1 |
#include <iostream> |
2 |
|
3 |
#include <cstdlib> |
4 |
#include <cstring> |
5 |
#include <cmath> |
6 |
|
7 |
|
8 |
#include "simError.h" |
9 |
#include "SimInfo.hpp" |
10 |
#include "ReadWrite.hpp" |
11 |
|
12 |
#include "latticeBuilder.hpp" |
13 |
#include "MoLocator.hpp" |
14 |
#include "sysBuild.hpp" |
15 |
#include "nanoBuilder.hpp" |
16 |
|
17 |
nanoBuilder::nanoBuilder(int &hasError){ |
18 |
int Errors; |
19 |
int foundCore,foundShell; |
20 |
int i; |
21 |
|
22 |
//Zero variables |
23 |
particleRadius = 0.0; |
24 |
coreRadius = 0.0; |
25 |
vacancyFraction = 0.0; |
26 |
vacancyRadius = 0.0; |
27 |
shellRadius = 0.0; |
28 |
latticeSpacing = 0.0; |
29 |
|
30 |
buildNmol = 0; |
31 |
|
32 |
nCoreMolecules = 0; |
33 |
nShellMolecules = 0; |
34 |
|
35 |
atomCount = 0; |
36 |
coreAtomCount = 0; |
37 |
shellAtomCount = 0; |
38 |
|
39 |
|
40 |
|
41 |
moleculeCount = 0; |
42 |
foundCore = 0; |
43 |
foundShell = 0; |
44 |
totalMolecules = 0; |
45 |
coreHasOrientation = 0; |
46 |
shellHasOrientation = 0; |
47 |
nInterface = 0; |
48 |
nMol = 0; |
49 |
|
50 |
hasError = 0; |
51 |
Errors = 0; |
52 |
|
53 |
//Initialize class members from bsInfo struct that sysbuilder provides. |
54 |
isRandom = bsInfo.isRandomParticle; |
55 |
hasVacancies = bsInfo.hasVacancies; |
56 |
latticeType = bsInfo.latticeType; |
57 |
particleRadius = bsInfo.particleRadius; |
58 |
coreRadius = bsInfo.coreRadius; |
59 |
vacancyFraction = bsInfo.vacancyFraction; |
60 |
latticeSpacing = bsInfo.latticeSpacing; |
61 |
soluteX = bsInfo.soluteX; //Mole fraction for random particle. |
62 |
|
63 |
|
64 |
|
65 |
|
66 |
|
67 |
for (i=0;bsInfo.nComponents;i++){ |
68 |
if( !strcmp( bsInfo.compStamps[i]->getID(),bsInfo.coreName )){ |
69 |
foundCore = 1; |
70 |
coreStamp = bsInfo.compStamps[i]; |
71 |
nCoreMolecules = bsInfo.componentsNmol[i]; |
72 |
} |
73 |
if( !strcmp( bsInfo.compStamps[i]->getID(),bsInfo.shellName)){ |
74 |
foundShell = 1; |
75 |
shellStamp = bsInfo.compStamps[i]; |
76 |
nShellMolecules = bsInfo.componentsNmol[i]; |
77 |
|
78 |
} |
79 |
|
80 |
} |
81 |
|
82 |
|
83 |
|
84 |
if( !foundCore ){ |
85 |
hasError = 1; |
86 |
return; |
87 |
} |
88 |
if( !foundShell ){ |
89 |
hasError = 1; |
90 |
return; |
91 |
} |
92 |
|
93 |
|
94 |
|
95 |
Errors = sanityCheck(); |
96 |
|
97 |
if (Errors){ |
98 |
hasError = 1; |
99 |
return; |
100 |
} |
101 |
|
102 |
|
103 |
|
104 |
|
105 |
|
106 |
|
107 |
|
108 |
nCoreModelAtoms = coreStamp->getNAtoms(); |
109 |
nShellModelAtoms = shellStamp->getNAtoms(); |
110 |
|
111 |
|
112 |
// We assume that if the core or shell model has more then one atom |
113 |
// the model has an orientational component... |
114 |
if (nCoreModelAtoms > 1) coreHasOrientation = 1; |
115 |
if (nShellModelAtoms > 1) shellHasOrientation = 1; |
116 |
|
117 |
maxModelNatoms = std::max(nCoreModelAtoms,nShellModelAtoms); |
118 |
|
119 |
/* If we specify a number of atoms in bass, we will try to build a nanopartice |
120 |
with that number. |
121 |
*/ |
122 |
|
123 |
|
124 |
if ((nShellMolecules != 0) && (nCoreMolecules != 0)){ |
