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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 72937 2013-08-14 13:20:38Z gcosmo $
>> 28 //
>> 29 //
>> 30 // --------------------------------------------------------------------
>> 31 // GEANT 4 class source file
>> 32 //
>> 33 //
>> 34 // G4IntersectingCone.cc
>> 35 //
>> 36 // Implementation of a utility class which calculates the intersection
>> 37 // of an arbitrary line with a fixed cone
30 // ------------------------------------------- 38 // --------------------------------------------------------------------
31 39
32 #include "G4IntersectingCone.hh" 40 #include "G4IntersectingCone.hh"
33 #include "G4GeometryTolerance.hh" 41 #include "G4GeometryTolerance.hh"
34 42
>> 43 //
35 // Constructor 44 // Constructor
36 // 45 //
37 G4IntersectingCone::G4IntersectingCone( const 46 G4IntersectingCone::G4IntersectingCone( const G4double r[2],
38 const 47 const G4double z[2] )
39 { << 48 {
40 const G4double halfCarTolerance 49 const G4double halfCarTolerance
41 = 0.5 * G4GeometryTolerance::GetInstance() 50 = 0.5 * G4GeometryTolerance::GetInstance()->GetSurfaceTolerance();
42 51
>> 52 //
43 // What type of cone are we? 53 // What type of cone are we?
44 // 54 //
45 type1 = (std::abs(z[1]-z[0]) > std::abs(r[1] << 55 type1 = (std::fabs(z[1]-z[0]) > std::fabs(r[1]-r[0]));
46 << 56
47 if (type1) // tube like << 57 if (type1)
48 { 58 {
49 B = (r[1] - r[0]) / (z[1] - z[0]); << 59 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]) << 60 A = 0.5*( r[1]+r[0] - B*(z[1]+z[0]) );
51 } 61 }
52 else // disk like << 62 else
53 { 63 {
54 B = (z[1] - z[0]) / (r[1] - r[0]); << 64 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] << 65 A = 0.5*( z[1]+z[0] - B*(r[1]+r[0]) );
56 } 66 }
57 << 67 //
58 // Calculate extent 68 // Calculate extent
59 // 69 //
60 rLo = std::min(r[0], r[1]) - halfCarToleranc << 70 if (r[0] < r[1])
61 rHi = std::max(r[0], r[1]) + halfCarToleranc << 71 {
62 zLo = std::min(z[0], z[1]) - halfCarToleranc << 72 rLo = r[0]-halfCarTolerance; rHi = r[1]+halfCarTolerance;
63 zHi = std::max(z[0], z[1]) + halfCarToleranc << 73 }
>> 74 else
>> 75 {
>> 76 rLo = r[1]-halfCarTolerance; rHi = r[0]+halfCarTolerance;
>> 77 }
>> 78
>> 79 if (z[0] < z[1])
>> 80 {
>> 81 zLo = z[0]-halfCarTolerance; zHi = z[1]+halfCarTolerance;
>> 82 }
>> 83 else
>> 84 {
>> 85 zLo = z[1]-halfCarTolerance; zHi = z[0]+halfCarTolerance;
>> 86 }
64 } 87 }
65 88
>> 89
>> 90 //
66 // Fake default constructor - sets only member 91 // Fake default constructor - sets only member data and allocates memory
67 // for usage restri 92 // for usage restricted to object persistency.
68 // 93 //
69 G4IntersectingCone::G4IntersectingCone( __void 94 G4IntersectingCone::G4IntersectingCone( __void__& )
70 : zLo(0.), zHi(0.), rLo(0.), rHi(0.), A(0.), << 95 : zLo(0.), zHi(0.), rLo(0.), rHi(0.), type1(false), A(0.), B(0.)
