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25 // 25 //
26 // G4TriangularFacet implementation << 26 // $Id$
27 // 27 //
28 // 31.10.2004, P R Truscott, QinetiQ Ltd, UK - << 28 // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
29 // 01.08.2007, P R Truscott, QinetiQ Ltd, UK << 29 //
>> 30 // CHANGE HISTORY
>> 31 // --------------
>> 32 //
>> 33 // 31 October 2004, P R Truscott, QinetiQ Ltd, UK - Created.
>> 34 //
>> 35 // 01 August 2007 P R Truscott, QinetiQ Ltd, UK
30 // Significant modification t 36 // Significant modification to correct for errors and enhance
31 // based on patches/observati 37 // based on patches/observations kindly provided by Rickard
32 // Holmberg. 38 // Holmberg.
33 // 12.10.2012, M Gayer, CERN << 39 //
>> 40 // 26 September 2007
>> 41 // P R Truscott, QinetiQ Ltd, UK
>> 42 // Further chamges implemented to the Intersect member
>> 43 // function to correctly treat rays nearly parallel to the
>> 44 // plane of the triangle.
>> 45 //
>> 46 // 12 April 2010 P R Truscott, QinetiQ, bug fixes to treat optical
>> 47 // photon transport, in particular internal reflection
>> 48 // at surface.
>> 49 //
>> 50 // 22 August 2011 I Hrivnacova, Orsay, fix in Intersect() to take into
>> 51 // account geometrical tolerance and cases of zero distance
>> 52 // from surface.
>> 53 //
>> 54 // 12 October 2012 M Gayer, CERN
34 // New implementation reducin 55 // New implementation reducing memory requirements by 50%,
35 // and considerable CPU speed 56 // and considerable CPU speedup together with the new
36 // implementation of G4Tessel 57 // implementation of G4TessellatedSolid.
37 // 23.02.2016, E Tcherniaev, CERN << 58 //
38 // Improved test to detect de << 59 // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
39 // too narrow) triangles. <<
40 // ------------------------------------------- <<
41 60
42 #include "G4TriangularFacet.hh" 61 #include "G4TriangularFacet.hh"
43 62
44 #include "Randomize.hh" 63 #include "Randomize.hh"
45 #include "G4TessellatedGeometryAlgorithms.hh" 64 #include "G4TessellatedGeometryAlgorithms.hh"
46 65
47 using namespace std; 66 using namespace std;
48 67
49 ////////////////////////////////////////////// 68 ///////////////////////////////////////////////////////////////////////////////
50 // 69 //
51 // Definition of triangular facet using absolu 70 // Definition of triangular facet using absolute vectors to fVertices.
52 // From this for first vector is retained to d 71 // From this for first vector is retained to define the facet location and
53 // two relative vectors (E0 and E1) define the 72 // two relative vectors (E0 and E1) define the sides and orientation of
54 // the outward surface normal. 73 // the outward surface normal.
55 // 74 //
56 G4TriangularFacet::G4TriangularFacet (const G4 << 75 G4TriangularFacet::G4TriangularFacet (const G4ThreeVector &vt0,
57 const G4 << 76 const G4ThreeVector &vt1,
58 const G4 << 77 const G4ThreeVector &vt2,
59 G4 78 G4FacetVertexType vertexType)
>> 79 : fSqrDist(0.)
60 { 80 {
61 fVertices = new vector<G4ThreeVector>(3); 81 fVertices = new vector<G4ThreeVector>(3);
62 82
63 SetVertex(0, vt0); 83 SetVertex(0, vt0);
64 if (vertexType == ABSOLUTE) 84 if (vertexType == ABSOLUTE)
65 { 85 {
66 SetVertex(1, vt1); 86 SetVertex(1, vt1);
67 SetVertex(2, vt2); 87 SetVertex(2, vt2);
68 fE1 = vt1 - vt0; 88 fE1 = vt1 - vt0;
69 fE2 = vt2 - vt0; 89 fE2 = vt2 - vt0;
70 } 90 }
71 else 91 else
72 { 92 {
73 SetVertex(1, vt0 + vt1); 93 SetVertex(1, vt0 + vt1);
74 SetVertex(2, vt0 + vt2); 94 SetVertex(2, vt0 + vt2);
75 fE1 = vt1; 95 fE1 = vt1;
76 fE2 = vt2; 96 fE2 = vt2;
77 } 97 }
78 98
79 G4ThreeVector E1xE2 = fE1.cross(fE2); <<
80 fArea = 0.5 * E1xE2.mag(); <<
81 for (G4int i = 0; i < 3; ++i) fIndices[i] = 99 for (G4int i = 0; i < 3; ++i) fIndices[i] = -1;
82 100
83 fIsDefined = true; << 101 G4double eMag1 = fE1.mag();
84 G4double delta = kCarTolerance; // Set toler << 102 G4double eMag2 = fE2.mag();
>> 103 G4double eMag3 = (fE2-fE1).mag();
85 104
86 // Check length of edges << 105 if (eMag1 <= kCarTolerance || eMag2 <= kCarTolerance
87 // << 106 || eMag3 <= kCarTolerance)
88 G4double leng1 = fE1.mag(); <<
89 G4double leng2 = (fE2-fE1).mag(); <<
90 G4double leng3 = fE2.mag(); <<
91 if (leng1 <= delta || leng2 <= delta || leng <<
92 { <<
93 fIsDefined = false; <<
94 } <<
95 <<
96 // Check min height of triangle <<
97 // <<
98 if (fIsDefined) <<
99 { <<
100 if (2.*fArea/std::max(std::max(leng1,leng2 <<
101 { <<
102 fIsDefined = false; <<
103 } <<
104 } <<
105 <<
106 // Define facet <<
107 // <<
108 if (!fIsDefined) <<
109 { 107 {
110 ostringstream message; 108 ostringstream message;
111 message << "Facet is too small or too narr << 109 message << "Length of sides of facet are too small." << endl
112 << "Triangle area = " << fArea << << 110 << "fVertices[0] = " << GetVertex(0) << endl
113 << "P0 = " << GetVertex(0) << G4en << 111 << "fVertices[1] = " << GetVertex(1) << endl
114 << "P1 = " << GetVertex(1) << G4en << 112 << "fVertices[2] = " << GetVertex(2) << endl
115 << "P2 = " << GetVertex(2) << G4en << 113 << "Side lengths = fVertices[0]->fVertices[1]" << eMag1 << endl
116 << "Side1 length (P0->P1) = " << l << 114 << "Side lengths = fVertices[0]->fVertices[2]" << eMag2 << endl
117 << "Side2 length (P1->P2) = " << l << 115 << "Side lengths = fVertices[1]->fVertices[2]" << eMag3;
118 << "Side3 length (P2->P0) = " << l <<
119 G4Exception("G4TriangularFacet::G4Triangul 116 G4Exception("G4TriangularFacet::G4TriangularFacet()",
120 "GeomSolids1001", JustWarning, message); << 117 "GeomSolids1001", JustWarning, message);
>> 118 fIsDefined = false;
121 fSurfaceNormal.set(0,0,0); 119 fSurfaceNormal.set(0,0,0);
