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gezelter |
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#include <math.h> |
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#include "RigidBody.hpp" |
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#include "VDWAtom.hpp" |
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#include "MatVec3.h" |
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RigidBody::RigidBody() { |
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is_linear = false; |
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linear_axis = -1; |
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momIntTol = 1e-6; |
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} |
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RigidBody::~RigidBody() { |
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} |
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void RigidBody::addAtom(VDWAtom* at) { |
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vec3 coords; |
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myAtoms.push_back(at); |
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at->getPos(coords.vec); |
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refCoords.push_back(coords); |
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} |
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void RigidBody::getPos(double theP[3]){ |
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for (int i = 0; i < 3 ; i++) |
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theP[i] = pos[i]; |
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} |
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void RigidBody::setPos(double theP[3]){ |
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for (int i = 0; i < 3 ; i++) |
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pos[i] = theP[i]; |
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} |
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void RigidBody::setEuler( double phi, double theta, double psi ){ |
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A[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
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A[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
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A[0][2] = sin(theta) * sin(psi); |
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A[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
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A[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
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A[1][2] = sin(theta) * cos(psi); |
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A[2][0] = sin(phi) * sin(theta); |
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A[2][1] = -cos(phi) * sin(theta); |
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A[2][2] = cos(theta); |
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} |
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void RigidBody::getQ( double q[4] ){ |
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double t, s; |
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double ad1, ad2, ad3; |
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t = A[0][0] + A[1][1] + A[2][2] + 1.0; |
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if( t > 0.0 ){ |
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s = 0.5 / sqrt( t ); |
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q[0] = 0.25 / s; |
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q[1] = (A[1][2] - A[2][1]) * s; |
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q[2] = (A[2][0] - A[0][2]) * s; |
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q[3] = (A[0][1] - A[1][0]) * s; |
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} |
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else{ |
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ad1 = fabs( A[0][0] ); |
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ad2 = fabs( A[1][1] ); |
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ad3 = fabs( A[2][2] ); |
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if( ad1 >= ad2 && ad1 >= ad3 ){ |
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s = 2.0 * sqrt( 1.0 + A[0][0] - A[1][1] - A[2][2] ); |
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q[0] = (A[1][2] + A[2][1]) / s; |
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q[1] = 0.5 / s; |
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q[2] = (A[0][1] + A[1][0]) / s; |
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q[3] = (A[0][2] + A[2][0]) / s; |
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} |
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else if( ad2 >= ad1 && ad2 >= ad3 ){ |
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s = sqrt( 1.0 + A[1][1] - A[0][0] - A[2][2] ) * 2.0; |
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q[0] = (A[0][2] + A[2][0]) / s; |
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q[1] = (A[0][1] + A[1][0]) / s; |
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q[2] = 0.5 / s; |
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q[3] = (A[1][2] + A[2][1]) / s; |
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} |
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else{ |
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s = sqrt( 1.0 + A[2][2] - A[0][0] - A[1][1] ) * 2.0; |
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q[0] = (A[0][1] + A[1][0]) / s; |
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q[1] = (A[0][2] + A[2][0]) / s; |
