forked from lijiext/lammps
git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@5975 f3b2605a-c512-4ea7-a41b-209d697bcdaa
This commit is contained in:
sjplimp
parent
fb1e5c2389
commit
59495dcf54
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@ -150,7 +150,7 @@ void FixNVEAsphere::richardson(double *q, double *m, double *moments)
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// compute omega at 1/2 step from m at 1/2 step and q at 0
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double w[3];
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omega_from_mq(q,m,moments,w);
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omega_from_mq(m,q,moments,w);
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// full update from dq/dt = 1/2 w q
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@ -176,7 +176,7 @@ void FixNVEAsphere::richardson(double *q, double *m, double *moments)
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// re-compute omega at 1/2 step from m at 1/2 step and q at 1/2 step
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// recompute wq
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omega_from_mq(qhalf,m,moments,w);
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omega_from_mq(m,qhalf,moments,w);
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MathExtra::vecquat(w,qhalf,wq);
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// 2nd half of update from dq/dt = 1/2 w q
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@ -204,7 +204,7 @@ void FixNVEAsphere::richardson(double *q, double *m, double *moments)
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and divide by principal moments
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------------------------------------------------------------------------- */
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void FixNVEAsphere::omega_from_mq(double *q, double *m, double *moments,
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void FixNVEAsphere::omega_from_mq(double *m, double *q, double *moments,
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double *w)
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{
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double rot[3][3];
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@ -589,7 +589,6 @@ void FixRigid::init()
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pre_neighbor();
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// compute 6 moments of inertia of each body
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// stored as 6-vector in Voigt ordering
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// dx,dy,dz = coords relative to center-of-mass
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double dx,dy,dz,rad;
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@ -633,7 +632,8 @@ void FixRigid::init()
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// extended particles may contribute extra terms to moments of inertia
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if (extended) {
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double ivec[6];
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double ex[3],ey[3],ez[3],idiag[3];
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double p[3][3],ptrans[3][3],ispace[3][3],itemp[3][3];
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double *shape,*quatatom;
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for (i = 0; i < nlocal; i++) {
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@ -652,13 +652,19 @@ void FixRigid::init()
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if (eflags[i] & INERTIA_ELLIPSOID) {
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shape = ebonus[ellipsoid[i]].shape;
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quatatom = ebonus[ellipsoid[i]].quat;
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MathExtra::inertia_ellipsoid(shape,quatatom,massone,ivec);
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sum[ibody][0] += ivec[0];
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sum[ibody][1] += ivec[1];
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sum[ibody][2] += ivec[2];
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sum[ibody][3] += ivec[3];
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sum[ibody][4] += ivec[4];
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sum[ibody][5] += ivec[5];
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MathExtra::quat_to_mat(quatatom,p);
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MathExtra::quat_to_mat_trans(quatatom,ptrans);
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idiag[0] = 0.2*massone * (shape[1]*shape[1]+shape[2]*shape[2]);
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idiag[1] = 0.2*massone * (shape[0]*shape[0]+shape[2]*shape[2]);
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idiag[2] = 0.2*massone * (shape[0]*shape[0]+shape[1]*shape[1]);
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MathExtra::diag_times3(idiag,ptrans,itemp);
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MathExtra::times3(p,itemp,ispace);
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sum[ibody][0] += ispace[0][0];
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sum[ibody][1] += ispace[1][1];
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sum[ibody][2] += ispace[2][2];
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sum[ibody][3] += ispace[0][1];
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sum[ibody][4] += ispace[1][2];
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sum[ibody][5] += ispace[0][2];
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}
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}
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}
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@ -669,8 +675,9 @@ void FixRigid::init()
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// ex_space,ey_space,ez_space = 3 eigenvectors = principal axes of rigid body
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double tensor[3][3],evectors[3][3];
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double ez0,ez1,ez2;
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int ierror;
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double ez0,ez1,ez2;
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for (ibody = 0; ibody < nbody; ibody++) {
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tensor[0][0] = all[ibody][0];
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@ -792,11 +799,10 @@ void FixRigid::init()
