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root/OpenMD/branches/development/src/primitives/RigidBody.cpp

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trunk/src/primitives/RigidBody.cpp (file contents), Revision 2 by gezelter, Fri Sep 24 04:16:43 2004 UTC vs.
branches/development/src/primitives/RigidBody.cpp (file contents), Revision 1842 by gezelter, Tue Jan 29 19:10:04 2013 UTC

#	Line 1 | Line 1
1	+	/*
2	+	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	+	*
4	+	* The University of Notre Dame grants you ("Licensee") a
5	+	* non-exclusive, royalty free, license to use, modify and
6	+	* redistribute this software in source and binary code form, provided
7	+	* that the following conditions are met:
8	+	*
9	+	* 1. Redistributions of source code must retain the above copyright
10	+	*    notice, this list of conditions and the following disclaimer.
11	+	*
12	+	* 2. Redistributions in binary form must reproduce the above copyright
13	+	*    notice, this list of conditions and the following disclaimer in the
14	+	*    documentation and/or other materials provided with the
15	+	*    distribution.
16	+	*
17	+	* This software is provided "AS IS," without a warranty of any
18	+	* kind. All express or implied conditions, representations and
19	+	* warranties, including any implied warranty of merchantability,
20	+	* fitness for a particular purpose or non-infringement, are hereby
21	+	* excluded.  The University of Notre Dame and its licensors shall not
22	+	* be liable for any damages suffered by licensee as a result of
23	+	* using, modifying or distributing the software or its
24	+	* derivatives. In no event will the University of Notre Dame or its
25	+	* licensors be liable for any lost revenue, profit or data, or for
26	+	* direct, indirect, special, consequential, incidental or punitive
27	+	* damages, however caused and regardless of the theory of liability,
28	+	* arising out of the use of or inability to use software, even if the
29	+	* University of Notre Dame has been advised of the possibility of
30	+	* such damages.
31	+	*
32	+	* SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33	+	* research, please cite the appropriate papers when you publish your
34	+	* work.  Good starting points are:
35	+	*
36	+	* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37	+	* [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38	+	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39	+	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41	+	*/
42	+	#include <algorithm>
43		#include <math.h>
44	<	#include "RigidBody.hpp"
45	<	#include "DirectionalAtom.hpp"
46	<	#include "simError.h"
47	<	#include "MatVec3.h"
48	<
49	<	RigidBody::RigidBody() : StuntDouble() {
50	<	objType = OT_RIGIDBODY;
9	<	is_linear = false;
10	<	linear_axis =  -1;
11	<	momIntTol = 1e-6;
12	<	}
13	<
14	<	RigidBody::~RigidBody() {
15	<	}
16	<
17	<	void RigidBody::addAtom(Atom* at, AtomStamp* ats) {
18	<
19	<	vec3 coords;
20	<	vec3 euler;
21	<	mat3x3 Atmp;
22	<
23	<	myAtoms.push_back(at);
24	<
25	<	if( !ats->havePosition() ){
26	<	sprintf( painCave.errMsg,
27	<	"RigidBody error.\n"
28	<	"\tAtom %s does not have a position specified.\n"
29	<	"\tThis means RigidBody cannot set up reference coordinates.\n",
30	<	ats->getType() );
31	<	painCave.isFatal = 1;
32	<	simError();
44	>	#include "primitives/RigidBody.hpp"
45	>	#include "utils/simError.h"
46	>	#include "utils/NumericConstant.hpp"
47	>	namespace OpenMD {
48	>
49	>	RigidBody::RigidBody() : StuntDouble(otRigidBody, &Snapshot::rigidbodyData),
50	>	inertiaTensor_(0.0){
51		}
52
53	<	coords[0] = ats->getPosX();
54	<	coords[1] = ats->getPosY();
55	<	coords[2] = ats->getPosZ();
56	<
57	<	refCoords.push_back(coords);
53	>	void RigidBody::setPrevA(const RotMat3x3d& a) {
54	>	((snapshotMan_->getPrevSnapshot())->*storage_).aMat[localIndex_] = a;
55	>
56	>	for (unsigned int i = 0 ; i < atoms_.size(); ++i){
57	>	if (atoms_[i]->isDirectional()) {
58	>	atoms_[i]->setPrevA(refOrients_[i].transpose() * a);
59	>	}
60	>	}
61	>
62	>	}
63
64	<	if (at->isDirectional()) {
64	>
65	>	void RigidBody::setA(const RotMat3x3d& a) {
66	>	((snapshotMan_->getCurrentSnapshot())->*storage_).aMat[localIndex_] = a;
67
68	<	if( !ats->haveOrientation() ){
69	<	sprintf( painCave.errMsg,
70	<	"RigidBody error.\n"
71	<	"\tAtom %s does not have an orientation specified.\n"
72	<	"\tThis means RigidBody cannot set up reference orientations.\n",
73	<	ats->getType() );
74	<	painCave.isFatal = 1;
75	<	simError();
