B == 0.0 ) // no intersection, quit |
---|
564 | return Dist; |
---|
565 | else { // B != 0 |
---|
566 | CoverB = -C / B; |
---|
567 | if ( std::fabs( CoverB ) > 1.0 ) |
---|
568 | return Dist; |
---|
569 | s[0] = std::acos( CoverB ); |
---|
570 | } |
---|
571 | } |
---|
572 | else { // A != 0, general quadratic solution |
---|
573 | radical = B * B - 4.0 * A * C; |
---|
574 | if ( radical < 0.0 ) |
---|
575 | return Dist; |
---|
576 | root = std::sqrt( radical ); |
---|
577 | s1 = ( -B + root ) / ( 2.0 * A ); |
---|
578 | s2 = ( -B - root ) / ( 2.0 * A ); |
---|
579 | if ( std::fabs( s1 ) <= 1.0 ) |
---|
580 | s[0] = std::acos( s1 ); |
---|
581 | if ( std::fabs( s2 ) <= 1.0 ) |
---|
582 | s[1] = std::acos( s2 ); |
---|
583 | } |
---|
584 | } |
---|
585 | // |
---|
586 | else if ( special_case == 4 ) { // exact solution |
---|
587 | exact = 1; |
---|
588 | F = gamma * gamma |
---|
589 | - ( ( gamma * ac ) * ( gamma * ac ) ) |
---|
590 | - rc * rc; |
---|
591 | G = 2.0 * ( rhp * rhp + gamma * alpha ); |
---|
592 | if ( G == 0.0 ) // no intersection, quit |
---|
593 | return Dist; |
---|
594 | G4double cs = 1.0 + ( F / G ); |
---|
595 | if ( std::fabs( cs ) > 1.0 ) // no intersection, quit |
---|
596 | return Dist; |
---|
597 | s[0] = std::acos( cs ); |
---|
598 | } |
---|
599 | // |
---|
600 | else // shouldn't get here |
---|
601 | return Dist; |
---|
602 | // |
---|
603 | // ************************************************************************** |
---|
604 | // |
---|
605 | // Order the possible solutions by increasing turning angle |
---|
606 | // (G4Sorting routines are in support/G4Sort.h). |
---|
607 | G4Sort_double( s, isoln, maxsoln-1 ); |
---|
608 | // |
---|
609 | // Now loop over each positive solution, keeping the first one (smallest |
---|
610 | // distance along the Helix) which is within the boundary of the sub-shape. |
---|
611 | for ( isoln = 0; isoln < maxsoln; isoln++ ) { |
---|
612 | if ( s[isoln] >= 0.0 ) { |
---|
613 | // Calculate distance along Helix and position and G4Vector3D vectors. |
---|
614 | Dist = s[isoln] * std::fabs( rhp ); |
---|
615 | p = hx->position( Dist ); |
---|
616 | G4Vector3D d = hx->direction( Dist ); |
---|
617 | if ( exact == 0 ) { // only for approximate solns |
---|
618 | // Now do approximation to get remaining distance to correct this solution |
---|
619 | // iterate it until the accuracy is below the user-set surface precision. |
---|
620 | G4double delta = 0.0; |
---|
621 | G4double delta0 = FLT_MAXX; |
---|
622 | G4int dummy = 1; |
---|
623 | G4int iter = 0; |
---|
624 | G4int in0 = Inside( hx->position ( 0.0 ) ); |
---|
625 | G4int in1 = Inside( p ); |
---|
626 | G4double sc = Scale(); |
---|
627 | while ( dummy ) { |
---|
628 | iter++; |
---|
629 | // Terminate loop after 50 iterations and Reset distance to large number, |
---|
630 | // indicating no intersection with G4CylindricalSurface. |
---|
631 | // This generally occurs if the Helix curls too tightly to Intersect it. |
---|
632 | if ( iter > 50 ) { |
---|
633 | Dist = FLT_MAXX; |
---|
634 | p = lv; |
---|
635 | break; |
---|
636 | } |
---|
637 | // Find distance from the current point along the above-calculated |
---|
638 | // G4Vector3D using a Ray. |
---|
639 | // The G4Vector3D of the Ray and the Sign of the distance are determined |
---|
640 | // by whether the starting point of the Helix is Inside or outside of |
---|
641 | // the G4CylindricalSurface. |
---|
642 | in1 = Inside( p ); |
---|
643 | if ( in1 ) { // current point Inside |
---|
644 | if ( in0 ) { // starting point Inside |
---|
645 | Ray* r = new Ray( p, d ); |
---|
646 | delta = |
---|
647 | distanceAlongRay( 1, r, p ); |
---|
648 | delete r; |
---|
649 | } |
---|
