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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 2006/06/29 18:48:38 gunter Exp $
>> 28 // GEANT4 tag $Name: geant4-08-02 $
>> 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" <<
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 //
41 = 0.5 * G4GeometryTolerance::GetInstance() <<
42 <<
43 // What type of cone are we? 50 // What type of cone are we?
44 // 51 //
45 type1 = (std::abs(z[1]-z[0]) > std::abs(r[1] << 52 type1 = (std::fabs(z[1]-z[0]) > std::fabs(r[1]-r[0]));
46 << 53
47 if (type1) // tube like << 54 if (type1)
48 { 55 {
49 B = (r[1] - r[0]) / (z[1] - z[0]); << 56 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]) << 57 A = 0.5*( r[1]+r[0] - B*(z[1]+z[0]) );
51 } 58 }
52 else // disk like << 59 else
53 { 60 {
54 B = (z[1] - z[0]) / (r[1] - r[0]); << 61 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] << 62 A = 0.5*( z[1]+z[0] - B*(r[1]+r[0]) );
56 } 63 }
57 64
>> 65 //
58 // Calculate extent 66 // Calculate extent
59 // 67 //
60 rLo = std::min(r[0], r[1]) - halfCarToleranc << 68 if (r[0] < r[1])
61 rHi = std::max(r[0], r[1]) + halfCarToleranc << 69 {
62 zLo = std::min(z[0], z[1]) - halfCarToleranc << 70 rLo = r[0]; rHi = r[1];
63 zHi = std::max(z[0], z[1]) + halfCarToleranc << 71 }
>> 72 else
>> 73 {
>> 74 rLo = r[1]; rHi = r[0];
>> 75 }
>> 76
>> 77 if (z[0] < z[1])
>> 78 {
>> 79 zLo = z[0]; zHi = z[1];
>> 80 }
>> 81 else
>> 82 {
>> 83 zLo = z[1]; zHi = z[0];
>> 84 }
64 } 85 }
65 86
>> 87
>> 88 //
66 // Fake default constructor - sets only member 89 // Fake default constructor - sets only member data and allocates memory
67 // for usage restri 90 // for usage restricted to object persistency.
68 // 91 //
69 G4IntersectingCone::G4IntersectingCone( __void 92 G4IntersectingCone::G4IntersectingCone( __void__& )
70 : zLo(0.), zHi(0.), rLo(0.), rHi(0.), A(0.), <<
71 { 93 {
72 } 94 }
73 95
>> 96
>> 97 //
74 // Destructor 98 // Destructor
75 // 99 //
76 G4IntersectingCone::~G4IntersectingCone() = de << 100 G4IntersectingCone::~G4IntersectingCone()
>> 101 {
>> 102 }
77 103
>> 104
>> 105 //
78 // HitOn 106 // HitOn
79 // 107 //
80 // Check r or z extent, as appropriate, to see 108 // Check r or z extent, as appropriate, to see if the point is possibly
81 // on the cone. 109 // on the cone.
82 // 110 //
83 G4bool G4IntersectingCone::HitOn( const G4doub 111 G4bool G4IntersectingCone::HitOn( const G4double r,
84 const G4doub 112 const G4double z )
85 { 113 {
86 // 114 //
87 // Be careful! The inequalities cannot be "< 115 // Be careful! The inequalities cannot be "<=" and ">=" here without
88 // punching a tiny hole in our shape! 116 // punching a tiny hole in our shape!
89 // 117 //
90 if (type1) 118 if (type1)
91 { 119 {
92 if (z < zLo || z > zHi) return false; 120 if (z < zLo || z > zHi) return false;
93 } 121 }
94 else 122 else
95 { 123 {
96 if (r < rLo || r > rHi) return false; 124 if (r < rLo || r > rHi) return false;
97 } 125 }
98 126
99 return true; 127 return true;
100 } 128 }
101 129
>> 130
>> 131 //
102 // LineHitsCone 132 // LineHitsCone
103 // 133 //
104 // Calculate the intersection of a line with o 134 // Calculate the intersection of a line with our conical surface, ignoring
105 // any phi division 135 // any phi division
106 // 136 //
107 G4int G4IntersectingCone::LineHitsCone( const << 137 G4int G4IntersectingCone::LineHitsCone( const G4ThreeVector &p,
108 const << 138 const G4ThreeVector &v,
109 << 139 G4double *s1, G4double *s2 )
110 { 140 {
111 if (type1) 141 if (type1)
112 { 142 {
113 return LineHitsCone1( p, v, s1, s2 ); 143 return LineHitsCone1( p, v, s1, s2 );
114 } 144 }
115 else 145 else
116 { 146 {
117 return LineHitsCone2( p, v, s1, s2 ); 147 return LineHitsCone2( p, v, s1, s2 );
118 } 148 }
119 } 149 }
120 150
>> 151
>> 152 //
121 // LineHitsCone1 153 // LineHitsCone1
122 // 154 //
123 // Calculate the intersections of a line with 155 // Calculate the intersections of a line with a conical surface. Only
124 // suitable if zPlane[0] != zPlane[1]. 156 // suitable if zPlane[0] != zPlane[1].