122 fA = fB = fC = 0.0; 120 fA = fB = fC = 0.0;
123 fDet = 0.0; 121 fDet = 0.0;
124 fCircumcentre = vt0 + 0.5*fE1 + 0.5*fE2; <<
125 fArea = fRadius = 0.0; 122 fArea = fRadius = 0.0;
126 } 123 }
127 else 124 else
128 { 125 {
129 fSurfaceNormal = E1xE2.unit(); << 126 fIsDefined = true;
>> 127 fSurfaceNormal = fE1.cross(fE2).unit();
130 fA = fE1.mag2(); 128 fA = fE1.mag2();
131 fB = fE1.dot(fE2); 129 fB = fE1.dot(fE2);
132 fC = fE2.mag2(); 130 fC = fE2.mag2();
133 fDet = std::fabs(fA*fC - fB*fB); << 131 fDet = fabs(fA*fC - fB*fB);
134 132
135 fCircumcentre = << 133 // sMin = -0.5*kCarTolerance/sqrt(fA);
136 vt0 + (E1xE2.cross(fE1)*fC + fE2.cross(E << 134 // sMax = 1.0 - sMin;
137 fRadius = (fCircumcentre - vt0).mag(); << 135 // tMin = -0.5*kCarTolerance/sqrt(fC);
>> 136 // G4ThreeVector vtmp = 0.25 * (fE1 + fE2);
>> 137
>> 138 fArea = 0.5 * (fE1.cross(fE2)).mag();
>> 139 G4double lambda0 = (fA-fB) * fC / (8.0*fArea*fArea);
>> 140 G4double lambda1 = (fC-fB) * fA / (8.0*fArea*fArea);
>> 141 G4ThreeVector p0 = GetVertex(0);
>> 142 fCircumcentre = p0 + lambda0*fE1 + lambda1*fE2;
>> 143 G4double radiusSqr = (fCircumcentre-p0).mag2();
>> 144 fRadius = sqrt(radiusSqr);
138 } 145 }
139 } 146 }
140 147
141 ////////////////////////////////////////////// 148 ///////////////////////////////////////////////////////////////////////////////
142 // 149 //
143 G4TriangularFacet::G4TriangularFacet () 150 G4TriangularFacet::G4TriangularFacet ()
>> 151 : fSqrDist(0.)
144 { 152 {
145 fVertices = new vector<G4ThreeVector>(3); 153 fVertices = new vector<G4ThreeVector>(3);
146 G4ThreeVector zero(0,0,0); 154 G4ThreeVector zero(0,0,0);
147 SetVertex(0, zero); 155 SetVertex(0, zero);
148 SetVertex(1, zero); 156 SetVertex(1, zero);
149 SetVertex(2, zero); 157 SetVertex(2, zero);
150 for (G4int i = 0; i < 3; ++i) fIndices[i] = 158 for (G4int i = 0; i < 3; ++i) fIndices[i] = -1;
151 fIsDefined = false; 159 fIsDefined = false;
152 fSurfaceNormal.set(0,0,0); 160 fSurfaceNormal.set(0,0,0);
153 fA = fB = fC = 0; 161 fA = fB = fC = 0;
154 fE1 = zero; 162 fE1 = zero;
155 fE2 = zero; 163 fE2 = zero;
156 fDet = 0.0; 164 fDet = 0.0;
157 fArea = fRadius = 0.0; 165 fArea = fRadius = 0.0;
158 } 166 }
159 167
160 ////////////////////////////////////////////// 168 ///////////////////////////////////////////////////////////////////////////////
161 // 169 //
162 G4TriangularFacet::~G4TriangularFacet () 170 G4TriangularFacet::~G4TriangularFacet ()
163 { 171 {
164 SetVertices(nullptr); << 172 SetVertices(0);
165 } 173 }
166 174
167 ////////////////////////////////////////////// 175 ///////////////////////////////////////////////////////////////////////////////
168 // 176 //
169 void G4TriangularFacet::CopyFrom (const G4Tria << 177 void G4TriangularFacet::CopyFrom (const G4TriangularFacet &rhs)
170 { 178 {
171 auto p = (char *) &rhs; << 179 char *p = (char *) &rhs;
172 copy(p, p + sizeof(*this), (char *)this); 180 copy(p, p + sizeof(*this), (char *)this);
173 181
174 if (fIndices[0] < 0 && fVertices == nullptr) << 182 if (fIndices[0] < 0 && fVertices)
175 { 183 {
176 fVertices = new vector<G4ThreeVector>(3); 184 fVertices = new vector<G4ThreeVector>(3);
177 for (G4int i = 0; i < 3; ++i) (*fVertices) 185 for (G4int i = 0; i < 3; ++i) (*fVertices)[i] = (*rhs.fVertices)[i];
178 } 186 }
179 } 187 }
180 188
181 ////////////////////////////////////////////// 189 ///////////////////////////////////////////////////////////////////////////////
182 // 190 //
183 void G4TriangularFacet::MoveFrom (G4Triangular << 191 G4TriangularFacet::G4TriangularFacet (const G4TriangularFacet &rhs)
184 { <<
185 fSurfaceNormal = std::move(rhs.fSurfaceNorma <<
186 fArea = rhs.fArea; <<
187 fCircumcentre = std::move(rhs.fCircumcentre) <<
188 fRadius = rhs.fRadius; <<
189 fIndices = rhs.fIndices; <<
190 fA = rhs.fA; fB = rhs.fB; fC = rhs.fC; <<
191 fDet = rhs.fDet; <<
192 fSqrDist = rhs.fSqrDist; <<
193 fE1 = std::move(rhs.fE1); fE2 = std::move(rh <<
194 fIsDefined = rhs.fIsDefined; <<
195 fVertices = rhs.fVertices; <<
196 rhs.fVertices = nullptr; <<
197 } <<
198 <<
199 ////////////////////////////////////////////// <<
200 // <<
201 G4TriangularFacet::G4TriangularFacet (const G4 <<
202 : G4VFacet(rhs) 192 : G4VFacet(rhs)
203 { 193 {
204 CopyFrom(rhs); 194 CopyFrom(rhs);
205 } 195 }
206 196
207 ////////////////////////////////////////////// 197 ///////////////////////////////////////////////////////////////////////////////
208 // 198 //
209 G4TriangularFacet::G4TriangularFacet (G4Triang << 199 G4TriangularFacet &
210 : G4VFacet(rhs) << 200 G4TriangularFacet::operator=(const G4TriangularFacet &rhs)
211 { <<
212 MoveFrom(rhs); <<
213 } <<
214 <<
215 ////////////////////////////////////////////// <<
216 // <<
217 G4TriangularFacet& <<
218 G4TriangularFacet::operator=(const G4Triangula <<
219 { 201 {
220 SetVertices(nullptr); << 202 SetVertices(0);
221 203
222 if (this != &rhs) 204 if (this != &rhs)
223 { <<
224 delete fVertices; <<
225 CopyFrom(rhs); 205 CopyFrom(rhs);
226 } <<
227 <<
228 return *this; <<
229 } <<
230 <<
231 ////////////////////////////////////////////// <<
232 // <<
233 G4TriangularFacet& <<
234 G4TriangularFacet::operator=(G4TriangularFacet <<
235 { <<
236 SetVertices(nullptr); <<
237 <<
238 if (this != &rhs) <<
239 { <<
240 delete fVertices; <<
241 MoveFrom(rhs); <<
242 } <<
243 206
244 return *this; 207 return *this;
245 } 208 }
246 209
247 ////////////////////////////////////////////// 210 ///////////////////////////////////////////////////////////////////////////////
248 // 211 //
249 // GetClone 212 // GetClone
250 // 213 //
251 // Simple member function to generate fA dupli 214 // Simple member function to generate fA duplicate of the triangular facet.