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// test for valid principal moments & axes
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// recompute moments of inertia around new axes
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// stored as 6-vector in Voigt ordering
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// 3 diagonal moments should equal principal moments
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// 3 off-diagonal moments should be 0.0
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// extended particles may contribute extra terms to moments of inertia
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for (ibody = 0; ibody < nbody; ibody++)
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for (i = 0; i < 6; i++) sum[ibody][i] = 0.0;
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@ -818,7 +824,8 @@ void FixRigid::init()
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}
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if (extended) {
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double ivec[6];
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double ex[3],ey[3],ez[3],idiag[3];
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double p[3][3],ptrans[3][3],ispace[3][3],itemp[3][3];
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double *shape;
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for (i = 0; i < nlocal; i++) {
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@ -836,13 +843,19 @@ void FixRigid::init()
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}
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if (eflags[i] & INERTIA_ELLIPSOID) {
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shape = ebonus[ellipsoid[i]].shape;
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MathExtra::inertia_ellipsoid(shape,qorient[i],massone,ivec);
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sum[ibody][0] += ivec[0];
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sum[ibody][1] += ivec[1];
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sum[ibody][2] += ivec[2];
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sum[ibody][3] += ivec[3];
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sum[ibody][4] += ivec[4];
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sum[ibody][5] += ivec[5];
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MathExtra::quat_to_mat(qorient[i],p);
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MathExtra::quat_to_mat_trans(qorient[i],ptrans);
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idiag[0] = 0.2*massone * (shape[1]*shape[1]+shape[2]*shape[2]);
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idiag[1] = 0.2*massone * (shape[0]*shape[0]+shape[2]*shape[2]);
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idiag[2] = 0.2*massone * (shape[0]*shape[0]+shape[1]*shape[1]);
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MathExtra::diag_times3(idiag,ptrans,itemp);
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MathExtra::times3(p,itemp,ispace);
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sum[ibody][0] += ispace[0][0];
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sum[ibody][1] += ispace[1][1];
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sum[ibody][2] += ispace[2][2];
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sum[ibody][3] += ispace[0][1];
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sum[ibody][4] += ispace[1][2];
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sum[ibody][5] += ispace[0][2];
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}
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}
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}
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@ -1220,6 +1233,7 @@ void FixRigid::richardson(double *q, double *w,
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qfull[1] = q[1] + dtq * wq[1];
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qfull[2] = q[2] + dtq * wq[2];
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qfull[3] = q[3] + dtq * wq[3];
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MathExtra::qnormalize(qfull);
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// 1st half update from dq/dt = 1/2 w q
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@ -1229,6 +1243,7 @@ void FixRigid::richardson(double *q, double *w,
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qhalf[1] = q[1] + 0.5*dtq * wq[1];
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qhalf[2] = q[2] + 0.5*dtq * wq[2];
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qhalf[3] = q[3] + 0.5*dtq * wq[3];
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MathExtra::qnormalize(qhalf);
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// udpate ex,ey,ez from qhalf
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@ -1245,6 +1260,7 @@ void FixRigid::richardson(double *q, double *w,
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qhalf[1] += 0.5*dtq * wq[1];
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qhalf[2] += 0.5*dtq * wq[2];
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qhalf[3] += 0.5*dtq * wq[3];
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MathExtra::qnormalize(qhalf);
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// corrected Richardson update
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@ -1253,8 +1269,8 @@ void FixRigid::richardson(double *q, double *w,
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q[1] = 2.0*qhalf[1] - qfull[1];
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q[2] = 2.0*qhalf[2] - qfull[2];
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q[3] = 2.0*qhalf[3] - qfull[3];
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MathExtra::qnormalize(q);
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MathExtra::qnormalize(q);
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MathExtra::q_to_exyz(q,ex,ey,ez);
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}
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@ -0,0 +1,436 @@
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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http://lammps.sandia.gov, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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/* ----------------------------------------------------------------------
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Contributing author: Mike Brown (SNL)