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q[2] = (A[1][2] + A[2][1]) / s; |
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q[3] = 0.5 / s; |
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} |
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} |
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} |
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void RigidBody::setQ( double the_q[4] ){ |
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double q0Sqr, q1Sqr, q2Sqr, q3Sqr; |
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q0Sqr = the_q[0] * the_q[0]; |
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q1Sqr = the_q[1] * the_q[1]; |
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q2Sqr = the_q[2] * the_q[2]; |
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q3Sqr = the_q[3] * the_q[3]; |
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A[0][0] = q0Sqr + q1Sqr - q2Sqr - q3Sqr; |
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A[0][1] = 2.0 * ( the_q[1] * the_q[2] + the_q[0] * the_q[3] ); |
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A[0][2] = 2.0 * ( the_q[1] * the_q[3] - the_q[0] * the_q[2] ); |
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A[1][0] = 2.0 * ( the_q[1] * the_q[2] - the_q[0] * the_q[3] ); |
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A[1][1] = q0Sqr - q1Sqr + q2Sqr - q3Sqr; |
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A[1][2] = 2.0 * ( the_q[2] * the_q[3] + the_q[0] * the_q[1] ); |
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A[2][0] = 2.0 * ( the_q[1] * the_q[3] + the_q[0] * the_q[2] ); |
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A[2][1] = 2.0 * ( the_q[2] * the_q[3] - the_q[0] * the_q[1] ); |
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A[2][2] = q0Sqr - q1Sqr -q2Sqr +q3Sqr; |
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} |
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void RigidBody::getA( double the_A[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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the_A[i][j] = A[i][j]; |
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} |
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void RigidBody::setA( double the_A[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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A[i][j] = the_A[i][j]; |
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} |
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void RigidBody::getI( double the_I[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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the_I[i][j] = I[i][j]; |
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} |
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void RigidBody::lab2Body( double r[3] ){ |
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double rl[3]; // the lab frame vector |
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rl[0] = r[0]; |
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rl[1] = r[1]; |
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rl[2] = r[2]; |
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r[0] = (A[0][0] * rl[0]) + (A[0][1] * rl[1]) + (A[0][2] * rl[2]); |
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r[1] = (A[1][0] * rl[0]) + (A[1][1] * rl[1]) + (A[1][2] * rl[2]); |
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r[2] = (A[2][0] * rl[0]) + (A[2][1] * rl[1]) + (A[2][2] * rl[2]); |
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} |
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void RigidBody::body2Lab( double r[3] ){ |
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double rb[3]; // the body frame vector |
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rb[0] = r[0]; |
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rb[1] = r[1]; |
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rb[2] = r[2]; |
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r[0] = (A[0][0] * rb[0]) + (A[1][0] * rb[1]) + (A[2][0] * rb[2]); |
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r[1] = (A[0][1] * rb[0]) + (A[1][1] * rb[1]) + (A[2][1] * rb[2]); |
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r[2] = (A[0][2] * rb[0]) + (A[1][2] * rb[1]) + (A[2][2] * rb[2]); |
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} |
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void RigidBody::calcRefCoords( ) { |
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chrisfen |
1279 |
int i, j, it, n_linear_coords, pAxis, maxAxis, midAxis; |
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gezelter |
1271 |
double mtmp; |
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vec3 apos; |
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double refCOM[3]; |
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vec3 ptmp; |
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double Itmp[3][3]; |
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chrisfen |
1279 |
double pAxisMat[3][3], pAxisRotMat[3][3]; |
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gezelter |
1271 |
double evals[3]; |
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chrisfen |
1279 |
double prePos[3], rotPos[3]; |
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gezelter |
1271 |
double r, r2, len; |
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chrisfen |
1279 |
double iMat[3][3]; |
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gezelter |
1271 |
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// First, find the center of mass: |
