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25 // 25 //
26 // Implementation of G4IntersectingCone, a uti <<
27 // the intersection of an arbitrary line with <<
28 // 26 //
29 // Author: David C. Williams (davidw@scipp.ucs << 27 // $Id: G4IntersectingCone.cc,v 1.8.8.2 2008/04/28 09:03:16 gcosmo Exp $
>> 28 // GEANT4 tag $Name: geant4-09-01-patch-03 $
>> 29 //
>> 30 //
>> 31 // --------------------------------------------------------------------
>> 32 // GEANT 4 class source file
>> 33 //
>> 34 //
>> 35 // G4IntersectingCone.cc
>> 36 //
>> 37 // Implementation of a utility class which calculates the intersection
>> 38 // of an arbitrary line with a fixed cone
30 // ------------------------------------------- 39 // --------------------------------------------------------------------
31 40
32 #include "G4IntersectingCone.hh" 41 #include "G4IntersectingCone.hh"
33 #include "G4GeometryTolerance.hh" 42 #include "G4GeometryTolerance.hh"
34 43
>> 44 //
35 // Constructor 45 // Constructor
36 // 46 //
37 G4IntersectingCone::G4IntersectingCone( const 47 G4IntersectingCone::G4IntersectingCone( const G4double r[2],
38 const 48 const G4double z[2] )
39 { << 49 {
40 const G4double halfCarTolerance <<
41 = 0.5 * G4GeometryTolerance::GetInstance() <<
42 50
>> 51
>> 52 half_kCarTolerance = 0.5 * G4GeometryTolerance::GetInstance()
>> 53 ->GetSurfaceTolerance();
>> 54 //
43 // What type of cone are we? 55 // What type of cone are we?
44 // 56 //
45 type1 = (std::abs(z[1]-z[0]) > std::abs(r[1] << 57 type1 = (std::fabs(z[1]-z[0]) > std::fabs(r[1]-r[0]));
46 << 58
47 if (type1) // tube like << 59 if (type1)
48 { 60 {
49 B = (r[1] - r[0]) / (z[1] - z[0]); << 61 B = (r[1]-r[0])/(z[1]-z[0]); // tube like
50 A = (r[0]*z[1] - r[1]*z[0]) / (z[1] -z[0]) << 62 A = 0.5*( r[1]+r[0] - B*(z[1]+z[0]) );
51 } 63 }
52 else // disk like << 64 else
53 { 65 {
54 B = (z[1] - z[0]) / (r[1] - r[0]); << 66 B = (z[1]-z[0])/(r[1]-r[0]); // disk like
55 A = (z[0]*r[1] - z[1]*r[0]) / (r[1] - r[0] << 67 A = 0.5*( z[1]+z[0] - B*(r[1]+r[0]) );
56 } 68 }
57 << 69 //
58 // Calculate extent 70 // Calculate extent
59 // 71 //
60 rLo = std::min(r[0], r[1]) - halfCarToleranc << 72 if (r[0] < r[1])
61 rHi = std::max(r[0], r[1]) + halfCarToleranc << 73 {
62 zLo = std::min(z[0], z[1]) - halfCarToleranc << 74 rLo = r[0]-half_kCarTolerance; rHi = r[1]+half_kCarTolerance;
63 zHi = std::max(z[0], z[1]) + halfCarToleranc << 75 }
>> 76 else
>> 77 {
>> 78 rLo = r[1]-half_kCarTolerance; rHi = r[0]+half_kCarTolerance;
>> 79 }
>> 80
>> 81 if (z[0] < z[1])
>> 82 {
>> 83 zLo = z[0]-half_kCarTolerance; zHi = z[1]+half_kCarTolerance;
>> 84 }
>> 85 else
>> 86 {
>> 87 zLo = z[1]-half_kCarTolerance; zHi = z[0]+half_kCarTolerance;
>> 88 }
64 } 89 }
65 90
>> 91
>> 92 //
66 // Fake default constructor - sets only member 93 // Fake default constructor - sets only member data and allocates memory
67 // for usage restri 94 // for usage restricted to object persistency.
68 // 95 //
69 G4IntersectingCone::G4IntersectingCone( __void 96 G4IntersectingCone::G4IntersectingCone( __void__& )
70 : zLo(0.), zHi(0.), rLo(0.), rHi(0.), A(0.), <<
71 { 97 {
72 } 98 }
73 99
>> 100
>> 101 //
74 // Destructor 102 // Destructor
75 // 103 //
76 G4IntersectingCone::~G4IntersectingCone() = de << 104 G4IntersectingCone::~G4IntersectingCone()
>> 105 {
>> 106 }
>> 107
77 108
>> 109 //
78 // HitOn 110 // HitOn
79 // 111 //
80 // Check r or z extent, as appropriate, to see 112 // Check r or z extent, as appropriate, to see if the point is possibly
81 // on the cone. 113 // on the cone.
