1 |
#include <cmath> |
2 |
#include "Mat3x3d.hpp" |
3 |
#include "Roll.hpp" |
4 |
#include "SimInfo.hpp" |
5 |
|
6 |
|
7 |
//////////////////////////////////////////////////////////////////////////////// |
8 |
//Implementation of DCRollAFunctor |
9 |
//////////////////////////////////////////////////////////////////////////////// |
10 |
int DCRollAFunctor::operator()(ConstraintAtom* consAtom1, ConstraintAtom* consAtom2){ |
11 |
Vector3d posA; |
12 |
Vector3d posB; |
13 |
Vector3d oldPosA; |
14 |
Vector3d oldPosB; |
15 |
Vector3d velA; |
16 |
Vector3d velB; |
17 |
Vector3d pab; |
18 |
Vector3d tempPab; |
19 |
Vector3d rab; |
20 |
Vector3d zetaA; |
21 |
Vector3d zetaB; |
22 |
Vector3d zeta; |
23 |
Vector3d consForce; |
24 |
Vector3d bondDirUnitVec; |
25 |
double dx, dy, dz; |
26 |
double rpab; |
27 |
double rabsq, pabsq, rpabsq; |
28 |
double diffsq; |
29 |
double gab; |
30 |
double dt; |
31 |
double pabDotZeta; |
32 |
double pabDotZeta2; |
33 |
double zeta2; |
34 |
double forceScalar; |
35 |
|
36 |
|
37 |
dt = info->dt; |
38 |
|
39 |
consAtom1->getOldPos(oldPosA.vec); |
40 |
consAtom2->getOldPos(oldPosB.vec); |
41 |
|
42 |
|
43 |
consAtom1->getPos(posA.vec); |
44 |
consAtom2->getPos(posB.vec); |
45 |
|
46 |
//discard the vector convention in alan tidesley's code |
47 |
//rij = rj - ri; |
48 |
pab = posB - posA; |
49 |
|
50 |
//periodic boundary condition |
51 |
|
52 |
info->wrapVector(pab.vec); |
53 |
|
54 |
pabsq = dotProduct(pab, pab); |
55 |
|
56 |
rabsq = curPair->getBondLength2(); |
57 |
diffsq = pabsq -rabsq; |
58 |
|
59 |
if (fabs(diffsq) > (consTolerance * rabsq * 2)){ |
60 |
rab = oldPosB - oldPosA; |
61 |
info->wrapVector(rab.vec); |
62 |
|
63 |
//rpab = dotProduct(rab, pab); |
64 |
|
65 |
//rpabsq = rpab * rpab; |
66 |
|
67 |
|
68 |
//if (rpabsq < (rabsq * -diffsq)){ |
69 |
// return consFail; |
70 |
//} |
71 |
|
72 |
bondDirUnitVec = pab; |
73 |
bondDirUnitVec.normalize(); |
74 |
|
75 |
calcZeta(consAtom1, bondDirUnitVec, zetaA); |
76 |
|
77 |
calcZeta(consAtom2, bondDirUnitVec, zetaB); |
78 |
|
79 |
zeta = zetaA + zetaB; |
80 |
zeta2 = dotProduct(zeta, zeta); |
81 |
|
82 |
pabDotZeta = dotProduct(pab, zeta); |
83 |
pabDotZeta2 = pabDotZeta * pabDotZeta; |
84 |
|
85 |
//solve quadratic equation |
86 |
//dt^4 * zeta^2 * G^2 + 2* h^2 * pab * zeta * G + pab^2 - d^2 |
87 |
//dt : time step |
88 |
// pab : |
89 |
//G : constraint force scalar |
90 |
//d: equilibrium bond length |
91 |
|
92 |
if (pabDotZeta2 - zeta2 * diffsq < 0) |
93 |
return consFail; |
94 |
|
95 |
//forceScalar = (pabDotZeta + sqrt(pabDotZeta2 - zeta2 * diffsq)) / dt * dt * zeta2; |
96 |
forceScalar = diffsq / (2 * dt * dt * pabDotZeta); |
97 |
//forceScalar = 1 / forceScalar; |
98 |
consForce = forceScalar * bondDirUnitVec; |
99 |
//integrate consRB1 using constraint force; |
100 |
integrate(consAtom1, consForce); |
101 |
|
102 |
//integrate consRB2 using constraint force; |
103 |