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------------------------------------------------------------------------- */
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#include "stdio.h"
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#include "string.h"
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#include "math_extra.h"
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#define MAXJACOBI 50
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namespace MathExtra {
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/* ----------------------------------------------------------------------
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output a matrix
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------------------------------------------------------------------------- */
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void MathExtra::write3(const double mat[3][3])
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{
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for (unsigned i = 0; i < 3; i++) {
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for (unsigned j = 0; j < 3; j++) printf("%g ",mat[i][j]);
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printf("\n");
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}
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}
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/* ----------------------------------------------------------------------
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solve Ax = b or M ans = v
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use gaussian elimination & partial pivoting on matrix
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------------------------------------------------------------------------- */
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int MathExtra::mldivide3(const double m[3][3], const double *v, double *ans)
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{
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// create augmented matrix for pivoting
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double aug[3][4];
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for (unsigned i = 0; i < 3; i++) {
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aug[i][3] = v[i];
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for (unsigned j = 0; j < 3; j++) aug[i][j] = m[i][j];
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}
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for (unsigned i = 0; i < 2; i++) {
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unsigned p = i;
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for (unsigned j = i+1; j < 3; j++) {
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if (fabs(aug[j][i]) > fabs(aug[i][i])) {
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double tempv[4];
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memcpy(tempv,aug[i],4*sizeof(double));
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memcpy(aug[i],aug[j],4*sizeof(double));
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memcpy(aug[j],tempv,4*sizeof(double));
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}
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}
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while (aug[p][i] == 0.0 && p < 3) p++;
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if (p == 3) return 1;
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else
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if (p != i) {
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double tempv[4];
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memcpy(tempv,aug[i],4*sizeof(double));
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memcpy(aug[i],aug[p],4*sizeof(double));
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memcpy(aug[p],tempv,4*sizeof(double));
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}
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for (unsigned j = i+1; j < 3; j++) {
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double m = aug[j][i]/aug[i][i];
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for (unsigned k=i+1; k<4; k++) aug[j][k]-=m*aug[i][k];
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}
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}
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if (aug[2][2] == 0.0) return 1;
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// back substitution
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ans[2] = aug[2][3]/aug[2][2];
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for (int i = 1; i >= 0; i--) {
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double sumax = 0.0;
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for (unsigned j = i+1; j < 3; j++) sumax += aug[i][j]*ans[j];
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ans[i] = (aug[i][3]-sumax) / aug[i][i];
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}
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return 0;
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}
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/* ----------------------------------------------------------------------
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compute evalues and evectors of 3x3 real symmetric matrix
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based on Jacobi rotations
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adapted from Numerical Recipes jacobi() function
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------------------------------------------------------------------------- */
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int MathExtra::jacobi(double matrix[3][3], double *evalues,
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double evectors[3][3])
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{
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int i,j,k;
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double tresh,theta,tau,t,sm,s,h,g,c,b[3],z[3];
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for (i = 0; i < 3; i++) {
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for (j = 0; j < 3; j++) evectors[i][j] = 0.0;
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evectors[i][i] = 1.0;
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}
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for (i = 0; i < 3; i++) {
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b[i] = evalues[i] = matrix[i][i];
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z[i] = 0.0;
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}
