[1350] | 1 | // |
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| 2 | // E.Medernach 2000 |
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| 3 | // |
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| 4 | |
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| 5 | #define EPSILON 1e-12 |
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| 6 | #define INFINITY 1e+12 |
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| 7 | #define TORUSPRECISION 0.001 //1.0 // or whatever you want for precision (it is TorusEquation related) |
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| 8 | |
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| 9 | #define NBPOINT 6 |
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| 10 | #define ITERATION 8 //20 But 8 is really enough for Newton with a good guess |
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| 11 | #define NOINTERSECTION -1//kInfinity |
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| 12 | |
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| 13 | #define DEBUGTORUS 0 |
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| 14 | |
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| 15 | /* |
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| 16 | Torus implementation with Newton Method and Bounding volume |
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| 17 | */ |
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| 18 | |
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| 19 | |
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| 20 | #define G4double double |
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| 21 | |
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| 22 | |
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| 23 | #include <stdio.h> |
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| 24 | #include <math.h> |
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| 25 | #include "torus.h" |
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| 26 | |
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| 27 | double cos(double x); |
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| 28 | double sin(double x); |
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| 29 | |
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| 30 | |
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| 31 | double sqrt(double x); |
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| 32 | double fabs(double x); |
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| 33 | |
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| 34 | |
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| 35 | inline int CheckAngle (double x,double y,double phi,double deltaphi) |
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| 36 | { |
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| 37 | /** Note: this is possble to avoid atan by projecing -PI;PI to -inf;inf **/ |
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| 38 | |
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| 39 | double theta ; |
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| 40 | |
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| 41 | theta = atan(x/y); |
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| 42 | if (y < 0.0) theta += M_PI; |
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| 43 | if (theta < 0.0) theta += 2*M_PI; |
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| 44 | |
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| 45 | if ((theta >= phi) && (theta <= (phi + deltaphi))) { |
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| 46 | return 1; |
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| 47 | } else { |
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| 48 | return 0; |
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| 49 | } |
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| 50 | } |
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| 51 | |
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| 52 | inline double IntersectPlanarSection (double x,double y,double dx,double dy,double phi,double deltaphi) |
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| 53 | { |
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| 54 | /*** Intersect a ray with plan (phi) and (phi + deltaphi) ***/ |
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| 55 | /*** the point is outside phi..phi+deltaphi ***/ |
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| 56 | double Lambda1,Lambda2 ; |
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| 57 | Lambda1 = -(y - x*tan(phi))/(dy - dx*tan(phi)); |
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| 58 | Lambda2 = -(y - x*tan(phi + deltaphi))/(dy - dx*tan(phi + deltaphi)); |
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| 59 | if (Lambda1 < Lambda2) { |
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| 60 | return Lambda1; |
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| 61 | } else { |
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| 62 | return Lambda2; |
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| 63 | } |
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| 64 | } |
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| 65 | |
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| 66 | inline double TorusEquation (x, y, z, R0, R1) |
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| 67 | double x; |
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| 68 | double y; |
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| 69 | double z; |
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| 70 | double R0; |
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| 71 | double R1; |
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| 72 | { |
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| 73 | /* |
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| 74 | An interesting property is that the sign |
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| 75 | tell if the point is inside or outside |
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| 76 | or if > EPSILON on the surface |
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| 77 | */ |
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| 78 | double temp; |
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| 79 | |
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| 80 | temp = ((x*x + y*y + z*z) + R0*R0 - R1*R1) ; |
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| 81 | temp = temp*temp ; |
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| 82 | temp = temp - 4*R0*R0*(x*x + y*y) ; |
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| 83 | |
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| 84 | /* |
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| 85 | > 0 Outside |
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| 86 | < 0 Inside |
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| 87 | */ |
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| 88 | return temp ; |
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| 89 | } |
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| 90 | |
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| 91 | |
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| 92 | inline double TorusDerivativeX (x, y, z, R0, R1) |
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| 93 | double x; |
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| 94 | double y; |
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| 95 | double z; |
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| 96 | double R0; |
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| 97 | double R1; |
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| 98 | { |
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| 99 | return 4*x*(x*x + y*y + z*z + R0*R0 - R1*R1) - 8*R0*R0*x ; |
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| 100 | } |
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| 101 | |
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| 102 | inline double TorusDerivativeY (x, y, z, R0, R1) |
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| 103 | double x; |
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| 104 | double y; |
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| 105 | double z; |
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| 106 | double R0; |
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| 107 | double R1; |
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| 108 | { |
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| 109 | return 4*y*(x*x + y*y + z*z + R0*R0 - R1*R1) - 8*R0*R0*y ; |
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| 110 | } |
