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// (c) 2007-2010 Vaclav Smilauer <eudoxos@arcig.cz>
#include "Clump.hpp"
#include <lib/high-precision/Constants.hpp>
#include <core/BodyContainer.hpp>
#include <core/Scene.hpp>
#include <core/State.hpp>
#include <pkg/common/Sphere.hpp>
namespace yade { // Cannot have #include directive inside.
using math::max;
using math::min; // using inside .cpp file is ok.
YADE_PLUGIN((Clump));
CREATE_LOGGER(Clump);
boost::python::dict Clump::members_get() const
{
boost::python::dict ret;
for (const auto& b : members) {
ret[b.first] = boost::python::make_tuple(b.second.position, b.second.orientation);
}
return ret;
}
void Clump::add(const shared_ptr<Body>& clumpBody, const shared_ptr<Body>& subBody)
{
Body::id_t subId = subBody->getId();
const shared_ptr<Clump> clump = YADE_PTR_CAST<Clump>(clumpBody->shape);
if (clump->members.count(subId) != 0)
throw std::invalid_argument(
("Body #" + boost::lexical_cast<string>(subId) + " is already part of this clump #" + boost::lexical_cast<string>(clumpBody->id))
.c_str());
if (subBody->isClumpMember())
throw std::invalid_argument(
("Body #" + boost::lexical_cast<string>(subId) + " is already a clump member of #" + boost::lexical_cast<string>(subBody->clumpId))
.c_str());
else if (subBody->isClump()) {
const shared_ptr<Clump> subClump = YADE_PTR_CAST<Clump>(subBody->shape);
for (const auto& mm : subClump->members) {
const Body::id_t& memberId = mm.first;
Scene* scene(Omega::instance().getScene().get()); // get scene
const shared_ptr<Body>& member = Body::byId(memberId, scene);
assert(member->isClumpMember());
member->clumpId = clumpBody->id;
clump->members[memberId] = Se3r(); // meaningful values will be put in by Clump::updateProperties
//LOG_DEBUG("Added body #"<<memberId->id<<" to clump #"<<clumpBody->id);
}
//LOG_DEBUG("Clump #"<<subClump->id<<" will be erased.");// see addToClump() in yadeWrapper.cpp
} else { // subBody must be a standalone!
clump->members[subId] = Se3r(); // meaningful values will be put in by Clump::updateProperties
subBody->clumpId = clumpBody->id;
}
clumpBody->clumpId = clumpBody->id; // just to make sure
clumpBody->setBounded(false); // disallow collisions with the clump itself
if (subBody->isStandalone()) { LOG_DEBUG("Added body #" << subBody->id << " to clump #" << clumpBody->id); }
}
void Clump::del(const shared_ptr<Body>& clumpBody, const shared_ptr<Body>& subBody)
{
// erase the subBody; removing body that is not part of the clump throws
const shared_ptr<Clump> clump = YADE_PTR_CAST<Clump>(clumpBody->shape);
if (clump->members.erase(subBody->id) != 1)
throw std::invalid_argument(("Body #" + boost::lexical_cast<string>(subBody->id) + " not part of clump #"
+ boost::lexical_cast<string>(clumpBody->id) + "; not removing.")
.c_str());
subBody->clumpId = Body::ID_NONE;
LOG_DEBUG("Removed body #" << subBody->id << " from clump #" << clumpBody->id);
}
void Clump::addForceTorqueFromMembers(const State* clumpState, Scene* scene, Vector3r& F, Vector3r& T)
{
for (const auto& mm : members) {
const Body::id_t& memberId = mm.first;
const shared_ptr<Body>& member = Body::byId(memberId, scene);
assert(member->isClumpMember());
State* memberState = member->state.get();
const Vector3r& f = scene->forces.getForce(memberId);
const Vector3r& t = scene->forces.getTorque(memberId);
F += f;
T += t + (memberState->pos - clumpState->pos).cross(f);
}
}
/*! Clump's se3 will be updated (origin at centroid and axes coincident with principal inertia axes) and subSe3 modified in such a way that members positions in world coordinates will not change.
Note: velocities and angularVelocities of constituents are zeroed.
OLD DOCS (will be cleaned up):
-# Clump::members values and Clump::physicalParameters::se3 are invalid from this point
-# M=0; S=vector3r(0,0,0); I=zero tensor; (ALL calculations are in world coordinates!)