252 // 215 //
253 G4VFacet* G4TriangularFacet::GetClone () << 216 G4VFacet *G4TriangularFacet::GetClone ()
254 { 217 {
255 auto fc = new G4TriangularFacet (GetVertex(0 << 218 G4TriangularFacet *fc =
256 GetVertex(2 << 219 new G4TriangularFacet (GetVertex(0), GetVertex(1), GetVertex(2), ABSOLUTE);
257 return fc; 220 return fc;
258 } 221 }
259 222
260 ////////////////////////////////////////////// 223 ///////////////////////////////////////////////////////////////////////////////
261 // 224 //
262 // GetFlippedFacet 225 // GetFlippedFacet
263 // 226 //
264 // Member function to generate an identical fa 227 // Member function to generate an identical facet, but with the normal vector
265 // pointing at 180 degrees. 228 // pointing at 180 degrees.
266 // 229 //
267 G4TriangularFacet* G4TriangularFacet::GetFlipp << 230 G4TriangularFacet *G4TriangularFacet::GetFlippedFacet ()
268 { 231 {
269 auto flipped = new G4TriangularFacet (GetVer << 232 G4TriangularFacet *flipped =
270 GetVer << 233 new G4TriangularFacet (GetVertex(0), GetVertex(1), GetVertex(2), ABSOLUTE);
271 return flipped; 234 return flipped;
272 } 235 }
273 236
274 ////////////////////////////////////////////// 237 ///////////////////////////////////////////////////////////////////////////////
275 // 238 //
276 // Distance (G4ThreeVector) 239 // Distance (G4ThreeVector)
277 // 240 //
278 // Determines the vector between p and the clo 241 // Determines the vector between p and the closest point on the facet to p.
279 // This is based on the algorithm published in 242 // This is based on the algorithm published in "Geometric Tools for Computer
280 // Graphics," Philip J Scheider and David H Eb 243 // Graphics," Philip J Scheider and David H Eberly, Elsevier Science (USA),
281 // 2003. at the time of writing, the algorith 244 // 2003. at the time of writing, the algorithm is also available in fA
282 // technical note "Distance between point and 245 // technical note "Distance between point and triangle in 3D," by David Eberly
283 // at http://www.geometrictools.com/Documentat 246 // at http://www.geometrictools.com/Documentation/DistancePoint3Triangle3.pdf
284 // 247 //
285 // The by-product is the square-distance fSqrD 248 // The by-product is the square-distance fSqrDist, which is retained
286 // in case needed by the other "Distance" memb 249 // in case needed by the other "Distance" member functions.
287 // 250 //
288 G4ThreeVector G4TriangularFacet::Distance (con << 251 G4ThreeVector G4TriangularFacet::Distance (const G4ThreeVector &p)
289 { 252 {
290 G4ThreeVector D = GetVertex(0) - p; 253 G4ThreeVector D = GetVertex(0) - p;
291 G4double d = fE1.dot(D); 254 G4double d = fE1.dot(D);
292 G4double e = fE2.dot(D); 255 G4double e = fE2.dot(D);
293 G4double f = D.mag2(); 256 G4double f = D.mag2();
294 G4double q = fB*e - fC*d; 257 G4double q = fB*e - fC*d;
295 G4double t = fB*d - fA*e; 258 G4double t = fB*d - fA*e;
296 fSqrDist = 0.; 259 fSqrDist = 0.;
297 260
298 if (q+t <= fDet) 261 if (q+t <= fDet)
299 { 262 {
300 if (q < 0.0) 263 if (q < 0.0)
301 { 264 {
302 if (t < 0.0) 265 if (t < 0.0)
303 { 266 {
304 // 267 //
305 // We are in region 4. 268 // We are in region 4.
306 // 269 //
307 if (d < 0.0) 270 if (d < 0.0)
308 { 271 {
309 t = 0.0; 272 t = 0.0;
310 if (-d >= fA) {q = 1.0; fSqrDist = f 273 if (-d >= fA) {q = 1.0; fSqrDist = fA + 2.0*d + f;}
311 else {q = -d/fA; fSqrDist = 274 else {q = -d/fA; fSqrDist = d*q + f;}
312 } 275 }
313 else 276 else
314 { 277 {
315 q = 0.0; 278 q = 0.0;
316 if (e >= 0.0) {t = 0.0; fSqrDi 279 if (e >= 0.0) {t = 0.0; fSqrDist = f;}
317 else if (-e >= fC) {t = 1.0; fSqrD 280 else if (-e >= fC) {t = 1.0; fSqrDist = fC + 2.0*e + f;}
318 else {t = -e/fC; fSqr 281 else {t = -e/fC; fSqrDist = e*t + f;}
319 } 282 }
320 } 283 }
321 else 284 else
322 { 285 {
323 // 286 //
324 // We are in region 3. 287 // We are in region 3.