71 { 96 {
72 } 97 }
73 98
>> 99
>> 100 //
74 // Destructor 101 // Destructor
75 // 102 //
76 G4IntersectingCone::~G4IntersectingCone() = de << 103 G4IntersectingCone::~G4IntersectingCone()
>> 104 {
>> 105 }
>> 106
77 107
>> 108 //
78 // HitOn 109 // HitOn
79 // 110 //
80 // Check r or z extent, as appropriate, to see 111 // Check r or z extent, as appropriate, to see if the point is possibly
81 // on the cone. 112 // on the cone.
82 // 113 //
83 G4bool G4IntersectingCone::HitOn( const G4doub 114 G4bool G4IntersectingCone::HitOn( const G4double r,
84 const G4doub 115 const G4double z )
85 { 116 {
86 // 117 //
87 // Be careful! The inequalities cannot be "< 118 // Be careful! The inequalities cannot be "<=" and ">=" here without
88 // punching a tiny hole in our shape! 119 // punching a tiny hole in our shape!
89 // 120 //
90 if (type1) 121 if (type1)
91 { 122 {
92 if (z < zLo || z > zHi) return false; 123 if (z < zLo || z > zHi) return false;
93 } 124 }
94 else 125 else
95 { 126 {
96 if (r < rLo || r > rHi) return false; 127 if (r < rLo || r > rHi) return false;
97 } 128 }
98 129
99 return true; 130 return true;
100 } 131 }
101 132
>> 133
>> 134 //
102 // LineHitsCone 135 // LineHitsCone
103 // 136 //
104 // Calculate the intersection of a line with o 137 // Calculate the intersection of a line with our conical surface, ignoring
105 // any phi division 138 // any phi division
106 // 139 //
107 G4int G4IntersectingCone::LineHitsCone( const << 140 G4int G4IntersectingCone::LineHitsCone( const G4ThreeVector &p,
108 const << 141 const G4ThreeVector &v,
109 << 142 G4double *s1, G4double *s2 )
110 { 143 {
111 if (type1) 144 if (type1)
112 { 145 {
113 return LineHitsCone1( p, v, s1, s2 ); 146 return LineHitsCone1( p, v, s1, s2 );
114 } 147 }
115 else 148 else
116 { 149 {
117 return LineHitsCone2( p, v, s1, s2 ); 150 return LineHitsCone2( p, v, s1, s2 );
118 } 151 }
119 } 152 }
120 153
>> 154
>> 155 //
121 // LineHitsCone1 156 // LineHitsCone1
122 // 157 //
123 // Calculate the intersections of a line with 158 // Calculate the intersections of a line with a conical surface. Only
124 // suitable if zPlane[0] != zPlane[1]. 159 // suitable if zPlane[0] != zPlane[1].
125 // 160 //
126 // Equation of a line: 161 // Equation of a line:
127 // 162 //
128 // x = x0 + s*tx y = y0 + s*ty 163 // x = x0 + s*tx y = y0 + s*ty z = z0 + s*tz
129 // 164 //
130 // Equation of a conical surface: 165 // Equation of a conical surface:
131 // 166 //
132 // x**2 + y**2 = (A + B*z)**2 167 // x**2 + y**2 = (A + B*z)**2
133 // 168 //
134 // Solution is quadratic: 169 // Solution is quadratic:
135 // 170 //
136 // a*s**2 + b*s + c = 0 171 // a*s**2 + b*s + c = 0
137 // 172 //
138 // where: 173 // where:
139 // 174 //
140 // a = tx**2 + ty**2 - (B*tz)**2 << 175 // a = x0**2 + y0**2 - (A + B*z0)**2
141 // 176 //
142 // b = 2*( px*vx + py*vy - B*(A + B*pz)*vz ) << 177 // b = 2*( x0*tx + y0*ty - (A*B - B*B*z0)*tz)
143 // 178 //
144 // c = x0**2 + y0**2 - (A + B*z0)**2 << 179 // c = tx**2 + ty**2 - (B*tz)**2
145 // 180 //
146 // Notice, that if a < 0, this indicates that 181 // Notice, that if a < 0, this indicates that the two solutions (assuming
147 // they exist) are in opposite cones (that is, 182 // 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 183 // and the other z > z0). For our shapes, the invalid solution is one
149 // which produces A + Bz < 0, or the one where 184 // 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 185 // Since Bz = B*s*tz, if B*tz > 0, we want the largest s, otherwise,
151 // the smaller. 186 // the smaller.