82 // 114 //
83 G4bool G4IntersectingCone::HitOn( const G4doub 115 G4bool G4IntersectingCone::HitOn( const G4double r,
84 const G4doub 116 const G4double z )
85 { 117 {
86 // 118 //
87 // Be careful! The inequalities cannot be "< 119 // Be careful! The inequalities cannot be "<=" and ">=" here without
88 // punching a tiny hole in our shape! 120 // punching a tiny hole in our shape!
89 // 121 //
90 if (type1) 122 if (type1)
91 { 123 {
92 if (z < zLo || z > zHi) return false; 124 if (z < zLo || z > zHi) return false;
93 } 125 }
94 else 126 else
95 { 127 {
96 if (r < rLo || r > rHi) return false; 128 if (r < rLo || r > rHi) return false;
97 } 129 }
98 130
99 return true; 131 return true;
100 } 132 }
101 133
>> 134
>> 135 //
102 // LineHitsCone 136 // LineHitsCone
103 // 137 //
104 // Calculate the intersection of a line with o 138 // Calculate the intersection of a line with our conical surface, ignoring
105 // any phi division 139 // any phi division
106 // 140 //
107 G4int G4IntersectingCone::LineHitsCone( const << 141 G4int G4IntersectingCone::LineHitsCone( const G4ThreeVector &p,
108 const << 142 const G4ThreeVector &v,
109 << 143 G4double *s1, G4double *s2 )
110 { 144 {
111 if (type1) 145 if (type1)
112 { 146 {
113 return LineHitsCone1( p, v, s1, s2 ); 147 return LineHitsCone1( p, v, s1, s2 );
114 } 148 }
115 else 149 else
116 { 150 {
117 return LineHitsCone2( p, v, s1, s2 ); 151 return LineHitsCone2( p, v, s1, s2 );
118 } 152 }
119 } 153 }
120 154
>> 155
>> 156 //
121 // LineHitsCone1 157 // LineHitsCone1
122 // 158 //
123 // Calculate the intersections of a line with 159 // Calculate the intersections of a line with a conical surface. Only
124 // suitable if zPlane[0] != zPlane[1]. 160 // suitable if zPlane[0] != zPlane[1].
125 // 161 //
126 // Equation of a line: 162 // Equation of a line:
127 // 163 //
128 // x = x0 + s*tx y = y0 + s*ty 164 // x = x0 + s*tx y = y0 + s*ty z = z0 + s*tz
129 // 165 //
130 // Equation of a conical surface: 166 // Equation of a conical surface:
131 // 167 //
132 // x**2 + y**2 = (A + B*z)**2 168 // x**2 + y**2 = (A + B*z)**2
133 // 169 //
134 // Solution is quadratic: 170 // Solution is quadratic:
135 // 171 //
136 // a*s**2 + b*s + c = 0 172 // a*s**2 + b*s + c = 0
137 // 173 //
138 // where: 174 // where:
139 // 175 //
140 // a = tx**2 + ty**2 - (B*tz)**2 << 176 // a = x0**2 + y0**2 - (A + B*z0)**2
141 // 177 //
142 // b = 2*( px*vx + py*vy - B*(A + B*pz)*vz ) << 178 // b = 2*( x0*tx + y0*ty - (A*B - B*B*z0)*tz)
143 // 179 //
144 // c = x0**2 + y0**2 - (A + B*z0)**2 << 180 // c = tx**2 + ty**2 - (B*tz)**2
145 // 181 //
146 // Notice, that if a < 0, this indicates that 182 // Notice, that if a < 0, this indicates that the two solutions (assuming
147 // they exist) are in opposite cones (that is, 183 // they exist) are in opposite cones (that is, given z0 = -A/B, one z < z0
148 // and the other z > z0). For our shapes, the 184 // and the other z > z0). For our shapes, the invalid solution is one
149 // which produces A + Bz < 0, or the one where 185 // which produces A + Bz < 0, or the one where Bz is smallest (most negative).
150 // Since Bz = B*s*tz, if B*tz > 0, we want the 186 // Since Bz = B*s*tz, if B*tz > 0, we want the largest s, otherwise,
151 // the smaller. 187 // the smaller.