-# loop over Clump::members (position x_i, mass m_i, inertia at subBody's centroid I_i) [this loop will be replaced by numerical integration (rasterization) for the intersecting case; the rest will be the same]
- M+=m_i
- S+=m_i*x_i (local static moments are zero (centroid)
- get inertia tensor of subBody in world coordinates, by rotating the principal (local) tensor against subBody->se3->orientation; then translate it to world origin (parallel axes theorem), then I+=I_i_world
-# clumpPos=S/M
-# translate aggregate's inertia tensor; parallel axes on I (R=clumpPos): I^c_jk=I'_jk-M*(delta_jk R.R - R_j*R_k) [http://en.wikipedia.org/wiki/Moments_of_inertia#Parallel_axes_theorem]
-# eigen decomposition of I, get principal inertia and rotation matrix of the clump
-# se3->orientation=quaternion(rotation_matrix); se3->position=clumpPos
-# update subSe3s
*/
void Clump::updateProperties(const shared_ptr<Body>& clumpBody, unsigned int discretization)
{
LOG_DEBUG("Updating clump #" << clumpBody->id << " parameters");
const shared_ptr<State> state(clumpBody->state);
const shared_ptr<Clump> clump(YADE_PTR_CAST<Clump>(clumpBody->shape));
if (clump->members.empty()) { throw std::runtime_error("Clump::updateProperties: clump has zero members."); }
// trivial case
if (clump->members.size() == 1) {
LOG_DEBUG("Clump of size one will be treated specially.")
MemberMap::iterator I = clump->members.begin();
shared_ptr<Body> subBody = Body::byId(I->first);
//const shared_ptr<RigidBodyParameters>& subRBP(YADE_PTR_CAST<RigidBodyParameters>(subBody->physicalParameters));
State* subState = subBody->state.get();
// se3 of the clump as whole is the same as the member's se3
state->pos = subState->pos;
state->ori = subState->ori;
// relative member's se3 is identity
I->second.position = Vector3r::Zero();
I->second.orientation = Quaternionr::Identity();
state->inertia = subState->inertia;
state->mass = subState->mass;
state->vel = Vector3r::Zero();
state->angVel = Vector3r::Zero();
return;
}
//check for intersections:
bool intersecting = false;
int Sph_Index = Sphere::getClassIndexStatic(); // get sphere index for checking if bodies are spheres
if (discretization > 0) {
for (const auto& mm : clump->members) {
const shared_ptr<Body> subBody1 = Body::byId(mm.first);
for (const auto& mmm : clump->members) {
const shared_ptr<Body> subBody2 = Body::byId(mmm.first);
if ((subBody1->shape->getClassIndex() == Sph_Index) && (subBody2->shape->getClassIndex() == Sph_Index)
&& (subBody1 != subBody2)) { //clump members should be spheres
Vector3r dist = subBody1->state->pos - subBody2->state->pos;
const Sphere* sphere1 = YADE_CAST<Sphere*>(subBody1->shape.get());
const Sphere* sphere2 = YADE_CAST<Sphere*>(subBody2->shape.get());
Real un = (sphere1->radius + sphere2->radius) - dist.norm();
if (un > 0.001 * min(sphere1->radius, sphere2->radius)) {
intersecting = true;
break;
}
} // non-spherical cases trigger a warning below (here would not be ideal because of above "break")
}
if (intersecting) break;
}
}
/* quantities suffixed by
g: global (world) coordinates
s: local subBody's coordinates
c: local clump coordinates
*/
Real M = 0; // mass
Real dens = 0; //density
Vector3r Sg(0, 0, 0); // static moment, for getting clump's centroid
Matrix3r Ig(Matrix3r::Zero()), Ic(Matrix3r::Zero()); // tensors of inertia; is upper triangular, zeros instead of symmetric elements
/**
algorithm for estimation of volumes and inertia tensor from clumps using summation/integration scheme with regular grid spacing
(some parts copied from woo: http://bazaar.launchpad.net/~eudoxos/woo/trunk/view/head:/pkg/dem/Clump.cpp)
*/
if (intersecting) {
//get boundaries of clump Body (in global frame):
AlignedBox3r aabb;
for (const auto& mm : clump->members) {
const shared_ptr<Body> subBody = Body::byId(mm.first);