76	<	}
68	>	for (unsigned int i = 0 ; i < atoms_.size(); ++i){
69	>	if (atoms_[i]->isDirectional()) {
70	>	atoms_[i]->setA(refOrients_[i].transpose() * a);
71	>	}
72	>	}
73	>	}
74	>
75	>	void RigidBody::setA(const RotMat3x3d& a, int snapshotNo) {
76	>	((snapshotMan_->getSnapshot(snapshotNo))->*storage_).aMat[localIndex_] = a;
77	>
78	>	for (unsigned int i = 0 ; i < atoms_.size(); ++i){
79	>	if (atoms_[i]->isDirectional()) {
80	>	atoms_[i]->setA(refOrients_[i].transpose() * a, snapshotNo);
81	>	}
82	>	}
83
84	<	euler[0] = ats->getEulerPhi();
85	<	euler[1] = ats->getEulerTheta();
86	<	euler[2] = ats->getEulerPsi();
84	>	}
85	>
86	>	Mat3x3d RigidBody::getI() {
87	>	return inertiaTensor_;
88	>	}
89	>
90	>	std::vector<RealType> RigidBody::getGrad() {
91	>	std::vector<RealType> grad(6, 0.0);
92	>	Vector3d force;
93	>	Vector3d torque;
94	>	Vector3d myEuler;
95	>	RealType phi, theta;
96	>	// RealType psi;
97	>	RealType cphi, sphi, ctheta, stheta;
98	>	Vector3d ephi;
99	>	Vector3d etheta;
100	>	Vector3d epsi;
101
102	<	doEulerToRotMat(euler, Atmp);
102	>	force = getFrc();
103	>	torque =getTrq();
104	>	myEuler = getA().toEulerAngles();
105
106	<	refOrients.push_back(Atmp);
106	>	phi = myEuler[0];
107	>	theta = myEuler[1];
108	>	// psi = myEuler[2];
109
110	<	}
111	<	}
112	<
113	<	void RigidBody::getPos(double theP[3]){
65	<	for (int i = 0; i < 3 ; i++)
66	<	theP[i] = pos[i];
67	<	}
68	<
69	<	void RigidBody::setPos(double theP[3]){
70	<	for (int i = 0; i < 3 ; i++)
71	<	pos[i] = theP[i];
72	<	}
73	<
74	<	void RigidBody::getVel(double theV[3]){
75	<	for (int i = 0; i < 3 ; i++)
76	<	theV[i] = vel[i];
77	<	}
78	<
79	<	void RigidBody::setVel(double theV[3]){
80	<	for (int i = 0; i < 3 ; i++)
81	<	vel[i] = theV[i];
82	<	}
83	<
84	<	void RigidBody::getFrc(double theF[3]){
85	<	for (int i = 0; i < 3 ; i++)
86	<	theF[i] = frc[i];
87	<	}
88	<
89	<	void RigidBody::addFrc(double theF[3]){
90	<	for (int i = 0; i < 3 ; i++)
91	<	frc[i] += theF[i];
92	<	}
93	<
94	<	void RigidBody::zeroForces() {
95	<
96	<	for (int i = 0; i < 3; i++) {
97	<	frc[i] = 0.0;
98	<	trq[i] = 0.0;
99	<	}
100	<
101	<	}
102	<
103	<	void RigidBody::setEuler( double phi, double theta, double psi ){
104	<
105	<	A[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi));
106	<	A[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi));
107	<	A[0][2] = sin(theta) * sin(psi);
110	>	cphi = cos(phi);
111	>	sphi = sin(phi);
112	>	ctheta = cos(theta);
113	>	stheta = sin(theta);
114
115	<	A[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi));
110	<	A[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi));
111	<	A[1][2] = sin(theta) * cos(psi);
115	>	// get unit vectors along the phi, theta and psi rotation axes
116
117	<	A[2][0] = sin(phi) * sin(theta);
118	<	A[2][1] = -cos(phi) * sin(theta);
119	<	A[2][2] = cos(theta);
116	<
117	<	}
118	<
119	<	void RigidBody::getQ( double q[4] ){
120	<
121	<	double t, s;
122	<	double ad1, ad2, ad3;
117	>	ephi[0] = 0.0;
118	>	ephi[1] = 0.0;
119	>	ephi[2] = 1.0;
120
121	<	t = A[0][0] + A[1][1] + A[2][2] + 1.0;
122	<	if( t > 0.0 ){
121	>	//etheta[0] = -sphi;
122	>	//etheta[1] =  cphi;
123	>	//etheta[2] =  0.0;
124
125	<	s = 0.5 / sqrt( t );
126	<	q[0] = 0.25 / s;
127	<	q[1] = (A[1][2] - A[2][1]) * s;
130	<	q[2] = (A[2][0] - A[0][2]) * s;
131	<	q[3] = (A[0][1] - A[1][0]) * s;
132	<	}
133	<	else{
125	>	etheta[0] = cphi;
126	>	etheta[1] = sphi;
127	>	etheta[2] =  0.0;
128
129	<	ad1 = fabs( A[0][0] );
130	<	ad2 = fabs( A[1][1] );
131	<	ad3 = fabs( A[2][2] );
129	>	epsi[0] = stheta * cphi;
130	>	epsi[1] = stheta * sphi;
131	>	epsi[2] = ctheta;
132
133	<	if( ad1 >= ad2 && ad1 >= ad3 ){
133	>	//gradient is equal to -force
134	>	for (int j = 0 ; j<3; j++)
135	>	grad[j] = -force[j];
136	>
137	>	for (int j = 0; j < 3; j++ ) {
138
139	<	s = 2.0 * sqrt( 1.0 + A[0][0] - A[1][1] - A[2][2] );
140	<	q[0] = (A[1][2] + A[2][1]) / s;
141	<	q[1] = 0.5 / s;
144	<	q[2] = (A[0][1] + A[1][0]) / s;
145	<	q[3] = (A[0][2] + A[2][0]) / s;
146	<	}
147	<	else if( ad2 >= ad1 && ad2 >= ad3 ){
139	>	grad[3] += torque[j]*ephi[j];
140	>	grad[4] += torque[j]*etheta[j];
141	>	grad[5] += torque[j]*epsi[j];
142
149	–	s = sqrt( 1.0 + A[1][1] - A[0][0] - A[2][2] ) * 2.0;
150	–	q[0] = (A[0][2] + A[2][0]) / s;
151	–	q[1] = (A[0][1] + A[1][0]) / s;
152	–	q[2] = 0.5 / s;
153	–	q[3] = (A[1][2] + A[2][1]) / s;
143		}
144	<	else{
144	>
145	>	return grad;
146	>	}
147	>
148	>	void RigidBody::accept(BaseVisitor* v) {
149	>	v->visit(this);
150	>	}
151	>
152	>	/**@todo need modification */