integrate(consAtom2, -consForce); |
104 |
|
105 |
return consSuccess; |
106 |
} |
107 |
else |
108 |
return consAlready; |
109 |
|
110 |
|
111 |
|
112 |
|
113 |
} |
114 |
void DCRollAFunctor::calcZeta(ConstraintAtom* consAtom, const Vector3d& bondDir, Vector3d&zeta){ |
115 |
double invMass; |
116 |
invMass = 1.0 / consAtom ->getMass(); |
117 |
|
118 |
zeta = invMass * bondDir; |
119 |
} |
120 |
|
121 |
void DCRollAFunctor::integrate(ConstraintAtom* consAtom, const Vector3d& force){ |
122 |
StuntDouble* sd; |
123 |
Vector3d vel; |
124 |
Vector3d pos; |
125 |
Vector3d tempPos; |
126 |
Vector3d tempVel; |
127 |
double mass; |
128 |
double dt; |
129 |
|
130 |
dt = info->dt; |
131 |
sd = consAtom->getStuntDouble(); |
132 |
|
133 |
sd->getVel(vel.vec); |
134 |
sd->getPos(pos.vec); |
135 |
|
136 |
mass = sd->getMass(); |
137 |
|
138 |
tempVel = dt/mass * force; |
139 |
tempPos = dt * tempVel; |
140 |
|
141 |
vel += tempVel; |
142 |
pos += tempPos; |
143 |
|
144 |
sd->setVel(vel.vec); |
145 |
sd->setPos(pos.vec); |
146 |
} |
147 |
|
148 |
int DCRollAFunctor::operator()(ConstraintRigidBody* consRB1, ConstraintRigidBody* consRB2){ |
149 |
Vector3d posA; |
150 |
Vector3d posB; |
151 |
Vector3d oldPosA; |
152 |
Vector3d oldPosB; |
153 |
Vector3d velA; |
154 |
Vector3d velB; |
155 |
Vector3d pab; |
156 |
Vector3d tempPab; |
157 |
Vector3d rab; |
158 |
Vector3d zetaA; |
159 |
Vector3d zetaB; |
160 |
Vector3d zeta; |
161 |
Vector3d consForce; |
162 |
Vector3d bondDirUnitVec; |
163 |
double dx, dy, dz; |
164 |
double rpab; |
165 |
double rabsq, pabsq, rpabsq; |
166 |
double diffsq; |
167 |
double gab; |
168 |
double dt; |
169 |
double pabDotZeta; |
170 |
double pabDotZeta2; |
171 |
double zeta2; |
172 |
double forceScalar; |
173 |
|
174 |
const int conRBMaxIter = 100; |
175 |
|
176 |
dt = info->dt; |
177 |
|
178 |
consRB1->getOldAtomPos(oldPosA.vec); |
179 |
consRB2->getOldAtomPos(oldPosB.vec); |
180 |
|
181 |
|
182 |
for(int i=0 ; i < conRBMaxIter; i++){ |
183 |
consRB1->getCurAtomPos(posA.vec); |
184 |
consRB2->getCurAtomPos(posB.vec); |
185 |
|
186 |
//discard the vector convention in alan tidesley's code |
187 |
//rij = rj - ri; |
188 |
pab = posB - posA; |
189 |
|
190 |
//periodic boundary condition |
191 |
|
192 |
info->wrapVector(pab.vec); |
193 |
|
194 |
pabsq = dotProduct(pab, pab); |
195 |
|
196 |
rabsq = curPair->getBondLength2(); |
197 |
diffsq = pabsq -rabsq; |
198 |
|
199 |
if (fabs(diffsq) > (consTolerance * rabsq * 2)){ |
200 |
rab = oldPosB - oldPosA; |
201 |
info->wrapVector(rab.vec); |
202 |
|
203 |
bondDirUnitVec = rab; |
204 |
bondDirUnitVec.normalize(); |
205 |
|
206 |
calcZeta(consRB1, bondDirUnitVec, zetaA); |
207 |
|
208 |
calcZeta(consRB2, bondDirUnitVec, zetaB); |
209 |
|
210 |
zeta = zetaA + zetaB; |
211 |
zeta2 = dotProduct(zeta, zeta); |
212 |
|
213 |
pabDotZeta = dotProduct(pab, zeta); |
214 |
pabDotZeta2 = pabDotZeta * pabDotZeta; |
215 |
|
216 |