152 // 187 //
153 // If there are two solutions on one side of t 188 // 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 189 // sure that they are on the "correct" side, that is A + B*z0 + s*B*tz >= 0.
155 // 190 //
156 // If a = 0, we have a linear problem: s = c/b 191 // If a = 0, we have a linear problem: s = c/b, which again gives one solution.
157 // This should be rare. 192 // This should be rare.
158 // 193 //
159 // For b*b - 4*a*c = 0, we also have one solut 194 // 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 << 195 // a line just grazing the surface of a the cone, which we want to ignore.
161 // However, there are two other, very rare, po 196 // However, there are two other, very rare, possibilities:
162 // a line intersecting the z axis and either: 197 // a line intersecting the z axis and either:
163 // 1. At the same angle std::atan(B) to 198 // 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 199 // 2. Intersecting the cone apex (0,0,-A/B)
165 // We *don't* want to miss these! How do we id 200 // We *don't* want to miss these! How do we identify them? Well, since
166 // this case is rare, we can at least swallow 201 // this case is rare, we can at least swallow a little more CPU than we would
167 // normally be comfortable with. Intersection 202 // normally be comfortable with. Intersection with the z axis means
168 // x0*ty - y0*tx = 0. Case (1) means a==0, and 203 // x0*ty - y0*tx = 0. Case (1) means a==0, and we've already dealt with that
169 // above. Case (2) means a < 0. 204 // above. Case (2) means a < 0.
170 // 205 //
171 // Now: x0*tx + y0*ty = 0 in terms of roundoff 206 // Now: x0*tx + y0*ty = 0 in terms of roundoff error. We can write:
172 // Delta = x0*tx + y0*ty 207 // Delta = x0*tx + y0*ty
173 // b = 2*( Delta - B*(A + B*z0)*tz << 208 // b = 2*( Delta - (A*B + B*B*z0)*tz )
174 // For: 209 // For:
175 // b*b - 4*a*c = epsilon 210 // b*b - 4*a*c = epsilon
176 // where epsilon is small, then: 211 // where epsilon is small, then:
177 // Delta = epsilon/2/B 212 // Delta = epsilon/2/B
178 // << 213 //
179 G4int G4IntersectingCone::LineHitsCone1( const << 214 G4int G4IntersectingCone::LineHitsCone1( const G4ThreeVector &p,
180 const << 215 const G4ThreeVector &v,
181 << 216 G4double *s1, G4double *s2 )
182 { 217 {
183 static const G4double EPS = DBL_EPSILON; // <<
184 // <<
185 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 218 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
186 G4double tx = v.x(), ty = v.y(), tz = v.z(); 219 G4double tx = v.x(), ty = v.y(), tz = v.z();
187 220
188 // Value of radical can be inaccurate due to << 221 G4double a = tx*tx + ty*ty - sqr(B*tz);
189 // if to calculate the coefficiets a,b,c lik << 222 G4double b = 2*( x0*tx + y0*ty - (A*B + B*B*z0)*tz);
190 // G4double a = tx*tx + ty*ty - sqr(B*tz << 223 G4double c = x0*x0 + y0*y0 - sqr(A + B*z0);
191 // G4double b = 2*( x0*tx + y0*ty - B*(A << 224
192 // G4double c = x0*x0 + y0*y0 - sqr(A + << 225 G4double radical = b*b - 4*a*c;
193 // << 226
194 // For more accurate calculation of radical << 227 if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution
