1 |
#include <math.h> |
2 |
#include <iostream> |
3 |
#include "RigidBody.hpp" |
4 |
#include "VDWAtom.hpp" |
5 |
#include "MatVec3.h" |
6 |
|
7 |
RigidBody::RigidBody() { |
8 |
is_linear = false; |
9 |
linear_axis = -1; |
10 |
momIntTol = 1e-6; |
11 |
} |
12 |
|
13 |
RigidBody::~RigidBody() { |
14 |
} |
15 |
|
16 |
void RigidBody::addAtom(VDWAtom* at) { |
17 |
|
18 |
vec3 coords; |
19 |
|
20 |
myAtoms.push_back(at); |
21 |
|
22 |
at->getPos(coords.vec); |
23 |
refCoords.push_back(coords); |
24 |
} |
25 |
|
26 |
void RigidBody::getPos(double theP[3]){ |
27 |
for (int i = 0; i < 3 ; i++) |
28 |
theP[i] = pos[i]; |
29 |
} |
30 |
|
31 |
void RigidBody::setPos(double theP[3]){ |
32 |
for (int i = 0; i < 3 ; i++) |
33 |
pos[i] = theP[i]; |
34 |
} |
35 |
|
36 |
|
37 |
void RigidBody::setEuler( double phi, double theta, double psi ){ |
38 |
|
39 |
A[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
40 |
A[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
41 |
A[0][2] = sin(theta) * sin(psi); |
42 |
|
43 |
A[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
44 |
A[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
45 |
A[1][2] = sin(theta) * cos(psi); |
46 |
|
47 |
A[2][0] = sin(phi) * sin(theta); |
48 |
A[2][1] = -cos(phi) * sin(theta); |
49 |
A[2][2] = cos(theta); |
50 |
|
51 |
} |
52 |
|
53 |
void RigidBody::getQ( double q[4] ){ |
54 |
|
55 |
double t, s; |
56 |
double ad1, ad2, ad3; |
57 |
|
58 |
t = A[0][0] + A[1][1] + A[2][2] + 1.0; |
59 |
if( t > 0.0 ){ |
60 |
|
61 |
s = 0.5 / sqrt( t ); |
62 |
q[0] = 0.25 / s; |
63 |
q[1] = (A[1][2] - A[2][1]) * s; |
64 |
q[2] = (A[2][0] - A[0][2]) * s; |
65 |
q[3] = (A[0][1] - A[1][0]) * s; |
66 |
} |
67 |
else{ |
68 |
|
69 |
ad1 = fabs( A[0][0] ); |
70 |
ad2 = fabs( A[1][1] ); |
71 |
ad3 = fabs( A[2][2] ); |
72 |
|
73 |
if( ad1 >= ad2 && ad1 >= ad3 ){ |
74 |
|
75 |
s = 2.0 * sqrt( 1.0 + A[0][0] - A[1][1] - A[2][2] ); |
76 |
q[0] = (A[1][2] + A[2][1]) / s; |
77 |
q[1] = 0.5 / s; |
78 |
q[2] = (A[0][1] + A[1][0]) / s; |
79 |
q[3] = (A[0][2] + A[2][0]) / s; |
80 |
} |
81 |
else if( ad2 >= ad1 && ad2 >= ad3 ){ |
82 |
|
83 |
s = sqrt( 1.0 + A[1][1] - A[0][0] - A[2][2] ) * 2.0; |
84 |
q[0] = (A[0][2] + A[2][0]) / s; |
85 |
q[1] = (A[0][1] + A[1][0]) / s; |
86 |
q[2] = 0.5 / s; |
87 |
q[3] = (A[1][2] + A[2][1]) / s; |
88 |
} |
89 |
else{ |
90 |
|
91 |
s = sqrt( 1.0 + A[2][2] - A[0][0] - A[1][1] ) * 2.0; |
92 |
q[0] = (A[0][1] + A[1][0]) / s; |
93 |
q[1] = (A[0][2] + A[2][0]) / s; |
94 |
q[2] = (A[1][2] + A[2][1]) / s; |
95 |
q[3] = 0.5 / s; |
96 |
} |
97 |
} |
98 |
} |
99 |
|
100 |
void RigidBody::setQ( double the_q[4] ){ |