125 // 157 //
126 // Equation of a line: 158 // Equation of a line:
127 // 159 //
128 // x = x0 + s*tx y = y0 + s*ty 160 // x = x0 + s*tx y = y0 + s*ty z = z0 + s*tz
129 // 161 //
130 // Equation of a conical surface: 162 // Equation of a conical surface:
131 // 163 //
132 // x**2 + y**2 = (A + B*z)**2 164 // x**2 + y**2 = (A + B*z)**2
133 // 165 //
134 // Solution is quadratic: 166 // Solution is quadratic:
135 // 167 //
136 // a*s**2 + b*s + c = 0 168 // a*s**2 + b*s + c = 0
137 // 169 //
138 // where: 170 // where:
139 // 171 //
140 // a = tx**2 + ty**2 - (B*tz)**2 << 172 // a = x0**2 + y0**2 - (A + B*z0)**2
141 // 173 //
142 // b = 2*( px*vx + py*vy - B*(A + B*pz)*vz ) << 174 // b = 2*( x0*tx + y0*ty - (A*B - B*B*z0)*tz)
143 // 175 //
144 // c = x0**2 + y0**2 - (A + B*z0)**2 << 176 // c = tx**2 + ty**2 - (B*tz)**2
145 // 177 //
146 // Notice, that if a < 0, this indicates that 178 // Notice, that if a < 0, this indicates that the two solutions (assuming
147 // they exist) are in opposite cones (that is, 179 // 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 180 // and the other z > z0). For our shapes, the invalid solution is one
149 // which produces A + Bz < 0, or the one where 181 // 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 182 // Since Bz = B*s*tz, if B*tz > 0, we want the largest s, otherwise,
151 // the smaller. 183 // the smaller.
152 // 184 //
153 // If there are two solutions on one side of t 185 // 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 186 // sure that they are on the "correct" side, that is A + B*z0 + s*B*tz >= 0.
155 // 187 //
156 // If a = 0, we have a linear problem: s = c/b 188 // If a = 0, we have a linear problem: s = c/b, which again gives one solution.
157 // This should be rare. 189 // This should be rare.
158 // 190 //
159 // For b*b - 4*a*c = 0, we also have one solut 191 // 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 << 192 // a line just grazing the surface of a the cone, which we want to ignore.
161 // However, there are two other, very rare, po 193 // However, there are two other, very rare, possibilities:
162 // a line intersecting the z axis and either: 194 // a line intersecting the z axis and either:
163 // 1. At the same angle std::atan(B) to 195 // 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 196 // 2. Intersecting the cone apex (0,0,-A/B)
165 // We *don't* want to miss these! How do we id 197 // We *don't* want to miss these! How do we identify them? Well, since
166 // this case is rare, we can at least swallow 198 // this case is rare, we can at least swallow a little more CPU than we would
167 // normally be comfortable with. Intersection 199 // normally be comfortable with. Intersection with the z axis means
168 // x0*ty - y0*tx = 0. Case (1) means a==0, and 200 // x0*ty - y0*tx = 0. Case (1) means a==0, and we've already dealt with that
169 // above. Case (2) means a < 0. 201 // above. Case (2) means a < 0.