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for (int iter = 1; iter <= MAXJACOBI; iter++) {
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sm = 0.0;
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for (i = 0; i < 2; i++)
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for (j = i+1; j < 3; j++)
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sm += fabs(matrix[i][j]);
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if (sm == 0.0) return 0;
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if (iter < 4) tresh = 0.2*sm/(3*3);
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else tresh = 0.0;
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for (i = 0; i < 2; i++) {
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for (j = i+1; j < 3; j++) {
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g = 100.0*fabs(matrix[i][j]);
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if (iter > 4 && fabs(evalues[i])+g == fabs(evalues[i])
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&& fabs(evalues[j])+g == fabs(evalues[j]))
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matrix[i][j] = 0.0;
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else if (fabs(matrix[i][j]) > tresh) {
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h = evalues[j]-evalues[i];
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if (fabs(h)+g == fabs(h)) t = (matrix[i][j])/h;
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else {
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theta = 0.5*h/(matrix[i][j]);
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t = 1.0/(fabs(theta)+sqrt(1.0+theta*theta));
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if (theta < 0.0) t = -t;
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}
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c = 1.0/sqrt(1.0+t*t);
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s = t*c;
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tau = s/(1.0+c);
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h = t*matrix[i][j];
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z[i] -= h;
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z[j] += h;
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evalues[i] -= h;
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evalues[j] += h;
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matrix[i][j] = 0.0;
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for (k = 0; k < i; k++) rotate(matrix,k,i,k,j,s,tau);
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for (k = i+1; k < j; k++) rotate(matrix,i,k,k,j,s,tau);
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for (k = j+1; k < 3; k++) rotate(matrix,i,k,j,k,s,tau);
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for (k = 0; k < 3; k++) rotate(evectors,k,i,k,j,s,tau);
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}
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}
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}
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for (i = 0; i < 3; i++) {
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evalues[i] = b[i] += z[i];
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z[i] = 0.0;
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}
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}
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return 1;
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}
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/* ----------------------------------------------------------------------
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perform a single Jacobi rotation
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------------------------------------------------------------------------- */
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void MathExtra::rotate(double matrix[3][3], int i, int j, int k, int l,
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double s, double tau)
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{
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double g = matrix[i][j];
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double h = matrix[k][l];
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matrix[i][j] = g-s*(h+g*tau);
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matrix[k][l] = h+s*(g-h*tau);
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}
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/* ----------------------------------------------------------------------
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compute rotation matrix from quaternion
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quat = [w i j k]
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------------------------------------------------------------------------- */
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void MathExtra::quat_to_mat(const double *quat, double mat[3][3])
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{
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double w2 = quat[0]*quat[0];
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double i2 = quat[1]*quat[1];
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double j2 = quat[2]*quat[2];
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double k2 = quat[3]*quat[3];
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double twoij = 2.0*quat[1]*quat[2];
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double twoik = 2.0*quat[1]*quat[3];
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double twojk = 2.0*quat[2]*quat[3];
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double twoiw = 2.0*quat[1]*quat[0];
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double twojw = 2.0*quat[2]*quat[0];
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double twokw = 2.0*quat[3]*quat[0];
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mat[0][0] = w2+i2-j2-k2;
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mat[0][1] = twoij-twokw;
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mat[0][2] = twojw+twoik;
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mat[1][0] = twoij+twokw;
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mat[1][1] = w2-i2+j2-k2;
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mat[1][2] = twojk-twoiw;
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mat[2][0] = twoik-twojw;
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mat[2][1] = twojk+twoiw;
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mat[2][2] = w2-i2-j2+k2;