101 |
|
102 |
double q0Sqr, q1Sqr, q2Sqr, q3Sqr; |
103 |
|
104 |
q0Sqr = the_q[0] * the_q[0]; |
105 |
q1Sqr = the_q[1] * the_q[1]; |
106 |
q2Sqr = the_q[2] * the_q[2]; |
107 |
q3Sqr = the_q[3] * the_q[3]; |
108 |
|
109 |
A[0][0] = q0Sqr + q1Sqr - q2Sqr - q3Sqr; |
110 |
A[0][1] = 2.0 * ( the_q[1] * the_q[2] + the_q[0] * the_q[3] ); |
111 |
A[0][2] = 2.0 * ( the_q[1] * the_q[3] - the_q[0] * the_q[2] ); |
112 |
|
113 |
A[1][0] = 2.0 * ( the_q[1] * the_q[2] - the_q[0] * the_q[3] ); |
114 |
A[1][1] = q0Sqr - q1Sqr + q2Sqr - q3Sqr; |
115 |
A[1][2] = 2.0 * ( the_q[2] * the_q[3] + the_q[0] * the_q[1] ); |
116 |
|
117 |
A[2][0] = 2.0 * ( the_q[1] * the_q[3] + the_q[0] * the_q[2] ); |
118 |
A[2][1] = 2.0 * ( the_q[2] * the_q[3] - the_q[0] * the_q[1] ); |
119 |
A[2][2] = q0Sqr - q1Sqr -q2Sqr +q3Sqr; |
120 |
|
121 |
} |
122 |
|
123 |
void RigidBody::getA( double the_A[3][3] ){ |
124 |
|
125 |
for (int i = 0; i < 3; i++) |
126 |
for (int j = 0; j < 3; j++) |
127 |
the_A[i][j] = A[i][j]; |
128 |
|
129 |
} |
130 |
|
131 |
void RigidBody::setA( double the_A[3][3] ){ |
132 |
|
133 |
for (int i = 0; i < 3; i++) |
134 |
for (int j = 0; j < 3; j++) |
135 |
A[i][j] = the_A[i][j]; |
136 |
|
137 |
} |
138 |
|
139 |
void RigidBody::getI( double the_I[3][3] ){ |
140 |
|
141 |
for (int i = 0; i < 3; i++) |
142 |
for (int j = 0; j < 3; j++) |
143 |
the_I[i][j] = I[i][j]; |
144 |
|
145 |
} |
146 |
|
147 |
void RigidBody::lab2Body( double r[3] ){ |
148 |
|
149 |
double rl[3]; // the lab frame vector |
150 |
|
151 |
rl[0] = r[0]; |
152 |
rl[1] = r[1]; |
153 |
rl[2] = r[2]; |
154 |
|
155 |
r[0] = (A[0][0] * rl[0]) + (A[0][1] * rl[1]) + (A[0][2] * rl[2]); |
156 |
r[1] = (A[1][0] * rl[0]) + (A[1][1] * rl[1]) + (A[1][2] * rl[2]); |
157 |
r[2] = (A[2][0] * rl[0]) + (A[2][1] * rl[1]) + (A[2][2] * rl[2]); |
158 |
|
159 |
} |
160 |
|
161 |
void RigidBody::body2Lab( double r[3] ){ |
162 |
|
163 |
double rb[3]; // the body frame vector |
164 |
|
165 |
rb[0] = r[0]; |
166 |
rb[1] = r[1]; |
167 |
rb[2] = r[2]; |
168 |
|
169 |
r[0] = (A[0][0] * rb[0]) + (A[1][0] * rb[1]) + (A[2][0] * rb[2]); |
170 |
r[1] = (A[0][1] * rb[0]) + (A[1][1] * rb[1]) + (A[2][1] * rb[2]); |
171 |
r[2] = (A[0][2] * rb[0]) + (A[1][2] * rb[1]) + (A[2][2] * rb[2]); |
172 |
|
173 |
} |
174 |
|
175 |
void RigidBody::calcRefCoords( ) { |
176 |
|
177 |
int i, j, it, n_linear_coords, pAxis, maxAxis, midAxis; |
178 |
double mtmp; |
179 |
vec3 apos; |
180 |
double refCOM[3]; |
181 |
vec3 ptmp; |
182 |
double Itmp[3][3]; |
183 |
double pAxisMat[3][3], pAxisRotMat[3][3]; |
184 |
double evals[3]; |
185 |
double r, r2, len; |
186 |