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| 111 | |
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| 112 | |
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| 113 | inline double TorusDerivativeZ (x, y, z, R0, R1) |
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| 114 | double x; |
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| 115 | double y; |
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| 116 | double z; |
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| 117 | double R0; |
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| 118 | double R1; |
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| 119 | { |
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| 120 | return 4*z*(x*x + y*y + z*z + R0*R0 - R1*R1) ; |
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| 121 | } |
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| 122 | |
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| 123 | |
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| 124 | inline double ParaboloidEquation (x, y, z, H, L) |
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| 125 | double x; |
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| 126 | double y; |
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| 127 | double z; |
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| 128 | double H; |
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| 129 | double L; |
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| 130 | |
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| 131 | { |
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| 132 | return z - H*(x*x + y*y)/(L*L) ; |
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| 133 | } |
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| 134 | |
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| 135 | inline double ParaboloidDerX (x, y, z, H, L) |
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| 136 | double x; |
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| 137 | double y; |
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| 138 | double z; |
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| 139 | double H; |
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| 140 | double L; |
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| 141 | |
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| 142 | { |
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| 143 | return - 2*H*x/(L*L) ; |
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| 144 | } |
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| 145 | |
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| 146 | inline double ParaboloidDerY (x, y, z, H, L) |
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| 147 | double x; |
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| 148 | double y; |
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| 149 | double z; |
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| 150 | double H; |
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| 151 | double L; |
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| 152 | |
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| 153 | { |
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| 154 | return - 2*H*y/(L*L) ; |
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| 155 | } |
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| 156 | |
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| 157 | inline double ParaboloidDerZ (x, y, z, H, L) |
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| 158 | double x; |
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| 159 | double y; |
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| 160 | double z; |
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| 161 | double H; |
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| 162 | double L; |
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| 163 | |
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| 164 | { |
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| 165 | return 1 ; |
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| 166 | } |
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| 167 | |
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| 168 | |
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| 169 | inline double HyperboloidEquation (x, y, z, H, L) |
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| 170 | double x; |
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| 171 | double y; |
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| 172 | double z; |
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| 173 | double H; |
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| 174 | double L; |
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| 175 | |
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| 176 | { |
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| 177 | return (x*x + y*y) - z*z + H*H - L*L ; |
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| 178 | } |
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| 179 | |
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| 180 | inline double HyperboloidDerX (x, y, z, H, L) |
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| 181 | double x; |
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| 182 | double y; |
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| 183 | double z; |
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| 184 | double H; |
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| 185 | double L; |
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| 186 | |
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| 187 | { |
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| 188 | return 2*x ; |
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| 189 | } |
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| 190 | |
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| 191 | inline double HyperboloidDerY (x, y, z, H, L) |
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| 192 | double x; |
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| 193 | double y; |
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| 194 | double z; |
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| 195 | double H; |
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| 196 | double L; |
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| 197 | |
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| 198 | { |
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| 199 | return 2*y ; |
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| 200 | } |
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| 201 | |
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| 202 | inline double HyperboloidDerZ (x, y, z, H, L) |
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| 203 | double x; |
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| 204 | double y; |
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| 205 | double z; |
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| 206 | double H; |
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| 207 | double L; |
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| 208 | |
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| 209 | { |
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| 210 | return -2*z ; |
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| 211 | } |
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| 212 | |
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| 213 | |
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| 214 | void BVMParaboloidIntersection (G4double x,G4double y,G4double z, |
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| 215 | G4double dx,G4double dy,G4double dz, |
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| 216 | G4double H, G4double L, |
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| 217 | G4double *NewL,int *valid) |
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| 218 | { |
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| 219 | /* We use the box [-L L]x[-L L]x[0 H] */ |
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| 220 | /* there is only one interval at maximum */ |
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| 221 | |
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| 222 | /* NewL and valid are array of 6 elements */ |
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| 223 | |
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| 224 | if (dz != 0) { |
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| 225 | /* z = 0 */ |
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| 226 | NewL[0] = -z/dz ; |