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}
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/* ----------------------------------------------------------------------
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compute rotation matrix from quaternion conjugate
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quat = [w i j k]
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------------------------------------------------------------------------- */
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void MathExtra::quat_to_mat_trans(const double *quat, double mat[3][3])
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{
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double w2 = quat[0]*quat[0];
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double i2 = quat[1]*quat[1];
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double j2 = quat[2]*quat[2];
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double k2 = quat[3]*quat[3];
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double twoij = 2.0*quat[1]*quat[2];
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double twoik = 2.0*quat[1]*quat[3];
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double twojk = 2.0*quat[2]*quat[3];
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double twoiw = 2.0*quat[1]*quat[0];
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double twojw = 2.0*quat[2]*quat[0];
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double twokw = 2.0*quat[3]*quat[0];
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mat[0][0] = w2+i2-j2-k2;
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mat[1][0] = twoij-twokw;
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mat[2][0] = twojw+twoik;
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mat[0][1] = twoij+twokw;
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mat[1][1] = w2-i2+j2-k2;
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mat[2][1] = twojk-twoiw;
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mat[0][2] = twoik-twojw;
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mat[1][2] = twojk+twoiw;
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mat[2][2] = w2-i2-j2+k2;
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}
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/* ----------------------------------------------------------------------
|
||||
compute omega from angular momentum, both in space frame
|
||||
only know Idiag so need to do M = Iw in body frame
|
||||
ex,ey,ez are column vectors of rotation matrix P
|
||||
Mbody = P_transpose Mspace
|
||||
wbody = Mbody / Idiag
|
||||
wspace = P wbody
|
||||
set wbody component to 0.0 if inertia component is 0.0
|
||||
otherwise body can spin easily around that axis
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::angmom_to_omega(double *m, double *ex, double *ey, double *ez,
|
||||
double *idiag, double *w)
|
||||
{
|
||||
double wbody[3];
|
||||
|
||||
if (idiag[0] == 0.0) wbody[0] = 0.0;
|
||||
else wbody[0] = (m[0]*ex[0] + m[1]*ex[1] + m[2]*ex[2]) / idiag[0];
|
||||
if (idiag[1] == 0.0) wbody[1] = 0.0;
|
||||
else wbody[1] = (m[0]*ey[0] + m[1]*ey[1] + m[2]*ey[2]) / idiag[1];
|
||||
if (idiag[2] == 0.0) wbody[2] = 0.0;
|
||||
else wbody[2] = (m[0]*ez[0] + m[1]*ez[1] + m[2]*ez[2]) / idiag[2];
|
||||
|
||||
w[0] = wbody[0]*ex[0] + wbody[1]*ey[0] + wbody[2]*ez[0];
|
||||
w[1] = wbody[0]*ex[1] + wbody[1]*ey[1] + wbody[2]*ez[1];
|
||||
w[2] = wbody[0]*ex[2] + wbody[1]*ey[2] + wbody[2]*ez[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute angular momentum from omega, both in space frame
|
||||
only know Idiag so need to do M = Iw in body frame
|
||||
ex,ey,ez are column vectors of rotation matrix P
|
||||
wbody = P_transpose wspace
|
||||
Mbody = Idiag wbody
|
||||
Mspace = P Mbody
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::omega_to_angmom(double *w,
|
||||
double *ex, double *ey, double *ez,
|
||||
double *idiag, double *m)
|
||||
{
|
||||
double mbody[3];
|
||||
|
||||
mbody[0] = (w[0]*ex[0] + w[1]*ex[1] + w[2]*ex[2]) * idiag[0];
|
||||
mbody[1] = (w[0]*ey[0] + w[1]*ey[1] + w[2]*ey[2]) * idiag[1];
|
||||
mbody[2] = (w[0]*ez[0] + w[1]*ez[1] + w[2]*ez[2]) * idiag[2];
|
||||
|
||||
m[0] = mbody[0]*ex[0] + mbody[1]*ey[0] + mbody[2]*ez[0];
|
||||
m[1] = mbody[0]*ex[1] + mbody[1]*ey[1] + mbody[2]*ez[1];
|
||||
m[2] = mbody[0]*ex[2] + mbody[1]*ey[2] + mbody[2]*ez[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
create unit quaternion from space-frame ex,ey,ez
|
||||
ex,ey,ez are columns of a rotation matrix
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::exyz_to_q(double *ex, double *ey, double *ez, double *q)
|
||||
{
|
||||
// squares of quaternion components
|
||||
|
||||
double q0sq = 0.25 * (ex[0] + ey[1] + ez[2] + 1.0);
|
||||
double q1sq = q0sq - 0.5 * (ey[1] + ez[2]);
|
||||
double q2sq = q0sq - 0.5 * (ex[0] + ez[2]);
|
||||
double q3sq = q0sq - 0.5 * (ex[0] + ey[1]);
|
||||
|
||||
// some component must be greater than 1/4 since they sum to 1
|
||||
// compute other components from it
|
||||
|
||||
if (q0sq >= 0.25) {
|
||||
q[0] = sqrt(q0sq);
|
||||
q[1] = (ey[2] - ez[1]) / (4.0*q[0]);
|
||||
q[2] = (ez[0] - ex[2]) / (4.0*q[0]);
|
||||
q[3] = (ex[1] - ey[0]) / (4.0*q[0]);
|
||||
} else if (q1sq >= 0.25) {
|
||||
q[1] = sqrt(q1sq);
|
||||
q[0] = (ey[2] - ez[1]) / (4.0*q[1]);
|
||||
q[2] = (ey[0] + ex[1]) / (4.0*q[1]);
|
||||
q[3] = (ex[2] + ez[0]) / (4.0*q[1]);
|
||||
} else if (q2sq >= 0.25) {
|
||||
q[2] = sqrt(q2sq);
|
||||
q[0] = (ez[0] - ex[2]) / (4.0*q[2]);
|
||||
q[1] = (ey[0] + ex[1]) / (4.0*q[2]);
|
||||
q[3] = (ez[1] + ey[2]) / (4.0*q[2]);
|
||||
} else if (q3sq >= 0.25) {
|
||||
q[3] = sqrt(q3sq);
|
||||
q[0] = (ex[1] - ey[0]) / (4.0*q[3]);
|
||||
q[1] = (ez[0] + ex[2]) / (4.0*q[3]);
|
||||
q[2] = (ez[1] + ey[2]) / (4.0*q[3]);
|
||||
}
|
||||
|
||||
qnormalize(q);
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute space-frame ex,ey,ez from current quaternion q
|
||||
ex,ey,ez = space-frame coords of 1st,2nd,3rd principal axis
|
||||
operation is ex = q' d q = Q d, where d is (1,0,0) = 1st axis in body frame
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::q_to_exyz(double *q, double *ex, double *ey, double *ez)
|
||||
{
|
||||
ex[0] = q[0]*q[0] + q[1]*q[1] - q[2]*q[2] - q[3]*q[3];
|
||||
ex[1] = 2.0 * (q[1]*q[2] + q[0]*q[3]);
|
||||
ex[2] = 2.0 * (q[1]*q[3] - q[0]*q[2]);
|
||||
|
||||
ey[0] = 2.0 * (q[1]*q[2] - q[0]*q[3]);
|
||||
ey[1] = q[0]*q[0] - q[1]*q[1] + q[2]*q[2] - q[3]*q[3];
|
||||
ey[2] = 2.0 * (q[2]*q[3] + q[0]*q[1]);
|
||||
|
||||