152 // 188 //
153 // If there are two solutions on one side of t 189 // If there are two solutions on one side of the cone, we want to make
154 // sure that they are on the "correct" side, t 190 // sure that they are on the "correct" side, that is A + B*z0 + s*B*tz >= 0.
155 // 191 //
156 // If a = 0, we have a linear problem: s = c/b 192 // If a = 0, we have a linear problem: s = c/b, which again gives one solution.
157 // This should be rare. 193 // This should be rare.
158 // 194 //
159 // For b*b - 4*a*c = 0, we also have one solut 195 // For b*b - 4*a*c = 0, we also have one solution, which is almost always
160 // a line just grazing the surface of a the co << 196 // a line just grazing the surface of a the cone, which we want to ignore.
161 // However, there are two other, very rare, po 197 // However, there are two other, very rare, possibilities:
162 // a line intersecting the z axis and either: 198 // a line intersecting the z axis and either:
163 // 1. At the same angle std::atan(B) to 199 // 1. At the same angle std::atan(B) to just miss one side of the cone, or
164 // 2. Intersecting the cone apex (0,0,-A 200 // 2. Intersecting the cone apex (0,0,-A/B)
165 // We *don't* want to miss these! How do we id 201 // We *don't* want to miss these! How do we identify them? Well, since
166 // this case is rare, we can at least swallow 202 // this case is rare, we can at least swallow a little more CPU than we would
167 // normally be comfortable with. Intersection 203 // normally be comfortable with. Intersection with the z axis means
168 // x0*ty - y0*tx = 0. Case (1) means a==0, and 204 // x0*ty - y0*tx = 0. Case (1) means a==0, and we've already dealt with that
169 // above. Case (2) means a < 0. 205 // above. Case (2) means a < 0.
170 // 206 //
171 // Now: x0*tx + y0*ty = 0 in terms of roundoff 207 // Now: x0*tx + y0*ty = 0 in terms of roundoff error. We can write:
172 // Delta = x0*tx + y0*ty 208 // Delta = x0*tx + y0*ty
173 // b = 2*( Delta - B*(A + B*z0)*tz << 209 // b = 2*( Delta - (A*B + B*B*z0)*tz )
174 // For: 210 // For:
175 // b*b - 4*a*c = epsilon 211 // b*b - 4*a*c = epsilon
176 // where epsilon is small, then: 212 // where epsilon is small, then:
177 // Delta = epsilon/2/B 213 // Delta = epsilon/2/B
178 // << 214 //
179 G4int G4IntersectingCone::LineHitsCone1( const << 215 G4int G4IntersectingCone::LineHitsCone1( const G4ThreeVector &p,
180 const << 216 const G4ThreeVector &v,
181 << 217 G4double *s1, G4double *s2 )
182 { 218 {
183 static const G4double EPS = DBL_EPSILON; // <<
184 // <<
185 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 219 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
186 G4double tx = v.x(), ty = v.y(), tz = v.z(); 220 G4double tx = v.x(), ty = v.y(), tz = v.z();
187 221
188 // Value of radical can be inaccurate due to << 222 G4double a = tx*tx + ty*ty - sqr(B*tz);
189 // if to calculate the coefficiets a,b,c lik << 223 G4double b = 2*( x0*tx + y0*ty - (A*B + B*B*z0)*tz);
190 // G4double a = tx*tx + ty*ty - sqr(B*tz << 224 G4double c = x0*x0 + y0*y0 - sqr(A + B*z0);
191 // G4double b = 2*( x0*tx + y0*ty - B*(A << 225
192 // G4double c = x0*x0 + y0*y0 - sqr(A + << 226 G4double radical = b*b - 4*a*c;
193 // << 227
194 // For more accurate calculation of radical << 228 if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution
195 // are splitted in two components, radial an << 229
196 // << 230 if (radical < 1E-6*std::fabs(b))
197 G4double ar = tx*tx + ty*ty; <<
198 G4double az = sqr(B*tz); <<