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| 227 | if ((fabs(x + NewL[0]*dx) < L) && (fabs(y + NewL[0]*dy) < L)) { |
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| 228 | valid[0] = 1; |
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| 229 | } else { |
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| 230 | valid[0] = 0; |
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| 231 | } |
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| 232 | |
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| 233 | /* z = H */ |
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| 234 | NewL[1] = -(z-H)/dz ; |
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| 235 | if ((fabs(x + NewL[1]*dx) < L) && (fabs(y + NewL[1]*dy) < L)) { |
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| 236 | valid[1] = 1; |
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| 237 | } else { |
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| 238 | valid[1] = 0; |
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| 239 | } |
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| 240 | |
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| 241 | } else { |
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| 242 | NewL[0] = -1.0 ; |
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| 243 | NewL[1] = -1.0 ; |
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| 244 | valid[0] = 0; |
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| 245 | valid[1] = 0; |
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| 246 | } |
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| 247 | |
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| 248 | if (dx != 0) { |
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| 249 | /* x = -L */ |
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| 250 | NewL[2] = -(x+L)/dx ; |
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| 251 | if ((fabs(z - H/2 +NewL[2]*dz) < H/2) && (fabs(y + NewL[2]*dy) < L)) { |
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| 252 | valid[2] = 1; |
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| 253 | } else { |
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| 254 | valid[2] = 0; |
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| 255 | } |
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| 256 | |
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| 257 | /* z = H */ |
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| 258 | NewL[3] = -(x-L)/dx ; |
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| 259 | if ((fabs(z - H/2 + NewL[3]*dz) < H/2) && (fabs(y + NewL[3]*dy) < L)) { |
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| 260 | valid[3] = 1; |
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| 261 | } else { |
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| 262 | valid[3] = 0; |
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| 263 | } |
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| 264 | |
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| 265 | } else { |
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| 266 | NewL[2] = -1.0 ; |
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| 267 | NewL[3] = -1.0 ; |
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| 268 | valid[2] = 0; |
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| 269 | valid[3] = 0; |
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| 270 | } |
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| 271 | |
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| 272 | if (dy != 0) { |
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| 273 | /* y = -L */ |
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| 274 | NewL[4] = -(y+L)/dy ; |
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| 275 | if ((fabs(z - H/2 +NewL[4]*dz) < H) && (fabs(y + NewL[4]*dy) < L)) { |
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| 276 | valid[4] = 1; |
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| 277 | } else { |
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| 278 | valid[4] = 0; |
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| 279 | } |
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| 280 | |
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| 281 | /* z = H */ |
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| 282 | NewL[5] = -(y-L)/dy ; |
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| 283 | if ((fabs(z - H/2 + NewL[5]*dz) < H) && (fabs(y + NewL[5]*dy) < L)) { |
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| 284 | valid[5] = 1; |
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| 285 | } else { |
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| 286 | valid[5] = 0; |
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| 287 | } |
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| 288 | |
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| 289 | } else { |
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| 290 | NewL[4] = -1.0 ; |
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| 291 | NewL[5] = -1.0 ; |
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| 292 | valid[4] = 0; |
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| 293 | valid[5] = 0; |
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| 294 | } |
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| 295 | |
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| 296 | } |
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| 297 | |
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| 298 | void BVMHyperboloidIntersection (G4double x,G4double y,G4double z, |
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| 299 | G4double dx,G4double dy,G4double dz, |
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| 300 | G4double H, G4double L, |
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| 301 | G4double *NewL,int *valid) |
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| 302 | { |
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| 303 | /* We use the box [-L L]x[-L L]x[-H H] */ |
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| 304 | /* there is only one interval at maximum */ |
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| 305 | |
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| 306 | /* NewL and valid are array of 6 elements */ |
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| 307 | |
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| 308 | if (dz != 0) { |
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| 309 | /* z = -H */ |
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| 310 | NewL[0] = -(z+H)/dz ; |
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| 311 | if ((fabs(x + NewL[0]*dx) < L) && (fabs(y + NewL[0]*dy) < L)) { |
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| 312 | valid[0] = 1; |
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| 313 | } else { |
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| 314 | valid[0] = 0; |
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| 315 | } |
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| 316 | |
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| 317 | /* z = H */ |
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| 318 | NewL[1] = -(z-H)/dz ; |
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| 319 | if ((fabs(x + NewL[1]*dx) < L) && (fabs(y + NewL[1]*dy) < L)) { |
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| 320 | valid[1] = 1; |
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| 321 | } else { |
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| 322 | valid[1] = 0; |
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| 323 | } |
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| 324 | |
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| 325 | } else { |
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| 326 | NewL[0] = -1.0 ; |
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| 327 | NewL[1] = -1.0 ; |
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| 328 | valid[0] = 0; |
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| 329 | valid[1] = 0; |
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| 330 | } |
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| 331 | |
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| 332 | if (dx != 0) { |
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| 333 | /* x = -L */ |
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| 334 | NewL[2] = -(x+L)/dx ; |
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| 335 | if ((fabs(z +NewL[2]*dz) < H) && (fabs(y + NewL[2]*dy) < L)) { |
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| 336 | valid[2] = 1; |