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mass = 0.0; |
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for (j=0; j<3; j++) |
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refCOM[j] = 0.0; |
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for (i = 0; i < myAtoms.size(); i++) { |
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mtmp = myAtoms[i]->getMass(); |
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mass += mtmp; |
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apos = refCoords[i]; |
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for(j = 0; j < 3; j++) { |
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refCOM[j] += apos[j]*mtmp; |
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} |
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} |
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for(j = 0; j < 3; j++) |
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refCOM[j] /= mass; |
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// Next, move the origin of the reference coordinate system to the COM: |
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for (i = 0; i < myAtoms.size(); i++) { |
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apos = refCoords[i]; |
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for (j=0; j < 3; j++) { |
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apos[j] = apos[j] - refCOM[j]; |
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} |
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refCoords[i] = apos; |
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} |
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// Moment of Inertia calculation |
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for (i = 0; i < 3; i++) |
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for (j = 0; j < 3; j++) |
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Itmp[i][j] = 0.0; |
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for (it = 0; it < myAtoms.size(); it++) { |
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mtmp = myAtoms[it]->getMass(); |
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ptmp = refCoords[it]; |
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r= norm3(ptmp.vec); |
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r2 = r*r; |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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if (i==j) Itmp[i][j] += mtmp * r2; |
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Itmp[i][j] -= mtmp * ptmp.vec[i]*ptmp.vec[j]; |
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} |
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} |
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} |
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diagonalize3x3(Itmp, evals, sU); |
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// zero out I and then fill the diagonals with the moments of inertia: |
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n_linear_coords = 0; |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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I[i][j] = 0.0; |
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} |
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I[i][i] = evals[i]; |
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if (fabs(evals[i]) < momIntTol) { |
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is_linear = true; |
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n_linear_coords++; |
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linear_axis = i; |
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} |
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} |
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if (n_linear_coords > 1) { |
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printf( |
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"RigidBody error.\n" |
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"\tOOPSE found more than one axis in this rigid body with a vanishing \n" |
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"\tmoment of inertia. This can happen in one of three ways:\n" |
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"\t 1) Only one atom was specified, or \n" |
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"\t 2) All atoms were specified at the same location, or\n" |
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"\t 3) The programmers did something stupid.\n" |
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"\tIt is silly to use a rigid body to describe this situation. Be smarter.\n" |
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); |
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exit(-1); |
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} |
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chrisfen |
1279 |
//sort and reorder the moment axes |
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if (evals[0] < evals[1] && evals[0] < evals[2]) |
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pAxis = 0; |
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else if (evals[1] < evals[2]) |
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pAxis = 1; |
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else |
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pAxis = 2; |
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| 281 |
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if (evals[0] > evals[1] && evals[0] > evals[2]) |
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maxAxis = 0; |
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else if (evals[1] > evals[2]) |