650 | else { // starting point outside |
---|
651 | Ray* r = new Ray( p, -d ); |
---|
652 | delta = |
---|
653 | -distanceAlongRay( 1, r, p ); |
---|
654 | delete r; |
---|
655 | } |
---|
656 | } |
---|
657 | else { // current point outside |
---|
658 | if ( in0 ) { // starting point Inside |
---|
659 | Ray* r = new Ray( p, -d ); |
---|
660 | delta = |
---|
661 | -distanceAlongRay( -1, r, p ); |
---|
662 | delete r; |
---|
663 | } |
---|
664 | else { // starting point outside |
---|
665 | Ray* r = new Ray( p, d ); |
---|
666 | delta = |
---|
667 | distanceAlongRay( -1, r, p ); |
---|
668 | delete r; |
---|
669 | } |
---|
670 | } |
---|
671 | // Test if distance is less than the surface precision, if so Terminate loop. |
---|
672 | if ( std::fabs( delta / sc ) <= SURFACE_PRECISION ) |
---|
673 | break; |
---|
674 | // If delta has not changed sufficiently from the previous iteration, |
---|
675 | // skip out of this loop. |
---|
676 | if ( std::fabs( ( delta - delta0 ) / sc ) <= |
---|
677 | SURFACE_PRECISION ) |
---|
678 | break; |
---|
679 | // If delta has increased in absolute value from the previous iteration |
---|
680 | // either the Helix doesn't Intersect the G4CylindricalSurface or the approximate |
---|
681 | // solution is too far from the real solution. Try groping for a solution. |
---|
682 | // If not found, Reset distance to large number, indicating no intersection with |
---|
683 | // the G4CylindricalSurface. |
---|
684 | if ( std::fabs( delta ) > std::fabs( delta0 ) ) { |
---|
685 | Dist = std::fabs( rhp ) * |
---|
686 | gropeAlongHelix( hx ); |
---|
687 | if ( Dist < 0.0 ) { |
---|
688 | Dist = FLT_MAXX; |
---|
689 | p = lv; |
---|
690 | } |
---|
691 | else |
---|
692 | p = hx->position( Dist ); |
---|
693 | break; |
---|
694 | } |
---|
695 | // Set old delta to new one. |
---|
696 | delta0 = delta; |
---|
697 | // Add distance to G4CylindricalSurface to distance along Helix. |
---|
698 | Dist += delta; |
---|
699 | // Negative distance along Helix means Helix doesn't Intersect |
---|
700 | // G4CylindricalSurface. |
---|
701 | // Reset distance to large number, indicating no intersection with |
---|
702 | // G4CylindricalSurface. |
---|
703 | if ( Dist < 0.0 ) { |
---|
704 | Dist = FLT_MAXX; |
---|
705 | p = lv; |
---|
706 | break; |
---|
707 | } |
---|
708 | // Recalculate point along Helix and the G4Vector3D. |
---|
709 | p = hx->position( Dist ); |
---|
710 | d = hx->direction( Dist ); |
---|
711 | } // end of while loop |
---|
712 | } // end of exact == 0 condition |
---|
713 | // Now have best value of distance along Helix and position for this |
---|
714 | // solution, so test if it is within the boundary of the sub-shape |
---|
715 | // and require that it point in the correct G4Vector3D with respect to |
---|
716 | // the Normal to the G4CylindricalSurface. |
---|
717 | if ( ( Dist < FLT_MAXX ) && |
---|
718 | ( ( hx->direction( Dist ) * Normal( p ) * |
---|
719 | which_way ) >= 0.0 ) && |
---|
720 | ( WithinBoundary( p ) == 1 ) ) |
---|
721 | return Dist; |
---|
722 | } // end of if s[isoln] >= 0.0 condition |
---|
723 | } // end of for loop over solutions |
---|
724 | // if one gets here, there is no solution, so set distance along Helix |
---|
725 | // and position to large numbers |
---|
726 | Dist = FLT_MAXX; |
---|
727 | p = lv; |
---|
728 | return Dist; |
---|
729 | } |
---|
730 | */ |
---|
731 | |
---|
732 | |
---|
733 | G4Vector3D G4CylindricalSurface::Normal( const G4Vector3D& p ) const |
---|
734 | { |
---|
735 | // return the Normal unit vector to the G4CylindricalSurface |
---|
736 | // at a point p on (or nearly on) the G4CylindricalSurface |
---|
737 | |
---|
738 | G4Vector3D n = ( p - origin ) - ( ( p - origin ) * axis ) * axis; |