//solve quadratic equation |
217 |
//dt^4 * zeta^2 * G^2 + 2* h^2 * pab * zeta * G + pab^2 - d^2 |
218 |
//dt : time step |
219 |
// pab : |
220 |
//G : constraint force scalar |
221 |
//d: equilibrium bond length |
222 |
|
223 |
if (pabDotZeta2 - zeta2 * diffsq < 0){ |
224 |
cerr << "DCRollAFunctor::operator() Error: Constraint Fail at " << info->getTime() << endl; |
225 |
return consFail; |
226 |
} |
227 |
//if pabDotZeta is close to 0, we can't neglect the square term |
228 |
if(fabs(pabDotZeta) < consTolerance) |
229 |
forceScalar = (pabDotZeta - sqrt(pabDotZeta2 - zeta2 * diffsq)) / dt * dt * zeta2; |
230 |
else |
231 |
forceScalar = diffsq / (2 * dt * dt * pabDotZeta); |
232 |
|
233 |
// |
234 |
consForce = forceScalar * bondDirUnitVec; |
235 |
//integrate consRB1 using constraint force; |
236 |
integrate(consRB1, consForce); |
237 |
|
238 |
//integrate consRB2 using constraint force; |
239 |
integrate(consRB2, -consForce); |
240 |
|
241 |
} |
242 |
else{ |
243 |
if (i ==0) |
244 |
return consAlready; |
245 |
else |
246 |
return consSuccess; |
247 |
} |
248 |
} |
249 |
|
250 |
cerr << "DCRollAFunctor::operator() Error: can not constrain the bond within maximum iteration at " << info->getTime() << endl; |
251 |
return consExceedMaxIter; |
252 |
|
253 |
} |
254 |
|
255 |
void DCRollAFunctor::calcZeta(ConstraintRigidBody* consRB, const Vector3d& bondDir, Vector3d& zeta){ |
256 |
double invMass; |
257 |
Vector3d tempVec1; |
258 |
Vector3d tempVec2; |
259 |
Vector3d refCoor; |
260 |
Vector3d refCrossBond; |
261 |
Mat3x3d IBody; |
262 |
Mat3x3d invIBody; |
263 |
Mat3x3d invILab; |
264 |
Mat3x3d a; |
265 |
Mat3x3d aTrans; |
266 |
|
267 |
invMass = 1.0 / consRB ->getMass(); |
268 |
|
269 |
zeta = invMass * bondDir; |
270 |
|
271 |
consRB->getRefCoor(refCoor.vec); |
272 |
//consRB->getA(a.element); |
273 |
consRB->getOldA(a.element); |
274 |
consRB->getI(IBody.element); |
275 |
|
276 |
aTrans = a.transpose(); |
277 |
invIBody = IBody.inverse(); |
278 |
|
279 |
invILab = aTrans * invIBody * a; |
280 |
|
281 |
refCrossBond = crossProduct(aTrans *refCoor, bondDir); |
282 |
|
283 |
tempVec1 = invILab * refCrossBond; |
284 |
tempVec2 = crossProduct(tempVec1, aTrans *refCoor); |
285 |
|
286 |
zeta += tempVec2; |
287 |
|
288 |
} |
289 |
|
290 |
void DCRollAFunctor::integrate(ConstraintRigidBody* consRB, const Vector3d& consForce){ |
291 |
RigidBody* rb; |
292 |
Vector3d frc; |
293 |
Vector3d totConsForce; |
294 |
Vector3d vel; |
295 |
Vector3d pos; |
296 |
Vector3d Tb; |
297 |
Vector3d ji; |
298 |
Vector3d refCoor; |
299 |
Vector3d consTorque; |
300 |
Vector3d totConsTorque; |
301 |
Mat3x3d a; |
302 |
double mass; |
303 |
double dt; |
304 |
double dtOver2; |
305 |
const double eConvert = 4.184e-4; |
306 |
|
307 |
dt = info->dt; |
308 |
dtOver2 = dt /2; |
309 |
|
310 |
//restore to old status |
311 |
consRB->restoreUnconsStatus(); |
312 |
|
313 |
//accumulate constraint force; |
314 |