125 |
totalMolecules = nShellMolecules + nCoreMolecules; |
126 |
nCells = ceil(pow((double)totalMolecules/4.0, 1/3)); |
127 |
buildNmol = 1; |
128 |
} |
129 |
else { |
130 |
nCells = 2.0 * particleRadius/latticeSpacing; |
131 |
shellRadius = particleRadius - coreRadius; |
132 |
} |
133 |
|
134 |
|
135 |
|
136 |
|
137 |
// Initialize random seed |
138 |
srand48( RAND_SEED ); |
139 |
|
140 |
|
141 |
} |
142 |
|
143 |
|
144 |
nanoBuilder::~nanoBuilder(){ |
145 |
} |
146 |
|
147 |
|
148 |
// Checks to make sure we aren't doing something the builder can't do. |
149 |
int nanoBuilder::sanityCheck(void){ |
150 |
|
151 |
// Right now we only do bimetallic nanoparticles |
152 |
if (bsInfo.nComponents > 2) return 1; |
153 |
|
154 |
//Check for vacancies and random |
155 |
if (hasVacancies && isRandom) return 1; |
156 |
|
157 |
// make sure we aren't trying to build a core larger then the total particle size |
158 |
if ((coreRadius >= particleRadius) && (particleRadius != 0)) return 1; |
159 |
|
160 |
// we initialize the lattice spacing to be 0.0, if the lattice spacing is still 0.0 |
161 |
// we have a problem |
162 |
if (latticeSpacing == 0.0) return 1; |
163 |
|
164 |
// Check to see if we are specifing the number of atoms in the particle correctly. |
165 |
if ((nShellMolecules == 0) && (nCoreMolecules != 0)){ |
166 |
cerr << "nShellParticles is zero and nCoreParticles != 0" << "\n"; |
167 |
return 1; |
168 |
} |
169 |
// Make sure there are more then two components if we are building a randomly mixed particle. |
170 |
if ((bsInfo.nComponents < 2) && (isRandom)){ |
171 |
cerr << "Two Components are needed to build a random particle." << "\n"; |
172 |
} |
173 |
// Make sure both the core and shell models specify a target nmol. |
174 |
if ((nShellMolecules != 0) && (nCoreMolecules == 0)){ |
175 |
cerr << "nCoreParticles is zero and nShellParticles != 0" << "\n"; |
176 |
return 1; |
177 |
} |
178 |
|
179 |
return 0; |
180 |
|
181 |
} |
182 |
|
183 |
|
184 |
|
185 |
int nanoBuilder::buildNanoParticle( void ){ |
186 |
|
187 |
int ix; |
188 |
int iy; |
189 |
int iz; |
190 |
double *rx; |
191 |
double *ry; |
192 |
double *rz; |
193 |
double pos[3]; |
194 |
double A[3][3]; |
195 |
double HmatI[3][3]; |
196 |
|
197 |
int nCellSites; |
198 |
int iref; |
199 |
int appNMols; |
200 |
int latticeCount = 0; |
201 |
|
202 |
int nAtoms; |
203 |
int nCoreAtomCounter = 0; |
204 |
int nShellAtomCounter = 0; |
205 |
int hasError; |
206 |
|
207 |
int i, j; |
208 |
|
209 |
int interfaceIndex = 0; |
210 |
double dist; |
211 |
double distsq; |
212 |
int latticeNpoints; |
213 |
int shesActualSizetoMe = 0; |
214 |
|
215 |
DumpWriter* writer; |
216 |
SimInfo* simnfo; |
217 |
|
218 |
Lattice *myLattice; |
219 |
MoLocator *coreLocate; |
220 |
MoLocator *shellLocate; |
221 |
|
222 |
|
223 |
Atom** atoms; |
224 |
|
225 |
hasError = 0; |
226 |
|
227 |
myLattice = new Lattice(FCC_LATTICE_TYPE,latticeSpacing); |
228 |
/* |
229 |
latticeNpoints = myLattice.getNpoints(); |
230 |
|
231 |
// Initializd atom vector to approximate size. |