---|
739 | G4double nmag = n.mag(); |
---|
740 | |
---|
741 | if ( nmag != 0.0 ) |
---|
742 | n = n * (1/nmag); |
---|
743 | |
---|
744 | return n; |
---|
745 | } |
---|
746 | |
---|
747 | |
---|
748 | G4Vector3D G4CylindricalSurface::SurfaceNormal( const G4Point3D& p ) const |
---|
749 | { |
---|
750 | // return the Normal unit vector to the G4CylindricalSurface at a point |
---|
751 | // p on (or nearly on) the G4CylindricalSurface |
---|
752 | |
---|
753 | G4Vector3D n = ( p - origin ) - ( ( p - origin ) * axis ) * axis; |
---|
754 | G4double nmag = n.mag(); |
---|
755 | |
---|
756 | if ( nmag != 0.0 ) |
---|
757 | n = n * (1/nmag); |
---|
758 | |
---|
759 | return n; |
---|
760 | } |
---|
761 | |
---|
762 | |
---|
763 | G4int G4CylindricalSurface::Inside ( const G4Vector3D& x ) const |
---|
764 | { |
---|
765 | // Return 0 if point x is outside G4CylindricalSurface, 1 if Inside. |
---|
766 | // Outside means that the distance to the G4CylindricalSurface would |
---|
767 | // be negative. |
---|
768 | // Use the HowNear function to calculate this distance. |
---|
769 | if ( HowNear( x ) >= -0.5*kCarTolerance ) |
---|
770 | return 1; |
---|
771 | else |
---|
772 | return 0; |
---|
773 | } |
---|
774 | |
---|
775 | |
---|
776 | G4int G4CylindricalSurface::WithinBoundary( const G4Vector3D& x ) const |
---|
777 | { |
---|
778 | // return 1 if point x is on the G4CylindricalSurface, otherwise return zero |
---|
779 | // base this on the surface precision factor set in support/globals.h |
---|
780 | if ( std::fabs( HowNear( x ) / Scale() ) <= SURFACE_PRECISION ) |
---|
781 | return 1; |
---|
782 | else |
---|
783 | return 0; |
---|
784 | } |
---|
785 | |
---|
786 | |
---|
787 | G4double G4CylindricalSurface::Scale() const |
---|
788 | { |
---|
789 | // Returns the radius of a G4CylindricalSurface unless it is zero, in which |
---|
790 | // case returns the arbitrary number 1.0. |
---|
791 | // This is ok since derived finite-sized classes will overwrite this. |
---|
792 | // Used for Scale-invariant tests of surface thickness. |
---|
793 | if ( radius == 0.0 ) |
---|
794 | return 1.0; |
---|
795 | else |
---|
796 | return radius; |
---|
797 | } |
---|
798 | |
---|
799 | |
---|
800 | //void G4CylindricalSurface::rotate( G4double alpha, G4double beta, |
---|
801 | // G4double gamma, G4ThreeMat& m, G4int inverse ) |
---|
802 | // // rotate G4CylindricalSurface first about global x-axis by angle alpha, |
---|
803 | // second about global y-axis by angle beta, |
---|
804 | // and third about global z-axis by angle gamma |
---|
805 | // by creating and using G4ThreeMat objects in Surface::rotate |
---|
806 | // angles are assumed to be given in radians |
---|
807 | // if inverse is non-zero, the order of rotations is reversed |
---|
808 | // the axis is rotated here, the origin is rotated by calling |
---|
809 | // Surface::rotate |
---|
810 | // G4Surface::rotate( alpha, beta, gamma, m, inverse ); |
---|
811 | // axis = m * axis; |
---|
812 | //} |
---|
813 | |
---|
814 | //void G4CylindricalSurface::rotate( G4double alpha, G4double beta, |
---|
815 | // G4double gamma, G4int inverse ) |
---|
816 | //{ // rotate G4CylindricalSurface first about global x-axis by angle alpha, |
---|
817 | // second about global y-axis by angle beta, |
---|
818 | // and third about global z-axis by angle gamma |
---|
819 | // by creating and using G4ThreeMat objects in Surface::rotate |
---|
820 | // angles are assumed to be given in radians |
---|
821 | // if inverse is non-zero, the order of rotations is reversed |
---|
822 | // the axis is rotated here, the origin is rotated by calling |
---|
823 | // Surface::rotate |
---|
824 | // G4ThreeMat m; |
---|