195 // are splitted in two components, radial an << 228
196 // << 229 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 { 230 {
218 // 231 //
219 // The radical is roughly zero: check for 232 // The radical is roughly zero: check for special, very rare, cases
220 // 233 //
221 if (std::fabs(a) > 1/kInfinity) 234 if (std::fabs(a) > 1/kInfinity)
222 { 235 {
223 if(B==0.) { return 0; } 236 if(B==0.) { return 0; }
224 if ( std::fabs(x0*ty - y0*tx) < std::fab << 237 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) )
225 { 238 {
226 *s1 = -0.5*b/a; 239 *s1 = -0.5*b/a;
227 return 1; 240 return 1;
228 } 241 }
229 return 0; 242 return 0;
230 } 243 }
231 } 244 }
232 else 245 else
233 { 246 {
234 radical = std::sqrt(radical); 247 radical = std::sqrt(radical);
235 } 248 }
236 << 249
237 if (a > 1/kInfinity) 250 if (a > 1/kInfinity)
238 { 251 {
239 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 252 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
240 sa = q/a; 253 sa = q/a;
241 sb = c/q; 254 sb = c/q;
242 if (sa < sb) { *s1 = sa; *s2 = sb; } else 255 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
243 if (A + B*(z0+(*s1)*tz) < 0) { return 0; 256 if (A + B*(z0+(*s1)*tz) < 0) { return 0; }
244 return 2; 257 return 2;
245 } 258 }
246 else if (a < -1/kInfinity) 259 else if (a < -1/kInfinity)
247 { 260 {
248 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 261 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
249 sa = q/a; 262 sa = q/a;
250 sb = c/q; 263 sb = c/q;
251 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa; 264 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa;
252 return 1; 265 return 1;
253 } 266 }
254 else if (std::fabs(b) < 1/kInfinity) 267 else if (std::fabs(b) < 1/kInfinity)
255 { 268 {
256 return 0; 269 return 0;
257 } 270 }
258 else 271 else
259 { 272 {
260 *s1 = -c/b; 273 *s1 = -c/b;
261 if (A + B*(z0+(*s1)*tz) < 0) { return 0; 274 if (A + B*(z0+(*s1)*tz) < 0) { return 0; }
262 return 1; 275 return 1;
263 } 276 }
264 } 277 }
265 278
>> 279
>> 280 //
266 // LineHitsCone2 281 // LineHitsCone2
267 // 282 //
268 // See comments under LineHitsCone1. In this r 283 // See comments under LineHitsCone1. In this routine, case2, we have:
269 // 284 //
270 // Z = A + B*R 285 // Z = A + B*R
271 // 286 //
272 // The solution is still quadratic: 287 // The solution is still quadratic:
273 // 288 //
274 // a = tz**2 - B*B*(tx**2 + ty**2) 289 // a = tz**2 - B*B*(tx**2 + ty**2)
275 // 290 //
276 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) ) 291 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) )
277 // 292 //
278 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) ) 293 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) )
279 // 294 //
280 // The rest is much the same, except some deta 295 // The rest is much the same, except some details.
281 // 296 //
282 // a > 0 now means we intersect only once in t 297 // a > 0 now means we intersect only once in the correct hemisphere.
283 // 298 //
284 // a > 0 ? We only want solution which produce << 299 // a > 0 ? We only want solution which produces R > 0.