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| 337 | } else { |
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| 338 | valid[2] = 0; |
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| 339 | } |
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| 340 | |
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| 341 | /* z = H */ |
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| 342 | NewL[3] = -(x-L)/dx ; |
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| 343 | if ((fabs(z + NewL[3]*dz) < H) && (fabs(y + NewL[3]*dy) < L)) { |
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| 344 | valid[3] = 1; |
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| 345 | } else { |
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| 346 | valid[3] = 0; |
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| 347 | } |
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| 348 | |
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| 349 | } else { |
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| 350 | NewL[2] = -1.0 ; |
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| 351 | NewL[3] = -1.0 ; |
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| 352 | valid[2] = 0; |
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| 353 | valid[3] = 0; |
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| 354 | } |
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| 355 | |
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| 356 | if (dy != 0) { |
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| 357 | /* y = -L */ |
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| 358 | NewL[4] = -(y+L)/dy ; |
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| 359 | if ((fabs(z +NewL[4]*dz) < H) && (fabs(y + NewL[4]*dy) < L)) { |
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| 360 | valid[4] = 1; |
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| 361 | } else { |
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| 362 | valid[4] = 0; |
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| 363 | } |
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| 364 | |
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| 365 | /* z = H */ |
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| 366 | NewL[5] = -(y-L)/dy ; |
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| 367 | if ((fabs(z + NewL[5]*dz) < H) && (fabs(y + NewL[5]*dy) < L)) { |
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| 368 | valid[5] = 1; |
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| 369 | } else { |
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| 370 | valid[5] = 0; |
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| 371 | } |
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| 372 | |
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| 373 | } else { |
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| 374 | NewL[4] = -1.0 ; |
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| 375 | NewL[5] = -1.0 ; |
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| 376 | valid[4] = 0; |
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| 377 | valid[5] = 0; |
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| 378 | } |
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| 379 | |
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| 380 | } |
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| 381 | |
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| 382 | void BVMIntersection(G4double x,G4double y,G4double z, |
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| 383 | G4double dx,G4double dy,G4double dz, |
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| 384 | G4double Rmax, G4double Rmin, |
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| 385 | G4double *NewL,int *valid) |
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| 386 | { |
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| 387 | |
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| 388 | if (dz != 0) { |
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| 389 | G4double DistToZ ; |
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| 390 | /* z = + Rmin */ |
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| 391 | NewL[0] = (Rmin - z)/dz ; |
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| 392 | /* z = - Rmin */ |
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| 393 | NewL[1] = (-Rmin - z)/dz ; |
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| 394 | /* Test validity here (*** To be optimized ***) */ |
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| 395 | if (NewL[0] < 0.0) valid[0] = 0; |
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| 396 | if (NewL[1] < 0.0) valid[1] = 0; |
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| 397 | DistToZ = (x+NewL[0]*dx)*(x+NewL[0]*dx) + (y+NewL[0]*dy)*(y+NewL[0]*dy); |
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| 398 | if (DistToZ - (Rmax + Rmin)*(Rmax + Rmin) > 0) |
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| 399 | valid[0] = 0; |
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| 400 | if (DistToZ - (Rmax - Rmin)*(Rmax - Rmin) < 0) |
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| 401 | valid[0] = 0; |
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| 402 | DistToZ = (x+NewL[1]*dx)*(x+NewL[1]*dx) + (y+NewL[1]*dy)*(y+NewL[1]*dy); |
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| 403 | if (DistToZ - (Rmax + Rmin)*(Rmax + Rmin) > 0) |
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| 404 | valid[1] = 0; |
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| 405 | if (DistToZ - (Rmax - Rmin)*(Rmax - Rmin) < 0) |
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| 406 | valid[1] = 0; |
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| 407 | } else { |
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| 408 | /* if dz == 0 we could know the exact solution */ |
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| 409 | /* Well, this is true but we have not expected precision issue from sqrt .. */ |
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| 410 | NewL[0] = -1.0; |
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| 411 | NewL[1] = -1.0; |
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| 412 | valid[0] = 0; |
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| 413 | valid[1] = 0; |
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| 414 | } |
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| 415 | |
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| 416 | /* x² + y² = (Rmax + Rmin)² */ |
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| 417 | if ((dx != 0) || (dy != 0)) { |
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| 418 | G4double a,b,c,d; |
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| 419 | |
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| 420 | a = dx*dx + dy*dy ; |
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| 421 | b = 2*(x*dx + y*dy) ; |
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| 422 | c = x*x + y*y - (Rmax + Rmin)*(Rmax + Rmin) ; |
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| 423 | d = b*b - 4*a*c ; |
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| 424 | |
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| 425 | if (d < 0) { |
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| 426 | valid[2] = 0; |
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| 427 | valid[3] = 0; |
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| 428 | NewL[2] = -1.0; |
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| 429 | NewL[3] = -1.0; |
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| 430 | } else { |
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| 431 | d = sqrt(d) ; |
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| 432 | NewL[2] = (d - b)/(2*a); |
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| 433 | NewL[3] = (-d - b)/(2*a); |
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| 434 | if (NewL[2] < 0.0) valid[2] = 0; |
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| 435 | if (fabs(z + NewL[2]*dz) - Rmin > EPSILON) valid[2] = 0; |
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| 436 | if (NewL[3] < 0.0) valid[3] = 0; |
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| 437 | if (fabs(z + NewL[3]*dz) - Rmin > EPSILON) valid[3] = 0; |
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| 438 | } |
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| 439 | } else { |
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| 440 | /* only dz != 0 so we could know the exact solution */ |
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| 441 | /* this depends only for the distance to Z axis */ |