825 | // G4Surface::rotate( alpha, beta, gamma, m, inverse ); |
---|
826 | // axis = m * axis; |
---|
827 | //} |
---|
828 | |
---|
829 | |
---|
830 | void G4CylindricalSurface::SetRadius( G4double r ) |
---|
831 | { |
---|
832 | // Reset the radius of the G4CylindricalSurface |
---|
833 | // Require radius to be non-negative |
---|
834 | if ( r >= 0.0 ) |
---|
835 | radius = r; |
---|
836 | // use old value (do not change radius) if out of the range, |
---|
837 | // but Print message |
---|
838 | else |
---|
839 | { |
---|
840 | G4cerr << "Error in G4CylindricalSurface::SetRadius" |
---|
841 | << "--asked for negative radius\n" |
---|
842 | << "\tDefault radius of " << radius << " is used.\n"; |
---|
843 | } |
---|
844 | } |
---|
845 | |
---|
846 | |
---|
847 | /* |
---|
848 | G4double G4CylindricalSurface::gropeAlongHelix( const Helix* hx ) const |
---|
849 | { // Grope for a solution of a Helix intersecting a G4CylindricalSurface. |
---|
850 | // This function returns the turning angle (in radians) where the |
---|
851 | // intersection occurs with only positive values allowed, or -1.0 if |
---|
852 | // no intersection is found. |
---|
853 | // The idea is to start at the beginning of the Helix, then take steps |
---|
854 | // of some fraction of a turn. If at the end of a Step, the current position |
---|
855 | // along the Helix and the previous position are on opposite sides of the |
---|
856 | // G4CylindricalSurface, then the solution must lie somewhere in between. |
---|
857 | G4int one_over_f = 8; // one over fraction of a turn to go in each Step |
---|
858 | G4double turn_angle = 0.0; |
---|
859 | G4double dist_along = 0.0; |
---|
860 | G4double d_new; |
---|
861 | G4double fk = 1.0 / G4double( one_over_f ); |
---|
862 | G4double scal = Scale(); |
---|
863 | G4double d_old = HowNear( hx->position( dist_along ) ); |
---|
864 | G4double rh = hx->GetRadius(); // radius of Helix |
---|
865 | G4Vector3D prp = hx->getPerp(); // perpendicular vector |
---|
866 | G4double prpmag = prp.Magnitude(); |
---|
867 | G4double rhp = rh / prpmag; |
---|
868 | G4int max_iter = one_over_f * HELIX_MAX_TURNS; |
---|
869 | // Take up to a user-settable number of turns along the Helix, |
---|
870 | // groping for an intersection point. |
---|
871 | for ( G4int k = 1; k < max_iter; k++ ) { |
---|
872 | turn_angle = 2.0 * pi * k / one_over_f; |
---|
873 | dist_along = turn_angle * std::fabs( rhp ); |
---|
874 | d_new = HowNear( hx->position( dist_along ) ); |
---|
875 | if ( ( d_old < 0.0 && d_new > 0.0 ) || |
---|
876 | ( d_old > 0.0 && d_new < 0.0 ) ) { |
---|
877 | d_old = d_new; |
---|
878 | // Old and new points are on opposite sides of the G4CylindricalSurface, therefore |
---|
879 | // a solution lies in between, use a binary search to pin the point down |
---|
880 | // to the surface precision, but don't do more than 50 iterations. |
---|
881 | G4int itr = 0; |
---|
882 | while ( std::fabs( d_new / scal ) > SURFACE_PRECISION ) { |
---|
883 | itr++; |
---|
884 | if ( itr > 50 ) |
---|
885 | return turn_angle; |
---|
886 | turn_angle -= fk * pi; |
---|
887 | dist_along = turn_angle * std::fabs( rhp ); |
---|
888 | d_new = HowNear( hx->position( dist_along ) ); |
---|
889 | if ( ( d_old < 0.0 && d_new > 0.0 ) || |
---|
890 | ( d_old > 0.0 && d_new < 0.0 ) ) |
---|
891 | fk *= -0.5; |
---|
892 | else |
---|
893 | fk *= 0.5; |
---|
894 | d_old = d_new; |
---|
895 | } // end of while loop |
---|
896 | return turn_angle; // this is the best solution |
---|
897 | } // end of if condition |
---|
898 | } // end of for loop |
---|
899 | // Get here only if no solution is found, so return -1.0 to indicate that. |
---|
900 | return -1.0; |
---|
901 | } |
---|
902 | */ |
---|