153	>	void  RigidBody::calcRefCoords() {
154	>	RealType mtmp;
155	>	Vector3d refCOM(0.0);
156	>	mass_ = 0.0;
157	>	for (std::size_t i = 0; i < atoms_.size(); ++i) {
158	>	mtmp = atoms_[i]->getMass();
159	>	mass_ += mtmp;
160	>	refCOM += refCoords_[i]*mtmp;
161	>	}
162	>	refCOM /= mass_;
163	>
164	>	// Next, move the origin of the reference coordinate system to the COM:
165	>	for (std::size_t i = 0; i < atoms_.size(); ++i) {
166	>	refCoords_[i] -= refCOM;
167	>	}
168	>
169	>	// Moment of Inertia calculation
170	>	Mat3x3d Itmp(0.0);
171	>	for (std::size_t i = 0; i < atoms_.size(); i++) {
172	>	Mat3x3d IAtom(0.0);
173	>	mtmp = atoms_[i]->getMass();
174	>	IAtom -= outProduct(refCoords_[i], refCoords_[i]) * mtmp;
175	>	RealType r2 = refCoords_[i].lengthSquare();
176	>	IAtom(0, 0) += mtmp * r2;
177	>	IAtom(1, 1) += mtmp * r2;
178	>	IAtom(2, 2) += mtmp * r2;
179	>	Itmp += IAtom;
180
181	<	s = sqrt( 1.0 + A[2][2] - A[0][0] - A[1][1] ) * 2.0;
182	<	q[0] = (A[0][1] + A[1][0]) / s;
183	<	q[1] = (A[0][2] + A[2][0]) / s;
184	<	q[2] = (A[1][2] + A[2][1]) / s;
161	<	q[3] = 0.5 / s;
181	>	//project the inertial moment of directional atoms into this rigid body
182	>	if (atoms_[i]->isDirectional()) {
183	>	Itmp += refOrients_[i].transpose() * atoms_[i]->getI() * refOrients_[i];
184	>	}
185		}
163	–	}
164	–	}
186
187	<	void RigidBody::setQ( double the_q[4] ){
187	>	//    std::cout << Itmp << std::endl;
188
189	<	double q0Sqr, q1Sqr, q2Sqr, q3Sqr;
190	<
191	<	q0Sqr = the_q[0] * the_q[0];
171	<	q1Sqr = the_q[1] * the_q[1];
172	<	q2Sqr = the_q[2] * the_q[2];
173	<	q3Sqr = the_q[3] * the_q[3];
174	<
175	<	A[0][0] = q0Sqr + q1Sqr - q2Sqr - q3Sqr;
176	<	A[0][1] = 2.0 * ( the_q[1] * the_q[2] + the_q[0] * the_q[3] );
177	<	A[0][2] = 2.0 * ( the_q[1] * the_q[3] - the_q[0] * the_q[2] );
178	<
179	<	A[1][0] = 2.0 * ( the_q[1] * the_q[2] - the_q[0] * the_q[3] );
180	<	A[1][1] = q0Sqr - q1Sqr + q2Sqr - q3Sqr;
181	<	A[1][2] = 2.0 * ( the_q[2] * the_q[3] + the_q[0] * the_q[1] );
182	<
183	<	A[2][0] = 2.0 * ( the_q[1] * the_q[3] + the_q[0] * the_q[2] );
184	<	A[2][1] = 2.0 * ( the_q[2] * the_q[3] - the_q[0] * the_q[1] );
185	<	A[2][2] = q0Sqr - q1Sqr -q2Sqr +q3Sqr;
189	>	//diagonalize
190	>	Vector3d evals;
191	>	Mat3x3d::diagonalize(Itmp, evals, sU_);
192
193	<	}
193	>	// zero out I and then fill the diagonals with the moments of inertia:
194	>	inertiaTensor_(0, 0) = evals[0];
195	>	inertiaTensor_(1, 1) = evals[1];
196	>	inertiaTensor_(2, 2) = evals[2];
197	>
198	>	int nLinearAxis = 0;
199	>	for (int i = 0; i < 3; i++) {
200	>	if (fabs(evals[i]) < OpenMD::epsilon) {
201	>	linear_ = true;
202	>	linearAxis_ = i;
203	>	++ nLinearAxis;
204	>	}
205	>	}
206
207	<	void RigidBody::getA( double the_A[3][3] ){
207	>	if (nLinearAxis > 1) {
208	>	sprintf( painCave.errMsg,
209	>	"RigidBody error.\n"
210	>	"\tOpenMD found more than one axis in this rigid body with a vanishing \n"
211	>	"\tmoment of inertia.  This can happen in one of three ways:\n"
212	>	"\t 1) Only one atom was specified, or \n"
213	>	"\t 2) All atoms were specified at the same location, or\n"
214	>	"\t 3) The programmers did something stupid.\n"
215	>	"\tIt is silly to use a rigid body to describe this situation.  Be smarter.\n"
216	>	);
217	>	painCave.isFatal = 1;
218	>	simError();
219	>	}
220
221	<	for (int i = 0; i < 3; i++)
192	<	for (int j = 0; j < 3; j++)
193	<	the_A[i][j] = A[i][j];
221	>	}
222
223	<	}
223	>	void  RigidBody::calcForcesAndTorques() {
224	>	Vector3d afrc;
225	>	Vector3d atrq;
226	>	Vector3d apos;
227	>	Vector3d rpos;
228	>	Vector3d frc(0.0);
229	>	Vector3d trq(0.0);
230	>	Vector3d ef(0.0);
231	>	Vector3d pos = this->getPos();
232
233	<	void RigidBody::setA( double the_A[3][3] ){
233	>	int sl = ((snapshotMan_->getCurrentSnapshot())->*storage_).getStorageLayout();
234
235	<	for (int i = 0; i < 3; i++)
200	<	for (int j = 0; j < 3; j++)
201	<	A[i][j] = the_A[i][j];
202	<
203	<	}
235	>	for (unsigned int i = 0; i < atoms_.size(); i++) {
236
237	<	void RigidBody::getJ( double theJ[3] ){
238	<
239	<	for (int i = 0; i < 3; i++)
240	<	theJ[i] = ji[i];
237	>	afrc = atoms_[i]->getFrc();
238	>	apos = atoms_[i]->getPos();
239	>	rpos = apos - pos;
240	>
241	>	frc += afrc;
242
243	<	}
243	>	trq[0] += rpos[1]*afrc[2] - rpos[2]*afrc[1];
244	>	trq[1] += rpos[2]*afrc[0] - rpos[0]*afrc[2];
245	>	trq[2] += rpos[0]*afrc[1] - rpos[1]*afrc[0];
246
247	<	void RigidBody::setJ( double theJ[3] ){
248	<
214	<	for (int i = 0; i < 3; i++)
215	<	ji[i] = theJ[i];