if (subBody->shape->getClassIndex() == Sph_Index) { //clump member should be a sphere
const Sphere* sphere = YADE_CAST<Sphere*>(subBody->shape.get());
aabb.extend(subBody->state->pos + Vector3r::Constant(sphere->radius));
aabb.extend(subBody->state->pos - Vector3r::Constant(sphere->radius));
} else { // since we have intersecting = 1 here, discretization is necessarily > 0
// and we might still face non-spherical members: intersecting can be for instance detected to be true with a (2 overlapping Spheres + 1 non-Sphere) clump
LOG_ERROR("Clump member " << mm.first << " is not spherical, discretization > 0 is not effective");
}
}
Real rMin = min(aabb.diagonal()[0], min(aabb.diagonal()[1], aabb.diagonal()[2]));
//get volume and inertia tensor using regular cubic cell array inside bounding box of the clump:
Real dx = rMin / discretization; //edge length of cell
Real dv = pow(dx, 3); //volume of cell
long nCells = long(math::round((aabb.sizes() / dx).prod()));
if (nCells > 1e7) LOG_WARN("Clump::updateProperties: Cell array has " << nCells << " cells. Integrate inertia may take a while ...");
Vector3r x; //position vector (center) of cell
for (x.x() = aabb.min().x() + dx / 2.; x.x() < aabb.max().x(); x.x() += dx) {
for (x.y() = aabb.min().y() + dx / 2.; x.y() < aabb.max().y(); x.y() += dx) {
for (x.z() = aabb.min().z() + dx / 2.; x.z() < aabb.max().z(); x.z() += dx) {
for (const auto& mm : clump->members) {
const shared_ptr<Body> subBody = Body::byId(mm.first);
if (subBody->shape->getClassIndex() == Sph_Index) { //clump member should be a sphere
dens = subBody->material->density;
const Sphere* sphere = YADE_CAST<Sphere*>(subBody->shape.get());
if ((x - subBody->state->pos).squaredNorm() < pow(sphere->radius, 2)) {
Real m = dens * dv;
M += m;
Sg += m * x;
//inertia I = sum_i( mass_i*dist^2 + I_s) ) //steiners theorem
Ig += m
* (x.dot(x) * Matrix3r::Identity() - x * x.transpose() /*dist^2*/
+ Matrix3r(
Vector3r::Constant(pow(dx, 2) / 6.)
.asDiagonal())) /*I_s/m = d^2: along princial axes of dv; perhaps negligible?*/
;
break;
}
}
}
}
}
}
} else { //not intersecting
for (const auto& mm : clump->members) {
// mm.first is Body::id_t, mm.second is Se3r of that body
const shared_ptr<Body> subBody = Body::byId(mm.first);
dens = subBody->material->density;
if (subBody->shape->getClassIndex() == Sph_Index) { //clump member should be a sphere
State* subState = subBody->state.get();
const Sphere* sphere = YADE_CAST<Sphere*>(subBody->shape.get());
Real vol = (4. / 3.) * Mathr::PI * pow(sphere->radius, 3.);
Real m = dens * vol;
M += m;
Sg += m * subState->pos;
Ig += Clump::inertiaTensorTranslate(
Vector3r::Constant((2 / 5.) * m * pow(sphere->radius, 2)).asDiagonal(), m, -1. * subState->pos);
} else { // non-spherical bodies
if (discretization > 0) LOG_ERROR("Clump member " << mm.first << " is not spherical, discretization > 0 is not effective");
State* subState = subBody->state.get();
const Real& m = subState->mass;
const Vector3r& inertia = subState->inertia;
const Vector3r& pos = subState->pos;
const Quaternionr& ori = subState->ori;
M += m;
Sg += m * pos;
Ig += inertiaTensorTranslate(inertiaTensorRotate(inertia.asDiagonal(), ori), m, -pos);
}
}
}
assert(M > 0);
LOG_TRACE("M=\n" << M << "\nIg=\n" << Ig << "\nSg=\n" << Sg);
// clump's centroid
state->pos = Sg / M;
// this will calculate translation only, since rotation is zero
Matrix3r Ic_orientG = inertiaTensorTranslate(
Ig, -M /* negative mass means towards centroid */, state->pos); // inertia at clump's centroid but with world orientation
LOG_TRACE("Ic_orientG=\n" << Ic_orientG);
Ic_orientG(1, 0) = Ic_orientG(0, 1);
Ic_orientG(2, 0) = Ic_orientG(0, 2);
Ic_orientG(2, 1) = Ic_orientG(1, 2); // symmetrize
Matrix3r R_g2c;
matrixEigenDecomposition(Ic_orientG, R_g2c, Ic);
// has NaNs for identity matrix??