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| 442 | /* BUT big precision problem near the border.. */ |
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| 443 | /* I like so much Newton to increase precision you know.. => */ |
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| 444 | |
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| 445 | NewL[2] = -1.0; |
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| 446 | NewL[3] = -1.0; |
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| 447 | valid[2] = 0; |
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| 448 | valid[3] = 0; |
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| 449 | |
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| 450 | /*** Try This to see precision issue with sqrt(~ 0) |
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| 451 | G4double DistToZ ; |
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| 452 | G4double result; |
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| 453 | G4double guess; |
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| 454 | |
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| 455 | DistToZ = sqrt(x*x + y*y) ; |
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| 456 | |
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| 457 | if ((DistToZ < (Rmax - Rmin)) || (DistToZ > (Rmax + Rmin))) { |
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| 458 | return -1.0 ; |
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| 459 | } |
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| 460 | |
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| 461 | result = sqrt((Rmin + Rmax - DistToZ)*(Rmin - Rmax + DistToZ)); |
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| 462 | |
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| 463 | if (dz < 0) { |
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| 464 | if (z > result) { |
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| 465 | return (result - z)/dz; |
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| 466 | } else { |
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| 467 | if (z > -result) { |
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| 468 | return (-result - z)/dz; |
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| 469 | } else |
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| 470 | return -1.0; |
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| 471 | } |
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| 472 | } else { |
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| 473 | if (z < -result) { |
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| 474 | return (z + result)/dz; |
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| 475 | } else { |
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| 476 | if (z < result) { |
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| 477 | return (z - result)/dz; |
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| 478 | } else |
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| 479 | return -1.0; |
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| 480 | } |
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| 481 | } |
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| 482 | */ |
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| 483 | } |
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| 484 | |
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| 485 | |
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| 486 | /* x² + y² = (Rmax - Rmin)² */ |
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| 487 | if ((dx != 0) || (dy != 0)) { |
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| 488 | G4double a,b,c,d; |
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| 489 | |
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| 490 | a = dx*dx + dy*dy ; |
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| 491 | b = 2*(x*dx + y*dy) ; |
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| 492 | c = x*x + y*y - (Rmax - Rmin)*(Rmax - Rmin) ; |
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| 493 | d = b*b - 4*a*c ; |
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| 494 | |
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| 495 | if (d < 0) { |
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| 496 | valid[4] = 0; |
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| 497 | valid[5] = 0; |
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| 498 | NewL[4] = -1.0; |
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| 499 | NewL[5] = -1.0; |
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| 500 | } else { |
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| 501 | d = sqrt(d) ; |
---|
| 502 | NewL[4] = (d - b)/(2*a); |
---|
| 503 | NewL[5] = (-d - b)/(2*a); |
---|
| 504 | if (NewL[4] < 0.0) valid[4] = 0; |
---|
| 505 | if (fabs(z + NewL[4]*dz) - Rmin > EPSILON) valid[4] = 0; |
---|
| 506 | if (NewL[5] < 0.0) valid[5] = 0; |
---|
| 507 | if (fabs(z + NewL[5]*dz) - Rmin > EPSILON) valid[5] = 0; |
---|
| 508 | } |
---|
| 509 | } else { |
---|
| 510 | /* only dz != 0 so we could know the exact solution */ |
---|
| 511 | /* OK but same as above .. */ |
---|
| 512 | valid[4] = 0; |
---|
| 513 | valid[5] = 0; |
---|
| 514 | NewL[4] = -1.0; |
---|
| 515 | NewL[5] = -1.0; |
---|
| 516 | } |
---|
| 517 | } |
---|
| 518 | |
---|
| 519 | void SortIntervals (int NbElem,G4double *SortL,G4double *NewL,int *valid,int *NbIntersection) |
---|
| 520 | { |
---|
| 521 | int i,j; |
---|
| 522 | G4double swap; |
---|
| 523 | |
---|
| 524 | (*NbIntersection) = 0; |
---|
| 525 | SortL[0] = -INFINITY; |
---|
| 526 | |
---|
| 527 | for (i=0;i<NbElem;i++) { |
---|
| 528 | if (valid[i] != 0) { |
---|
| 529 | SortL[(*NbIntersection)] = NewL[i] ; |
---|
| 530 | for (j=(*NbIntersection);j>0;j--) { |
---|
| 531 | if (SortL[j] < SortL[j-1]) { |
---|
| 532 | swap = SortL[j-1] ; |
---|
| 533 | SortL[j-1] = SortL[j]; |
---|
| 534 | SortL[j] = swap; |
---|
| 535 | } |
---|
| 536 | } |
---|
| 537 | |
---|
| 538 | (*NbIntersection) ++; |
---|
| 539 | } |
---|
| 540 | } |
---|
| 541 | /* Delete double value */ |
---|
| 542 | /* When the ray hits a corner we have a double value */ |
---|
| 543 | for (i=0;i<(*NbIntersection)-1;i++) { |
---|
| 544 | if (SortL[i+1] - SortL[i] < EPSILON) { |
---|
| 545 | if (((*NbIntersection) & (1)) == 1) { |
---|
| 546 | /* If the NbIntersection is odd then we keep one value */ |
---|
| 547 | for (j=i+1;j<(*NbIntersection);j++) { |
---|
| 548 | SortL[j-1] = SortL[j] ; |
---|
| 549 | } |
---|
| 550 | (*NbIntersection) --; |
---|
| 551 | } else { |
---|
| 552 | /* If it is even we delete the 2 values */ |
---|
| 553 | for (j=i+2;j<(*NbIntersection);j++) { |
---|
| 554 | SortL[j-2] = SortL[j] ; |
---|
| 555 | } |
---|
| 556 | (*NbIntersection) -= 2; |
---|
| 557 | } |
---|
| 558 | } |
---|
| 559 | } |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | |
---|
| 563 | /* TODO: |
---|
| 564 | check if the root is entering the torus (with gradient) |
---|
| 565 | clean problems when Rmin ~ Rmax (BVM is not good when near Z axis) |
---|
| 566 | */ |
---|
| 567 | |
---|
| 568 | /** Now the interesting part .. **/ |
---|
| 569 | |
---|
| 570 | int SafeNewton(G4double x, G4double y, G4double z, |
---|
| 571 | G4double dx, G4double dy, G4double dz, |
---|
| 572 | G4double Rmax, G4double Rmin, |
---|
| 573 | G4double *Lmin,G4double *Lmax) |
---|
| 574 | { |
---|
| 575 | /** SafeNewton is a clipping interval Newton method **/ |
---|
| 576 | G4double P[5][2],D[2] ; |
---|
| 577 | G4double Lx,Ly,Lz ; |
---|
| 578 | G4double NewMin,NewMax; |
---|
| 579 | |
---|
| 580 | int IntervalIsVoid = 1; |
---|
| 581 | int NewtonIsSafe = 0; |
---|
| 582 | |
---|
| 583 | /*** Calculating Control Points ***/ |
---|
| 584 | |
---|
| 585 | /* |
---|
| 586 | 0 p0 = F((*Lmin)) |
---|
| 587 | 1/4 p1 = F((*Lmin)) + ((*Lmax) - (*Lmin))/4 * F'((*Lmin)) |
---|
| 588 | 2/4 p2 = 1/6 * (32*F(((*Lmax) + (*Lmin))/2) - (p0 + 4*p1 + 4*p3 + p4)) |
---|
| 589 | 3/4 p3 = F((*Lmax)) - ((*Lmax) - (*Lmin))/4 * F'((*Lmax)) |
---|
| 590 | 1 p4 = F((*Lmax)) |
---|
| 591 | */ |
---|
| 592 | |
---|
| 593 | |
---|
| 594 | Lx = x + (*Lmin)*dx; |
---|
| 595 | Ly = y + (*Lmin)*dy; |
---|
| 596 | Lz = z + (*Lmin)*dz; |
---|
| 597 | |
---|
| 598 | D[0] = dx*HyperboloidDerX(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 599 | D[0] += dy*HyperboloidDerY(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 600 | D[0] += dz*HyperboloidDerZ(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 601 | |
---|
| 602 | P[0][0] = (*Lmin); |
---|
| 603 | P[0][1] = HyperboloidEquation(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 604 | |