199 G4double br = 2*(x0*tx + y0*ty); <<
200 G4double bz = 2*B*(A + B*z0)*tz; <<
201 G4double cr = x0*x0 + y0*y0; <<
202 G4double cz = sqr(A + B*z0); <<
203 <<
204 // Instead radical = b*b - 4*a*c <<
205 G4double arcz = 4*ar*cz; <<
206 G4double azcr = 4*az*cr; <<
207 G4double radical = (br*br - 4*ar*cr) + ((std <<
208 <<
209 // Find the coefficients <<
210 G4double a = ar - az; <<
211 G4double b = br - bz; <<
212 G4double c = cr - cz; <<
213 <<
214 if (radical < -EPS*std::fabs(b)) { return 0 <<
215 <<
216 if (radical < EPS*std::fabs(b)) <<
217 { 231 {
218 // 232 //
219 // The radical is roughly zero: check for 233 // The radical is roughly zero: check for special, very rare, cases
220 // 234 //
221 if (std::fabs(a) > 1/kInfinity) 235 if (std::fabs(a) > 1/kInfinity)
222 { 236 {
223 if(B==0.) { return 0; } 237 if(B==0.) { return 0; }
224 if ( std::fabs(x0*ty - y0*tx) < std::fab << 238 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) )
225 { 239 {
226 *s1 = -0.5*b/a; 240 *s1 = -0.5*b/a;
227 return 1; 241 return 1;
228 } 242 }
229 return 0; 243 return 0;
230 } 244 }
231 } 245 }
232 else 246 else
233 { 247 {
234 radical = std::sqrt(radical); 248 radical = std::sqrt(radical);
235 } 249 }
236 << 250
237 if (a > 1/kInfinity) 251 if (a > 1/kInfinity)
238 { 252 {
239 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 253 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
240 sa = q/a; 254 sa = q/a;
241 sb = c/q; 255 sb = c/q;
242 if (sa < sb) { *s1 = sa; *s2 = sb; } else 256 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
243 if (A + B*(z0+(*s1)*tz) < 0) { return 0; 257 if (A + B*(z0+(*s1)*tz) < 0) { return 0; }
244 return 2; 258 return 2;
245 } 259 }
246 else if (a < -1/kInfinity) 260 else if (a < -1/kInfinity)
247 { 261 {
248 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 262 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
249 sa = q/a; 263 sa = q/a;
250 sb = c/q; 264 sb = c/q;
251 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa; 265 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa;
252 return 1; 266 return 1;
253 } 267 }
254 else if (std::fabs(b) < 1/kInfinity) 268 else if (std::fabs(b) < 1/kInfinity)
255 { 269 {
256 return 0; 270 return 0;
257 } 271 }
258 else 272 else
259 { 273 {
260 *s1 = -c/b; 274 *s1 = -c/b;
261 if (A + B*(z0+(*s1)*tz) < 0) { return 0; 275 if (A + B*(z0+(*s1)*tz) < 0) { return 0; }
262 return 1; 276 return 1;
263 } 277 }
264 } 278 }
265 279
>> 280
>> 281 //
266 // LineHitsCone2 282 // LineHitsCone2
267 // 283 //
268 // See comments under LineHitsCone1. In this r 284 // See comments under LineHitsCone1. In this routine, case2, we have:
269 // 285 //
270 // Z = A + B*R 286 // Z = A + B*R
271 // 287 //
272 // The solution is still quadratic: 288 // The solution is still quadratic:
273 // 289 //
274 // a = tz**2 - B*B*(tx**2 + ty**2) 290 // a = tz**2 - B*B*(tx**2 + ty**2)
275 // 291 //
276 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) ) 292 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) )
277 // 293 //
278 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) ) 294 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) )
279 // 295 //
280 // The rest is much the same, except some deta 296 // The rest is much the same, except some details.
281 // 297 //
282 // a > 0 now means we intersect only once in t 298 // a > 0 now means we intersect only once in the correct hemisphere.
283 // 299 //
284 // a > 0 ? We only want solution which produce << 300 // a > 0 ? We only want solution which produces R > 0.