LOG_TRACE("R_g2c=\n" << R_g2c);
// set quaternion from rotation matrix
state->ori = Quaternionr(R_g2c);
state->ori.normalize();
state->inertia = Ic.diagonal();
state->mass = M;
// TODO: these might be calculated from members... but complicated... - someone needs that?!
state->vel = state->angVel = Vector3r::Zero();
clumpBody->setAspherical(state->inertia[0] != state->inertia[1] || state->inertia[0] != state->inertia[2]);
// update subBodySe3s; subtract clump orientation (=apply its inverse first) to subBody's orientation
for (auto& I : clump->members) {
shared_ptr<Body> subBody = Body::byId(I.first);
State* subState = subBody->state.get();
I.second.orientation = state->ori.conjugate() * subState->ori;
I.second.position = state->ori.conjugate() * (subState->pos - state->pos);
}
}
void Clump::updatePropertiesNonSpherical(const shared_ptr<Body>& clumpBody, bool intersecting, shared_ptr<Scene> rb)
{ //FIXME
//LOG_DEBUG("Updating clump #"<<getId()<<" parameters");
//LOG_DEBUG("Updating clump #"<<getId()<<" parameters");
//assert(members.size()>0);
const shared_ptr<State> state(clumpBody->state);
const shared_ptr<Clump> clump(YADE_PTR_CAST<Clump>(clumpBody->shape));
// trivial case
if (clump->members.size() == 1) {
LOG_DEBUG("Clump of size one will be treated specially.")
MemberMap::iterator I = clump->members.begin();
shared_ptr<Body> subBody = Body::byId(I->first, rb);
//const shared_ptr<RigidBodyParameters>& subRBP(YADE_PTR_CAST<RigidBodyParameters>(subBody->physicalParameters));
State* subState = subBody->state.get();
// se3 of the clump as whole is the same as the member's se3
state->pos = subState->pos;
state->ori = subState->ori;
// relative member's se3 is identity
I->second.position = Vector3r::Zero();
I->second.orientation = Quaternionr::Identity();
state->inertia = subState->inertia;
state->mass = subState->mass;
state->vel = Vector3r::Zero();
state->angVel = Vector3r::Zero();
return;
}
/* quantities suffixed by
g: global (world) coordinates
s: local subBody's coordinates
c: local clump coordinates
*/
Real M = 0; // mass
Vector3r Sg(0, 0, 0); // static moment, for getting clump's centroid
Matrix3r Ig(Matrix3r::Zero()), Ic(Matrix3r::Zero()); // tensors of inertia; is upper triangular, zeros instead of symmetric elements
if (intersecting) {
LOG_WARN("Self-intersecting clumps not yet implemented, intersections will be ignored.");
intersecting = false;
}
// begin non-intersecting loop here
if (!intersecting) {
for (const auto& I : clump->members) {
// I.first is Body::id_t, I.second is Se3r of that body
shared_ptr<Body> subBody = Body::byId(I.first, rb);
State* subState = subBody->state.get();
M += subState->mass;
Sg += subState->mass * subState->pos;
// transform from local to global coords
Quaternionr subState_ori_conjugate = subState->ori.conjugate();
Matrix3r Imatrix = Matrix3r::Zero();
Imatrix.diagonal() = subState->inertia;
// TRWM3MAT(Imatrix); TRWM3QUAT(subRBP_orientation_conjugate);
Ig += Clump::inertiaTensorTranslate(Clump::inertiaTensorRotate(Imatrix, subState_ori_conjugate), subState->mass, -1. * subState->pos);
//TRWM3MAT(Clump::inertiaTensorRotate(Matrix3r(subRBP->inertia),subRBP_orientation_conjugate));
}
}
//TRVAR1(M); TRWM3MAT(Ig); TRWM3VEC(Sg);
assert(M > 0);
state->pos = Sg / M; // clump's centroid
// this will calculate translation only, since rotation is zero
Matrix3r Ic_orientG = Clump::inertiaTensorTranslate(
Ig, -M /* negative mass means towards centroid */, state->pos); // inertia at clump's centroid but with world orientation
//TRWM3MAT(Ic_orientG);
Matrix3r R_g2c(Matrix3r::Zero()); //rotation matrix
Ic_orientG(1, 0) = Ic_orientG(0, 1);
Ic_orientG(2, 0) = Ic_orientG(0, 2);
Ic_orientG(2, 1) = Ic_orientG(1, 2); // symmetrize
//TRWM3MAT(Ic_orientG);
matrixEigenDecomposition(Ic_orientG, R_g2c, Ic);
// set quaternion from rotation matrix
state->ori = Quaternionr(R_g2c);
state->ori.normalize();
state->inertia = Ic.diagonal();
state->mass = M;
// TODO: these might be calculated from members... but complicated... - someone needs that?!