232 |
switch (buildType){ |
233 |
|
234 |
case BUILD_NMOL_PARTICLE: |
235 |
|
236 |
break; |
237 |
case BUILD_CORE_SHELL_VACANCY: |
238 |
// Make space in the vector for all atoms except the last full cells |
239 |
// We will have to add at most (latticeNpoints-1)^3 to vector |
240 |
appNMols = latticeNPoints * pow((double)(nCells - 1),3); |
241 |
moleculeVector.pushBack(); |
242 |
|
243 |
default: |
244 |
// Make space in the vector for all atoms except the last full cells |
245 |
// We will have to add at most (latticeNpoints-1)^3 to vector |
246 |
appNMols = latticeNPoints * pow((double)(nCells - 1),3); |
247 |
|
248 |
} |
249 |
*/ |
250 |
|
251 |
|
252 |
|
253 |
|
254 |
// Create molocator and atom arrays. |
255 |
coreLocate = new MoLocator(coreStamp); |
256 |
shellLocate = new MoLocator(shellStamp); |
257 |
|
258 |
|
259 |
|
260 |
|
261 |
|
262 |
|
263 |
for(iz=-nCells;iz < nCells;iz++){ |
264 |
for(iy=-nCells;iy<nCells;iy++){ |
265 |
for(ix=-nCells;ix<nCells;ix++){ |
266 |
nCellSites = myLattice->getLatticePoints(&rx,&ry,&rz, |
267 |
ix,iy,iz); |
268 |
for (iref=1;iref<nCellSites;iref++){ |
269 |
latticeCount++; |
270 |
|
271 |
pos[0] = rx[iref]; |
272 |
pos[1] = ry[iref]; |
273 |
pos[2] = rz[iref]; |
274 |
|
275 |
distsq = rx[iref]*rx[iref] + ry[iref]*ry[iref] +rz[iref]*rz[iref]; |
276 |
dist = sqrt(distsq); |
277 |
|
278 |
switch(buildType){ |
279 |
|
280 |
case BUILD_CORE_SHELL: |
281 |
nanoBuilder::buildWithCoreShell(dist,pos); |
282 |
break; |
283 |
case BUILD_CORE_SHELL_VACANCY: |
284 |
nanoBuilder::buildWithVacancies(dist,pos); |
285 |
break; |
286 |
|
287 |
case BUILD_RANDOM_PARTICLE: |
288 |
nanoBuilder::buildRandomlyMixed(dist,pos); |
289 |
break; |
290 |
case BUILD_NMOL_PARTICLE: |
291 |
nanoBuilder::buildNmolParticle(dist,pos); |
292 |
} |
293 |
} |
294 |
} |
295 |
} |
296 |
} |
297 |
|
298 |
|
299 |
|
300 |
// Create vacancies |
301 |
if (hasVacancies) buildVacancies(); |
302 |
|
303 |
// Find the size of the atom vector not including Null atoms |
304 |
for (i=0;i<moleculeVector.size();i++){ |
305 |
if (! moleculeVector[i].isVacancy){ |
306 |
shesActualSizetoMe++; |
307 |
nAtoms = moleculeVector[i].myStamp->getNAtoms(); |
308 |
} |
309 |
} |
310 |
|
311 |
// Make a random particle. |
312 |
if (isRandom){ |
313 |
placeRandom(shesActualSizetoMe); |
314 |
|
315 |
// Loop back thru and count natoms since they may have changed |
316 |
for (i=0;i<moleculeVector.size();i++){ |
317 |
if (! moleculeVector[i].isVacancy){ |
318 |
shesActualSizetoMe++; |
319 |
nAtoms = moleculeVector[i].myStamp->getNAtoms(); |
320 |
} |
321 |
} |
322 |
} |
323 |
|
324 |
|
325 |
Atom::createArrays( nAtoms ); |
326 |
atoms = new Atom*[nAtoms]; |
327 |
|
328 |
|
329 |
|
330 |
shesActualSizetoMe = 0; |
331 |
/* Use the information from the molecule vector to place the atoms. |
332 |
*/ |
333 |
for (i= 0;i<moleculeVector.size();i++){ |
334 |
if (! moleculeVector[i].isVacancy) { |
335 |
orientationMunger( A ); |
336 |
if( moleculeVector[i].isCore){ |
337 |
nCoreAtomCounter += nCoreModelAtoms; |
338 |