247	>	// If the atom has a torque associated with it, then we also need to
248	>	// migrate the torques onto the center of mass:
249
250	<	}
250	>	if (atoms_[i]->isDirectional()) {
251	>	atrq = atoms_[i]->getTrq();
252	>	trq += atrq;
253	>	}
254
255	<	void RigidBody::getTrq(double theT[3]){
256	<	for (int i = 0; i < 3 ; i++)
257	<	theT[i] = trq[i];
258	<	}
255	>	if (sl & DataStorage::dslElectricField) {
256	>	ef += atoms_[i]->getElectricField();
257	>	}
258	>	}
259	>	addFrc(frc);
260	>	addTrq(trq);
261
262	<	void RigidBody::addTrq(double theT[3]){
263	<	for (int i = 0; i < 3 ; i++)
264	<	trq[i] += theT[i];
265	<	}
262	>	if (sl & DataStorage::dslElectricField) {
263	>	ef /= atoms_.size();
264	>	setElectricField(ef);
265	>	}
266
267	<	void RigidBody::getI( double the_I[3][3] ){
267	>	}
268
269	<	for (int i = 0; i < 3; i++)
270	<	for (int j = 0; j < 3; j++)
271	<	the_I[i][j] = I[i][j];
269	>	Mat3x3d RigidBody::calcForcesAndTorquesAndVirial() {
270	>	Vector3d afrc;
271	>	Vector3d atrq;
272	>	Vector3d apos;
273	>	Vector3d rpos;
274	>	Vector3d dfrc;
275	>	Vector3d frc(0.0);
276	>	Vector3d trq(0.0);
277	>	Vector3d ef(0.0);
278	>
279	>	Vector3d pos = this->getPos();
280	>	Mat3x3d tau_(0.0);
281
282	<	}
282	>	int sl = ((snapshotMan_->getCurrentSnapshot())->*storage_).getStorageLayout();
283
284	<	void RigidBody::lab2Body( double r[3] ){
284	>	for (unsigned int i = 0; i < atoms_.size(); i++) {
285	>
286	>	afrc = atoms_[i]->getFrc();
287	>	apos = atoms_[i]->getPos();
288	>	rpos = apos - pos;
289	>
290	>	frc += afrc;
291
292	<	double rl[3]; // the lab frame vector
292	>	trq[0] += rpos[1]*afrc[2] - rpos[2]*afrc[1];
293	>	trq[1] += rpos[2]*afrc[0] - rpos[0]*afrc[2];
294	>	trq[2] += rpos[0]*afrc[1] - rpos[1]*afrc[0];
295	>
296	>	// If the atom has a torque associated with it, then we also need to
297	>	// migrate the torques onto the center of mass:
298	>
299	>	if (atoms_[i]->isDirectional()) {
300	>	atrq = atoms_[i]->getTrq();
301	>	trq += atrq;
302	>	}
303	>	if (sl & DataStorage::dslElectricField) {
304	>	ef += atoms_[i]->getElectricField();
305	>	}
306	>
307	>	tau_(0,0) -= rpos[0]*afrc[0];
308	>	tau_(0,1) -= rpos[0]*afrc[1];
309	>	tau_(0,2) -= rpos[0]*afrc[2];
310	>	tau_(1,0) -= rpos[1]*afrc[0];
311	>	tau_(1,1) -= rpos[1]*afrc[1];
312	>	tau_(1,2) -= rpos[1]*afrc[2];
313	>	tau_(2,0) -= rpos[2]*afrc[0];
314	>	tau_(2,1) -= rpos[2]*afrc[1];
315	>	tau_(2,2) -= rpos[2]*afrc[2];
316	>
317	>	}
318	>	addFrc(frc);
319	>	addTrq(trq);
320	>
321	>	if (sl & DataStorage::dslElectricField) {
322	>	ef /= atoms_.size();
323	>	setElectricField(ef);
324	>	}
325	>
326	>	return tau_;
327	>	}
328	>
329	>	void  RigidBody::updateAtoms() {
330	>	unsigned int i;
331	>	Vector3d ref;
332	>	Vector3d apos;
333	>	DirectionalAtom* dAtom;
334	>	Vector3d pos = getPos();
335	>	RotMat3x3d a = getA();
336	>
337	>	for (i = 0; i < atoms_.size(); i++) {
338	>
339	>	ref = body2Lab(refCoords_[i]);
340	>
341	>	apos = pos + ref;
342	>
343	>	atoms_[i]->setPos(apos);
344	>
345	>	if (atoms_[i]->isDirectional()) {
346	>
347	>	dAtom = (DirectionalAtom *) atoms_[i];
348	>	dAtom->setA(refOrients_[i].transpose() * a);
349	>	}
350	>
351	>	}
352
353	<	rl[0] = r[0];
242	<	rl[1] = r[1];
243	<	rl[2] = r[2];
244	<
245	<	r[0] = (A[0][0] * rl[0]) + (A[0][1] * rl[1]) + (A[0][2] * rl[2]);
246	<	r[1] = (A[1][0] * rl[0]) + (A[1][1] * rl[1]) + (A[1][2] * rl[2]);
247	<	r[2] = (A[2][0] * rl[0]) + (A[2][1] * rl[1]) + (A[2][2] * rl[2]);
353	>	}
354
249	–	}
355
356	<	void RigidBody::body2Lab( double r[3] ){
356	>	void  RigidBody::updateAtoms(int frame) {
357	>	unsigned int i;
358	>	Vector3d ref;
359	>	Vector3d apos;
360	>	DirectionalAtom* dAtom;
361	>	Vector3d pos = getPos(frame);
362	>	RotMat3x3d a = getA(frame);
363	>
364	>	for (i = 0; i < atoms_.size(); i++) {
365	>
366	>	ref = body2Lab(refCoords_[i], frame);
367
368	<	double rb[3]; // the body frame vector
368	>	apos = pos + ref;
369	>
370	>	atoms_[i]->setPos(apos, frame);
371	>
372	>	if (atoms_[i]->isDirectional()) {
373	>
374	>	dAtom = (DirectionalAtom *) atoms_[i];
375	>	dAtom->setA(refOrients_[i].transpose() * a, frame);
376	>	}
377	>
378	>	}
379
380	<	rb[0] = r[0];
256	<	rb[1] = r[1];
257	<	rb[2] = r[2];
258	<
259	<	r[0] = (A[0][0] * rb[0]) + (A[1][0] * rb[1]) + (A[2][0] * rb[2]);
260	<	r[1] = (A[0][1] * rb[0]) + (A[1][1] * rb[1]) + (A[2][1] * rb[2]);
261	<	r[2] = (A[0][2] * rb[0]) + (A[1][2] * rb[1]) + (A[2][2] * rb[2]);
380	>	}
381
382	<	}
382	>	void RigidBody::updateAtomVel() {
383	>	Mat3x3d skewMat;;
384
385	<	double RigidBody::getZangle( ){