state->vel = state->angVel = Vector3r::Zero();
clumpBody->setAspherical(state->inertia[0] != state->inertia[1] || state->inertia[0] != state->inertia[2]);
// update subBodySe3s; subtract clump orientation (=apply its inverse first) to subBody's orientation
for (auto& I : clump->members) {
// now, I->first is Body::id_t, I->second is Se3r of that body
shared_ptr<Body> subBody = Body::byId(I.first, rb);
//const shared_ptr<RigidBodyParameters>& subRBP(YADE_PTR_CAST<RigidBodyParameters>(subBody->physicalParameters));
State* subState = subBody->state.get();
I.second.orientation = state->ori.conjugate() * subState->ori;
I.second.position = state->ori.conjugate() * (subState->pos - state->pos);
}
}
void Clump::updatePropertiesNonSpherical(const shared_ptr<Body>& clumpBody, bool intersecting)
{ //FIXME
//LOG_DEBUG("Updating clump #"<<getId()<<" parameters");
//assert(members.size()>0);
const shared_ptr<State> state(clumpBody->state);
const shared_ptr<Clump> clump(YADE_PTR_CAST<Clump>(clumpBody->shape));
// trivial case
if (clump->members.size() == 1) {
LOG_DEBUG("Clump of size one will be treated specially.")
MemberMap::iterator I = clump->members.begin();
shared_ptr<Body> subBody = Body::byId(I->first);
//const shared_ptr<RigidBodyParameters>& subRBP(YADE_PTR_CAST<RigidBodyParameters>(subBody->physicalParameters));
State* subState = subBody->state.get();
// se3 of the clump as whole is the same as the member's se3
state->pos = subState->pos;
state->ori = subState->ori;
// relative member's se3 is identity
I->second.position = Vector3r::Zero();
I->second.orientation = Quaternionr::Identity();
state->inertia = subState->inertia;
state->mass = subState->mass;
state->vel = Vector3r::Zero();
state->angVel = Vector3r::Zero();
return;
}
/* quantities suffixed by
g: global (world) coordinates
s: local subBody's coordinates
c: local clump coordinates
*/
Real M = 0; // mass
Vector3r Sg(0, 0, 0); // static moment, for getting clump's centroid
Matrix3r Ig(Matrix3r::Zero()), Ic(Matrix3r::Zero()); // tensors of inertia; is upper triangular, zeros instead of symmetric elements
if (intersecting) {
LOG_WARN("Self-intersecting clumps not yet implemented, intersections will be ignored.");
intersecting = false;
}
// begin non-intersecting loop here
if (!intersecting) {
for (const auto& I : clump->members) {
// I.first is Body::id_t, I.second is Se3r of that body
shared_ptr<Body> subBody = Body::byId(I.first);
State* subState = subBody->state.get();
M += subState->mass;
Sg += subState->mass * subState->pos;
// transform from local to global coords
Quaternionr subState_ori_conjugate = subState->ori.conjugate();
Matrix3r Imatrix = Matrix3r::Zero();
Imatrix.diagonal() = subState->inertia;
// TRWM3MAT(Imatrix); TRWM3QUAT(subRBP_orientation_conjugate);
Ig += Clump::inertiaTensorTranslate(Clump::inertiaTensorRotate(Imatrix, subState_ori_conjugate), subState->mass, -1. * subState->pos);
//TRWM3MAT(Clump::inertiaTensorRotate(Matrix3r(subRBP->inertia),subRBP_orientation_conjugate));
}
}
//TRVAR1(M); TRWM3MAT(Ig); TRWM3VEC(Sg);
assert(M > 0);
state->pos = Sg / M; // clump's centroid
// this will calculate translation only, since rotation is zero
Matrix3r Ic_orientG = Clump::inertiaTensorTranslate(
Ig, -M /* negative mass means towards centroid */, state->pos); // inertia at clump's centroid but with world orientation
//TRWM3MAT(Ic_orientG);
Matrix3r R_g2c(Matrix3r::Zero()); //rotation matrix
Ic_orientG(1, 0) = Ic_orientG(0, 1);
Ic_orientG(2, 0) = Ic_orientG(0, 2);
Ic_orientG(2, 1) = Ic_orientG(1, 2); // symmetrize
//TRWM3MAT(Ic_orientG);
matrixEigenDecomposition(Ic_orientG, R_g2c, Ic);
/*! @bug eigendecomposition might be wrong. see http://article.gmane.org/gmane.science.physics.yade.devel/99 for message. It is worked around below, however.