325 // 288 //
326 q = 0.0; 289 q = 0.0;
327 if (e >= 0.0) {t = 0.0; fSqrDist 290 if (e >= 0.0) {t = 0.0; fSqrDist = f;}
328 else if (-e >= fC) {t = 1.0; fSqrDist 291 else if (-e >= fC) {t = 1.0; fSqrDist = fC + 2.0*e + f;}
329 else {t = -e/fC; fSqrDis 292 else {t = -e/fC; fSqrDist = e*t + f;}
330 } 293 }
331 } 294 }
332 else if (t < 0.0) 295 else if (t < 0.0)
333 { 296 {
334 // 297 //
335 // We are in region 5. 298 // We are in region 5.
336 // 299 //
337 t = 0.0; 300 t = 0.0;
338 if (d >= 0.0) {q = 0.0; fSqrDist = 301 if (d >= 0.0) {q = 0.0; fSqrDist = f;}
339 else if (-d >= fA) {q = 1.0; fSqrDist = 302 else if (-d >= fA) {q = 1.0; fSqrDist = fA + 2.0*d + f;}
340 else {q = -d/fA; fSqrDist 303 else {q = -d/fA; fSqrDist = d*q + f;}
341 } 304 }
342 else 305 else
343 { 306 {
344 // 307 //
345 // We are in region 0. 308 // We are in region 0.
346 // 309 //
347 G4double dist = fSurfaceNormal.dot(D); << 310 q = q / fDet;
348 fSqrDist = dist*dist; << 311 t = t / fDet;
349 return fSurfaceNormal*dist; << 312 fSqrDist = q*(fA*q + fB*t + 2.0*d) + t*(fB*q + fC*t + 2.0*e) + f;
350 } 313 }
351 } 314 }
352 else 315 else
353 { 316 {
354 if (q < 0.0) 317 if (q < 0.0)
355 { 318 {
356 // 319 //
357 // We are in region 2. 320 // We are in region 2.
358 // 321 //
359 G4double tmp0 = fB + d; 322 G4double tmp0 = fB + d;
360 G4double tmp1 = fC + e; 323 G4double tmp1 = fC + e;
361 if (tmp1 > tmp0) 324 if (tmp1 > tmp0)
362 { 325 {
363 G4double numer = tmp1 - tmp0; 326 G4double numer = tmp1 - tmp0;
364 G4double denom = fA - 2.0*fB + fC; 327 G4double denom = fA - 2.0*fB + fC;
365 if (numer >= denom) {q = 1.0; t = 0.0; 328 if (numer >= denom) {q = 1.0; t = 0.0; fSqrDist = fA + 2.0*d + f;}
366 else 329 else
367 { 330 {
368 q = numer/denom; 331 q = numer/denom;
369 t = 1.0 - q; 332 t = 1.0 - q;
370 fSqrDist = q*(fA*q + fB*t +2.0*d) + 333 fSqrDist = q*(fA*q + fB*t +2.0*d) + t*(fB*q + fC*t + 2.0*e) + f;
371 } 334 }
372 } 335 }
373 else 336 else
374 { 337 {
375 q = 0.0; 338 q = 0.0;
376 if (tmp1 <= 0.0) {t = 1.0; fSqrDi 339 if (tmp1 <= 0.0) {t = 1.0; fSqrDist = fC + 2.0*e + f;}
377 else if (e >= 0.0) {t = 0.0; fSqrDi 340 else if (e >= 0.0) {t = 0.0; fSqrDist = f;}
378 else {t = -e/fC; fSqr 341 else {t = -e/fC; fSqrDist = e*t + f;}
379 } 342 }
380 } 343 }
381 else if (t < 0.0) 344 else if (t < 0.0)
382 { 345 {
383 // 346 //
384 // We are in region 6. 347 // We are in region 6.
385 // 348 //
386 G4double tmp0 = fB + e; 349 G4double tmp0 = fB + e;
387 G4double tmp1 = fA + d; 350 G4double tmp1 = fA + d;
388 if (tmp1 > tmp0) 351 if (tmp1 > tmp0)
389 { 352 {
390 G4double numer = tmp1 - tmp0; 353 G4double numer = tmp1 - tmp0;
391 G4double denom = fA - 2.0*fB + fC; 354 G4double denom = fA - 2.0*fB + fC;
392 if (numer >= denom) {t = 1.0; q = 0.0; 355 if (numer >= denom) {t = 1.0; q = 0.0; fSqrDist = fC + 2.0*e + f;}
393 else 356 else
394 { 357 {
395 t = numer/denom; 358 t = numer/denom;
396 q = 1.0 - t; 359 q = 1.0 - t;
397 fSqrDist = q*(fA*q + fB*t +2.0*d) + 360 fSqrDist = q*(fA*q + fB*t +2.0*d) + t*(fB*q + fC*t + 2.0*e) + f;
398 } 361 }
399 } 362 }
400 else 363 else
401 { 364 {
402 t = 0.0; 365 t = 0.0;
403 if (tmp1 <= 0.0) {q = 1.0; fSqrDi 366 if (tmp1 <= 0.0) {q = 1.0; fSqrDist = fA + 2.0*d + f;}
404 else if (d >= 0.0) {q = 0.0; fSqrDi 367 else if (d >= 0.0) {q = 0.0; fSqrDist = f;}
405 else {q = -d/fA; fSqr 368 else {q = -d/fA; fSqrDist = d*q + f;}
406 } 369 }
407 } 370 }
408 else 371 else
409 // 372 //
410 // We are in region 1. 373 // We are in region 1.
411 // 374 //
412 { 375 {
413 G4double numer = fC + e - fB - d; 376 G4double numer = fC + e - fB - d;
414 if (numer <= 0.0) 377 if (numer <= 0.0)
415 { 378 {
416 q = 0.0; 379 q = 0.0;
417 t = 1.0; 380 t = 1.0;
418 fSqrDist = fC + 2.0*e + f; 381 fSqrDist = fC + 2.0*e + f;
419 } 382 }
420 else 383 else
421 { 384 {
422 G4double denom = fA - 2.0*fB + fC; 385 G4double denom = fA - 2.0*fB + fC;
423 if (numer >= denom) {q = 1.0; t = 0.0; 386 if (numer >= denom) {q = 1.0; t = 0.0; fSqrDist = fA + 2.0*d + f;}
424 else 387 else
425 { 388 {
426 q = numer/denom; 389 q = numer/denom;
427 t = 1.0 - q; 390 t = 1.0 - q;
428 fSqrDist = q*(fA*q + fB*t + 2.0*d) + 391 fSqrDist = q*(fA*q + fB*t + 2.0*d) + t*(fB*q + fC*t + 2.0*e) + f;
429 } 392 }
430 } 393 }
431 } 394 }
432 } 395 }
433 // 396 //
434 // 397 //
435 // Do fA check for rounding errors in the di 398 // Do fA check for rounding errors in the distance-squared. It appears that
436 // the conventional methods for calculating 399 // the conventional methods for calculating fSqrDist breaks down when very
437 // near to or at the surface (as required by 400 // near to or at the surface (as required by transport).