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maxAxis = 1; |
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else |
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maxAxis = 2; |
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midAxis = 0; |
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if (midAxis == pAxis || midAxis == pAxis) |
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midAxis = 1; |
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if (midAxis == pAxis || midAxis == pAxis) |
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midAxis = 2; |
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if (pAxis != maxAxis){ |
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//zero out our matrices |
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for (i=0; i<3; i++){ |
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for (j=0; j<3; j++) { |
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pAxisMat[i][j] = 0.0; |
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pAxisRotMat[i][j] = 0.0; |
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} |
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} |
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//let z be the smallest and x be the largest eigenvalue axes |
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for (i=0; i<3; i++){ |
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pAxisMat[i][2] = I[i][pAxis]; |
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pAxisMat[i][1] = I[i][midAxis]; |
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pAxisMat[i][0] = I[i][maxAxis]; |
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} |
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//calculate the proper rotation matrix |
| 311 |
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transposeMat3(pAxisMat, pAxisRotMat); |
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//rotate the rigid body to the principle axis frame |
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for (i = 0; i < myAtoms.size(); i++) { |
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apos = refCoords[i]; |
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for (j=0; j<3; j++) |
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prePos[j] = apos[j]; |
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matVecMul3(pAxisRotMat, prePos, rotPos); |
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for (j=0; j < 3; j++) |
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apos[j] = rotPos[j]; |
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refCoords[i] = apos; |
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} |
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//the lab and the body frame match up at this point, so A = Identity Matrix |
| 328 |
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for (i=0; i<3; i++){ |
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for (j=0; j<3; j++){ |
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if (i == j) |
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iMat[i][j] = 1.0; |
| 332 |
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else |
| 333 |
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iMat[i][j] = 0.0; |
| 334 |
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} |
| 335 |
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} |
| 336 |
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setA(iMat); |
| 337 |
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} |
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| 339 |
gezelter |
1271 |
// renormalize column vectors: |
| 340 |
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| 341 |
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for (i=0; i < 3; i++) { |
| 342 |
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len = 0.0; |
| 343 |
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for (j = 0; j < 3; j++) { |
| 344 |
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len += sU[i][j]*sU[i][j]; |
| 345 |
|
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} |
| 346 |
|
|
len = sqrt(len); |
| 347 |
|
|
for (j = 0; j < 3; j++) { |
| 348 |
|
|
sU[i][j] /= len; |
| 349 |
|
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} |
| 350 |
|
|
} |
| 351 |
|
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} |
| 352 |
|
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|
| 353 |
chrisfen |
1276 |
void RigidBody::doEulerToRotMat(double euler[3], double myA[3][3] ){ |
| 354 |
gezelter |
1271 |
|
| 355 |
|
|
double phi, theta, psi; |
| 356 |
|
|
|
| 357 |
|
|
phi = euler[0]; |
| 358 |
|
|
theta = euler[1]; |
| 359 |
|
|
psi = euler[2]; |
| 360 |
|
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|
| 361 |
|
|
myA[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
| 362 |
|
|
myA[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
| 363 |
|
|
myA[0][2] = sin(theta) * sin(psi); |
| 364 |
|
|
|
| 365 |
|
|
myA[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
| 366 |
|
|
myA[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
| 367 |
|
|
myA[1][2] = sin(theta) * cos(psi); |
| 368 |
|
|
|
| 369 |
|
|
myA[2][0] = sin(phi) * sin(theta); |
| 370 |
|
|
myA[2][1] = -cos(phi) * sin(theta); |
| 371 |
|
|
myA[2][2] = cos(theta); |
| 372 |
|
|
|
| 373 |
|
|
} |
| 374 |
|
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|
| 375 |
|
|
void RigidBody::updateAtoms() { |
| 376 |
|
|
int i, j; |
| 377 |
|
|
vec3 ref; |
| 378 |
|
|
double apos[3]; |
| 379 |
|
|
|
| 380 |
|
|
for (i = 0; i < myAtoms.size(); i++) { |