coreLocate->placeMol(moleculeVector[i].pos,A,atoms,nShellAtomCounter); |
339 |
} |
340 |
else { |
341 |
nShellAtomCounter += nShellModelAtoms; |
342 |
shellLocate->placeMol(moleculeVector[i].pos,A,atoms,nCoreAtomCounter); |
343 |
} |
344 |
shesActualSizetoMe++; |
345 |
} |
346 |
} |
347 |
|
348 |
|
349 |
// shellLocate.placeMol(pos, A, moleculeVector,shellAtomCount); |
350 |
|
351 |
for (i=0;i<3;i++) |
352 |
for (j=0; j<3; j++) |
353 |
simnfo->Hmat[i][j] = 0.0; |
354 |
|
355 |
simnfo->Hmat[0][0] = 1.0; |
356 |
simnfo->Hmat[1][1] = 1.0; |
357 |
simnfo->Hmat[2][2] = 1.0; |
358 |
|
359 |
// set up the SimInfo object |
360 |
|
361 |
simnfo = new SimInfo(); |
362 |
simnfo->n_atoms = nAtoms; |
363 |
|
364 |
sprintf( simnfo->sampleName, "%s.dump", bsInfo.outPrefix ); |
365 |
sprintf( simnfo->finalName, "%s.init", bsInfo.outPrefix ); |
366 |
|
367 |
simnfo->atoms = atoms; |
368 |
|
369 |
// set up the writer and write out |
370 |
|
371 |
writer = new DumpWriter( simnfo ); |
372 |
writer->writeFinal(0.0); |
373 |
|
374 |
// clean up |
375 |
|
376 |
delete[] myLattice; |
377 |
|
378 |
return hasError; |
379 |
} |
380 |
|
381 |
// Begin Builder routines-------------------------------> |
382 |
|
383 |
/* Builds a standard core-shell nanoparticle. |
384 |
*/ |
385 |
void nanoBuilder::buildWithCoreShell(double dist, double pos[3]){ |
386 |
|
387 |
|
388 |
if ( dist <= particleRadius ){ |
389 |
moleculeVector.push_back(myMol); |
390 |
|
391 |
if (dist <= coreRadius){ |
392 |
coreAtomCount += nCoreModelAtoms; |
393 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
394 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
395 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
396 |
moleculeVector[moleculeCount].myStamp = coreStamp; |
397 |
moleculeVector[moleculeCount].isCore = 1; |
398 |
moleculeVector[moleculeCount].isShell = 0; |
399 |
|
400 |
} |
401 |
// Place shell |
402 |
else{ |
403 |
shellAtomCount += nShellModelAtoms; |
404 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
405 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
406 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
407 |
moleculeVector[moleculeCount].myStamp = shellStamp; |
408 |
moleculeVector[moleculeCount].isCore = 0; |
409 |
moleculeVector[moleculeCount].isShell = 1; |
410 |
|
411 |
} |
412 |
moleculeCount++; |
413 |
} |
414 |
|
415 |
} |
416 |
/* |
417 |
Builds a core-shell nanoparticle and tracks the number of molecules at the |
418 |
interface between the core-shell. These are recorded in vacancyInterface which is just |
419 |
an integer vector. |
420 |
*/ |
421 |
void nanoBuilder::buildWithVacancies(double dist, double pos[3]){ |
422 |
if ( dist <= particleRadius ){ |
423 |
|
424 |
moleculeVector.push_back(myMol); |
425 |
if (dist <= coreRadius){ |
426 |
|
427 |
coreAtomCount += nCoreModelAtoms; |
428 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
429 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
430 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
431 |
moleculeVector[moleculeCount].myStamp = coreStamp; |