*/
// has NaNs for identity matrix!
//TRWM3MAT(R_g2c);
// set quaternion from rotation matrix
state->ori = Quaternionr(R_g2c);
state->ori.normalize();
// now Ic is diagonal
state->inertia = Ic.diagonal();
state->mass = M;
// this block will be removed once EigenDecomposition works for diagonal matrices
//#if 1
// if(isnan(R_g2c(0,0))||isnan(R_g2c(0,1))||isnan(R_g2c(0,2))||isnan(R_g2c(1,0))||isnan(R_g2c(1,1))||isnan(R_g2c(1,2))||isnan(R_g2c(2,0))||isnan(R_g2c(2,1))||isnan(R_g2c(2,2))){
// throw std::logic_error("Clump::updateProperties: NaNs in eigen-decomposition of inertia matrix?!");
// }
//#endif
//TRWM3VEC(state->inertia);
// TODO: these might be calculated from members... but complicated... - someone needs that?!
state->vel = state->angVel = Vector3r::Zero();
clumpBody->setAspherical(state->inertia[0] != state->inertia[1] || state->inertia[0] != state->inertia[2]);
// update subBodySe3s; subtract clump orientation (=apply its inverse first) to subBody's orientation
for (auto& I : clump->members) {
// now, I->first is Body::id_t, I->second is Se3r of that body
shared_ptr<Body> subBody = Body::byId(I.first);
//const shared_ptr<RigidBodyParameters>& subRBP(YADE_PTR_CAST<RigidBodyParameters>(subBody->physicalParameters));
State* subState = subBody->state.get();
I.second.orientation = state->ori.conjugate() * subState->ori;
I.second.position = state->ori.conjugate() * (subState->pos - state->pos);
}
}
void Clump::addNonSpherical(const shared_ptr<Body>& clumpBody, const shared_ptr<Body>& subBody)
{ //FIXME
Body::id_t subId = subBody->getId();
if (subBody->clumpId != Body::ID_NONE)
throw std::invalid_argument(
("Body #" + boost::lexical_cast<string>(subId) + " is already in clump #" + boost::lexical_cast<string>(subBody->clumpId)).c_str());
const shared_ptr<Clump> clump = YADE_PTR_CAST<Clump>(clumpBody->shape);
if (clump->members.count(subId) != 0)
throw std::invalid_argument(
("Body #" + boost::lexical_cast<string>(subId) + " is already part of this clump #" + boost::lexical_cast<string>(clumpBody->id))
.c_str());
clump->members[subId] = Se3r(); // meaningful values will be put in by Clump::updateProperties
subBody->clumpId = clumpBody->id;
clumpBody->clumpId = clumpBody->id; // just to make sure
clumpBody->setBounded(false); // disallow collisions with the clump itself
//LOG_DEBUG("Added body #"<<subId<<" to clump #"<<getId());
}
/*! @brief Recalculates inertia tensor of a body after translation away from (default) or towards its centroid.
*
* @param I inertia tensor in the original coordinates; it is assumed to be upper-triangular (elements below the diagonal are ignored).
* @param m mass of the body; if positive, translation is away from the centroid; if negative, towards centroid.
* @param off offset of the new origin from the original origin
* @return inertia tensor in the new coordinate system; the matrix is symmetric.
*/
Matrix3r Clump::inertiaTensorTranslate(const Matrix3r& I, const Real m, const Vector3r& off)
{
return I + m * (off.dot(off) * Matrix3r::Identity() - off * off.transpose());
}
/*! @brief Recalculate body's inertia tensor in rotated coordinates.
*
* @param I inertia tensor in old coordinates
* @param T rotation matrix from old to new coordinates
* @return inertia tensor in new coordinates
*/
Matrix3r Clump::inertiaTensorRotate(const Matrix3r& I, const Matrix3r& T)
{
/* [http://www.kwon3d.com/theory/moi/triten.html] */
return T.transpose() * I * T;
}
/*! @brief Recalculate body's inertia tensor in rotated coordinates.
*
* @param I inertia tensor in old coordinates
* @param rot quaternion that describes rotation from old to new coordinates
* @return inertia tensor in new coordinates
*/
Matrix3r Clump::inertiaTensorRotate(const Matrix3r& I, const Quaternionr& rot)
{
Matrix3r T = rot.toRotationMatrix();
return inertiaTensorRotate(I, T);
}
} // namespace yade
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