| 381 |
|
|
|
| 382 |
|
|
ref = refCoords[i]; |
| 383 |
|
|
|
| 384 |
|
|
body2Lab(ref.vec); |
| 385 |
|
|
|
| 386 |
|
|
for (j = 0; j<3; j++) |
| 387 |
|
|
apos[j] = pos[j] + ref.vec[j]; |
| 388 |
|
|
|
| 389 |
|
|
myAtoms[i]->setPos(apos); |
| 390 |
|
|
|
| 391 |
|
|
} |
| 392 |
|
|
} |
| 393 |
|
|
|
| 394 |
|
|
/** |
| 395 |
|
|
* getEulerAngles computes a set of Euler angle values consistent |
| 396 |
|
|
* with an input rotation matrix. They are returned in the following |
| 397 |
|
|
* order: |
| 398 |
|
|
* myEuler[0] = phi; |
| 399 |
|
|
* myEuler[1] = theta; |
| 400 |
|
|
* myEuler[2] = psi; |
| 401 |
|
|
*/ |
| 402 |
|
|
void RigidBody::getEulerAngles(double myEuler[3]) { |
| 403 |
|
|
|
| 404 |
|
|
// We use so-called "x-convention", which is the most common |
| 405 |
|
|
// definition. In this convention, the rotation given by Euler |
| 406 |
|
|
// angles (phi, theta, psi), where the first rotation is by an angle |
| 407 |
|
|
// phi about the z-axis, the second is by an angle theta (0 <= theta |
| 408 |
|
|
// <= 180) about the x-axis, and the third is by an angle psi about |
| 409 |
|
|
// the z-axis (again). |
| 410 |
|
|
|
| 411 |
|
|
|
| 412 |
|
|
double phi,theta,psi,eps; |
| 413 |
chrisfen |
1276 |
double ctheta; |
| 414 |
|
|
double stheta; |
| 415 |
|
|
|
| 416 |
gezelter |
1271 |
// set the tolerance for Euler angles and rotation elements |
| 417 |
|
|
|
| 418 |
|
|
eps = 1.0e-8; |
| 419 |
|
|
|
| 420 |
|
|
theta = acos(min(1.0,max(-1.0,A[2][2]))); |
| 421 |
|
|
ctheta = A[2][2]; |
| 422 |
|
|
stheta = sqrt(1.0 - ctheta * ctheta); |
| 423 |
|
|
|
| 424 |
|
|
// when sin(theta) is close to 0, we need to consider the |
| 425 |
|
|
// possibility of a singularity. In this case, we can assign an |
| 426 |
|
|
// arbitary value to phi (or psi), and then determine the psi (or |
| 427 |
|
|
// phi) or vice-versa. We'll assume that phi always gets the |
| 428 |
|
|
// rotation, and psi is 0 in cases of singularity. we use atan2 |
| 429 |
|
|
// instead of atan, since atan2 will give us -Pi to Pi. Since 0 <= |
| 430 |
|
|
// theta <= 180, sin(theta) will be always non-negative. Therefore, |
| 431 |
|
|
// it never changes the sign of both of the parameters passed to |
| 432 |
|
|
// atan2. |
| 433 |
|
|
|
| 434 |
|
|
if (fabs(stheta) <= eps){ |
| 435 |
|
|
psi = 0.0; |
| 436 |
|
|
phi = atan2(-A[1][0], A[0][0]); |
| 437 |
|
|
} |
| 438 |
|
|
// we only have one unique solution |
| 439 |
|
|
else{ |
| 440 |
|
|
phi = atan2(A[2][0], -A[2][1]); |
| 441 |
|
|
psi = atan2(A[0][2], A[1][2]); |
| 442 |
|
|
} |
| 443 |
|
|
|
| 444 |
|
|
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
| 445 |
|
|
//if (phi < 0) |
| 446 |
|
|
// phi += M_PI; |
| 447 |
|
|
|
| 448 |
|
|
//if (psi < 0) |
| 449 |
|
|
// psi += M_PI; |
| 450 |
|
|
|
| 451 |
|
|
myEuler[0] = phi; |
| 452 |
|
|
myEuler[1] = theta; |
| 453 |
|
|
myEuler[2] = psi; |
| 454 |
|
|
|
| 455 |
|
|
return; |
| 456 |
|
|
} |
| 457 |
|
|
|
| 458 |
|
|
double RigidBody::max(double x, double y) { |
| 459 |
|
|
return (x > y) ? x : y; |
| 460 |
|
|
} |
| 461 |
|
|
|
| 462 |
|
|
double RigidBody::min(double x, double y) { |
| 463 |
|
|
return (x > y) ? y : x; |
| 464 |
|
|
} |
| 465 |
|
|
|
| 466 |
chrisfen |
1276 |
double RigidBody::findMaxExtent(){ |
| 467 |
|
|
int i; |
| 468 |
|
|
double refAtomPos[3]; |
| 469 |
|
|
double maxExtent; |
| 470 |
|
|
double tempExtent; |
| 471 |
|
|
|
| 472 |
|
|
//zero the extent variables |
| 473 |
|
|
maxExtent = 0.0; |
| 474 |
|
|
tempExtent = 0.0; |
| 475 |
|
|
for (i=0; i<3; i++) |
| 476 |
|
|
refAtomPos[i] = 0.0; |
| 477 |
|
|
|
| 478 |
|
|
//loop over all atoms |
| 479 |
|
|
for (i=0; i<myAtoms.size(); i++){ |
| 480 |
|
|
getAtomRefCoor(refAtomPos, i); |
| 481 |
|
|
tempExtent = sqrt(refAtomPos[0]*refAtomPos[0] + refAtomPos[1]*refAtomPos[1] |
| 482 |
|
|
+ refAtomPos[2]*refAtomPos[2]); |
| 483 |
|
|
if (tempExtent > maxExtent) |
| 484 |
|
|
maxExtent = tempExtent; |
| 485 |
|
|
} |
| 486 |
|
|
return maxExtent; |
| 487 |
|
|
} |
| 488 |
|
|
|
| 489 |
gezelter |
1271 |
void RigidBody::findCOM() { |
| 490 |
|
|
|
| 491 |
|
|
size_t i; |
| 492 |
|
|
int j; |
| 493 |
|
|
double mtmp; |
| 494 |
|
|
double ptmp[3]; |
| 495 |
chrisfen |
1276 |
|
| 496 |
gezelter |
1271 |
for(j = 0; j < 3; j++) { |
| 497 |
|
|
pos[j] = 0.0; |
| 498 |
|
|
} |
| 499 |
|
|
mass = 0.0; |
| 500 |
|
|
|
| 501 |
|
|
for (i = 0; i < myAtoms.size(); i++) { |
| 502 |
|
|
|
| 503 |
|
|
mtmp = myAtoms[i]->getMass(); |
| 504 |
|
|
myAtoms[i]->getPos(ptmp); |
| 505 |
|
|
|
| 506 |
|
|
mass += mtmp; |
| 507 |
|
|
|
| 508 |
|
|
for(j = 0; j < 3; j++) { |
| 509 |
|
|
pos[j] += ptmp[j]*mtmp; |
| 510 |
|
|
} |
| 511 |
|
|
|
| 512 |
|
|
} |
| 513 |
|
|
|
| 514 |
|
|
for(j = 0; j < 3; j++) { |
| 515 |
|
|
pos[j] /= mass; |
| 516 |
|
|
} |
| 517 |
|
|
|
| 518 |
|
|
} |
| 519 |
|
|
|
| 520 |
|
|
void RigidBody::getAtomPos(double theP[3], int index){ |
| 521 |
|
|
vec3 ref; |
| 522 |
|
|
|
| 523 |
|
|
if (index >= myAtoms.size()) |
| 524 |
|
|
printf( "%d is an invalid index, current rigid body contains " |
| 525 |
|
|
"%d atoms\n", index, myAtoms.size()); |
| 526 |
|
|
|
| 527 |
|
|
ref = refCoords[index]; |
| 528 |
|
|
body2Lab(ref.vec); |
| 529 |
|
|
|
| 530 |
|
|
theP[0] = pos[0] + ref[0]; |
| 531 |
|
|
theP[1] = pos[1] + ref[1]; |
| 532 |
|
|
theP[2] = pos[2] + ref[2]; |
| 533 |
|
|
} |
| 534 |
|
|
|
| 535 |
|
|
|
| 536 |
|
|
void RigidBody::getAtomRefCoor(double pos[3], int index){ |
| 537 |
|
|
vec3 ref; |
| 538 |
|
|
|
| 539 |
|
|
ref = refCoords[index]; |
| 540 |
|
|
pos[0] = ref[0]; |
| 541 |
|
|
pos[1] = ref[1]; |
| 542 |
|
|
pos[2] = ref[2]; |
| 543 |
|
|
|
| 544 |
|
|
} |