170 // 202 //
171 // Now: x0*tx + y0*ty = 0 in terms of roundoff 203 // Now: x0*tx + y0*ty = 0 in terms of roundoff error. We can write:
172 // Delta = x0*tx + y0*ty 204 // Delta = x0*tx + y0*ty
173 // b = 2*( Delta - B*(A + B*z0)*tz << 205 // b = 2*( Delta - (A*B + B*B*z0)*tz )
174 // For: 206 // For:
175 // b*b - 4*a*c = epsilon 207 // b*b - 4*a*c = epsilon
176 // where epsilon is small, then: 208 // where epsilon is small, then:
177 // Delta = epsilon/2/B 209 // Delta = epsilon/2/B
178 // << 210 //
179 G4int G4IntersectingCone::LineHitsCone1( const << 211 G4int G4IntersectingCone::LineHitsCone1( const G4ThreeVector &p,
180 const << 212 const G4ThreeVector &v,
181 << 213 G4double *s1, G4double *s2 )
182 { 214 {
183 static const G4double EPS = DBL_EPSILON; // <<
184 // <<
185 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 215 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
186 G4double tx = v.x(), ty = v.y(), tz = v.z(); 216 G4double tx = v.x(), ty = v.y(), tz = v.z();
187 217
188 // Value of radical can be inaccurate due to << 218 G4double a = tx*tx + ty*ty - sqr(B*tz);
189 // if to calculate the coefficiets a,b,c lik << 219 G4double b = 2*( x0*tx + y0*ty - (A*B + B*B*z0)*tz);
190 // G4double a = tx*tx + ty*ty - sqr(B*tz << 220 G4double c = x0*x0 + y0*y0 - sqr(A + B*z0);
191 // G4double b = 2*( x0*tx + y0*ty - B*(A << 221
192 // G4double c = x0*x0 + y0*y0 - sqr(A + << 222 G4double radical = b*b - 4*a*c;
193 // << 223
194 // For more accurate calculation of radical << 224 if (radical < -1E-6*std::fabs(b)) return 0; // No solution
195 // are splitted in two components, radial an << 225
196 // << 226 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 { 227 {
218 // 228 //
219 // The radical is roughly zero: check for 229 // The radical is roughly zero: check for special, very rare, cases
220 // 230 //
221 if (std::fabs(a) > 1/kInfinity) 231 if (std::fabs(a) > 1/kInfinity)
>> 232 {
>> 233 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B))
222 { 234 {
223 if(B==0.) { return 0; } << 235 *s1 = -0.5*b/a;
224 if ( std::fabs(x0*ty - y0*tx) < std::fab << 236 return 1;
225 { <<
226 *s1 = -0.5*b/a; <<
227 return 1; <<
228 } 237 }
229 return 0; 238 return 0;
230 } 239 }
231 } 240 }
232 else 241 else
233 { 242 {
234 radical = std::sqrt(radical); 243 radical = std::sqrt(radical);
235 } 244 }
236 << 245
237 if (a > 1/kInfinity) 246 if (a > 1/kInfinity)
238 { 247 {
239 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 248 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
240 sa = q/a; 249 sa = q/a;
241 sb = c/q; 250 sb = c/q;
242 if (sa < sb) { *s1 = sa; *s2 = sb; } else 251 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
243 if (A + B*(z0+(*s1)*tz) < 0) { return 0; << 252 if (A + B*(z0+(*s1)*tz) < 0) return 0;
244 return 2; 253 return 2;
245 } 254 }
246 else if (a < -1/kInfinity) 255 else if (a < -1/kInfinity)
247 { 256 {
248 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 257 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
249 sa = q/a; 258 sa = q/a;
250 sb = c/q; 259 sb = c/q;
251 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa; 260 *s1 = (B*tz > 0)^(sa > sb) ? sb : sa;
252 return 1; 261 return 1;
253 } 262 }
254 else if (std::fabs(b) < 1/kInfinity) 263 else if (std::fabs(b) < 1/kInfinity)
255 { 264 {
256 return 0; 265 return 0;
257 } 266 }
258 else 267 else
259 { 268 {
260 *s1 = -c/b; 269 *s1 = -c/b;
261 if (A + B*(z0+(*s1)*tz) < 0) { return 0; << 270 if (A + B*(z0+(*s1)*tz) < 0) return 0;
262 return 1; 271 return 1;
263 } 272 }
264 } 273 }
265 274
>> 275
>> 276 //
266 // LineHitsCone2 277 // LineHitsCone2
267 // 278 //
268 // See comments under LineHitsCone1. In this r 279 // See comments under LineHitsCone1. In this routine, case2, we have:
269 // 280 //
270 // Z = A + B*R 281 // Z = A + B*R
271 // 282 //
272 // The solution is still quadratic: 283 // The solution is still quadratic:
273 // 284 //
274 // a = tz**2 - B*B*(tx**2 + ty**2) 285 // a = tz**2 - B*B*(tx**2 + ty**2)
275 // 286 //
276 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) ) 287 // b = 2*( (z0-A)*tz - B*B*(x0*tx+y0*ty) )
277 // 288 //
278 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) ) 289 // c = ( (z0-A)**2 - B*B*(x0**2 + y0**2) )
279 // 290 //
280 // The rest is much the same, except some deta 291 // The rest is much the same, except some details.
281 // 292 //
282 // a > 0 now means we intersect only once in t 293 // a > 0 now means we intersect only once in the correct hemisphere.
283 // 294 //
284 // a > 0 ? We only want solution which produce << 295 // a > 0 ? We only want solution which produces R > 0.