438 // We'll therefore also use the magnitude-sq 401 // We'll therefore also use the magnitude-squared of the vector displacement.
439 // (Note that I've also tried to get around 402 // (Note that I've also tried to get around this problem by using the
440 // existing equations for 403 // existing equations for
441 // 404 //
442 // fSqrDist = function(fA,fB,fC,d,q,t) 405 // fSqrDist = function(fA,fB,fC,d,q,t)
443 // 406 //
444 // and use fA more accurate addition process 407 // and use fA more accurate addition process which minimises errors and
445 // breakdown of cummutitivity [where (A+B)+C 408 // breakdown of cummutitivity [where (A+B)+C != A+(B+C)] but this still
446 // doesn't work. 409 // doesn't work.
447 // Calculation from u = D + q*fE1 + t*fE2 is 410 // Calculation from u = D + q*fE1 + t*fE2 is less efficient, but appears
448 // more robust. 411 // more robust.
449 // 412 //
450 if (fSqrDist < 0.0) fSqrDist = 0.; 413 if (fSqrDist < 0.0) fSqrDist = 0.;
451 G4ThreeVector u = D + q*fE1 + t*fE2; 414 G4ThreeVector u = D + q*fE1 + t*fE2;
452 G4double u2 = u.mag2(); 415 G4double u2 = u.mag2();
453 // 416 //
454 // The following (part of the roundoff error 417 // The following (part of the roundoff error check) is from Oliver Merle'q
455 // updates. 418 // updates.
456 // 419 //
457 if (fSqrDist > u2) fSqrDist = u2; 420 if (fSqrDist > u2) fSqrDist = u2;
458 421
459 return u; 422 return u;
460 } 423 }
461 424
462 ////////////////////////////////////////////// 425 ///////////////////////////////////////////////////////////////////////////////
463 // 426 //
464 // Distance (G4ThreeVector, G4double) 427 // Distance (G4ThreeVector, G4double)
465 // 428 //
466 // Determines the closest distance between poi 429 // Determines the closest distance between point p and the facet. This makes
467 // use of G4ThreeVector G4TriangularFacet::Dis 430 // use of G4ThreeVector G4TriangularFacet::Distance, which stores the
468 // square of the distance in variable fSqrDist 431 // square of the distance in variable fSqrDist. If approximate methods show
469 // the distance is to be greater than minDist, 432 // the distance is to be greater than minDist, then forget about further
470 // computation and return fA very large number 433 // computation and return fA very large number.
471 // 434 //
472 G4double G4TriangularFacet::Distance (const G4 << 435 G4double G4TriangularFacet::Distance (const G4ThreeVector &p,
473 G4 436 G4double minDist)
474 { 437 {
475 // 438 //
476 // Start with quicky test to determine if th 439 // Start with quicky test to determine if the surface of the sphere enclosing
477 // the triangle is any closer to p than minD 440 // the triangle is any closer to p than minDist. If not, then don't bother
478 // about more accurate test. 441 // about more accurate test.
479 // 442 //
480 G4double dist = kInfinity; 443 G4double dist = kInfinity;
481 if ((p-fCircumcentre).mag()-fRadius < minDis 444 if ((p-fCircumcentre).mag()-fRadius < minDist)
482 { 445 {
483 // 446 //
484 // It's possible that the triangle is clos 447 // It's possible that the triangle is closer than minDist,
485 // so do more accurate assessment. 448 // so do more accurate assessment.
486 // 449 //
487 dist = Distance(p).mag(); 450 dist = Distance(p).mag();
488 } 451 }
489 return dist; 452 return dist;
490 } 453 }
491 454
492 ////////////////////////////////////////////// 455 ///////////////////////////////////////////////////////////////////////////////
493 // 456 //
494 // Distance (G4ThreeVector, G4double, G4bool) 457 // Distance (G4ThreeVector, G4double, G4bool)
495 // 458 //
496 // Determine the distance to point p. kInfini 459 // Determine the distance to point p. kInfinity is returned if either:
497 // (1) outgoing is TRUE and the dot product of 460 // (1) outgoing is TRUE and the dot product of the normal vector to the facet
498 // and the displacement vector from p to t 461 // and the displacement vector from p to the triangle is negative.
499 // (2) outgoing is FALSE and the dot product o 462 // (2) outgoing is FALSE and the dot product of the normal vector to the facet
500 // and the displacement vector from p to t 463 // and the displacement vector from p to the triangle is positive.
501 // If approximate methods show the distance is 464 // If approximate methods show the distance is to be greater than minDist, then
502 // forget about further computation and return 465 // forget about further computation and return fA very large number.
503 // 466 //
504 // This method has been heavily modified thank 467 // This method has been heavily modified thanks to the valuable comments and
505 // corrections of Rickard Holmberg. 468 // corrections of Rickard Holmberg.
506 // 469 //
507 G4double G4TriangularFacet::Distance (const G4 << 470 G4double G4TriangularFacet::Distance (const G4ThreeVector &p,
508 G4 471 G4double minDist,
509 const G4 472 const G4bool outgoing)
510 { 473 {
511 // 474 //
512 // Start with quicky test to determine if th 475 // Start with quicky test to determine if the surface of the sphere enclosing
513 // the triangle is any closer to p than minD 476 // the triangle is any closer to p than minDist. If not, then don't bother
514 // about more accurate test. 477 // about more accurate test.
515 // 478 //
516 G4double dist = kInfinity; 479 G4double dist = kInfinity;
517 if ((p-fCircumcentre).mag()-fRadius < minDis 480 if ((p-fCircumcentre).mag()-fRadius < minDist)
518 { 481 {
519 // 482 //
520 // It's possible that the triangle is clos 483 // It's possible that the triangle is closer than minDist,
521 // so do more accurate assessment. 484 // so do more accurate assessment.