double iMat[3][3]; |
187 |
double test[3]; |
188 |
|
189 |
// First, find the center of mass: |
190 |
|
191 |
mass = 0.0; |
192 |
for (j=0; j<3; j++) |
193 |
refCOM[j] = 0.0; |
194 |
|
195 |
for (i = 0; i < myAtoms.size(); i++) { |
196 |
mtmp = myAtoms[i]->getMass(); |
197 |
mass += mtmp; |
198 |
|
199 |
apos = refCoords[i]; |
200 |
for(j = 0; j < 3; j++) { |
201 |
refCOM[j] += apos[j]*mtmp; |
202 |
} |
203 |
} |
204 |
|
205 |
for(j = 0; j < 3; j++) |
206 |
refCOM[j] /= mass; |
207 |
|
208 |
// Next, move the origin of the reference coordinate system to the COM: |
209 |
|
210 |
for (i = 0; i < myAtoms.size(); i++) { |
211 |
apos = refCoords[i]; |
212 |
for (j=0; j < 3; j++) { |
213 |
apos[j] = apos[j] - refCOM[j]; |
214 |
} |
215 |
refCoords[i] = apos; |
216 |
} |
217 |
|
218 |
// Moment of Inertia calculation |
219 |
|
220 |
for (i = 0; i < 3; i++) |
221 |
for (j = 0; j < 3; j++) |
222 |
Itmp[i][j] = 0.0; |
223 |
|
224 |
for (it = 0; it < myAtoms.size(); it++) { |
225 |
|
226 |
mtmp = myAtoms[it]->getMass(); |
227 |
ptmp = refCoords[it]; |
228 |
r= norm3(ptmp.vec); |
229 |
r2 = r*r; |
230 |
|
231 |
for (i = 0; i < 3; i++) { |
232 |
for (j = 0; j < 3; j++) { |
233 |
|
234 |
if (i==j) Itmp[i][j] += mtmp * r2; |
235 |
|
236 |
Itmp[i][j] -= mtmp * ptmp.vec[i]*ptmp.vec[j]; |
237 |
} |
238 |
} |
239 |
} |
240 |
|
241 |
diagonalize3x3(Itmp, evals, sU); |
242 |
|
243 |
// zero out I and then fill the diagonals with the moments of inertia: |
244 |
|
245 |
n_linear_coords = 0; |
246 |
|
247 |
for (i = 0; i < 3; i++) { |
248 |
for (j = 0; j < 3; j++) { |
249 |
I[i][j] = 0.0; |
250 |
} |
251 |
I[i][i] = evals[i]; |
252 |
|
253 |
if (fabs(evals[i]) < momIntTol) { |
254 |
is_linear = true; |
255 |
n_linear_coords++; |
256 |
linear_axis = i; |
257 |
} |
258 |
} |
259 |
|
260 |
if (n_linear_coords > 1) { |
261 |
printf( |
262 |
"RigidBody error.\n" |
263 |
"\tSHAPES found more than one axis in this rigid body with a vanishing \n" |
264 |
"\tmoment of inertia. This can happen in one of three ways:\n" |
265 |
"\t 1) Only one atom was specified, or \n" |
266 |
"\t 2) All atoms were specified at the same location, or\n" |
267 |
"\t 3) The programmers did something stupid.\n" |
268 |
"\tIt is silly to use a rigid body to describe this situation. Be smarter.\n" |
269 |
); |
270 |
exit(-1); |
271 |
} |
272 |
|
273 |
// renormalize column vectors: |
274 |
|
275 |
for (i=0; i < 3; i++) { |
276 |
len = 0.0; |
277 |
for (j = 0; j < 3; j++) { |
278 |
len += sU[i][j]*sU[i][j]; |
279 |
} |
280 |
len = sqrt(len); |
281 |
for (j = 0; j < 3; j++) { |
282 |
sU[i][j] /= len; |
283 |
} |
284 |