285 // since R = (z0+s*tz-A)/B, for tz/B > 0, this 301 // since R = (z0+s*tz-A)/B, for tz/B > 0, this is the largest s
286 // for tz/B < 0, this is the smallest 302 // for tz/B < 0, this is the smallest s
287 // thus, same as in case 1 ( since sign(tz/B) 303 // thus, same as in case 1 ( since sign(tz/B) = sign(tz*B) )
288 // 304 //
289 G4int G4IntersectingCone::LineHitsCone2( const << 305 G4int G4IntersectingCone::LineHitsCone2( const G4ThreeVector &p,
290 const << 306 const G4ThreeVector &v,
291 << 307 G4double *s1, G4double *s2 )
292 { 308 {
293 static const G4double EPS = DBL_EPSILON; // <<
294 // <<
295 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 309 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
296 G4double tx = v.x(), ty = v.y(), tz = v.z(); 310 G4double tx = v.x(), ty = v.y(), tz = v.z();
297 << 311
>> 312
298 // Special case which might not be so rare: 313 // Special case which might not be so rare: B = 0 (precisely)
299 // 314 //
300 if (B==0) 315 if (B==0)
301 { 316 {
302 if (std::fabs(tz) < 1/kInfinity) { return 317 if (std::fabs(tz) < 1/kInfinity) { return 0; }
303 << 318
304 *s1 = (A-z0)/tz; 319 *s1 = (A-z0)/tz;
305 return 1; 320 return 1;
306 } 321 }
307 322
308 // Value of radical can be inaccurate due to <<
309 // if to calculate the coefficiets a,b,c lik <<
310 // G4double a = tz*tz - B2*(tx*tx + ty*ty) <<
311 // G4double b = 2*( (z0-A)*tz - B2*(x0*tx <<
312 // G4double c = sqr(z0-A) - B2*( x0*x0 + y <<
313 // <<
314 // For more accurate calculation of radical <<
315 // are splitted in two components, radial an <<
316 // <<
317 G4double B2 = B*B; 323 G4double B2 = B*B;
318 324
319 G4double az = tz*tz; << 325 G4double a = tz*tz - B2*(tx*tx + ty*ty);
320 G4double ar = B2*(tx*tx + ty*ty); << 326 G4double b = 2*( (z0-A)*tz - B2*(x0*tx + y0*ty) );
321 G4double bz = 2*(z0-A)*tz; << 327 G4double c = sqr(z0-A) - B2*( x0*x0 + y0*y0 );
322 G4double br = 2*B2*(x0*tx + y0*ty); << 328
323 G4double cz = sqr(z0-A); << 329 G4double radical = b*b - 4*a*c;
324 G4double cr = B2*(x0*x0 + y0*y0); << 330
325 << 331 if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution
326 // Instead radical = b*b - 4*a*c << 332
327 G4double arcz = 4*ar*cz; << 333 if (radical < 1E-6*std::fabs(b))
328 G4double azcr = 4*az*cr; <<
329 G4double radical = (br*br - 4*ar*cr) + ((std <<
330 <<
331 // Find the coefficients <<
332 G4double a = az - ar; <<
333 G4double b = bz - br; <<
334 G4double c = cz - cr; <<
335 <<
336 if (radical < -EPS*std::fabs(b)) { return 0; <<
337 <<
338 if (radical < EPS*std::fabs(b)) <<
339 { 334 {
340 // 335 //
341 // The radical is roughly zero: check for 336 // The radical is roughly zero: check for special, very rare, cases
342 // 337 //
343 if (std::fabs(a) > 1/kInfinity) 338 if (std::fabs(a) > 1/kInfinity)
344 { 339 {
345 if ( std::fabs(x0*ty - y0*tx) < std::fab << 340 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) )
346 { 341 {
347 *s1 = -0.5*b/a; 342 *s1 = -0.5*b/a;
348 return 1; 343 return 1;
349 } 344 }
350 return 0; 345 return 0;
351 } 346 }
352 } 347 }
353 else 348 else
354 { 349 {
355 radical = std::sqrt(radical); 350 radical = std::sqrt(radical);
356 } 351 }
357 << 352
358 if (a < -1/kInfinity) 353 if (a < -1/kInfinity)
359 { 354 {
360 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 355 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
361 sa = q/a; 356 sa = q/a;
362 sb = c/q; 357 sb = c/q;
363 if (sa < sb) { *s1 = sa; *s2 = sb; } else 358 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
364 if ((z0 + (*s1)*tz - A)/B < 0) { return 359 if ((z0 + (*s1)*tz - A)/B < 0) { return 0; }
365 return 2; 360 return 2;
366 } 361 }
367 else if (a > 1/kInfinity) 362 else if (a > 1/kInfinity)
368 { 363 {
369 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 364 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
370 sa = q/a; 365 sa = q/a;
371 sb = c/q; 366 sb = c/q;
372 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa; 367 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa;
373 return 1; 368 return 1;
374 } 369 }
375 else if (std::fabs(b) < 1/kInfinity) 370 else if (std::fabs(b) < 1/kInfinity)
376 { 371 {
377 return 0; 372 return 0;
378 } 373 }
379 else 374 else
380 { 375 {
381 *s1 = -c/b; 376 *s1 = -c/b;
382 if ((z0 + (*s1)*tz - A)/B < 0) { return 377 if ((z0 + (*s1)*tz - A)/B < 0) { return 0; }
383 return 1; 378 return 1;
384 } 379 }
385 } 380 }
386 381