432 |
moleculeVector[moleculeCount].isCore = 1; |
433 |
moleculeVector[moleculeCount].isShell = 0; |
434 |
|
435 |
if ((dist >= coreRadius - vacancyRadius/2.0) && |
436 |
(dist <= coreRadius + vacancyRadius/2.0)){ |
437 |
|
438 |
vacancyInterface.push_back(moleculeCount); |
439 |
nInterface++; |
440 |
} |
441 |
} else { |
442 |
// Place shell |
443 |
shellAtomCount += nShellModelAtoms; |
444 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
445 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
446 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
447 |
moleculeVector[moleculeCount].myStamp = shellStamp; |
448 |
moleculeVector[moleculeCount].isCore = 0; |
449 |
moleculeVector[moleculeCount].isShell = 1; |
450 |
|
451 |
} |
452 |
moleculeCount++; |
453 |
} |
454 |
|
455 |
|
456 |
|
457 |
} |
458 |
|
459 |
/* Builds a core-shell nanoparticle where the number of core and shell |
460 |
molecules is known. |
461 |
*/ |
462 |
void nanoBuilder::buildNmolParticle(double dist, double pos[3]){ |
463 |
static int nMolCounter = 0; |
464 |
static int nCoreMolCounter = 0; |
465 |
|
466 |
|
467 |
if (nMolCounter < totalMolecules){ |
468 |
moleculeVector.push_back(myMol); |
469 |
if (nCoreMolCounter < nCoreMolecules){ |
470 |
|
471 |
coreAtomCount += nCoreModelAtoms; |
472 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
473 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
474 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
475 |
moleculeVector[moleculeCount].myStamp = coreStamp; |
476 |
moleculeVector[moleculeCount].isCore = 1; |
477 |
moleculeVector[moleculeCount].isShell = 0; |
478 |
|
479 |
|
480 |
} else { |
481 |
shellAtomCount += nShellModelAtoms; |
482 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
483 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
484 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
485 |
moleculeVector[moleculeCount].myStamp = shellStamp; |
486 |
moleculeVector[moleculeCount].isCore = 0; |
487 |
moleculeVector[moleculeCount].isShell = 1; |
488 |
|
489 |
|
490 |
} |
491 |
|
492 |
} |
493 |
} |
494 |
|
495 |
|
496 |
/* Builds a randomly mixed nanoparticle. We build the particle to be |
497 |
entirely the core model, then randomly switch identities after the particle is built. |
498 |
*/ |
499 |
void nanoBuilder::buildRandomlyMixed(double dist, double pos[3]){ |
500 |
|
501 |
|
502 |
if ( dist <= particleRadius ){ |
503 |
moleculeCount++; |
504 |
|
505 |
|
506 |
moleculeVector[moleculeCount].pos[0] = pos[0]; |
507 |
moleculeVector[moleculeCount].pos[1] = pos[1]; |
508 |
moleculeVector[moleculeCount].pos[2] = pos[2]; |
509 |
moleculeVector[moleculeCount].myStamp = coreStamp; |
510 |
moleculeVector[moleculeCount].isCore = 1; |
511 |
moleculeVector[moleculeCount].isShell = 0; |
512 |
|
513 |
} |
514 |
|
515 |
|
516 |
|
517 |
} |
518 |
|
519 |
|
520 |
// -----------------------END Builder routines. |
521 |
|
522 |
|
523 |
|
524 |
//------------------------Begin Helper routines. |
525 |
void nanoBuilder::placeRandom(int totalMol){ |