consRB->addConsForce(consForce/eConvert); |
315 |
totConsForce = consRB->getConsForce(); |
316 |
|
317 |
rb = consRB->getRigidBody(); |
318 |
|
319 |
rb->addFrc(totConsForce.vec); |
320 |
|
321 |
rb->getVel(vel.vec); |
322 |
rb->getPos(pos.vec); |
323 |
rb->getFrc(frc.vec); |
324 |
mass = rb->getMass(); |
325 |
|
326 |
// velocity half step |
327 |
vel += eConvert * dtOver2 / mass * frc; |
328 |
// position whole step |
329 |
pos += dt * vel; |
330 |
|
331 |
rb->setVel(vel.vec); |
332 |
rb->setPos(pos.vec); |
333 |
|
334 |
//evolve orientational part |
335 |
consRB->getRefCoor(refCoor.vec); |
336 |
rb->getA(a.element); |
337 |
|
338 |
//calculate constraint torque in lab frame |
339 |
consTorque = crossProduct(a.transpose() * refCoor, consForce); |
340 |
consRB->addConsTorque(consTorque/eConvert); |
341 |
|
342 |
//add constraint torque |
343 |
totConsTorque = consRB->getConsTorque(); |
344 |
rb->addTrq(totConsTorque.vec); |
345 |
|
346 |
//get and convert the torque to body frame |
347 |
|
348 |
rb->getTrq(Tb.vec); |
349 |
rb->lab2Body(Tb.vec); |
350 |
|
351 |
//get the angular momentum, and propagate a half step |
352 |
|
353 |
rb->getJ(ji.vec); |
354 |
|
355 |
ji += eConvert * dtOver2 * Tb; |
356 |
|
357 |
rotationPropagation( rb, ji.vec ); |
358 |
|
359 |
rb->setJ(ji.vec); |
360 |
|
361 |
} |
362 |
|
363 |
void DCRollAFunctor::rotationPropagation(StuntDouble* sd, double ji[3]){ |
364 |
double angle; |
365 |
double A[3][3], I[3][3]; |
366 |
int i, j, k; |
367 |
double dtOver2; |
368 |
double dt; |
369 |
dt = info->dt; |
370 |
dtOver2 = dt /2; |
371 |
// use the angular velocities to propagate the rotation matrix a |
372 |
// full time step |
373 |
|
374 |
sd->getA(A); |
375 |
sd->getI(I); |
376 |
|
377 |
if (sd->isLinear()) { |
378 |
i = sd->linearAxis(); |
379 |
j = (i+1)%3; |
380 |
k = (i+2)%3; |
381 |
|
382 |
angle = dtOver2 * ji[j] / I[j][j]; |
383 |
this->rotate( k, i, angle, ji, A ); |
384 |
|
385 |
angle = dt* ji[k] / I[k][k]; |
386 |
this->rotate( i, j, angle, ji, A); |
387 |
|
388 |
angle = dtOver2 * ji[j] / I[j][j]; |
389 |
this->rotate( k, i, angle, ji, A ); |
390 |
|
391 |
} else { |
392 |
// rotate about the x-axis |
393 |
angle = dtOver2 * ji[0] / I[0][0]; |
394 |
this->rotate( 1, 2, angle, ji, A ); |
395 |
|
396 |
// rotate about the y-axis |
397 |
angle = dtOver2 * ji[1] / I[1][1]; |
398 |
this->rotate( 2, 0, angle, ji, A ); |
399 |
|
400 |
// rotate about the z-axis |
401 |
angle = dt * ji[2] / I[2][2]; |
402 |
this->rotate( 0, 1, angle, ji, A); |
403 |
|
404 |
// rotate about the y-axis |
405 |
angle = dtOver2 * ji[1] / I[1][1]; |
406 |
this->rotate( 2, 0, angle, ji, A ); |
407 |
|
408 |
// rotate about the x-axis |
409 |
angle = dtOver2 * ji[0] / I[0][0]; |
410 |
this->rotate( 1, 2, angle, ji, A ); |
411 |
|
412 |
} |
413 |
sd->setA( A ); |
414 |
} |
415 |
|
416 |
void DCRollAFunctor::rotate(int axes1, int axes2, double angle, double ji[3], double A[3][3]){ |