386	<	return zAngle;
267	<	}
385	>	Vector3d ji = getJ();
386	>	Mat3x3d I =  getI();
387
388	<	void RigidBody::setZangle( double zAng ){
389	<	zAngle = zAng;
390	<	}
388	>	skewMat(0, 0) =0;
389	>	skewMat(0, 1) = ji[2] /I(2, 2);
390	>	skewMat(0, 2) = -ji[1] /I(1, 1);
391	>
392	>	skewMat(1, 0) = -ji[2] /I(2, 2);
393	>	skewMat(1, 1) = 0;
394	>	skewMat(1, 2) = ji[0]/I(0, 0);
395	>
396	>	skewMat(2, 0) =ji[1] /I(1, 1);
397	>	skewMat(2, 1) = -ji[0]/I(0, 0);
398	>	skewMat(2, 2) = 0;
399	>
400	>	Mat3x3d mat = (getA() * skewMat).transpose();
401	>	Vector3d rbVel = getVel();
402	>
403	>
404	>	Vector3d velRot;
405	>	for (unsigned int i = 0 ; i < refCoords_.size(); ++i) {
406	>	atoms_[i]->setVel(rbVel + mat * refCoords_[i]);
407	>	}
408	>
409	>	}
410	>
411	>	void RigidBody::updateAtomVel(int frame) {
412	>	Mat3x3d skewMat;;
413	>
414	>	Vector3d ji = getJ(frame);
415	>	Mat3x3d I =  getI();
416	>
417	>	skewMat(0, 0) =0;
418	>	skewMat(0, 1) = ji[2] /I(2, 2);
419	>	skewMat(0, 2) = -ji[1] /I(1, 1);
420	>
421	>	skewMat(1, 0) = -ji[2] /I(2, 2);
422	>	skewMat(1, 1) = 0;
423	>	skewMat(1, 2) = ji[0]/I(0, 0);
424	>
425	>	skewMat(2, 0) =ji[1] /I(1, 1);
426	>	skewMat(2, 1) = -ji[0]/I(0, 0);
427	>	skewMat(2, 2) = 0;
428
429	<	void RigidBody::addZangle( double zAng ){
430	<	zAngle += zAng;
275	<	}
429	>	Mat3x3d mat = (getA(frame) * skewMat).transpose();
430	>	Vector3d rbVel = getVel(frame);
431
277	–	void RigidBody::calcRefCoords( ) {
432
433	<	int i,j,k, it, n_linear_coords;
434	<	double mtmp;
435	<	vec3 apos;
436	<	double refCOM[3];
283	<	vec3 ptmp;
284	<	double Itmp[3][3];
285	<	double evals[3];
286	<	double evects[3][3];
287	<	double r, r2, len;
433	>	Vector3d velRot;
434	>	for (unsigned int i = 0 ; i < refCoords_.size(); ++i) {
435	>	atoms_[i]->setVel(rbVel + mat * refCoords_[i], frame);
436	>	}
437
438	<	// First, find the center of mass:
290	<
291	<	mass = 0.0;
292	<	for (j=0; j<3; j++)
293	<	refCOM[j] = 0.0;
294	<
295	<	for (i = 0; i < myAtoms.size(); i++) {
296	<	mtmp = myAtoms[i]->getMass();
297	<	mass += mtmp;
438	>	}
439
440	<	apos = refCoords[i];
441	<
442	<	for(j = 0; j < 3; j++) {
443	<	refCOM[j] += apos[j]*mtmp;
440	>
441	>
442	>	bool RigidBody::getAtomPos(Vector3d& pos, unsigned int index) {
443	>	if (index < atoms_.size()) {
444	>
445	>	Vector3d ref = body2Lab(refCoords_[index]);
446	>	pos = getPos() + ref;
447	>	return true;
448	>	} else {
449	>	std::cerr << index << " is an invalid index, current rigid body contains "
450	>	<< atoms_.size() << "atoms" << std::endl;
451	>	return false;
452		}
453		}
305	–
306	–	for(j = 0; j < 3; j++)
307	–	refCOM[j] /= mass;
454
455	<	// Next, move the origin of the reference coordinate system to the COM:
456	<
457	<	for (i = 0; i < myAtoms.size(); i++) {
458	<	apos = refCoords[i];
459	<	for (j=0; j < 3; j++) {
460	<	apos[j] = apos[j] - refCOM[j];
455	>	bool RigidBody::getAtomPos(Vector3d& pos, Atom* atom) {
456	>	std::vector<Atom*>::iterator i;
457	>	i = std::find(atoms_.begin(), atoms_.end(), atom);
458	>	if (i != atoms_.end()) {
459	>	//RigidBody class makes sure refCoords_ and atoms_ match each other
460	>	Vector3d ref = body2Lab(refCoords_[i - atoms_.begin()]);
461	>	pos = getPos() + ref;
462	>	return true;
463	>	} else {
464	>	std::cerr << "Atom " << atom->getGlobalIndex()
465	>	<<" does not belong to Rigid body "<< getGlobalIndex() << std::endl;
466	>	return false;
467		}
316	–	refCoords[i] = apos;
468		}
469	+	bool RigidBody::getAtomVel(Vector3d& vel, unsigned int index) {
470
471	<	// Moment of Inertia calculation
471	>	//velRot = $(A\cdot skew(I^{-1}j))^{T}refCoor$
472
473	<	for (i = 0; i < 3; i++)
322	<	for (j = 0; j < 3; j++)
323	<	Itmp[i][j] = 0.0;
324	<
325	<	for (it = 0; it < myAtoms.size(); it++) {
473	>	if (index < atoms_.size()) {
474
475	<	mtmp = myAtoms[it]->getMass();
476	<	ptmp = refCoords[it];
477	<	r= norm3(ptmp.vec);
478	<	r2 = r*r;
479	<
332	<	for (i = 0; i < 3; i++) {
333	<	for (j = 0; j < 3; j++) {
334	<
335	<	if (i==j) Itmp[i][j] += mtmp * r2;
475	>	Vector3d velRot;
476	>	Mat3x3d skewMat;;
477	>	Vector3d ref = refCoords_[index];
478	>	Vector3d ji = getJ();
479	>	Mat3x3d I =  getI();
480
481	<	Itmp[i][j] -= mtmp * ptmp.vec[i]*ptmp.vec[j];
482	<	}
483	<	}
340	<	}
341	<
342	<	diagonalize3x3(Itmp, evals, sU);
343	<
344	<	// zero out I and then fill the diagonals with the moments of inertia:
481	>	skewMat(0, 0) =0;
482	>	skewMat(0, 1) = ji[2] /I(2, 2);
483	>	skewMat(0, 2) = -ji[1] /I(1, 1);
484
485	<	n_linear_coords = 0;
485	>	skewMat(1, 0) = -ji[2] /I(2, 2);