526 |
int nSolute; |
527 |
int nSolvent; |
528 |
int i; |
529 |
int notfound; |
530 |
double solute_x; |
531 |
double solvent_x; |
532 |
|
533 |
int tester; |
534 |
|
535 |
nSolute = floor(soluteX * (double)totalMolecules); //CHECK ME |
536 |
nSolvent = totalMolecules - nSolute; |
537 |
|
538 |
solute_x = (double)nSolute/(double)totalMolecules; |
539 |
solvent_x = 1.0 - solute_x; |
540 |
|
541 |
|
542 |
|
543 |
|
544 |
for(i=0;nSolute-1;i++){ |
545 |
notfound = 1; |
546 |
|
547 |
while(notfound){ |
548 |
|
549 |
tester = floor((double)totalMolecules * drand48()); //Pick a molecule |
550 |
|
551 |
if (moleculeVector[tester].isCore){ // Make sure we select a core atom to change |
552 |
|
553 |
moleculeVector[tester].isCore = 0; |
554 |
moleculeVector[tester].isShell = 1; |
555 |
moleculeVector[tester].myStamp = shellStamp; |
556 |
notfound = 0; //set notfound = false. |
557 |
} |
558 |
|
559 |
} |
560 |
|
561 |
} |
562 |
} |
563 |
|
564 |
|
565 |
void nanoBuilder::buildVacancies(void){ |
566 |
int i; |
567 |
int* VacancyList; //logical nInterface long. |
568 |
int notfound; |
569 |
int index = 0; |
570 |
int nVacancies; |
571 |
int tester; |
572 |
|
573 |
if (nInterface != 0){ |
574 |
nVacancies = floor((double)nInterface * vacancyFraction); |
575 |
|
576 |
VacancyList = new int[nInterface]; |
577 |
|
578 |
// make vacancy list all false |
579 |
for(i=0;i<nInterface-1;i++){ |
580 |
VacancyList[i] = 0; |
581 |
} |
582 |
|
583 |
// Build a vacancy list.... |
584 |
for(i=0;nVacancies-1;i++){ |
585 |
notfound = 1; |
586 |
while(notfound){ |
587 |
|
588 |
tester = floor((double)nInterface * drand48()); |
589 |
|
590 |
if(! VacancyList[tester]){ |
591 |
VacancyList[tester] = 1; |
592 |
notfound = 0; |
593 |
} |
594 |
|
595 |
} |
596 |
} |
597 |
} |
598 |
// Loop through and kill the vacancies from atom vector. |
599 |
|
600 |
for (i=0;i<nInterface;i++){ |
601 |
if (VacancyList[i]){ |
602 |
moleculeVector[vacancyInterface[i]].isVacancy = 1; |
603 |
} // End Vacancy List |
604 |
} // for nInterface |
605 |
|
606 |
|
607 |
delete[] VacancyList; |
608 |
} |
609 |
|
610 |
|
611 |
|
612 |
|
613 |
void nanoBuilder::orientationMunger(double rot[3][3]){ |
614 |
|
615 |
double theta, phi, psi; |
616 |
double cosTheta; |
617 |
|
618 |
// select random phi, psi, and cosTheta |
619 |
|
620 |
phi = 2.0 * M_PI * drand48(); |
621 |
psi = 2.0 * M_PI * drand48(); |
622 |
cosTheta = (2.0 * drand48()) - 1.0; // sample cos -1 to 1 |
623 |
|
624 |
theta = acos( cosTheta ); |
625 |
|
626 |
rot[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
627 |
rot[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
628 |
rot[0][2] = sin(theta) * sin(psi); |
629 |
|
630 |
rot[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
631 |
rot[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
632 |
rot[1][2] = sin(theta) * cos(psi); |
633 |
|
634 |
rot[2][0] = sin(phi) * sin(theta); |
635 |
rot[2][1] = -cos(phi) * sin(theta); |
636 |
rot[2][2] = cos(theta); |
637 |
|
638 |
} |
639 |
|
640 |
|
641 |
|
642 |
|
643 |
|
644 |
|
645 |
|