} |
285 |
|
286 |
//sort and reorder the moment axes |
287 |
|
288 |
// The only problem below is for molecules like C60 with 3 nearly identical |
289 |
// non-zero moments of inertia. In this case it doesn't really matter which is |
290 |
// the principal axis, so they get assigned nearly randomly depending on the |
291 |
// floating point comparison between eigenvalues |
292 |
if (! is_linear) { |
293 |
pAxis = 0; |
294 |
maxAxis = 0; |
295 |
|
296 |
for (i = 0; i < 3; i++) { |
297 |
if (evals[i] < evals[pAxis]) pAxis = i; |
298 |
if (evals[i] > evals[maxAxis]) maxAxis = i; |
299 |
} |
300 |
|
301 |
midAxis = 0; |
302 |
for (i=0; i < 3; i++) { |
303 |
if (pAxis != i && maxAxis != i) midAxis = i; |
304 |
} |
305 |
} else { |
306 |
pAxis = linear_axis; |
307 |
// linear molecules have one zero moment of inertia and two identical |
308 |
// moments of inertia. In this case, it doesn't matter which is chosen |
309 |
// as mid and which is max, so just permute from the pAxis: |
310 |
midAxis = (pAxis + 1)%3; |
311 |
maxAxis = (pAxis + 2)%3; |
312 |
} |
313 |
|
314 |
//let z be the smallest and x be the largest eigenvalue axes |
315 |
for (i=0; i<3; i++){ |
316 |
pAxisMat[i][2] = sU[i][pAxis]; |
317 |
pAxisMat[i][1] = sU[i][midAxis]; |
318 |
pAxisMat[i][0] = sU[i][maxAxis]; |
319 |
} |
320 |
|
321 |
|
322 |
//calculate the proper rotation matrix |
323 |
transposeMat3(pAxisMat, pAxisRotMat); |
324 |
|
325 |
|
326 |
//rotate the rigid body to the principle axis frame |
327 |
for (i = 0; i < myAtoms.size(); i++) { |
328 |
matVecMul3(pAxisRotMat, refCoords[i].vec, refCoords[i].vec); |
329 |
myAtoms[i]->setPos(refCoords[i].vec); |
330 |
} |
331 |
|
332 |
identityMat3(iMat); |
333 |
setA(iMat); |
334 |
|
335 |
//and resort the moments of intertia to match the new orientation |
336 |
for (i=0; i<3; i++) |
337 |
if (evals[i]<momIntTol) |
338 |
evals[i] = 0.0; |
339 |
I[0][0] = evals[maxAxis]; |
340 |
I[1][1] = evals[midAxis]; |
341 |
I[2][2] = evals[pAxis]; |
342 |
} |
343 |
|
344 |
void RigidBody::doEulerToRotMat(double euler[3], double myA[3][3] ){ |
345 |
|
346 |
double phi, theta, psi; |
347 |
|
348 |
phi = euler[0]; |
349 |
theta = euler[1]; |
350 |
psi = euler[2]; |
351 |
|
352 |
myA[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
353 |
myA[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
354 |
myA[0][2] = sin(theta) * sin(psi); |
355 |
|
356 |
myA[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
357 |
myA[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
358 |
myA[1][2] = sin(theta) * cos(psi); |
359 |
|
360 |
myA[2][0] = sin(phi) * sin(theta); |