ez[0] = 2.0 * (q[1]*q[3] + q[0]*q[2]);
|
||||
ez[1] = 2.0 * (q[2]*q[3] - q[0]*q[1]);
|
||||
ez[2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute space-frame inertia tensor of an ellipsoid
|
||||
quat = orientiation quaternion of ellipsoid
|
||||
radii = 3 radii of ellipsoid
|
||||
return symmetric inertia tensor as 6-vector in Voigt notation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::inertia_ellipsoid(double *radii, double *quat, double mass,
|
||||
double *inertia)
|
||||
{
|
||||
double p[3][3],ptrans[3][3],itemp[3][3],tensor[3][3];
|
||||
double idiag[3];
|
||||
|
||||
quat_to_mat(quat,p);
|
||||
quat_to_mat_trans(quat,ptrans);
|
||||
idiag[0] = 0.2*mass * (radii[1]*radii[1] + radii[2]*radii[2]);
|
||||
idiag[1] = 0.2*mass * (radii[0]*radii[0] + radii[2]*radii[2]);
|
||||
idiag[2] = 0.2*mass * (radii[0]*radii[0] + radii[1]*radii[1]);
|
||||
diag_times3(idiag,ptrans,itemp);
|
||||
times3(p,itemp,tensor);
|
||||
inertia[0] = tensor[0][0];
|
||||
inertia[1] = tensor[1][1];
|
||||
inertia[2] = tensor[2][2];
|
||||
inertia[3] = tensor[1][2];
|
||||
inertia[4] = tensor[0][2];
|
||||
inertia[5] = tensor[0][1];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute space-frame inertia tensor of a triangle
|
||||
v0,v1,v2 = 3 vertices of triangle
|
||||
from http://en.wikipedia.org/wiki/Inertia_tensor_of_triangle:
|
||||
inertia tensor = a/24 (v0^2 + v1^2 + v2^2 + (v0+v1+v2)^2) I - a Vt S V
|
||||
a = 2*area of tri = |(v1-v0) x (v2-v0)|
|
||||
I = 3x3 identity matrix
|
||||
V = 3x3 matrix with v0,v1,v2 as rows
|
||||
Vt = 3x3 matrix with v0,v1,v2 as columns
|
||||
S = 1/24 [2 1 1]
|
||||
[1 2 1]
|
||||
[1 1 2]
|
||||
return symmetric inertia tensor as 6-vector in Voigt notation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::inertia_triangle(double *v0, double *v1, double *v2,
|
||||
double mass, double *inertia)
|
||||
{
|
||||
double s[3][3] = {{2.0, 1.0, 1.0}, {1.0, 2.0, 1.0}, {1.0, 1.0, 2.0}};
|
||||
double v[3][3],sv[3][3],vtsv[3][3];
|
||||
double vvv[3],v1mv0[3],v2mv0[3],normal[3];
|
||||
|
||||
v[0][0] = v0[0]; v[0][1] = v0[2]; v[0][2] = v0[3];
|
||||
v[1][0] = v1[0]; v[1][1] = v1[2]; v[1][2] = v1[3];
|
||||
v[2][0] = v2[0]; v[2][1] = v2[2]; v[2][2] = v2[3];
|
||||
|
||||
times3(s,v,sv);
|
||||
transpose_times3(v,sv,vtsv);
|
||||
|
||||
double sum = lensq3(v0) + lensq3(v1) + lensq3(v2);
|
||||
vvv[0] = v0[0] + v1[0] + v2[0];
|
||||
vvv[1] = v0[1] + v1[1] + v2[1];
|
||||
vvv[2] = v0[2] + v1[2] + v2[2];
|
||||
sum += lensq3(vvv);
|
||||
|
||||
sub3(v1,v0,v1mv0);
|
||||
sub3(v2,v0,v2mv0);
|
||||
cross3(v1mv0,v2mv0,normal);
|
||||
double a = len3(normal);
|
||||
double inv24 = 1.0/24.0;
|
||||
|
||||
// NOTE: use mass
|
||||
|
||||
inertia[0] = inv24*a * (sum-vtsv[0][0]);
|
||||
inertia[1] = inv24*a * (sum-vtsv[1][1]);
|
||||
inertia[2] = inv24*a * (sum-vtsv[2][2]);
|
||||
inertia[3] = -inv24*a*vtsv[1][2];
|
||||
inertia[4] = -inv24*a*vtsv[0][2];
|
||||
inertia[5] = -inv24*a*vtsv[0][1];
|
||||
}
|
||||
|
||||
/* ---------------------------------------------------------------------- */
|
||||
|
||||
}
|
||||
227
src/math_extra.h
227
src/math_extra.h
|
|
@ -19,8 +19,9 @@
|
|||
#define LMP_MATH_EXTRA_H
|
||||
|
||||
#include "math.h"
|
||||
|
||||
// short methods are inlined, others are in math_extra.cpp
|
||||
#include "stdio.h"
|
||||
#include "string.h"
|
||||
#include "error.h"
|
||||
|
||||
namespace MathExtra {
|
||||
|
||||
|
|
@ -67,22 +68,23 @@ namespace MathExtra {
|
|||
int jacobi(double matrix[3][3], double *evalues, double evectors[3][3]);
|
||||
void rotate(double matrix[3][3], int i, int j, int k, int l,
|
||||
double s, double tau);
|
||||
|
||||
|
||||
// shape matrix operations
|
||||
// upper-triangular 3x3 matrix stored in Voigt notation as 6-vector
|
||||
|
||||
inline void multiply_shape_shape(const double *one, const double *two,
|
||||
double *ans);
|
||||
|
||||
// quaternion operations
|
||||
|
||||
inline void axisangle_to_quat(const double *v, const double angle,
|
||||
double *quat);
|
||||
|
||||
inline void qnormalize(double *q);
|
||||
inline void qconjugate(double *q, double *qc);
|
||||
inline void vecquat(double *a, double *b, double *c);
|
||||
inline void quatvec(double *a, double *b, double *c);
|
||||
inline void quatquat(double *a, double *b, double *c);
|
||||
inline void invquatvec(double *a, double *b, double *c);
|
||||
inline void qconjugate(double *q, double *qc);
|
||||
inline void qnormalize(double *q);
|
||||
inline void axisangle_to_quat(const double *v, const double angle,
|
||||
double *quat);
|
||||
inline void matvec_rows(double *x, double *y, double *z,
|
||||
double *b, double *c);
|
||||
inline void matvec_cols(double *x, double *y, double *z,
|
||||
|
|
@ -96,6 +98,8 @@ namespace MathExtra {
|
|||
void q_to_exyz(double *q, double *ex, double *ey, double *ez);
|
||||
void quat_to_mat(const double *quat, double mat[3][3]);
|
||||
void quat_to_mat_trans(const double *quat, double mat[3][3]);
|
||||
void quat_to_mat(const double *quat, double mat[3][3]);
|
||||
void quat_to_mat_trans(const double *quat, double mat[3][3]);
|
||||
|
||||
// rotation operations
|
||||
|
||||
|
|
@ -109,6 +113,7 @@ namespace MathExtra {
|
|||
double *inertia);
|
||||
void inertia_triangle(double *v0, double *v1, double *v2,
|
||||
double mass, double *inertia);
|
||||
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -193,7 +198,7 @@ double MathExtra::lensq3(const double *v)
|
|||
|
||||
double MathExtra::dot3(const double *v1, const double *v2)
|
||||
{
|
||||
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
|
||||
return v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -202,9 +207,9 @@ double MathExtra::dot3(const double *v1, const double *v2)
|
|||
|
||||
void MathExtra::cross3(const double *v1, const double *v2, double *ans)
|
||||
{
|
||||
ans[0] = v1[1]*v2[2] - v1[2]*v2[1];
|
||||
ans[1] = v1[2]*v2[0] - v1[0]*v2[2];
|
||||
ans[2] = v1[0]*v2[1] - v1[1]*v2[0];
|
||||
ans[0] = v1[1]*v2[2]-v1[2]*v2[1];
|
||||
ans[1] = v1[2]*v2[0]-v1[0]*v2[2];
|
||||
ans[2] = v1[0]*v2[1]-v1[1]*v2[0];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -213,8 +218,7 @@ void MathExtra::cross3(const double *v1, const double *v2, double *ans)
|
|||
|
||||
double MathExtra::det3(const double m[3][3])
|
||||
{
|
||||
double ans =
|
||||
m[0][0]*m[1][1]*m[2][2] - m[0][0]*m[1][2]*m[2][1] -
|
||||
double ans = m[0][0]*m[1][1]*m[2][2] - m[0][0]*m[1][2]*m[2][1] -
|
||||
m[1][0]*m[0][1]*m[2][2] + m[1][0]*m[0][2]*m[2][1] +
|
||||
m[2][0]*m[0][1]*m[1][2] - m[2][0]*m[0][2]*m[1][1];
|
||||
return ans;
|
||||
|
|
@ -245,15 +249,15 @@ void MathExtra::diag_times3(const double *d, const double m[3][3],