486	>	skewMat(1, 1) = 0;
487	>	skewMat(1, 2) = ji[0]/I(0, 0);
488
489	<	for (i = 0; i < 3; i++) {
490	<	for (j = 0; j < 3; j++) {
491	<	I[i][j] = 0.0;
351	<	}
352	<	I[i][i] = evals[i];
489	>	skewMat(2, 0) =ji[1] /I(1, 1);
490	>	skewMat(2, 1) = -ji[0]/I(0, 0);
491	>	skewMat(2, 2) = 0;
492
493	<	if (fabs(evals[i]) < momIntTol) {
355	<	is_linear = true;
356	<	n_linear_coords++;
357	<	linear_axis = i;
358	<	}
359	<	}
493	>	velRot = (getA() * skewMat).transpose() * ref;
494
495	<	if (n_linear_coords > 1) {
496	<	sprintf( painCave.errMsg,
497	<	"RigidBody error.\n"
498	<	"\tOOPSE found more than one axis in this rigid body with a vanishing \n"
499	<	"\tmoment of inertia.  This can happen in one of three ways:\n"
500	<	"\t 1) Only one atom was specified, or \n"
501	<	"\t 2) All atoms were specified at the same location, or\n"
368	<	"\t 3) The programmers did something stupid.\n"
369	<	"\tIt is silly to use a rigid body to describe this situation.  Be smarter.\n"
370	<	);
371	<	painCave.isFatal = 1;
372	<	simError();
373	<	}
374	<
375	<	// renormalize column vectors:
376	<
377	<	for (i=0; i < 3; i++) {
378	<	len = 0.0;
379	<	for (j = 0; j < 3; j++) {
380	<	len += sU[i][j]*sU[i][j];
495	>	vel =getVel() + velRot;
496	>	return true;
497	>
498	>	} else {
499	>	std::cerr << index << " is an invalid index, current rigid body contains "
500	>	<< atoms_.size() << "atoms" << std::endl;
501	>	return false;
502		}
382	–	len = sqrt(len);
383	–	for (j = 0; j < 3; j++) {
384	–	sU[i][j] /= len;
385	–	}
503		}
387	–	}
504
505	<	void RigidBody::doEulerToRotMat(vec3 &euler, mat3x3 &myA ){
505	>	bool RigidBody::getAtomVel(Vector3d& vel, Atom* atom) {
506
507	<	double phi, theta, psi;
508	<
509	<	phi = euler[0];
510	<	theta = euler[1];
511	<	psi = euler[2];
512	<
513	<	myA[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi));
514	<	myA[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi));
515	<	myA[0][2] = sin(theta) * sin(psi);
516	<
401	<	myA[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi));
402	<	myA[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi));
403	<	myA[1][2] = sin(theta) * cos(psi);
404	<
405	<	myA[2][0] = sin(phi) * sin(theta);
406	<	myA[2][1] = -cos(phi) * sin(theta);
407	<	myA[2][2] = cos(theta);
507	>	std::vector<Atom*>::iterator i;
508	>	i = std::find(atoms_.begin(), atoms_.end(), atom);
509	>	if (i != atoms_.end()) {
510	>	return getAtomVel(vel, i - atoms_.begin());
511	>	} else {
512	>	std::cerr << "Atom " << atom->getGlobalIndex()
513	>	<<" does not belong to Rigid body "<< getGlobalIndex() << std::endl;
514	>	return false;
515	>	}
516	>	}
517
518	<	}
518	>	bool RigidBody::getAtomRefCoor(Vector3d& coor, unsigned int index) {
519	>	if (index < atoms_.size()) {
520
521	<	void RigidBody::calcForcesAndTorques() {
522	<
523	<	// Convert Atomic forces and torques to total forces and torques:
524	<	int i, j;
525	<	double apos[3];
526	<	double afrc[3];
417	<	double atrq[3];
418	<	double rpos[3];
419	<
420	<	zeroForces();
421	<
422	<	for (i = 0; i < myAtoms.size(); i++) {
423	<
424	<	myAtoms[i]->getPos(apos);
425	<	myAtoms[i]->getFrc(afrc);
426	<
427	<	for (j=0; j<3; j++) {
428	<	rpos[j] = apos[j] - pos[j];
429	<	frc[j] += afrc[j];
521	>	coor = refCoords_[index];
522	>	return true;
523	>	} else {
524	>	std::cerr << index << " is an invalid index, current rigid body contains "
525	>	<< atoms_.size() << "atoms" << std::endl;
526	>	return false;
527		}
431	–
432	–	trq[0] += rpos[1]*afrc[2] - rpos[2]*afrc[1];
433	–	trq[1] += rpos[2]*afrc[0] - rpos[0]*afrc[2];
434	–	trq[2] += rpos[0]*afrc[1] - rpos[1]*afrc[0];
528
529	<	// If the atom has a torque associated with it, then we also need to
437	<	// migrate the torques onto the center of mass:
529	>	}
530
531	<	if (myAtoms[i]->isDirectional()) {
532	<
533	<	myAtoms[i]->getTrq(atrq);
534	<
535	<	for (j=0; j<3; j++)
536	<	trq[j] += atrq[j];
531	>	bool RigidBody::getAtomRefCoor(Vector3d& coor, Atom* atom) {
532	>	std::vector<Atom*>::iterator i;
533	>	i = std::find(atoms_.begin(), atoms_.end(), atom);
534	>	if (i != atoms_.end()) {
535	>	//RigidBody class makes sure refCoords_ and atoms_ match each other
536	>	coor = refCoords_[i - atoms_.begin()];
537	>	return true;
538	>	} else {
539	>	std::cerr << "Atom " << atom->getGlobalIndex()
540	>	<<" does not belong to Rigid body "<< getGlobalIndex() << std::endl;
541	>	return false;
542		}
543	+
544		}
545
448	–	// Convert Torque to Body-fixed coordinates:
449	–	// (Actually, on second thought, don't.  Integrator does this now.)