522 // 485 //
523 G4ThreeVector v = Distance(p); 486 G4ThreeVector v = Distance(p);
524 G4double dist1 = sqrt(fSqrDist); 487 G4double dist1 = sqrt(fSqrDist);
525 G4double dir = v.dot(fSurfaceNormal); 488 G4double dir = v.dot(fSurfaceNormal);
526 G4bool wrongSide = (dir > 0.0 && !outgoing 489 G4bool wrongSide = (dir > 0.0 && !outgoing) || (dir < 0.0 && outgoing);
527 if (dist1 <= kCarTolerance) 490 if (dist1 <= kCarTolerance)
528 { 491 {
529 // 492 //
530 // Point p is very close to triangle. C 493 // Point p is very close to triangle. Check if it's on the wrong side,
531 // in which case return distance of 0.0 494 // in which case return distance of 0.0 otherwise .
532 // 495 //
533 if (wrongSide) dist = 0.0; 496 if (wrongSide) dist = 0.0;
534 else dist = dist1; 497 else dist = dist1;
535 } 498 }
536 else if (!wrongSide) dist = dist1; 499 else if (!wrongSide) dist = dist1;
537 } 500 }
538 return dist; 501 return dist;
539 } 502 }
540 503
541 ////////////////////////////////////////////// 504 ///////////////////////////////////////////////////////////////////////////////
542 // 505 //
543 // Extent 506 // Extent
544 // 507 //
545 // Calculates the furthest the triangle extend 508 // Calculates the furthest the triangle extends in fA particular direction
546 // defined by the vector axis. 509 // defined by the vector axis.
547 // 510 //
548 G4double G4TriangularFacet::Extent (const G4Th 511 G4double G4TriangularFacet::Extent (const G4ThreeVector axis)
549 { 512 {
550 G4double ss = GetVertex(0).dot(axis); 513 G4double ss = GetVertex(0).dot(axis);
551 G4double sp = GetVertex(1).dot(axis); 514 G4double sp = GetVertex(1).dot(axis);
552 if (sp > ss) ss = sp; 515 if (sp > ss) ss = sp;
553 sp = GetVertex(2).dot(axis); 516 sp = GetVertex(2).dot(axis);
554 if (sp > ss) ss = sp; 517 if (sp > ss) ss = sp;
555 return ss; 518 return ss;
556 } 519 }
557 520
558 ////////////////////////////////////////////// 521 ///////////////////////////////////////////////////////////////////////////////
559 // 522 //
560 // Intersect 523 // Intersect
561 // 524 //
562 // Member function to find the next intersecti 525 // Member function to find the next intersection when going from p in the
563 // direction of v. If: 526 // direction of v. If:
564 // (1) "outgoing" is TRUE, only consider the f 527 // (1) "outgoing" is TRUE, only consider the face if we are going out through
565 // the face. 528 // the face.
566 // (2) "outgoing" is FALSE, only consider the 529 // (2) "outgoing" is FALSE, only consider the face if we are going in through
567 // the face. 530 // the face.
568 // Member functions returns TRUE if there is a 531 // Member functions returns TRUE if there is an intersection, FALSE otherwise.
569 // Sets the distance (distance along w), distF 532 // Sets the distance (distance along w), distFromSurface (orthogonal distance)
570 // and normal. 533 // and normal.
571 // 534 //
572 // Also considers intersections that happen wi 535 // Also considers intersections that happen with negative distance for small
573 // distances of distFromSurface = 0.5*kCarTole 536 // distances of distFromSurface = 0.5*kCarTolerance in the wrong direction.
574 // This is to detect kSurface without doing fA 537 // This is to detect kSurface without doing fA full Inside(p) in
575 // G4TessellatedSolid::Distance(p,v) calculati 538 // G4TessellatedSolid::Distance(p,v) calculation.
576 // 539 //
577 // This member function is thanks the valuable 540 // This member function is thanks the valuable work of Rickard Holmberg. PT.
578 // However, "gotos" are the Work of the Devil 541 // However, "gotos" are the Work of the Devil have been exorcised with
579 // extreme prejudice!! 542 // extreme prejudice!!
580 // 543 //
581 // IMPORTANT NOTE: These calculations are pre 544 // IMPORTANT NOTE: These calculations are predicated on v being fA unit
582 // vector. If G4TessellatedSolid or other cla 545 // vector. If G4TessellatedSolid or other classes call this member function
583 // with |v| != 1 then there will be errors. 546 // with |v| != 1 then there will be errors.
584 // 547 //
585 G4bool G4TriangularFacet::Intersect (const G4T << 548 G4bool G4TriangularFacet::Intersect (const G4ThreeVector &p,
586 const G4T << 549 const G4ThreeVector &v,
587 G4b 550 G4bool outgoing,
588 G4d << 551 G4double &distance,
589 G4d << 552 G4double &distFromSurface,
590 G4T << 553 G4ThreeVector &normal)
591 { 554 {
592 // 555 //
593 // Check whether the direction of the facet 556 // Check whether the direction of the facet is consistent with the vector v
594 // and the need to be outgoing or ingoing. 557 // and the need to be outgoing or ingoing. If inconsistent, disregard and
595 // return false. 558 // return false.
596 // 559 //
597 G4double w = v.dot(fSurfaceNormal); 560 G4double w = v.dot(fSurfaceNormal);
598 if ((outgoing && w < -dirTolerance) || (!out 561 if ((outgoing && w < -dirTolerance) || (!outgoing && w > dirTolerance))
599 { 562 {
600 distance = kInfinity; 563 distance = kInfinity;
601 distFromSurface = kInfinity; 564 distFromSurface = kInfinity;
602 normal.set(0,0,0); 565 normal.set(0,0,0);
603 return false; 566 return false;
604 } 567 }
605 // 568 //
606 // Calculate the orthogonal distance from p 569 // Calculate the orthogonal distance from p to the surface containing the
607 // triangle. Then determine if we're on the 570 // triangle. Then determine if we're on the right or wrong side of the
608 // surface (at fA distance greater than kCar 571 // surface (at fA distance greater than kCarTolerance to be consistent with
609 // "outgoing". 572 // "outgoing".
610 // 573 //
611 const G4ThreeVector& p0 = GetVertex(0); << 574 const G4ThreeVector &p0 = GetVertex(0);
612 G4ThreeVector D = p0 - p; 575 G4ThreeVector D = p0 - p;
613 distFromSurface = D.dot(fSurfaceNormal); 576 distFromSurface = D.dot(fSurfaceNormal);
614 G4bool wrongSide = (outgoing && distFromSurf 577 G4bool wrongSide = (outgoing && distFromSurface < -0.5*kCarTolerance) ||
615 (!outgoing && distFromSurface > 0.5*kCarT 578 (!outgoing && distFromSurface > 0.5*kCarTolerance);
616 <<
617 if (wrongSide) 579 if (wrongSide)
618 { 580 {
619 distance = kInfinity; 581 distance = kInfinity;
620 distFromSurface = kInfinity; 582 distFromSurface = kInfinity;
621 normal.set(0,0,0); 583 normal.set(0,0,0);
622 return false; 584 return false;
623 } 585 }
624 586
625 wrongSide = (outgoing && distFromSurface < 0 587 wrongSide = (outgoing && distFromSurface < 0.0)
626 || (!outgoing && distFromSurface > 588 || (!outgoing && distFromSurface > 0.0);
627 if (wrongSide) 589 if (wrongSide)
628 { 590 {
629 // 591 //
630 // We're slightly on the wrong side of the 592 // We're slightly on the wrong side of the surface. Check if we're close
631 // enough using fA precise distance calcul 593 // enough using fA precise distance calculation.