|
|||
void MathExtra::plus3(const double m[3][3], const double m2[3][3],
|
||||
double ans[3][3])
|
||||
{
|
||||
ans[0][0] = m[0][0] + m2[0][0];
|
||||
ans[0][1] = m[0][1] + m2[0][1];
|
||||
ans[0][2] = m[0][2] + m2[0][2];
|
||||
ans[1][0] = m[1][0] + m2[1][0];
|
||||
ans[1][1] = m[1][1] + m2[1][1];
|
||||
ans[1][2] = m[1][2] + m2[1][2];
|
||||
ans[2][0] = m[2][0] + m2[2][0];
|
||||
ans[2][1] = m[2][1] + m2[2][1];
|
||||
ans[2][2] = m[2][2] + m2[2][2];
|
||||
ans[0][0] = m[0][0]+m2[0][0];
|
||||
ans[0][1] = m[0][1]+m2[0][1];
|
||||
ans[0][2] = m[0][2]+m2[0][2];
|
||||
ans[1][0] = m[1][0]+m2[1][0];
|
||||
ans[1][1] = m[1][1]+m2[1][1];
|
||||
ans[1][2] = m[1][2]+m2[1][2];
|
||||
ans[2][0] = m[2][0]+m2[2][0];
|
||||
ans[2][1] = m[2][1]+m2[2][1];
|
||||
ans[2][2] = m[2][2]+m2[2][2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -263,15 +267,15 @@ void MathExtra::plus3(const double m[3][3], const double m2[3][3],
|
|||
void MathExtra::times3(const double m[3][3], const double m2[3][3],
|
||||
double ans[3][3])
|
||||
{
|
||||
ans[0][0] = m[0][0]*m2[0][0] + m[0][1]*m2[1][0] + m[0][2]*m2[2][0];
|
||||
ans[0][1] = m[0][0]*m2[0][1] + m[0][1]*m2[1][1] + m[0][2]*m2[2][1];
|
||||
ans[0][2] = m[0][0]*m2[0][2] + m[0][1]*m2[1][2] + m[0][2]*m2[2][2];
|
||||
ans[1][0] = m[1][0]*m2[0][0] + m[1][1]*m2[1][0] + m[1][2]*m2[2][0];
|
||||
ans[1][1] = m[1][0]*m2[0][1] + m[1][1]*m2[1][1] + m[1][2]*m2[2][1];
|
||||
ans[1][2] = m[1][0]*m2[0][2] + m[1][1]*m2[1][2] + m[1][2]*m2[2][2];
|
||||
ans[2][0] = m[2][0]*m2[0][0] + m[2][1]*m2[1][0] + m[2][2]*m2[2][0];
|
||||
ans[2][1] = m[2][0]*m2[0][1] + m[2][1]*m2[1][1] + m[2][2]*m2[2][1];
|
||||
ans[2][2] = m[2][0]*m2[0][2] + m[2][1]*m2[1][2] + m[2][2]*m2[2][2];
|
||||
ans[0][0] = m[0][0]*m2[0][0]+m[0][1]*m2[1][0]+m[0][2]*m2[2][0];
|
||||
ans[0][1] = m[0][0]*m2[0][1]+m[0][1]*m2[1][1]+m[0][2]*m2[2][1];
|
||||
ans[0][2] = m[0][0]*m2[0][2]+m[0][1]*m2[1][2]+m[0][2]*m2[2][2];
|
||||
ans[1][0] = m[1][0]*m2[0][0]+m[1][1]*m2[1][0]+m[1][2]*m2[2][0];
|
||||
ans[1][1] = m[1][0]*m2[0][1]+m[1][1]*m2[1][1]+m[1][2]*m2[2][1];
|
||||
ans[1][2] = m[1][0]*m2[0][2]+m[1][1]*m2[1][2]+m[1][2]*m2[2][2];
|
||||
ans[2][0] = m[2][0]*m2[0][0]+m[2][1]*m2[1][0]+m[2][2]*m2[2][0];
|
||||
ans[2][1] = m[2][0]*m2[0][1]+m[2][1]*m2[1][1]+m[2][2]*m2[2][1];
|
||||
ans[2][2] = m[2][0]*m2[0][2]+m[2][1]*m2[1][2]+m[2][2]*m2[2][2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -281,15 +285,15 @@ void MathExtra::times3(const double m[3][3], const double m2[3][3],
|
|||
void MathExtra::transpose_times3(const double m[3][3], const double m2[3][3],
|
||||
double ans[3][3])
|
||||
{
|
||||
ans[0][0] = m[0][0]*m2[0][0] + m[1][0]*m2[1][0] + m[2][0]*m2[2][0];
|
||||
ans[0][1] = m[0][0]*m2[0][1] + m[1][0]*m2[1][1] + m[2][0]*m2[2][1];
|
||||
ans[0][2] = m[0][0]*m2[0][2] + m[1][0]*m2[1][2] + m[2][0]*m2[2][2];
|
||||
ans[1][0] = m[0][1]*m2[0][0] + m[1][1]*m2[1][0] + m[2][1]*m2[2][0];
|
||||
ans[1][1] = m[0][1]*m2[0][1] + m[1][1]*m2[1][1] + m[2][1]*m2[2][1];
|
||||
ans[1][2] = m[0][1]*m2[0][2] + m[1][1]*m2[1][2] + m[2][1]*m2[2][2];
|
||||
ans[2][0] = m[0][2]*m2[0][0] + m[1][2]*m2[1][0] + m[2][2]*m2[2][0];
|
||||
ans[2][1] = m[0][2]*m2[0][1] + m[1][2]*m2[1][1] + m[2][2]*m2[2][1];
|
||||
ans[2][2] = m[0][2]*m2[0][2] + m[1][2]*m2[1][2] + m[2][2]*m2[2][2];
|
||||
ans[0][0] = m[0][0]*m2[0][0]+m[1][0]*m2[1][0]+m[2][0]*m2[2][0];
|
||||
ans[0][1] = m[0][0]*m2[0][1]+m[1][0]*m2[1][1]+m[2][0]*m2[2][1];
|
||||
ans[0][2] = m[0][0]*m2[0][2]+m[1][0]*m2[1][2]+m[2][0]*m2[2][2];
|
||||
ans[1][0] = m[0][1]*m2[0][0]+m[1][1]*m2[1][0]+m[2][1]*m2[2][0];
|
||||
ans[1][1] = m[0][1]*m2[0][1]+m[1][1]*m2[1][1]+m[2][1]*m2[2][1];
|
||||
ans[1][2] = m[0][1]*m2[0][2]+m[1][1]*m2[1][2]+m[2][1]*m2[2][2];
|
||||
ans[2][0] = m[0][2]*m2[0][0]+m[1][2]*m2[1][0]+m[2][2]*m2[2][0];
|
||||
ans[2][1] = m[0][2]*m2[0][1]+m[1][2]*m2[1][1]+m[2][2]*m2[2][1];
|
||||
ans[2][2] = m[0][2]*m2[0][2]+m[1][2]*m2[1][2]+m[2][2]*m2[2][2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -299,20 +303,20 @@ void MathExtra::transpose_times3(const double m[3][3], const double m2[3][3],
|
|||
void MathExtra::times3_transpose(const double m[3][3], const double m2[3][3],
|
||||
double ans[3][3])
|
||||
{
|
||||
ans[0][0] = m[0][0]*m2[0][0] + m[0][1]*m2[0][1] + m[0][2]*m2[0][2];
|
||||
ans[0][1] = m[0][0]*m2[1][0] + m[0][1]*m2[1][1] + m[0][2]*m2[1][2];
|
||||
ans[0][2] = m[0][0]*m2[2][0] + m[0][1]*m2[2][1] + m[0][2]*m2[2][2];
|
||||
ans[1][0] = m[1][0]*m2[0][0] + m[1][1]*m2[0][1] + m[1][2]*m2[0][2];
|
||||
ans[1][1] = m[1][0]*m2[1][0] + m[1][1]*m2[1][1] + m[1][2]*m2[1][2];
|
||||
ans[1][2] = m[1][0]*m2[2][0] + m[1][1]*m2[2][1] + m[1][2]*m2[2][2];
|
||||
ans[2][0] = m[2][0]*m2[0][0] + m[2][1]*m2[0][1] + m[2][2]*m2[0][2];
|
||||
ans[2][1] = m[2][0]*m2[1][0] + m[2][1]*m2[1][1] + m[2][2]*m2[1][2];
|
||||
ans[2][2] = m[2][0]*m2[2][0] + m[2][1]*m2[2][1] + m[2][2]*m2[2][2];
|
||||
ans[0][0] = m[0][0]*m2[0][0]+m[0][1]*m2[0][1]+m[0][2]*m2[0][2];
|
||||
ans[0][1] = m[0][0]*m2[1][0]+m[0][1]*m2[1][1]+m[0][2]*m2[1][2];
|
||||
ans[0][2] = m[0][0]*m2[2][0]+m[0][1]*m2[2][1]+m[0][2]*m2[2][2];
|
||||
ans[1][0] = m[1][0]*m2[0][0]+m[1][1]*m2[0][1]+m[1][2]*m2[0][2];
|
||||
ans[1][1] = m[1][0]*m2[1][0]+m[1][1]*m2[1][1]+m[1][2]*m2[1][2];
|
||||
ans[1][2] = m[1][0]*m2[2][0]+m[1][1]*m2[2][1]+m[1][2]*m2[2][2];
|
||||
ans[2][0] = m[2][0]*m2[0][0]+m[2][1]*m2[0][1]+m[2][2]*m2[0][2];
|
||||
ans[2][1] = m[2][0]*m2[1][0]+m[2][1]*m2[1][1]+m[2][2]*m2[1][2];
|
||||
ans[2][2] = m[2][0]*m2[2][0]+m[2][1]*m2[2][1]+m[2][2]*m2[2][2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
invert a matrix
|
||||
does NOT check for singular or badly scaled matrix
|
||||
does NOT checks for singular or badly scaled matrix
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::invert3(const double m[3][3], double ans[3][3])
|
||||
|
|
@ -339,9 +343,9 @@ void MathExtra::invert3(const double m[3][3], double ans[3][3])
|
|||
void MathExtra::times_column3(const double m[3][3], const double *v,
|
||||
double *ans)
|
||||
{
|
||||
ans[0] = m[0][0]*v[0] + m[0][1]*v[1] + m[0][2]*v[2];
|
||||
ans[1] = m[1][0]*v[0] + m[1][1]*v[1] + m[1][2]*v[2];
|
||||
ans[2] = m[2][0]*v[0] + m[2][1]*v[1] + m[2][2]*v[2];
|
||||
ans[0] = m[0][0]*v[0]+m[0][1]*v[1]+m[0][2]*v[2];
|
||||
ans[1] = m[1][0]*v[0]+m[1][1]*v[1]+m[1][2]*v[2];
|
||||
ans[2] = m[2][0]*v[0]+m[2][1]*v[1]+m[2][2]*v[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -351,9 +355,9 @@ void MathExtra::times_column3(const double m[3][3], const double *v,
|
|||
void MathExtra::transpose_times_column3(const double m[3][3], const double *v,
|
||||
double *ans)
|
||||
{