450	–	// lab2Body(trq);
546
547	<	}
547	>	void RigidBody::addAtom(Atom* at, AtomStamp* ats) {
548
549	<	void RigidBody::updateAtoms() {
550	<	int i, j;
456	<	vec3 ref;
457	<	double apos[3];
458	<	DirectionalAtom* dAtom;
549	>	Vector3d coords;
550	>	Vector3d euler;
551
460	–	for (i = 0; i < myAtoms.size(); i++) {
461	–
462	–	ref = refCoords[i];
552
553	<	body2Lab(ref.vec);
554	<
555	<	for (j = 0; j<3; j++)
556	<	apos[j] = pos[j] + ref.vec[j];
557	<
558	<	myAtoms[i]->setPos(apos);
559	<
560	<	if (myAtoms[i]->isDirectional()) {
561	<
562	<	dAtom = (DirectionalAtom *) myAtoms[i];
474	<	dAtom->rotateBy( A );
475	<
553	>	atoms_.push_back(at);
554	>
555	>	if( !ats->havePosition() ){
556	>	sprintf( painCave.errMsg,
557	>	"RigidBody error.\n"
558	>	"\tAtom %s does not have a position specified.\n"
559	>	"\tThis means RigidBody cannot set up reference coordinates.\n",
560	>	ats->getType().c_str() );
561	>	painCave.isFatal = 1;
562	>	simError();
563		}
477	–	}
478	–	}
479	–
480	–	void RigidBody::getGrad( double grad[6] ) {
481	–
482	–	double myEuler[3];
483	–	double phi, theta, psi;
484	–	double cphi, sphi, ctheta, stheta;
485	–	double ephi[3];
486	–	double etheta[3];
487	–	double epsi[3];
564
565	<	this->getEulerAngles(myEuler);
565	>	coords[0] = ats->getPosX();
566	>	coords[1] = ats->getPosY();
567	>	coords[2] = ats->getPosZ();
568
569	<	phi = myEuler[0];
492	<	theta = myEuler[1];
493	<	psi = myEuler[2];
569	>	refCoords_.push_back(coords);
570
571	<	cphi = cos(phi);
496	<	sphi = sin(phi);
497	<	ctheta = cos(theta);
498	<	stheta = sin(theta);
499	<
500	<	// get unit vectors along the phi, theta and psi rotation axes
501	<
502	<	ephi[0] = 0.0;
503	<	ephi[1] = 0.0;
504	<	ephi[2] = 1.0;
505	<
506	<	etheta[0] = cphi;
507	<	etheta[1] = sphi;
508	<	etheta[2] = 0.0;
571	>	RotMat3x3d identMat = RotMat3x3d::identity();
572
573	<	epsi[0] = stheta * cphi;
511	<	epsi[1] = stheta * sphi;
512	<	epsi[2] = ctheta;
513	<
514	<	for (int j = 0 ; j<3; j++)
515	<	grad[j] = frc[j];
573	>	if (at->isDirectional()) {
574
575	<	grad[3] = 0.0;
576	<	grad[4] = 0.0;
577	<	grad[5] = 0.0;
578	<
579	<	for (int j = 0; j < 3; j++ ) {
575	>	if( !ats->haveOrientation() ){
576	>	sprintf( painCave.errMsg,
577	>	"RigidBody error.\n"
578	>	"\tAtom %s does not have an orientation specified.\n"
579	>	"\tThis means RigidBody cannot set up reference orientations.\n",
580	>	ats->getType().c_str() );
581	>	painCave.isFatal = 1;
582	>	simError();
583	>	}
584
585	<	grad[3] += trq[j]*ephi[j];
586	<	grad[4] += trq[j]*etheta[j];
587	<	grad[5] += trq[j]*epsi[j];
526	<
527	<	}
528	<
529	<	}
585	>	euler[0] = ats->getEulerPhi() * NumericConstant::PI /180.0;
586	>	euler[1] = ats->getEulerTheta() * NumericConstant::PI /180.0;
587	>	euler[2] = ats->getEulerPsi() * NumericConstant::PI /180.0;
588
589	<	/**
590	<	* getEulerAngles computes a set of Euler angle values consistent
533	<	* with an input rotation matrix.  They are returned in the following
534	<	* order:
535	<	*  myEuler[0] = phi;
536	<	*  myEuler[1] = theta;
537	<	*  myEuler[2] = psi;
538	<	*/
539	<	void RigidBody::getEulerAngles(double myEuler[3]) {
540	<
541	<	// We use so-called "x-convention", which is the most common
542	<	// definition.  In this convention, the rotation given by Euler
543	<	// angles (phi, theta, psi), where the first rotation is by an angle
544	<	// phi about the z-axis, the second is by an angle theta (0 <= theta
545	<	// <= 180) about the x-axis, and the third is by an angle psi about
546	<	// the z-axis (again).