361 |
myA[2][1] = -cos(phi) * sin(theta); |
362 |
myA[2][2] = cos(theta); |
363 |
|
364 |
} |
365 |
|
366 |
void RigidBody::updateAtoms() { |
367 |
int i, j; |
368 |
vec3 ref; |
369 |
double apos[3]; |
370 |
|
371 |
for (i = 0; i < myAtoms.size(); i++) { |
372 |
|
373 |
ref = refCoords[i]; |
374 |
|
375 |
body2Lab(ref.vec); |
376 |
|
377 |
for (j = 0; j<3; j++) |
378 |
apos[j] = pos[j] + ref.vec[j]; |
379 |
|
380 |
myAtoms[i]->setPos(apos); |
381 |
|
382 |
} |
383 |
} |
384 |
|
385 |
/** |
386 |
* getEulerAngles computes a set of Euler angle values consistent |
387 |
* with an input rotation matrix. They are returned in the following |
388 |
* order: |
389 |
* myEuler[0] = phi; |
390 |
* myEuler[1] = theta; |
391 |
* myEuler[2] = psi; |
392 |
*/ |
393 |
void RigidBody::getEulerAngles(double myEuler[3]) { |
394 |
|
395 |
// We use so-called "x-convention", which is the most common |
396 |
// definition. In this convention, the rotation given by Euler |
397 |
// angles (phi, theta, psi), where the first rotation is by an angle |
398 |
// phi about the z-axis, the second is by an angle theta (0 <= theta |
399 |
// <= 180) about the x-axis, and the third is by an angle psi about |
400 |
// the z-axis (again). |
401 |
|
402 |
|
403 |
double phi,theta,psi,eps; |
404 |
double ctheta; |
405 |
double stheta; |
406 |
|
407 |
// set the tolerance for Euler angles and rotation elements |
408 |
|
409 |
eps = 1.0e-8; |
410 |
|
411 |
theta = acos(min(1.0,max(-1.0,A[2][2]))); |
412 |
ctheta = A[2][2]; |
413 |
stheta = sqrt(1.0 - ctheta * ctheta); |
414 |
|
415 |
// when sin(theta) is close to 0, we need to consider the |
416 |
// possibility of a singularity. In this case, we can assign an |
417 |
// arbitary value to phi (or psi), and then determine the psi (or |
418 |
// phi) or vice-versa. We'll assume that phi always gets the |
419 |
// rotation, and psi is 0 in cases of singularity. we use atan2 |
420 |
// instead of atan, since atan2 will give us -Pi to Pi. Since 0 <= |
421 |
// theta <= 180, sin(theta) will be always non-negative. Therefore, |
422 |
// it never changes the sign of both of the parameters passed to |
423 |
// atan2. |
424 |
|
425 |
if (fabs(stheta) <= eps){ |
426 |
psi = 0.0; |
427 |
phi = atan2(-A[1][0], A[0][0]); |
428 |
} |
429 |
// we only have one unique solution |
430 |
else{ |
431 |
phi = atan2(A[2][0], -A[2][1]); |
432 |
psi = atan2(A[0][2], A[1][2]); |
433 |
} |
434 |
|
435 |
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
436 |
//if (phi < 0) |
437 |
// phi += M_PI; |
438 |
|
439 |
//if (psi < 0) |
440 |
// psi += M_PI; |
441 |
|