---|
| 605 | if (fabs(P[0][1]) < TORUSPRECISION) { |
---|
| 606 | NewtonIsSafe = 1; |
---|
| 607 | //fprintf(stderr,"(fabs(P[0][1]) < TORUSPRECISION)\n"); |
---|
| 608 | return NewtonIsSafe; |
---|
| 609 | } |
---|
| 610 | |
---|
| 611 | if (((*Lmax) - (*Lmin)) < EPSILON) { |
---|
| 612 | //fprintf(stderr,"(((*Lmax) - (*Lmin)) < EPSILON)\n"); |
---|
| 613 | return 1; |
---|
| 614 | } |
---|
| 615 | |
---|
| 616 | P[1][0] = (*Lmin) + ((*Lmax) - (*Lmin))/4; |
---|
| 617 | P[1][1] = P[0][1] + (((*Lmax) - (*Lmin))/4.0) * D[0]; |
---|
| 618 | |
---|
| 619 | Lx = x + (*Lmax)*dx; |
---|
| 620 | Ly = y + (*Lmax)*dy; |
---|
| 621 | Lz = z + (*Lmax)*dz; |
---|
| 622 | |
---|
| 623 | D[1] = dx*HyperboloidDerX(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 624 | D[1] += dy*HyperboloidDerY(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 625 | D[1] += dz*HyperboloidDerZ(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 626 | |
---|
| 627 | P[4][0] = (*Lmax); |
---|
| 628 | P[4][1] = HyperboloidEquation(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 629 | P[3][0] = (*Lmax) - ((*Lmax) - (*Lmin))/4; |
---|
| 630 | P[3][1] = P[4][1] - ((*Lmax) - (*Lmin))/4 * D[1]; |
---|
| 631 | |
---|
| 632 | Lx = x + ((*Lmax)+(*Lmin))/2*dx; |
---|
| 633 | Ly = y + ((*Lmax)+(*Lmin))/2*dy; |
---|
| 634 | Lz = z + ((*Lmax)+(*Lmin))/2*dz; |
---|
| 635 | |
---|
| 636 | P[2][0] = ((*Lmax) + (*Lmin))/2; |
---|
| 637 | P[2][1] = (16*HyperboloidEquation(Lx,Ly,Lz,Rmax,Rmin) - (P[0][1] + 4*P[1][1] + 4*P[3][1] + P[4][1]))/6 ; |
---|
| 638 | |
---|
| 639 | |
---|
| 640 | |
---|
| 641 | //fprintf(stderr,"\n"); |
---|
| 642 | //fprintf(stderr,"Lmin = %14f\n",(*Lmin)); |
---|
| 643 | //fprintf(stderr,"Lmax = %14f\n",(*Lmax)); |
---|
| 644 | //fprintf(stderr,"P[0] = %14f\n",P[0][1]); |
---|
| 645 | //fprintf(stderr,"P[1] = %14f\n",P[1][1]); |
---|
| 646 | //fprintf(stderr,"P[2] = %14f\n",P[2][1]); |
---|
| 647 | //fprintf(stderr,"P[3] = %14f\n",P[3][1]); |
---|
| 648 | //fprintf(stderr,"P[4] = %14f\n",P[4][1]); |
---|
| 649 | |
---|
| 650 | #if DEBUGTORUS |
---|
| 651 | G4cout << "G4Torus::SafeNewton Lmin = " << (*Lmin) << G4endl ; |
---|
| 652 | G4cout << "G4Torus::SafeNewton Lmax = " << (*Lmax) << G4endl ; |
---|
| 653 | G4cout << "G4Torus::SafeNewton P[0] = " << P[0][1] << G4endl ; |
---|
| 654 | G4cout << "G4Torus::SafeNewton P[1] = " << P[1][1] << G4endl ; |
---|
| 655 | G4cout << "G4Torus::SafeNewton P[2] = " << P[2][1] << G4endl ; |
---|
| 656 | G4cout << "G4Torus::SafeNewton P[3] = " << P[3][1] << G4endl ; |
---|
| 657 | G4cout << "G4Torus::SafeNewton P[4] = " << P[4][1] << G4endl ; |
---|
| 658 | #endif |
---|
| 659 | |
---|
| 660 | /** Ok now we have all control points, we could compute the convex area **/ |
---|
| 661 | /** Problems: |
---|
| 662 | - if there is one point with a ~ 0 coordinate and all the other the same sign we |
---|
| 663 | miss the value |
---|
| 664 | - if there are more than a root in the interval then the interval length does not |
---|
| 665 | decrease to 0. A solution may be to split intervals in the middle but how to |
---|
| 666 | know that we must split ? |
---|
| 667 | - we have to compute convex area of the control point before applying intersection |
---|
| 668 | with y=0 |
---|
| 669 | **/ |
---|
| 670 | |
---|
| 671 | /*** For each points make 2 sets. A set of positive points and a set of negative points ***/ |
---|
| 672 | /*** Note: could be better done with scalar product .. ***/ |
---|
| 673 | |
---|
| 674 | /* there is an intersection only if each have different signs */ |
---|
| 675 | /* PROBLEM : If a control point have a 0.00 value the sign check is wrong */ |
---|
| 676 | { |
---|
| 677 | G4double Intersection ; |
---|
| 678 | int i,j; |
---|
| 679 | |
---|
| 680 | NewMin = (*Lmax) ; |
---|
| 681 | NewMax = (*Lmin) ; |
---|
| 682 | |
---|
| 683 | for (i=0;i<5;i++) |
---|
| 684 | for (j=i+1;j<5;j++) |
---|
| 685 | { |
---|
| 686 | /* there is an intersection only if each have different signs */ |
---|
| 687 | if (((P[j][1] > -TORUSPRECISION) && (P[i][1] < TORUSPRECISION)) || |
---|
| 688 | ((P[j][1] < TORUSPRECISION) && (P[i][1] > -TORUSPRECISION))) { |
---|
| 689 | IntervalIsVoid = 0; |
---|
| 690 | Intersection = P[j][0] - P[j][1]*((P[i][0] - P[j][0])/(P[i][1] - P[j][1])); |
---|
| 691 | if (Intersection < NewMin) { |
---|
| 692 | NewMin = Intersection; |
---|
| 693 | } |
---|
| 694 | if (Intersection > NewMax) { |
---|
| 695 | NewMax = Intersection; |
---|
| 696 | } |
---|
| 697 | } |
---|
| 698 | } |
---|
| 699 | if (IntervalIsVoid != 1) { |
---|
| 700 | (*Lmax) = NewMax; |
---|
| 701 | (*Lmin) = NewMin; |
---|
| 702 | } |
---|
| 703 | } |
---|
| 704 | |
---|
| 705 | if (IntervalIsVoid == 1) { |
---|
| 706 | //fprintf(stderr,"(IntervalIsVoid == 1)\n"); |
---|
| 707 | return -1; |
---|
| 708 | } |
---|
| 709 | |
---|
| 710 | //fprintf(stderr,"NewMin = %f NewMax = %f\n",NewMin,NewMax); |
---|
| 711 | /** Now we have each Extrema point of the new interval **/ |
---|
| 712 | |
---|
| 713 | return NewtonIsSafe; |
---|
| 714 | } |
---|
| 715 | |
---|
| 716 | |
---|
| 717 | G4double Newton (G4double guess, |
---|
| 718 | G4double x, G4double y, G4double z, |
---|
| 719 | G4double dx, G4double dy, G4double dz, |
---|
| 720 | G4double Rmax, G4double Rmin, |
---|
| 721 | G4double Lmin,G4double Lmax) |
---|
| 722 | { |
---|
| 723 | /* So now we have a good guess and an interval where if there are an intersection the root must be */ |
---|
| 724 | |
---|
| 725 | G4double Lx = 0; |
---|
| 726 | G4double Ly = 0; |
---|
| 727 | G4double Lz = 0; |
---|
| 728 | G4double Value = 0; |
---|
| 729 | G4double Gradient = 0; |
---|
| 730 | G4double Lambda ; |
---|
| 731 | |
---|
| 732 | int i=0; |
---|
| 733 | |
---|
| 734 | /* Reduce interval before applying Newton Method */ |
---|
| 735 | { |
---|
| 736 | int NewtonIsSafe ; |
---|
| 737 | |
---|
| 738 | while ((NewtonIsSafe = SafeNewton(x,y,z,dx,dy,dz,Rmax,Rmin,&Lmin,&Lmax)) == 0) ; |
---|
| 739 | |
---|
| 740 | guess = Lmin; |
---|
| 741 | } |
---|
| 742 | |
---|
| 743 | /*** BEWARE ***/ |
---|
| 744 | /* A typical problem is when Gradient is zero */ |
---|
| 745 | /* This is due to some 0 values in point or direction */ |
---|
| 746 | /* To solve that we move a little the guess |
---|
| 747 | if ((((x == 0) || (y == 0)) || (z == 0)) || |
---|
| 748 | (((dx == 0) || (dy == 0)) || (dz == 0))) |
---|
| 749 | guess += EPSILON;*/ |
---|
| 750 | |
---|
| 751 | Lambda = guess; |
---|
| 752 | Value = HyperboloidEquation(x + Lambda*dx,y + Lambda*dy,z + Lambda*dz,Rmax,Rmin); |
---|
| 753 | |
---|
| 754 | //fprintf(stderr,"NEWTON begin with L = %f and V = %f\n",Lambda,Value); |
---|
| 755 | |
---|
| 756 | /*** Beware: we must eliminate case with no root ***/ |
---|
| 757 | /*** Beware: In some rare case we converge to the false root (internal border)***/ |
---|
| 758 | /*** |
---|
| 759 | { |
---|
| 760 | FILE *fi; |
---|
| 761 | int i; |
---|
| 762 | fi = fopen("GNUplot.out","w+"); |
---|
| 763 | //fprintf(fi,"# Newton plot\n"); |
---|
| 764 | |
---|
| 765 | for (i = 0; i < 1000 ; i ++) { |
---|
| 766 | Lx = x + (Lmin + i*(Lmax - Lmin)/1000.0)*dx; |
---|
| 767 | Ly = y + (Lmin + i*(Lmax - Lmin)/1000.0)*dy; |
---|
| 768 | Lz = z + (Lmin + i*(Lmax - Lmin)/1000.0)*dz; |
---|
| 769 | Value = HyperboloidEquation(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 770 | //fprintf(fi," %f %f\n",Lmin + i*(Lmax - Lmin)/1000.0,Value ); |
---|
| 771 | } |
---|
| 772 | |
---|
| 773 | fclose(fi); |
---|
| 774 | } |
---|
| 775 | |
---|
| 776 | ***/ |
---|
| 777 | |
---|
| 778 | /* In fact The Torus Equation give big number so TORUS PRECISION is not EPSILON */ |
---|
| 779 | while (/* ?? (fabs(Value/Gradient) > 1e-2) ||*/ (fabs(Value) > TORUSPRECISION)) { |
---|
| 780 | |
---|
| 781 | // do { |
---|
| 782 | Lx = x + Lambda*dx; |
---|
| 783 | Ly = y + Lambda*dy; |
---|
| 784 | Lz = z + Lambda*dz; |
---|
| 785 | Value = HyperboloidEquation(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 786 | |
---|
| 787 | Gradient = dx*HyperboloidDerX(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 788 | Gradient += dy*HyperboloidDerY(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 789 | Gradient += dz*HyperboloidDerZ(Lx,Ly,Lz,Rmax,Rmin); |
---|
| 790 | |
---|
| 791 | /* |
---|
| 792 | if (Gradient > -EPSILON) |
---|
| 793 | return Lmin; |
---|
| 794 | */ |
---|
| 795 | |
---|
| 796 | /*** |
---|
| 797 | if ((beware != 0) && (Gradient > -EPSILON)) { |
---|
| 798 | ***/ |
---|
| 799 | |
---|
| 800 | /** Newton does not go to the root because interval is too big **/ |
---|
| 801 | /** In fact Newton is known to converge if |f.f''/(f'^2)| < 1 **/ |
---|
| 802 | /** There is two cases: ray hits or not **/ |
---|
| 803 | /** If ray hits we must search for a better intervals **/ |