632 // 594 //
633 G4ThreeVector u = Distance(p); 595 G4ThreeVector u = Distance(p);
634 if (fSqrDist <= kCarTolerance*kCarToleranc 596 if (fSqrDist <= kCarTolerance*kCarTolerance)
635 { 597 {
636 // 598 //
637 // We're very close. Therefore return f 599 // We're very close. Therefore return fA small negative number
638 // to pretend we intersect. 600 // to pretend we intersect.
639 // 601 //
640 // distance = -0.5*kCarTolerance 602 // distance = -0.5*kCarTolerance
641 distance = 0.0; 603 distance = 0.0;
642 normal = fSurfaceNormal; 604 normal = fSurfaceNormal;
643 return true; 605 return true;
644 } 606 }
645 else 607 else
646 { 608 {
647 // 609 //
648 // We're close to the surface containing 610 // We're close to the surface containing the triangle, but sufficiently
649 // far from the triangle, and on the wro 611 // far from the triangle, and on the wrong side compared to the directions
650 // of the surface normal and v. There i 612 // of the surface normal and v. There is no intersection.
651 // 613 //
652 distance = kInfinity; 614 distance = kInfinity;
653 distFromSurface = kInfinity; 615 distFromSurface = kInfinity;
654 normal.set(0,0,0); 616 normal.set(0,0,0);
655 return false; 617 return false;
656 } 618 }
657 } 619 }
658 if (w < dirTolerance && w > -dirTolerance) 620 if (w < dirTolerance && w > -dirTolerance)
659 { 621 {
660 // 622 //
661 // The ray is within the plane of the tria 623 // The ray is within the plane of the triangle. Project the problem into 2D
662 // in the plane of the triangle. First try 624 // in the plane of the triangle. First try to create orthogonal unit vectors
663 // mu and nu, where mu is fE1/|fE1|. This 625 // mu and nu, where mu is fE1/|fE1|. This is kinda like
664 // the original algorithm due to Rickard H 626 // the original algorithm due to Rickard Holmberg, but with better
665 // mathematical justification than the ori 627 // mathematical justification than the original method ... however,
666 // beware Rickard's was less time-consumin 628 // beware Rickard's was less time-consuming.
667 // 629 //
668 // Note that vprime is not fA unit vector. 630 // Note that vprime is not fA unit vector. We need to keep it unnormalised
669 // since the values of distance along vpri 631 // since the values of distance along vprime (s0 and s1) for intersection
670 // with the triangle will be used to deter 632 // with the triangle will be used to determine if we cut the plane at the
671 // same time. 633 // same time.
672 // 634 //
673 G4ThreeVector mu = fE1.unit(); 635 G4ThreeVector mu = fE1.unit();
674 G4ThreeVector nu = fSurfaceNormal.cross(mu 636 G4ThreeVector nu = fSurfaceNormal.cross(mu);
675 G4TwoVector pprime(p.dot(mu), p.dot(nu)); 637 G4TwoVector pprime(p.dot(mu), p.dot(nu));
676 G4TwoVector vprime(v.dot(mu), v.dot(nu)); 638 G4TwoVector vprime(v.dot(mu), v.dot(nu));
677 G4TwoVector P0prime(p0.dot(mu), p0.dot(nu) 639 G4TwoVector P0prime(p0.dot(mu), p0.dot(nu));
678 G4TwoVector E0prime(fE1.mag(), 0.0); 640 G4TwoVector E0prime(fE1.mag(), 0.0);
679 G4TwoVector E1prime(fE2.dot(mu), fE2.dot(n 641 G4TwoVector E1prime(fE2.dot(mu), fE2.dot(nu));
680 G4TwoVector loc[2]; 642 G4TwoVector loc[2];
681 if (G4TessellatedGeometryAlgorithms::Inter 643 if (G4TessellatedGeometryAlgorithms::IntersectLineAndTriangle2D(pprime,
682 vprime, P0 644 vprime, P0prime, E0prime, E1prime, loc))
683 { 645 {
684 // 646 //
685 // There is an intersection between the 647 // There is an intersection between the line and triangle in 2D.
686 // Now check which part of the line inte 648 // Now check which part of the line intersects with the plane
687 // containing the triangle in 3D. 649 // containing the triangle in 3D.
688 // 650 //
689 G4double vprimemag = vprime.mag(); 651 G4double vprimemag = vprime.mag();
690 G4double s0 = (loc[0] - pprime).m 652 G4double s0 = (loc[0] - pprime).mag()/vprimemag;
691 G4double s1 = (loc[1] - pprime).m 653 G4double s1 = (loc[1] - pprime).mag()/vprimemag;
692 G4double normDist0 = fSurfaceNormal.dot( 654 G4double normDist0 = fSurfaceNormal.dot(s0*v) - distFromSurface;
693 G4double normDist1 = fSurfaceNormal.dot( 655 G4double normDist1 = fSurfaceNormal.dot(s1*v) - distFromSurface;
694 656
695 if ((normDist0 < 0.0 && normDist1 < 0.0) 657 if ((normDist0 < 0.0 && normDist1 < 0.0)
696 || (normDist0 > 0.0 && normDist1 > 0.0) 658 || (normDist0 > 0.0 && normDist1 > 0.0)
697 || (normDist0 == 0.0 && normDist1 == 0. 659 || (normDist0 == 0.0 && normDist1 == 0.0) )
698 { 660 {
699 distance = kInfinity; 661 distance = kInfinity;
700 distFromSurface = kInfinity; 662 distFromSurface = kInfinity;
701 normal.set(0,0,0); 663 normal.set(0,0,0);
702 return false; 664 return false;
703 } 665 }
704 else 666 else
705 { 667 {
706 G4double dnormDist = normDist1 - normD 668 G4double dnormDist = normDist1 - normDist0;
707 if (fabs(dnormDist) < DBL_EPSILON) 669 if (fabs(dnormDist) < DBL_EPSILON)
708 { 670 {
709 distance = s0; 671 distance = s0;
710 normal = fSurfaceNormal; 672 normal = fSurfaceNormal;
711 if (!outgoing) distFromSurface = -di 673 if (!outgoing) distFromSurface = -distFromSurface;
712 return true; 674 return true;
713 } 675 }
714 else 676 else
715 { 677 {
716 distance = s0 - normDist0*(s1-s0)/dn 678 distance = s0 - normDist0*(s1-s0)/dnormDist;
717 normal = fSurfaceNormal; 679 normal = fSurfaceNormal;
718 if (!outgoing) distFromSurface = -di 680 if (!outgoing) distFromSurface = -distFromSurface;
719 return true; 681 return true;
720 } 682 }
721 } 683 }
722 } 684 }
723 else 685 else
724 { 686 {
725 distance = kInfinity; 687 distance = kInfinity;
726 distFromSurface = kInfinity; 688 distFromSurface = kInfinity;
727 normal.set(0,0,0); 689 normal.set(0,0,0);
728 return false; 690 return false;
729 } 691 }
730 } 692 }
731 // 693 //
732 // 694 //
733 // Use conventional algorithm to determine t 695 // Use conventional algorithm to determine the whether there is an
734 // intersection. This involves determining 696 // intersection. This involves determining the point of intersection of the
735 // line with the plane containing the triang 697 // line with the plane containing the triangle, and then calculating if the
736 // point is within the triangle. 698 // point is within the triangle.