|
||||
ans[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
|
||||
ans[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
|
||||
ans[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
|
||||
ans[0] = m[0][0]*v[0]+m[1][0]*v[1]+m[2][0]*v[2];
|
||||
ans[1] = m[0][1]*v[0]+m[1][1]*v[1]+m[2][1]*v[2];
|
||||
ans[2] = m[0][2]*v[0]+m[1][2]*v[1]+m[2][2]*v[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -381,9 +385,9 @@ void MathExtra::transpose_times_diag3(const double m[3][3],
|
|||
void MathExtra::row_times3(const double *v, const double m[3][3],
|
||||
double *ans)
|
||||
{
|
||||
ans[0] = m[0][0]*v[0] + v[1]*m[1][0] + v[2]*m[2][0];
|
||||
ans[1] = v[0]*m[0][1] + m[1][1]*v[1] + v[2]*m[2][1];
|
||||
ans[2] = v[0]*m[0][2] + v[1]*m[1][2] + m[2][2]*v[2];
|
||||
ans[0] = m[0][0]*v[0]+v[1]*m[1][0]+v[2]*m[2][0];
|
||||
ans[1] = v[0]*m[0][1]+m[1][1]*v[1]+v[2]*m[2][1];
|
||||
ans[2] = v[0]*m[0][2]+v[1]*m[1][2]+m[2][2]*v[2];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -392,20 +396,14 @@ void MathExtra::row_times3(const double *v, const double m[3][3],
|
|||
|
||||
inline void MathExtra::scalar_times3(const double f, double m[3][3])
|
||||
{
|
||||
m[0][0] *= f;
|
||||
m[0][1] *= f;
|
||||
m[0][2] *= f;
|
||||
m[1][0] *= f;
|
||||
m[1][1] *= f;
|
||||
m[1][2] *= f;
|
||||
m[2][0] *= f;
|
||||
m[2][1] *= f;
|
||||
m[2][2] *= f;
|
||||
m[0][0] *= f; m[0][1] *= f; m[0][2] *= f;
|
||||
m[1][0] *= f; m[1][1] *= f; m[1][2] *= f;
|
||||
m[2][0] *= f; m[2][1] *= f; m[2][2] *= f;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
multiply 2 shape matrices to yield a 3rd shape matrix
|
||||
upper-triangular 3x3 matrices stored in Voigt notation as 6-vectors
|
||||
multiply 2 shape matrices
|
||||
upper-triangular 3x3, stored as 6-vector in Voigt notation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::multiply_shape_shape(const double *one, const double *two,
|
||||
|
|
@ -420,19 +418,29 @@ void MathExtra::multiply_shape_shape(const double *one, const double *two,
|
|||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute quaternion from axis-angle rotation
|
||||
v MUST be a unit vector
|
||||
normalize a quaternion
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::axisangle_to_quat(const double *v, const double angle,
|
||||
double *quat)
|
||||
void MathExtra::qnormalize(double *q)
|
||||
{
|
||||
double halfa = 0.5*angle;
|
||||
double sina = sin(halfa);
|
||||
quat[0] = cos(halfa);
|
||||
quat[1] = v[0]*sina;
|
||||
quat[2] = v[1]*sina;
|
||||
quat[3] = v[2]*sina;
|
||||
double norm = 1.0 / sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
|
||||
q[0] *= norm;
|
||||
q[1] *= norm;
|
||||
q[2] *= norm;
|
||||
q[3] *= norm;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
conjugate of a quaternion: qc = conjugate of q
|
||||
assume q is of unit length
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::qconjugate(double *q, double *qc)
|
||||
{
|
||||
qc[0] = q[0];
|
||||
qc[1] = -q[1];
|
||||
qc[2] = -q[2];
|
||||
qc[3] = -q[3];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -461,7 +469,6 @@ void MathExtra::quatvec(double *a, double *b, double *c)
|
|||
|
||||
/* ----------------------------------------------------------------------
|
||||
quaternion-quaternion multiply: c = a*b
|
||||
NOT a commutative operation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::quatquat(double *a, double *b, double *c)
|
||||
|
|
@ -487,29 +494,19 @@ void MathExtra::invquatvec(double *a, double *b, double *c)
|
|||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
conjugate of a quaternion: qc = conjugate of q
|
||||
assume q is of unit length
|
||||
compute quaternion from axis-angle rotation
|
||||
v MUST be a unit vector
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::qconjugate(double *q, double *qc)
|
||||
void MathExtra::axisangle_to_quat(const double *v, const double angle,
|
||||
double *quat)
|
||||
{
|
||||
qc[0] = q[0];
|
||||
qc[1] = -q[1];
|
||||
qc[2] = -q[2];
|
||||
qc[3] = -q[3];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
normalize a quaternion
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::qnormalize(double *q)
|
||||
{
|
||||
double norm = 1.0 / sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
|
||||
q[0] *= norm;
|
||||
q[1] *= norm;
|
||||
q[2] *= norm;
|
||||
q[3] *= norm;
|
||||
double halfa = 0.5*angle;
|
||||
double sina = sin(halfa);
|
||||
quat[0] = cos(halfa);
|
||||
quat[1] = v[0]*sina;
|
||||
quat[2] = v[1]*sina;
|
||||
quat[3] = v[2]*sina;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
|
|
@ -537,54 +534,54 @@ void MathExtra::matvec_cols(double *x, double *y, double *z,
|
|||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
apply principal rotation generator about x to rotation matrix m
|
||||
Apply principal rotation generator about x to rotation matrix m
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::rotation_generator_x(const double m[3][3], double ans[3][3])
|
||||
{
|
||||
ans[0][0] = 0.0;
|
||||
ans[0][0] = 0;
|
||||
ans[0][1] = -m[0][2];
|
||||
ans[0][2] = m[0][1];
|
||||
ans[1][0] = 0.0;
|
||||
ans[1][0] = 0;
|
||||
ans[1][1] = -m[1][2];
|
||||
ans[1][2] = m[1][1];
|
||||
ans[2][0] = 0.0;
|
||||
ans[2][0] = 0;
|
||||
ans[2][1] = -m[2][2];
|
||||
ans[2][2] = m[2][1];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
apply principal rotation generator about y to rotation matrix m
|
||||
Apply principal rotation generator about y to rotation matrix m
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::rotation_generator_y(const double m[3][3], double ans[3][3])
|
||||
{
|
||||
ans[0][0] = m[0][2];
|
||||
ans[0][1] = 0.0;
|
||||
ans[0][1] = 0;
|
||||
ans[0][2] = -m[0][0];
|
||||
ans[1][0] = m[1][2];
|
||||
ans[1][1] = 0.0;
|
||||
ans[1][1] = 0;
|
||||
ans[1][2] = -m[1][0];
|
||||
ans[2][0] = m[2][2];
|
||||
ans[2][1] = 0.0;
|
||||
ans[2][1] = 0;
|
||||
ans[2][2] = -m[2][0];
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
apply principal rotation generator about z to rotation matrix m
|
||||
Apply principal rotation generator about z to rotation matrix m
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void MathExtra::rotation_generator_z(const double m[3][3], double ans[3][3])
|
||||
{
|
||||
ans[0][0] = -m[0][1];
|
||||
ans[0][1] = m[0][0];
|
||||
ans[0][2] = 0.0;
|
||||
ans[0][2] = 0;
|
||||
ans[1][0] = -m[1][1];
|
||||
ans[1][1] = m[1][0];
|
||||
ans[1][2] = 0.0;
|
||||
ans[1][2] = 0;
|
||||
ans[2][0] = -m[2][1];
|
||||
ans[2][1] = m[2][0];
|
||||
ans[2][2] = 0.0;
|
||||
ans[2][2] = 0;
|
||||
}
|
||||
|
||||
|
||||
#endif
|
||||
|
|
|
|||
Loading…
Reference in New Issue