---|
| 804 | /** but if there are no hits then we could not .. **/ |
---|
| 805 | /** So the easier way the best: if Newton encounter a problem |
---|
| 806 | it says to the BVM that the guess is no good |
---|
| 807 | then the BVM search for a better intervals, possibly none |
---|
| 808 | in this case no intersection, else we go back to Newton |
---|
| 809 | **/ |
---|
| 810 | |
---|
| 811 | /** |
---|
| 812 | Perhaps we have not to break Newton at the beginning because we could converge after some move |
---|
| 813 | May be not: If we are here this means that the root we want is rejecting. We could converge to |
---|
| 814 | another root. |
---|
| 815 | PROBLEMS |
---|
| 816 | **/ |
---|
| 817 | /* root is repulsive from this guess could you give me another guess ? |
---|
| 818 | Note: that it may be no root in this area .. |
---|
| 819 | Note: Lmin and Lmax are always outside the torus as a part of the BVM. |
---|
| 820 | We just want a point in this direction with a gradient < 0 |
---|
| 821 | |
---|
| 822 | guess = FindABetterGuess(Rmax,Rmin,guess,Lmin,Lmax); |
---|
| 823 | */ |
---|
| 824 | Lambda = Lambda - Value/Gradient ; |
---|
| 825 | |
---|
| 826 | #if DEBUGTORUS |
---|
| 827 | G4cout << "Newton Iteration " << i << G4endl ; |
---|
| 828 | G4cout << "Newton Lambda = " << Lambda << " Value = " << Value << " Grad = " << Gradient << G4endl; |
---|
| 829 | G4cout << "Newton Lmin = " << Lmin << " Lmax = " << Lmax << G4endl ; |
---|
| 830 | #endif |
---|
| 831 | //fprintf(stderr,"Newton Iteration %d\n",i); |
---|
| 832 | //fprintf(stderr,"Newton Lambda = %f Value = %f Grad = %f\n",Lambda,Value,Gradient); |
---|
| 833 | |
---|
| 834 | i ++; |
---|
| 835 | |
---|
| 836 | if (i > ITERATION) |
---|
| 837 | return NOINTERSECTION; //no convergency ?? |
---|
| 838 | |
---|
| 839 | } //while (/* ?? (fabs(Value/Gradient) > 1e-2) ||*/ (fabs(Value) > TORUSPRECISION)); |
---|
| 840 | |
---|
| 841 | |
---|
| 842 | #if DEBUGTORUS |
---|
| 843 | G4cout << "Newton Exiting with Lambda = " << Lambda << G4endl ; |
---|
| 844 | G4cout << "Newton Exiting with Value = " << Value << G4endl ; |
---|
| 845 | #endif |
---|
| 846 | |
---|
| 847 | //just a check |
---|
| 848 | if (Lambda < 0.0) { |
---|
| 849 | //fprintf(stderr,"Newton end with a negative solution ..\n"); |
---|
| 850 | return NOINTERSECTION; |
---|
| 851 | } |
---|
| 852 | //fprintf(stderr,"NEWTON: Lamdba = %f\n",Lambda); |
---|
| 853 | return Lambda ; |
---|
| 854 | } |
---|
| 855 | |
---|
| 856 | /* |
---|
| 857 | G4double DistanceToTorus (G4double x,G4double y,G4double z, |
---|
| 858 | G4double dx,G4double dy,G4double dz, |
---|
| 859 | G4double Rmax,G4double Rmin) |
---|
| 860 | */ |
---|
| 861 | double DistanceToTorus (Intersect * Inter) |
---|
| 862 | { |
---|
| 863 | static int Vstatic = 0; |
---|
| 864 | G4double Lmin,Lmax; |
---|
| 865 | G4double guess; |
---|
| 866 | G4double SortL[4]; |
---|
| 867 | |
---|
| 868 | int NbIntersection = 0; |
---|
| 869 | |
---|
| 870 | G4double NewL[NBPOINT]; |
---|
| 871 | int valid[] = {1,1,1,1,1,1} ; |
---|
| 872 | int j; |
---|
| 873 | |
---|
| 874 | double x,y,z,dx,dy,dz; |
---|
| 875 | double Rmax,Rmin; |
---|
| 876 | double phi,deltaphi; |
---|
| 877 | |
---|
| 878 | j = 0; |
---|
| 879 | |
---|
| 880 | |
---|
| 881 | dx = Inter->dx; |
---|
| 882 | dy = Inter->dy; |
---|
| 883 | dz = Inter->dz; |
---|
| 884 | x = Inter->x; |
---|
| 885 | y = Inter->y; |
---|
| 886 | z = Inter->z; |
---|
| 887 | Rmax = Inter->R0 ; |
---|
| 888 | Rmin = Inter->R1 ; |
---|
| 889 | phi = Inter->phi; |
---|
| 890 | deltaphi = Inter->deltaphi; |
---|
| 891 | |
---|
| 892 | |
---|
| 893 | /*** Compute Intervals from Bounding Volume ***/ |
---|
| 894 | |
---|
| 895 | //BVMIntersection(x,y,z,dx,dy,dz,Rmax,Rmin,NewL,valid); |
---|
| 896 | BVMHyperboloidIntersection(x,y,z,dx,dy,dz,Rmax,Rmin,NewL,valid); |
---|
| 897 | |
---|
| 898 | /* |
---|
| 899 | We could compute intervals value |
---|
| 900 | Sort all valid NewL to SortL. |
---|
| 901 | There must be 4 values at max and |
---|
| 902 | odd one if point is inside |
---|
| 903 | */ |
---|
| 904 | |
---|
| 905 | SortIntervals(6,SortL,NewL,valid,&NbIntersection); |
---|
| 906 | if (BVM_ONLY == 1) |
---|
| 907 | return SortL[0] ; |
---|
| 908 | |
---|
| 909 | #if 0 |
---|
| 910 | // Torus Only |
---|
| 911 | { |
---|
| 912 | /*** Length check ***/ |
---|
| 913 | G4double LengthMin = 0.82842712*Rmin; |
---|
| 914 | |
---|
| 915 | switch(NbIntersection) { |
---|
| 916 | case 1: |
---|
| 917 | if (SortL[0] < EPSILON) { |
---|
| 918 | if (fabs(HyperboloidEquation(x,y,z,Rmax,Rmin)) < TORUSPRECISION) { |
---|
| 919 | return 0.0; |
---|
| 920 | } else { |
---|
| 921 | return NOINTERSECTION; |
---|
| 922 | } |
---|
| 923 | } |
---|
| 924 | break; |
---|
| 925 | case 2: |
---|
| 926 | if ((SortL[1] - SortL[0]) < LengthMin) NbIntersection = 0; |
---|
| 927 | break; |
---|
| 928 | case 3: |
---|
| 929 | if (SortL[0] < EPSILON) { |
---|
| 930 | if (fabs(HyperboloidEquation(x,y,z,Rmax,Rmin)) < TORUSPRECISION) { |
---|
| 931 | return 0.0; |
---|
| 932 | } else { |
---|
| 933 | NbIntersection --; |
---|
| 934 | SortL[0] = SortL[1] ; |
---|
| 935 | SortL[1] = SortL[2] ; |
---|
| 936 | if ((SortL[1] - SortL[0]) < LengthMin) NbIntersection = 0; |
---|
| 937 | } |
---|
| 938 | } else { |
---|
| 939 | if ((SortL[2] - SortL[1]) < LengthMin) NbIntersection -= 2; |
---|
| 940 | } |
---|
| 941 | break; |
---|
| 942 | case 4: |
---|
| 943 | if ((SortL[1] - SortL[0]) < LengthMin) { |
---|
| 944 | NbIntersection -= 2; |
---|
| 945 | SortL[0] = SortL[2]; |
---|
| 946 | SortL[1] = SortL[3]; |
---|
| 947 | if ((SortL[1] - SortL[0]) < LengthMin) NbIntersection -= 2; |
---|
| 948 | } |
---|
| 949 | break; |
---|
| 950 | } |
---|
| 951 | } |
---|
| 952 | #endif |
---|
| 953 | |
---|
| 954 | #if DEBUGTORUS |
---|
| 955 | { |
---|
| 956 | int i; |
---|
| 957 | G4cout.precision(16); |
---|
| 958 | G4cout << "DistanceToTorus INTERVALS" << G4endl ; |
---|
| 959 | for (i=0;i<NbIntersection;i++) { |
---|
| 960 | G4cout << "DistanceToTorus " << SortL[i] << G4endl ; |
---|
| 961 | } |
---|
| 962 | } |
---|
| 963 | #endif |
---|
| 964 | |
---|
| 965 | Vstatic ++; |
---|
| 966 | |
---|
| 967 | //if ((Vstatic % 2) == 0) return SortL[0]; |
---|
| 968 | //printf("NbIntersection = %d\n",NbIntersection); |
---|
| 969 | |
---|
| 970 | |
---|
| 971 | /* BVM Test |
---|
| 972 | |
---|
| 973 | switch(NbIntersection) { |
---|
| 974 | case 0: |
---|
| 975 | return -1.0; |
---|
| 976 | break; |
---|
| 977 | case 1: |
---|
| 978 | return -1.0; |
---|
| 979 | break; |
---|
| 980 | case 2: |
---|
| 981 | return -1.0; |
---|
| 982 | break; |
---|
| 983 | case 3: |
---|
| 984 | return -1.0; |
---|
| 985 | break; |
---|
| 986 | case 4: |
---|
| 987 | return -1.0; |
---|
| 988 | break; |
---|
| 989 | } |
---|
| 990 | */ |
---|
| 991 | |
---|
| 992 | /*** If the ray intersects the torus it necessary intersects the BVMax ***/ |
---|
| 993 | /*** So it is necessary into *an* interval from the BVM ***/ |
---|
| 994 | |
---|
| 995 | /** Note : In general there are only 2 intersections so computing the second interval |
---|
| 996 | could be done only if the first one does not contain any root */ |
---|
| 997 | |
---|
| 998 | /* NOW there is 2 possibilities */ |
---|
| 999 | /* If inside the BVM (or Torus instead), take "0, SortL[0] .." */ |
---|
| 1000 | /* If outside the BVM, we have intervals where if there is an intersection the root must be */ |
---|
| 1001 | /* Now Lmin1 <= Lambda <= Lmax and there is a *unique* root */ |
---|
| 1002 | /* Newton Methods in this interval from the guess */ |
---|
| 1003 | |
---|
| 1004 | /*** Beware The first interval could be the bad one and we have to see other one ***/ |
---|
| 1005 | /*** We must have a way to decide if an interval contains root or not .. ***/ |
---|
| 1006 | |
---|
| 1007 | /*** |
---|
| 1008 | Beware: If the original point is near the torus (into the BVM not the torus) |
---|
| 1009 | we have serious precision issue (bad guess value) try it with a big Rmin |
---|
| 1010 | ***/ |
---|
| 1011 | |
---|
| 1012 | /* We are Inside the BVM if the number of intersection is odd */ |
---|
| 1013 | /* Not necessary an intersection with Torus if point outside Torus and Inside BVM ! */ |
---|
| 1014 | |
---|
| 1015 | if (((NbIntersection) & (1)) != 0) { |
---|
| 1016 | /*** If we are Inside the BVM Lmin = 0. Lmax is the point ***/ |
---|
| 1017 | /*** there is necessary an intersection if the point is inside the Torus ***/ |
---|
| 1018 | int InsideTorus = 0; |
---|
| 1019 | |
---|
| 1020 | Lmin = 0.0 ; |
---|
| 1021 | Lmax = SortL[0] ; |
---|
| 1022 | |
---|
| 1023 | if (HyperboloidEquation(x,y,z,Rmax,Rmin) < 0.0) { |
---|
| 1024 | |
---|
| 1025 | InsideTorus = 1; |
---|
| 1026 | /* As we are inside the torus it must have an intersection */ |