417 |
int i, j, k; |
418 |
double sinAngle; |
419 |
double cosAngle; |
420 |
double angleSqr; |
421 |
double angleSqrOver4; |
422 |
double top, bottom; |
423 |
double rot[3][3]; |
424 |
double tempA[3][3]; |
425 |
double tempJ[3]; |
426 |
|
427 |
// initialize the tempA |
428 |
|
429 |
for (i = 0; i < 3; i++){ |
430 |
for (j = 0; j < 3; j++){ |
431 |
tempA[j][i] = A[i][j]; |
432 |
} |
433 |
} |
434 |
|
435 |
// initialize the tempJ |
436 |
|
437 |
for (i = 0; i < 3; i++) |
438 |
tempJ[i] = ji[i]; |
439 |
|
440 |
// initalize rot as a unit matrix |
441 |
|
442 |
rot[0][0] = 1.0; |
443 |
rot[0][1] = 0.0; |
444 |
rot[0][2] = 0.0; |
445 |
|
446 |
rot[1][0] = 0.0; |
447 |
rot[1][1] = 1.0; |
448 |
rot[1][2] = 0.0; |
449 |
|
450 |
rot[2][0] = 0.0; |
451 |
rot[2][1] = 0.0; |
452 |
rot[2][2] = 1.0; |
453 |
|
454 |
// use a small angle aproximation for sin and cosine |
455 |
|
456 |
angleSqr = angle * angle; |
457 |
angleSqrOver4 = angleSqr / 4.0; |
458 |
top = 1.0 - angleSqrOver4; |
459 |
bottom = 1.0 + angleSqrOver4; |
460 |
|
461 |
cosAngle = top / bottom; |
462 |
sinAngle = angle / bottom; |
463 |
|
464 |
rot[axes1][axes1] = cosAngle; |
465 |
rot[axes2][axes2] = cosAngle; |
466 |
|
467 |
rot[axes1][axes2] = sinAngle; |
468 |
rot[axes2][axes1] = -sinAngle; |
469 |
|
470 |
// rotate the momentum acoording to: ji[] = rot[][] * ji[] |
471 |
|
472 |
for (i = 0; i < 3; i++){ |
473 |
ji[i] = 0.0; |
474 |
for (k = 0; k < 3; k++){ |
475 |
ji[i] += rot[i][k] * tempJ[k]; |
476 |
} |
477 |
} |
478 |
|
479 |
// rotate the Rotation matrix acording to: |
480 |
// A[][] = A[][] * transpose(rot[][]) |
481 |
|
482 |
|
483 |
// NOte for as yet unknown reason, we are performing the |
484 |
// calculation as: |
485 |
// transpose(A[][]) = transpose(A[][]) * transpose(rot[][]) |
486 |
|
487 |
for (i = 0; i < 3; i++){ |
488 |
for (j = 0; j < 3; j++){ |
489 |
A[j][i] = 0.0; |
490 |
for (k = 0; k < 3; k++){ |
491 |
A[j][i] += tempA[i][k] * rot[j][k]; |
492 |
} |
493 |
} |
494 |
} |
495 |
} |
496 |
//////////////////////////////////////////////////////////////////////////////// |
497 |
//Implementation of DCRollBFunctor |
498 |
//////////////////////////////////////////////////////////////////////////////// |
499 |
int DCRollBFunctor::operator()(ConstraintRigidBody* consRB1, ConstraintRigidBody* consRB2){ |
500 |
Vector3d posA; |
501 |
Vector3d posB; |
502 |
Vector3d velA; |
503 |
Vector3d velB; |
504 |
Vector3d pab; |
505 |
Vector3d rab; |
506 |
Vector3d vab; |
507 |
Vector3d zetaA; |
508 |
Vector3d zetaB; |
509 |
Vector3d zeta; |
510 |
Vector3d consForce; |
511 |
Vector3d bondDirUnitVec; |
512 |
double dt; |
513 |
double pabDotvab; |
514 |
double pabDotZeta; |
515 |
double pvab; |
516 |
|
517 |
const int conRBMaxIter = 20; |
518 |
|
519 |
dt = info->dt; |
520 |
|
521 |
for(int i=0 ; i < conRBMaxIter; i++){ |
522 |
consRB1->getCurAtomPos(posA.vec); |
523 |
consRB2->getCurAtomPos(posB.vec); |