547	<
548	<
549	<	double phi,theta,psi,eps;
550	<	double pi;
551	<	double cphi,ctheta,cpsi;
552	<	double sphi,stheta,spsi;
553	<	double b[3];
554	<	int flip[3];
555	<
556	<	// set the tolerance for Euler angles and rotation elements
557	<
558	<	eps = 1.0e-8;
559	<
560	<	theta = acos(min(1.0,max(-1.0,A[2][2])));
561	<	ctheta = A[2][2];
562	<	stheta = sqrt(1.0 - ctheta * ctheta);
563	<
564	<	// when sin(theta) is close to 0, we need to consider the
565	<	// possibility of a singularity. In this case, we can assign an
566	<	// arbitary value to phi (or psi), and then determine the psi (or
567	<	// phi) or vice-versa.  We'll assume that phi always gets the
568	<	// rotation, and psi is 0 in cases of singularity.  we use atan2
569	<	// instead of atan, since atan2 will give us -Pi to Pi.  Since 0 <=
570	<	// theta <= 180, sin(theta) will be always non-negative. Therefore,
571	<	// it never changes the sign of both of the parameters passed to
572	<	// atan2.
573	<
574	<	if (fabs(stheta) <= eps){
575	<	psi = 0.0;
576	<	phi = atan2(-A[1][0], A[0][0]);
577	<	}
578	<	// we only have one unique solution
579	<	else{
580	<	phi = atan2(A[2][0], -A[2][1]);
581	<	psi = atan2(A[0][2], A[1][2]);
582	<	}
583	<
584	<	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
585	<	//if (phi < 0)
586	<	//  phi += M_PI;
587	<
588	<	//if (psi < 0)
589	<	//  psi += M_PI;
590	<
591	<	myEuler[0] = phi;
592	<	myEuler[1] = theta;
593	<	myEuler[2] = psi;
594	<
595	<	return;
596	<	}
597	<
598	<	double RigidBody::max(double x, double  y) {
599	<	return (x > y) ? x : y;
600	<	}
601	<
602	<	double RigidBody::min(double x, double  y) {
603	<	return (x > y) ? y : x;
604	<	}
605	<
606	<	void RigidBody::findCOM() {
607	<
608	<	size_t i;
609	<	int j;
610	<	double mtmp;
611	<	double ptmp[3];
612	<	double vtmp[3];
613	<
614	<	for(j = 0; j < 3; j++) {
615	<	pos[j] = 0.0;
616	<	vel[j] = 0.0;
617	<	}
618	<	mass = 0.0;
619	<
620	<	for (i = 0; i < myAtoms.size(); i++) {
589	>	RotMat3x3d Atmp(euler);
590	>	refOrients_.push_back(Atmp);
591
592	<	mtmp = myAtoms[i]->getMass();
593	<	myAtoms[i]->getPos(ptmp);
624	<	myAtoms[i]->getVel(vtmp);
625	<
626	<	mass += mtmp;
627	<
628	<	for(j = 0; j < 3; j++) {
629	<	pos[j] += ptmp[j]*mtmp;
630	<	vel[j] += vtmp[j]*mtmp;
592	>	}else {
593	>	refOrients_.push_back(identMat);
594		}
632	–
633	–	}
595
596	<	for(j = 0; j < 3; j++) {
636	<	pos[j] /= mass;
637	<	vel[j] /= mass;
596	>
597		}
598
599		}
600
642	–	void RigidBody::accept(BaseVisitor* v){
643	–	vector<Atom*>::iterator atomIter;
644	–	v->visit(this);
645	–
646	–	//for(atomIter = myAtoms.begin(); atomIter != myAtoms.end(); ++atomIter)
647	–	//  (*atomIter)->accept(v);
648	–	}
649	–	void RigidBody::getAtomRefCoor(double pos[3], int index){
650	–	vec3 ref;
651	–
652	–	ref = refCoords[index];
653	–	pos[0] = ref[0];
654	–	pos[1] = ref[1];
655	–	pos[2] = ref[2];
656	–
657	–	}
658	–
659	–
660	–	void RigidBody::getAtomPos(double theP[3], int index){
661	–	vec3 ref;
662	–
663	–	if (index >= myAtoms.size())
664	–	cerr << index << " is an invalid index, current rigid body contains " << myAtoms.size() << "atoms" << endl;
665	–
666	–	ref = refCoords[index];
667	–	body2Lab(ref.vec);
668	–
669	–	theP[0] = pos[0] + ref[0];
670	–	theP[1] = pos[1] + ref[1];
671	–	theP[2] = pos[2] + ref[2];
672	–	}
673	–
674	–
675	–	void RigidBody::getAtomVel(double theV[3], int index){
676	–	vec3 ref;
677	–	double velRot[3];
678	–	double skewMat[3][3];
679	–	double aSkewMat[3][3];
680	–	double aSkewTransMat[3][3];
681	–
682	–	//velRot = $(A\cdot skew(I^{-1}j))^{T}refCoor$
683	–
684	–	if (index >= myAtoms.size())
685	–	cerr << index << " is an invalid index, current rigid body contains " << myAtoms.size() << "atoms" << endl;
686	–
687	–	ref = refCoords[index];
688	–
689	–	skewMat[0][0] =0;
690	–	skewMat[0][1] = ji[2] /I[2][2];
691	–	skewMat[0][2] = -ji[1] /I[1][1];
692	–
693	–	skewMat[1][0] = -ji[2] /I[2][2];
694	–	skewMat[1][1] = 0;
695	–	skewMat[1][2] = ji[0]/I[0][0];
696	–
697	–	skewMat[2][0] =ji[1] /I[1][1];
698	–	skewMat[2][1] = -ji[0]/I[0][0];
699	–	skewMat[2][2] = 0;
700	–
701	–	matMul3(A, skewMat, aSkewMat);
702	–
703	–	transposeMat3(aSkewMat, aSkewTransMat);
704	–
705	–	matVecMul3(aSkewTransMat, ref.vec, velRot);
706	–	theV[0] = vel[0] + velRot[0];
707	–	theV[1] = vel[1] + velRot[1];
708	–	theV[2] = vel[2] + velRot[2];
709	–	}
710	–
711	–

Comparing:
trunk/src/primitives/RigidBody.cpp (property svn:keywords), Revision 2 by gezelter, Fri Sep 24 04:16:43 2004 UTC vs.
branches/development/src/primitives/RigidBody.cpp (property svn:keywords), Revision 1842 by gezelter, Tue Jan 29 19:10:04 2013 UTC

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