442 |
myEuler[0] = phi; |
443 |
myEuler[1] = theta; |
444 |
myEuler[2] = psi; |
445 |
|
446 |
return; |
447 |
} |
448 |
|
449 |
double RigidBody::max(double x, double y) { |
450 |
return (x > y) ? x : y; |
451 |
} |
452 |
|
453 |
double RigidBody::min(double x, double y) { |
454 |
return (x > y) ? y : x; |
455 |
} |
456 |
|
457 |
double RigidBody::findMaxExtent(){ |
458 |
int i; |
459 |
double refAtomPos[3]; |
460 |
double maxExtent; |
461 |
double tempExtent; |
462 |
|
463 |
//zero the extent variables |
464 |
maxExtent = 0.0; |
465 |
tempExtent = 0.0; |
466 |
for (i=0; i<3; i++) |
467 |
refAtomPos[i] = 0.0; |
468 |
|
469 |
//loop over all atoms |
470 |
for (i=0; i<myAtoms.size(); i++){ |
471 |
getAtomRefCoor(refAtomPos, i); |
472 |
tempExtent = sqrt(refAtomPos[0]*refAtomPos[0] + refAtomPos[1]*refAtomPos[1] |
473 |
+ refAtomPos[2]*refAtomPos[2]); |
474 |
if (tempExtent > maxExtent) |
475 |
maxExtent = tempExtent; |
476 |
} |
477 |
return maxExtent; |
478 |
} |
479 |
|
480 |
void RigidBody::findCOM() { |
481 |
|
482 |
size_t i; |
483 |
int j; |
484 |
double mtmp; |
485 |
double ptmp[3]; |
486 |
|
487 |
for(j = 0; j < 3; j++) { |
488 |
pos[j] = 0.0; |
489 |
} |
490 |
mass = 0.0; |
491 |
|
492 |
for (i = 0; i < myAtoms.size(); i++) { |
493 |
|
494 |
mtmp = myAtoms[i]->getMass(); |
495 |
myAtoms[i]->getPos(ptmp); |
496 |
|
497 |
mass += mtmp; |
498 |
|
499 |
for(j = 0; j < 3; j++) { |
500 |
pos[j] += ptmp[j]*mtmp; |
501 |
} |
502 |
|
503 |
} |
504 |
|
505 |
for(j = 0; j < 3; j++) { |
506 |
pos[j] /= mass; |
507 |
} |
508 |
|
509 |
} |
510 |
|
511 |
void RigidBody::getAtomPos(double theP[3], int index){ |
512 |
vec3 ref; |
513 |
|
514 |
if (index >= myAtoms.size()) |
515 |
printf( "%d is an invalid index, current rigid body contains " |
516 |
"%d atoms\n", index, myAtoms.size()); |
517 |
|
518 |
ref = refCoords[index]; |
519 |
body2Lab(ref.vec); |
520 |
|
521 |
theP[0] = pos[0] + ref[0]; |
522 |
theP[1] = pos[1] + ref[1]; |
523 |
theP[2] = pos[2] + ref[2]; |
524 |
} |
525 |
|
526 |
|
527 |
void RigidBody::getAtomRefCoor(double pos[3], int index){ |
528 |
vec3 ref; |
529 |
|
530 |
ref = refCoords[index]; |
531 |
pos[0] = ref[0]; |
532 |
pos[1] = ref[1]; |
533 |
pos[2] = ref[2]; |
534 |
|
535 |
} |
536 |
|
537 |
double RigidBody::getAtomRpar(int index){ |
538 |
|
539 |
return myAtoms[index]->getRpar(); |
540 |
|
541 |
} |
542 |
|
543 |
double RigidBody::getAtomEps(int index){ |
544 |
|
545 |
return myAtoms[index]->getEps(); |
546 |
|
547 |
} |
548 |
|
549 |
char *RigidBody::getAtomBase(int index){ |
550 |
|
551 |
return myAtoms[index]->getBase(); |
552 |
|
553 |
} |