524 |
pab = posB - posA; |
525 |
|
526 |
//periodic boundary condition |
527 |
info->wrapVector(pab.vec); |
528 |
|
529 |
consRB1->getCurAtomVel(velA.vec); |
530 |
consRB2->getCurAtomVel(velB.vec); |
531 |
vab = velB -velA; |
532 |
|
533 |
pvab = dotProduct(pab, vab); |
534 |
|
535 |
if (fabs(pvab) > consTolerance ){ |
536 |
|
537 |
|
538 |
bondDirUnitVec = pab; |
539 |
bondDirUnitVec.normalize(); |
540 |
|
541 |
getZeta(consRB1, bondDirUnitVec, zetaA); |
542 |
getZeta(consRB2, bondDirUnitVec, zetaB); |
543 |
zeta = zetaA + zetaB; |
544 |
|
545 |
pabDotZeta = dotProduct(pab, zeta); |
546 |
|
547 |
consForce = 2 * pvab / (dt * pabDotZeta) * bondDirUnitVec; |
548 |
//integrate consRB1 using constraint force; |
549 |
integrate(consRB1, consForce); |
550 |
|
551 |
//integrate consRB2 using constraint force; |
552 |
integrate(consRB2, -consForce); |
553 |
|
554 |
} |
555 |
else{ |
556 |
if (i ==0) |
557 |
return consAlready; |
558 |
else |
559 |
return consSuccess; |
560 |
} |
561 |
} |
562 |
|
563 |
cerr << "DCRollBFunctor::operator() Error: can not constrain the bond within maximum iteration at " << info->getTime() << endl; |
564 |
return consExceedMaxIter; |
565 |
|
566 |
} |
567 |
|
568 |
void DCRollBFunctor::getZeta(ConstraintRigidBody* consRB, const Vector3d& bondDir, Vector3d& zeta){ |
569 |
double invMass; |
570 |
Vector3d tempVec1; |
571 |
Vector3d tempVec2; |
572 |
Vector3d refCoor; |
573 |
Vector3d refCrossBond; |
574 |
Mat3x3d IBody; |
575 |
Mat3x3d ILab; |
576 |
Mat3x3d invIBody; |
577 |
Mat3x3d invILab; |
578 |
Mat3x3d a; |
579 |
|
580 |
invMass = 1.0 / consRB ->getMass(); |
581 |
|
582 |
zeta = invMass * bondDir; |
583 |
|
584 |
consRB->getRefCoor(refCoor.vec); |
585 |
consRB->getA(a.element); |
586 |
consRB->getI(IBody.element); |
587 |
|
588 |
invIBody = IBody.inverse(); |
589 |
|
590 |
|
591 |
refCrossBond = crossProduct(refCoor, a * bondDir); |
592 |
|
593 |
tempVec1 = invIBody * refCrossBond; |
594 |
|
595 |
tempVec2 = (a * tempVec1.makeSkewMat()).transpose() * refCoor; |
596 |
|
597 |
zeta += tempVec2; |
598 |
|
599 |
} |
600 |
|
601 |
void DCRollBFunctor::integrate(ConstraintRigidBody* consRB, const Vector3d& force){ |
602 |
Vector3d vel; |
603 |
Vector3d ji; |
604 |
Vector3d tempJi; |
605 |
Vector3d tempTrq; |
606 |
Vector3d refCoor; |
607 |
double mass; |
608 |
double dtOver2; |
609 |
Mat3x3d a; |
610 |
StuntDouble* sd; |
611 |
|
612 |
sd = consRB->getStuntDouble(); |
613 |
dtOver2 = info->dt/2; |
614 |
|
615 |
sd->getVel(vel.vec); |
616 |
mass = sd->getMass(); |
617 |
vel +=dtOver2 /mass * force; |
618 |
sd->setVel(vel.vec); |
619 |
|
620 |
if (sd->isDirectional()){ |
621 |
sd->getA(a.element); |
622 |
consRB->getRefCoor(refCoor.vec); |
623 |
tempTrq = crossProduct(refCoor, a *force); |
624 |
|
625 |
tempJi = dtOver2* tempTrq; |
626 |
sd->getJ(ji.vec); |
627 |
ji += tempJi; |
628 |
sd->setJ(ji.vec); |
629 |
} |
630 |
|
631 |
} |