285 // since R = (z0+s*tz-A)/B, for tz/B > 0, this 296 // 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 297 // for tz/B < 0, this is the smallest s
287 // thus, same as in case 1 ( since sign(tz/B) 298 // thus, same as in case 1 ( since sign(tz/B) = sign(tz*B) )
288 // 299 //
289 G4int G4IntersectingCone::LineHitsCone2( const << 300 G4int G4IntersectingCone::LineHitsCone2( const G4ThreeVector &p,
290 const << 301 const G4ThreeVector &v,
291 << 302 G4double *s1, G4double *s2 )
292 { 303 {
293 static const G4double EPS = DBL_EPSILON; // <<
294 // <<
295 G4double x0 = p.x(), y0 = p.y(), z0 = p.z(); 304 G4double x0 = p.x(), y0 = p.y(), z0 = p.z();
296 G4double tx = v.x(), ty = v.y(), tz = v.z(); 305 G4double tx = v.x(), ty = v.y(), tz = v.z();
297 << 306
>> 307 //
298 // Special case which might not be so rare: 308 // Special case which might not be so rare: B = 0 (precisely)
299 // 309 //
300 if (B==0) 310 if (B==0)
301 { 311 {
302 if (std::fabs(tz) < 1/kInfinity) { return << 312 if (std::fabs(tz) < 1/kInfinity) return 0;
303 << 313
304 *s1 = (A-z0)/tz; 314 *s1 = (A-z0)/tz;
305 return 1; 315 return 1;
306 } 316 }
307 317
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; 318 G4double B2 = B*B;
318 319
319 G4double az = tz*tz; << 320 G4double a = tz*tz - B2*(tx*tx + ty*ty);
320 G4double ar = B2*(tx*tx + ty*ty); << 321 G4double b = 2*( (z0-A)*tz - B2*(x0*tx + y0*ty) );
321 G4double bz = 2*(z0-A)*tz; << 322 G4double c = sqr(z0-A) - B2*( x0*x0 + y0*y0 );
322 G4double br = 2*B2*(x0*tx + y0*ty); << 323
323 G4double cz = sqr(z0-A); << 324 G4double radical = b*b - 4*a*c;
324 G4double cr = B2*(x0*x0 + y0*y0); << 325
325 << 326 if (radical < -1E-6*std::fabs(b)) return 0; // No solution
326 // Instead radical = b*b - 4*a*c << 327
327 G4double arcz = 4*ar*cz; << 328 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 { 329 {
340 // 330 //
341 // The radical is roughly zero: check for 331 // The radical is roughly zero: check for special, very rare, cases
342 // 332 //
343 if (std::fabs(a) > 1/kInfinity) 333 if (std::fabs(a) > 1/kInfinity)
344 { 334 {
345 if ( std::fabs(x0*ty - y0*tx) < std::fab << 335 if ( std::fabs(x0*ty - y0*tx) < std::fabs(1E-6/B))
346 { 336 {
347 *s1 = -0.5*b/a; 337 *s1 = -0.5*b/a;
348 return 1; 338 return 1;
349 } 339 }
350 return 0; 340 return 0;
351 } 341 }
352 } 342 }
353 else 343 else
354 { 344 {
355 radical = std::sqrt(radical); 345 radical = std::sqrt(radical);
356 } 346 }
357 << 347
358 if (a < -1/kInfinity) 348 if (a < -1/kInfinity)
359 { 349 {
360 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 350 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
361 sa = q/a; 351 sa = q/a;
362 sb = c/q; 352 sb = c/q;
363 if (sa < sb) { *s1 = sa; *s2 = sb; } else 353 if (sa < sb) { *s1 = sa; *s2 = sb; } else { *s1 = sb; *s2 = sa; }
364 if ((z0 + (*s1)*tz - A)/B < 0) { return << 354 if ((z0 + (*s1)*tz - A)/B < 0) return 0;
365 return 2; 355 return 2;
366 } 356 }
367 else if (a > 1/kInfinity) 357 else if (a > 1/kInfinity)
368 { 358 {
369 G4double sa, sb, q = -0.5*( b + (b < 0 ? - 359 G4double sa, sb, q = -0.5*( b + (b < 0 ? -radical : +radical) );
370 sa = q/a; 360 sa = q/a;
371 sb = c/q; 361 sb = c/q;
372 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa; 362 *s1 = (tz*B > 0)^(sa > sb) ? sb : sa;
373 return 1; 363 return 1;
374 } 364 }
375 else if (std::fabs(b) < 1/kInfinity) 365 else if (std::fabs(b) < 1/kInfinity)
376 { 366 {
377 return 0; 367 return 0;
378 } 368 }
379 else 369 else
380 { 370 {
381 *s1 = -c/b; 371 *s1 = -c/b;
382 if ((z0 + (*s1)*tz - A)/B < 0) { return << 372 if ((z0 + (*s1)*tz - A)/B < 0) return 0;
383 return 1; 373 return 1;
384 } 374 }
385 } 375 }
386 376