737 // 699 //
738 distance = distFromSurface / w; 700 distance = distFromSurface / w;
739 G4ThreeVector pp = p + v*distance; 701 G4ThreeVector pp = p + v*distance;
740 G4ThreeVector DD = p0 - pp; 702 G4ThreeVector DD = p0 - pp;
741 G4double d = fE1.dot(DD); 703 G4double d = fE1.dot(DD);
742 G4double e = fE2.dot(DD); 704 G4double e = fE2.dot(DD);
743 G4double ss = fB*e - fC*d; 705 G4double ss = fB*e - fC*d;
744 G4double t = fB*d - fA*e; 706 G4double t = fB*d - fA*e;
745 707
746 G4double sTolerance = (fabs(fB)+ fabs(fC) + 708 G4double sTolerance = (fabs(fB)+ fabs(fC) + fabs(d) + fabs(e))*kCarTolerance;
747 G4double tTolerance = (fabs(fA)+ fabs(fB) + 709 G4double tTolerance = (fabs(fA)+ fabs(fB) + fabs(d) + fabs(e))*kCarTolerance;
748 G4double detTolerance = (fabs(fA)+ fabs(fC) 710 G4double detTolerance = (fabs(fA)+ fabs(fC) + 2*fabs(fB) )*kCarTolerance;
749 711
750 //if (ss < 0.0 || t < 0.0 || ss+t > fDet) 712 //if (ss < 0.0 || t < 0.0 || ss+t > fDet)
751 if (ss < -sTolerance || t < -tTolerance || ( 713 if (ss < -sTolerance || t < -tTolerance || ( ss+t - fDet ) > detTolerance)
752 { 714 {
753 // 715 //
754 // The intersection is outside of the tria 716 // The intersection is outside of the triangle.
755 // 717 //
756 distance = distFromSurface = kInfinity; 718 distance = distFromSurface = kInfinity;
757 normal.set(0,0,0); 719 normal.set(0,0,0);
758 return false; 720 return false;
759 } 721 }
760 else 722 else
761 { 723 {
762 // 724 //
763 // There is an intersection. Now we only 725 // There is an intersection. Now we only need to set the surface normal.
764 // 726 //
765 normal = fSurfaceNormal; 727 normal = fSurfaceNormal;
766 if (!outgoing) distFromSurface = -distFrom 728 if (!outgoing) distFromSurface = -distFromSurface;
767 return true; 729 return true;
768 } 730 }
769 } 731 }
770 732
771 ////////////////////////////////////////////// 733 ////////////////////////////////////////////////////////////////////////
772 // 734 //
773 // GetPointOnFace 735 // GetPointOnFace
774 // 736 //
775 // Auxiliary method, returns a uniform random << 737 // Auxiliary method for get fA random point on surface
776 // 738 //
777 G4ThreeVector G4TriangularFacet::GetPointOnFac 739 G4ThreeVector G4TriangularFacet::GetPointOnFace() const
778 { 740 {
779 G4double u = G4UniformRand(); << 741 G4double alpha = G4RandFlat::shoot(0., 1.);
780 G4double v = G4UniformRand(); << 742 G4double beta = G4RandFlat::shoot(0., 1.);
781 if (u+v > 1.) { u = 1. - u; v = 1. - v; } << 743 G4double lambda1 = alpha*beta;
782 return GetVertex(0) + u*fE1 + v*fE2; << 744 G4double lambda0 = alpha-lambda1;
>> 745
>> 746 return GetVertex(0) + lambda0*fE1 + lambda1*fE2;
783 } 747 }
784 748
785 ////////////////////////////////////////////// 749 ////////////////////////////////////////////////////////////////////////
786 // 750 //
787 // GetArea 751 // GetArea
788 // 752 //
789 // Auxiliary method for returning the surface 753 // Auxiliary method for returning the surface fArea
790 // 754 //
791 G4double G4TriangularFacet::GetArea() const << 755 G4double G4TriangularFacet::GetArea()
792 { 756 {
793 return fArea; 757 return fArea;
794 } 758 }
795 759
796 ////////////////////////////////////////////// 760 ////////////////////////////////////////////////////////////////////////
797 // 761 //
798 G4GeometryType G4TriangularFacet::GetEntityTyp 762 G4GeometryType G4TriangularFacet::GetEntityType () const
799 { 763 {
800 return "G4TriangularFacet"; 764 return "G4TriangularFacet";
801 } 765 }
802 766
803 ////////////////////////////////////////////// 767 ////////////////////////////////////////////////////////////////////////
804 // 768 //
805 G4ThreeVector G4TriangularFacet::GetSurfaceNor 769 G4ThreeVector G4TriangularFacet::GetSurfaceNormal () const
806 { 770 {
807 return fSurfaceNormal; 771 return fSurfaceNormal;
808 } 772 }
809 773
810 ////////////////////////////////////////////// 774 ////////////////////////////////////////////////////////////////////////
811 // 775 //
812 void G4TriangularFacet::SetSurfaceNormal (cons << 776 void G4TriangularFacet::SetSurfaceNormal (G4ThreeVector normal)
813 { 777 {
814 fSurfaceNormal = normal; 778 fSurfaceNormal = normal;
815 } 779 }
816 780