285 // since R = (z0+s*tz-A)/B, for tz/B > 0, this 300 // 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 301 // for tz/B < 0, this is the smallest s
287 // thus, same as in case 1 ( since sign(tz/B) 302 // thus, same as in case 1 ( since sign(tz/B) = sign(tz*B) )
288 // 303 //
289 G4int G4IntersectingCone::LineHitsCone2( const << 304 G4int G4IntersectingCone::LineHitsCone2( const G4ThreeVector &p,
290 const << 305 const G4ThreeVector &v,
291 << 306 G4double *s1, G4double *s2 )
292 { 307 {
293 static const G4double EPS = DBL_EPSILON; // <<
294 // <<
295 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 308 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
296 G4double tx = v.x(), ty = v.y(), tz = v.z(); 309 G4double tx = v.x(), ty = v.y(), tz = v.z();
297 << 310
>> 311
298 // Special case which might not be so rare: 312 // Special case which might not be so rare: B = 0 (precisely)
299 // 313 //
300 if (B==0) 314 if (B==0)
301 { 315 {
302 if (std::fabs(tz) < 1/kInfinity) { return 316 if (std::fabs(tz) < 1/kInfinity) { return 0; }
303 << 317
304 *s1 = (A-z0)/tz; 318 *s1 = (A-z0)/tz;
305 return 1; 319 return 1;
306 } 320 }
307 321
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; 322 G4double B2 = B*B;
318 323
319 G4double az = tz*tz; << 324 G4double a = tz*tz - B2*(tx*tx + ty*ty);
320 G4double ar = B2*(tx*tx + ty*ty); << 325 G4double b = 2*( (z0-A)*tz - B2*(x0*tx + y0*ty) );
321 G4double bz = 2*(z0-A)*tz; << 326 G4double c = sqr(z0-A) - B2*( x0*x0 + y0*y0 );
322 G4double br = 2*B2*(x0*tx + y0*ty); << 327
323 G4double cz = sqr(z0-A); << 328 G4double radical = b*b - 4*a*c;
324 G4double cr = B2*(x0*x0 + y0*y0); << 329
325 << 330 if (radical < -1E-6*std::fabs(b)) { return 0; } // No solution
326 // Instead radical = b*b - 4*a*c << 331
327 G4double arcz = 4*ar*cz; << 332 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 { 333 {
340 // 334 //
341 // The radical is roughly zero: check for 335 // The radical is roughly zero: check for special, very rare, cases
342 // 336 //
343 if (std::fabs(a) > 1/kInfinity) 337 if (std::fabs(a) > 1/kInfinity)
344 { 338 {
345 if ( std::fabs(x0*ty - y0*tx) < std::fab << 339 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B) )
346 { 340 {
347 *s1 = -0.5*b/a; 341 *s1 = -0.5*b/a;
348 return 1; 342 return 1;
349 } 343 }
350 return 0; 344 return 0;
351 } 345 }
352 } 346 }
353 else 347 else
354 { 348 {
355 radical = std::sqrt(radical); 349 radical = std::sqrt(radical);
356 } 350 }
357 << 351
358 if (a < -1/kInfinity) 352 if (a < -1/kInfinity)
359 { 353 {
360 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 354 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
361 sa = q/a; 355 sa = q/a;
362 sb = c/q; 356 sb = c/q;
363 if (sa < sb) { *s1 = sa; *s2 = sb; } else 357 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
364 if ((z0 + (*s1)*tz - A)/B < 0) { return 358 if ((z0 + (*s1)*tz - A)/B < 0) { return 0; }
365 return 2; 359 return 2;
366 } 360 }
367 else if (a > 1/kInfinity) 361 else if (a > 1/kInfinity)
368 { 362 {
369 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 363 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
370 sa = q/a; 364 sa = q/a;
371 sb = c/q; 365 sb = c/q;
372 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa; 366 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa;
373 return 1; 367 return 1;
374 } 368 }
375 else if (std::fabs(b) < 1/kInfinity) 369 else if (std::fabs(b) < 1/kInfinity)
376 { 370 {
377 return 0; 371 return 0;
378 } 372 }
379 else 373 else
380 { 374 {
381 *s1 = -c/b; 375 *s1 = -c/b;
382 if ((z0 + (*s1)*tz - A)/B < 0) { return 376 if ((z0 + (*s1)*tz - A)/B < 0) { return 0; }
383 return 1; 377 return 1;
384 } 378 }
385 } 379 }
386 380