---|
| 1027 | /* To have a good guess we take Lmax - Rmin/8.0 */ |
---|
| 1028 | /*(What is the best value for a square to be like a circle ?) */ |
---|
| 1029 | /* If we are inside the torus the upper bound is better */ |
---|
| 1030 | //return 1000.0; |
---|
| 1031 | guess = Lmax - Rmin*0.125; |
---|
| 1032 | //printf("DistanceToTorus Inside the torus\n"); |
---|
| 1033 | |
---|
| 1034 | #if DEBUGTORUS |
---|
| 1035 | G4cout << "DistanceToTorus Inside the torus" << G4endl ; |
---|
| 1036 | G4cout << "DistanceToTorus Initial Guess is " << guess << G4endl ; |
---|
| 1037 | #endif |
---|
| 1038 | |
---|
| 1039 | } else { |
---|
| 1040 | // return 1000.0; |
---|
| 1041 | //printf("DistanceToTorus Outside the torus\n"); |
---|
| 1042 | #if DEBUGTORUS |
---|
| 1043 | G4cout.precision(16); |
---|
| 1044 | G4cout << "DistanceToTorus point " << x << ", " << y << ", " << z << ", " << " is outside the torus " |
---|
| 1045 | << " Rmax = " << Rmax << " Rmin = " << Rmin << " Teq = " << HyperboloidEquation(x,y,z,Rmax,Rmin) << G4endl ; |
---|
| 1046 | #endif |
---|
| 1047 | InsideTorus = 0; |
---|
| 1048 | /* PROBLEMS what to choose ? 0.0 ? */ |
---|
| 1049 | /* 0.0 is generally a good guess, but there is case that it is very bad (hit center torus when inside BVM) */ |
---|
| 1050 | |
---|
| 1051 | if (Lmax > Rmin) { |
---|
| 1052 | /* we are in the case where we hit center torus */ |
---|
| 1053 | |
---|
| 1054 | //return 100000.0; |
---|
| 1055 | guess = Lmax; |
---|
| 1056 | |
---|
| 1057 | } else { |
---|
| 1058 | /* general case */ |
---|
| 1059 | guess = 0.0; |
---|
| 1060 | } |
---|
| 1061 | } |
---|
| 1062 | |
---|
| 1063 | /* Ready to do Newton */ |
---|
| 1064 | guess = Newton(guess,x,y,z,dx,dy,dz,Rmax,Rmin,Lmin,Lmax); |
---|
| 1065 | |
---|
| 1066 | #if DEBUGTORUS |
---|
| 1067 | G4cout << "DistanceToTorus First Newton guess = " << guess << G4endl ; |
---|
| 1068 | G4cout << "DistanceToTorus Lmin = " << Lmin << " Lmax = " << Lmax << G4endl ; |
---|
| 1069 | #endif |
---|
| 1070 | |
---|
| 1071 | /* In case we are the origin point is just in the surface |
---|
| 1072 | the NbIntersection will be odd and guess will be zero |
---|
| 1073 | Anyway, it is correct to say that distance is zero but |
---|
| 1074 | we want to return +inf if we are exiting the solid |
---|
| 1075 | So .. |
---|
| 1076 | */ |
---|
| 1077 | |
---|
| 1078 | /* Check here is the root found is into interval */ |
---|
| 1079 | |
---|
| 1080 | if ((guess >= (Lmin - EPSILON)) && (guess <= (Lmax + EPSILON))) { |
---|
| 1081 | return guess ; |
---|
| 1082 | } else { |
---|
| 1083 | if (NbIntersection == 3) { |
---|
| 1084 | /** OK we are in the small part around the BVM **/ |
---|
| 1085 | /** So we check the second interval **/ |
---|
| 1086 | Lmin = SortL[1]; |
---|
| 1087 | Lmax = SortL[2]; |
---|
| 1088 | guess = Lmin; |
---|
| 1089 | |
---|
| 1090 | guess = Newton(guess,x,y,z,dx,dy,dz,Rmax,Rmin,Lmin,Lmax); |
---|
| 1091 | #if DEBUGTORUS |
---|
| 1092 | G4cout << "DistanceToTorus Second Newton guess = " << guess << G4endl ; |
---|
| 1093 | G4cout << "DistanceToTorus Lmin = " << Lmin << " Lmax = " << Lmax << G4endl ; |
---|
| 1094 | #endif |
---|
| 1095 | if ((guess >= (Lmin - EPSILON)) && (guess <= (Lmax + EPSILON))) { |
---|
| 1096 | return guess; |
---|
| 1097 | } else { |
---|
| 1098 | return NOINTERSECTION; |
---|
| 1099 | } |
---|
| 1100 | } else { |
---|
| 1101 | if (InsideTorus == 1) { |
---|
| 1102 | /* Incredible : sometimes precisions errors bring us here |
---|
| 1103 | with guess = SortL[0] |
---|
| 1104 | So we return guess .. |
---|
| 1105 | |
---|
| 1106 | PROBLEMS 99% |
---|
| 1107 | |
---|
| 1108 | |
---|
| 1109 | printf("Torus: Root not found final (guess - Limit) = %f\n" |
---|
| 1110 | ,guess - SortL[0]); |
---|
| 1111 | printf("point: %f %f %f\n",x,y,z); |
---|
| 1112 | printf("dir : %f %f %f\n",dx,dy,dz); |
---|
| 1113 | */ |
---|
| 1114 | |
---|
| 1115 | return 100000.0;//guess; |
---|
| 1116 | exit(1); |
---|
| 1117 | |
---|
| 1118 | } |
---|
| 1119 | return NOINTERSECTION; |
---|
| 1120 | } |
---|
| 1121 | } |
---|
| 1122 | |
---|
| 1123 | |
---|
| 1124 | |
---|
| 1125 | } else { // Outside |
---|
| 1126 | /*** If we are Out then we need more to know if intersection exists ***/ |
---|
| 1127 | /*** there is 2 intersection points at least (perhaps the same) with BVMax ***/ |
---|
| 1128 | |
---|
| 1129 | /*** Return if no intersection with BVMax ***/ |
---|
| 1130 | |
---|
| 1131 | if (NbIntersection == 0) |
---|
| 1132 | return NOINTERSECTION ; |
---|
| 1133 | |
---|
| 1134 | |
---|
| 1135 | Lmin = SortL[0] ; |
---|
| 1136 | Lmax = SortL[1] ; |
---|
| 1137 | /** Lmin because it is probably near the BVM entry point **/ |
---|
| 1138 | /** PROBLEM if the ray hits the top of BVM with a small angle |
---|
| 1139 | then the interval is too big and the guess is bad **/ |
---|
| 1140 | |
---|
| 1141 | guess = Lmin ; |
---|
| 1142 | |
---|
| 1143 | |
---|
| 1144 | /*** We know only that if there is a solution, it is between Lmin and Lmax ***/ |
---|
| 1145 | /*** But we are not sure that there is one ... ***/ |
---|
| 1146 | |
---|
| 1147 | /* Ready to do Newton */ |
---|
| 1148 | guess = Newton(guess,x,y,z,dx,dy,dz,Rmax,Rmin,Lmin,Lmax); |
---|
| 1149 | |
---|
| 1150 | #if DEBUGTORUS |
---|
| 1151 | G4cout << "DistanceToTorus Newton with 2 or 4 points : " << guess << G4endl ; |
---|
| 1152 | #endif |
---|
| 1153 | |
---|
| 1154 | /* Check here is the root found is into interval */ |
---|
| 1155 | if ((guess >= (Lmin - EPSILON)) && (guess <= (Lmax + EPSILON))) { |
---|
| 1156 | #if DEBUGTORUS |
---|
| 1157 | G4cout << "DistanceToTorus Newton gives a point into interval (Ok)" << G4endl ; |
---|
| 1158 | #endif |
---|
| 1159 | return guess; |
---|
| 1160 | } else { |
---|
| 1161 | #if DEBUGTORUS |
---|
| 1162 | G4cout << "DistanceToTorus Newton does not give a point into interval (Ko)" << G4endl ; |
---|
| 1163 | #endif |
---|
| 1164 | if (NbIntersection == 4) { |
---|
| 1165 | /* Well if that does not converge with the first interval try with the other one */ |
---|
| 1166 | Lmin = SortL[2] ; |
---|
| 1167 | Lmax = SortL[3] ; |
---|
| 1168 | |
---|
| 1169 | guess = Lmin; |
---|
| 1170 | guess = Newton(guess,x,y,z,dx,dy,dz,Rmax,Rmin,Lmin,Lmax); |
---|
| 1171 | |
---|
| 1172 | if ((guess >= (Lmin - EPSILON)) && (guess <= (Lmax + EPSILON))) { |
---|
| 1173 | return guess; |
---|
| 1174 | } else { |
---|
| 1175 | return NOINTERSECTION; |
---|
| 1176 | } |
---|
| 1177 | } else { |
---|
| 1178 | /* Certainly this is due to the BVM part that is not in Torus */ |
---|
| 1179 | |
---|
| 1180 | return NOINTERSECTION ; |
---|
| 1181 | } |
---|
| 1182 | } |
---|
| 1183 | } |
---|
| 1184 | } |
---|
| 1185 | |
---|
| 1186 | inline G4double TorusGradient(G4double dx, |
---|
| 1187 | G4double dy, |
---|
| 1188 | G4double dz, |
---|
| 1189 | G4double x, |
---|
| 1190 | G4double y, |
---|
| 1191 | G4double z, |
---|
| 1192 | G4double Rmax, |
---|
| 1193 | G4double Rmin) |
---|
| 1194 | { |
---|
| 1195 | /* This tell the normal at a surface point */ |
---|
| 1196 | G4double result; |
---|
| 1197 | result = 0; |
---|
| 1198 | result += dx*HyperboloidDerX(x,y,z,Rmax,Rmin); |
---|
| 1199 | result += dy*HyperboloidDerY(x,y,z,Rmax,Rmin); |
---|
| 1200 | result += dz*HyperboloidDerZ(x,y,z,Rmax,Rmin); |
---|
| 1201 | |
---|
| 1202 | return result; |
---|
| 1203 | } |
---|
| 1204 | |
---|
| 1205 | |
---|
| 1206 | inline G4double ParaboloidGradient(G4double dx, |
---|
| 1207 | G4double dy, |
---|
| 1208 | G4double dz, |
---|
| 1209 | G4double x, |
---|
| 1210 | G4double y, |
---|
| 1211 | G4double z, |
---|
| 1212 | G4double Rmax, |
---|
| 1213 | G4double Rmin) |
---|
| 1214 | { |
---|
| 1215 | /* This tell the normal at a surface point */ |
---|
| 1216 | G4double result; |
---|
| 1217 | result = 0; |
---|
| 1218 | result += dx*ParaboloidDerX(x,y,z,Rmax,Rmin); |
---|
| 1219 | result += dy*ParaboloidDerY(x,y,z,Rmax,Rmin); |
---|
| 1220 | result += dz*ParaboloidDerZ(x,y,z,Rmax,Rmin); |
---|
| 1221 | |
---|
| 1222 | return result; |
---|
| 1223 | } |
---|
| 1224 | |
---|
| 1225 | inline G4double HyperboloidGradient(G4double dx, |
---|
| 1226 | G4double dy, |
---|
| 1227 | G4double dz, |
---|
| 1228 | G4double x, |
---|
| 1229 | G4double y, |
---|
| 1230 | G4double z, |
---|
| 1231 | G4double Rmax, |
---|
| 1232 | G4double Rmin) |
---|
| 1233 | { |
---|
| 1234 | /* This tell the normal at a surface point */ |
---|
| 1235 | G4double result; |
---|
| 1236 | result = 0; |
---|
| 1237 | result += dx*HyperboloidDerX(x,y,z,Rmax,Rmin); |
---|
| 1238 | result += dy*HyperboloidDerY(x,y,z,Rmax,Rmin); |
---|
| 1239 | result += dz*HyperboloidDerZ(x,y,z,Rmax,Rmin); |
---|
| 1240 | |
---|
| 1241 | return result; |
---|
| 1242 | } |
---|
| 1243 | |
---|