// http://en.wikipedia.org/wiki/Inertia_tensor_of_triangle
Matrix3r woo::Volumetric::triangleInertia(const Vector3r& v0, const Vector3r& v1, const Vector3r& v2){
Matrix3r V; V<<v0.transpose(),v1.transpose(),v2.transpose(); // rows!
Real a=((v1-v0).cross(v2-v0)).norm(); // twice the triangle area
Matrix3r S; S<<2,1,1, 1,2,1, 1,1,2; S*=(1/24.);
Matrix3r C=a*V.transpose()*S*V;
return Matrix3r::Identity()*C.trace()-C;
};
Matrix3r MeasureCapStress::matBp_BodyGlob(Real alpha,Real wettAngle, Real radius,Vector3r vecN){ // matrix B prime (the surface tension coefficient excepted), defined at body scale (see (3.49) p.65), expressed in global framework
Matrix3r Bp_BodyGlob ;
Bp_BodyGlob << - pow(sin(alpha),2) * cos(alpha+wettAngle) , 0 , 0 ,
0 , - pow(sin(alpha),2) * cos(alpha+wettAngle) , 0 ,
0 , 0 , sin(2*alpha) * sin(alpha+wettAngle);
Bp_BodyGlob *= Mathr::PI * pow(radius,2.0);
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * Bp_BodyGlob * globToLocRet.transpose() ;
}
Matrix3r MeasureCapStress::matLG_bridgeGlob(Real nn11,Real nn33, Vector3r vecN){
Matrix3r LG_bridgeGlob ;
LG_bridgeGlob << nn11 + nn33 , 0 , 0 , // useless to write lgArea - nn11 = 2*nn11 + nn33 - nn11
0 , nn11 + nn33 , 0 ,
0 , 0 , 2*nn11; // trace = 2*(2*nn11 + nn33) = 2*lgArea
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * LG_bridgeGlob * globToLocRet.transpose() ;
}
Matrix3r MeasureCapStress::matA_BodyGlob(Real alpha,Real radius,Vector3r vecN){
Matrix3r A_BodyGlob ;
A_BodyGlob << pow( 1 - cos(alpha),2) * (2 + cos(alpha)) , 0 , 0 ,
0 , pow( 1 - cos(alpha),2) * (2 + cos(alpha)) , 0 ,
0 , 0 , 2 * ( 1-pow(cos(alpha),3) );
A_BodyGlob *= Mathr::PI * pow(radius,3.0)/3.0;
Matrix3r globToLocRet = matGlobToLoc(vecN);
return globToLocRet * A_BodyGlob * globToLocRet.transpose() ;
}
// draw periodic cell, if active
void Renderer::drawPeriodicCell(){
if(!scene->isPeriodic || !cell) return;
glColor3v(Vector3r(1,1,0));
glPushMatrix();
const Matrix3r& hSize=scene->cell->hSize;
if(scaleOn && dispScale!=Vector3r::Ones()){
const Matrix3r& refHSize(scene->cell->refHSize);
Matrix3r scaledHSize;
for(int i=0; i<3; i++) scaledHSize.col(i)=refHSize.col(i)+((dispScale-Vector3r::Ones()).array()*Vector3r(hSize.col(i)-refHSize.col(i)).array()).matrix();
GLUtils::Parallelepiped(scaledHSize.col(0),scaledHSize.col(1),scaledHSize.col(2));
} else
{
GLUtils::Parallelepiped(hSize.col(0),hSize.col(1),hSize.col(2));
}
glPopMatrix();
}
// draw periodic cell, if active
void OpenGLRenderer::drawPeriodicCell(){
if(!scene->isPeriodic) return;
glColor3v(cellColor);
glPushMatrix();
// Vector3r size=scene->cell->getSize();
const Matrix3r& hSize=scene->cell->hSize;
if(dispScale!=Vector3r::Ones()){
const Matrix3r& refHSize(scene->cell->refHSize);
Matrix3r scaledHSize;
for(int i=0; i<3; i++) scaledHSize.col(i)=refHSize.col(i)+dispScale.cwiseProduct(Vector3r(hSize.col(i)-refHSize.col(i)));
GLUtils::Parallelepiped(scaledHSize.col(0),scaledHSize.col(1),scaledHSize.col(2));
} else {
GLUtils::Parallelepiped(hSize.col(0),hSize.col(1),hSize.col(2));
}
glPopMatrix();
}
void woo::Sphere::lumpMassInertia(const shared_ptr<Node>& n, Real density, Real& mass, Matrix3r& I, bool& rotateOk){
if(n.get()!=nodes[0].get()) return;
checkNodesHaveDemData();
rotateOk=true;
Real m=(4/3.)*M_PI*pow(radius,3)*density;
mass+=m;
I.diagonal()+=Vector3r::Ones()*(2./5.)*m*pow(radius,2);
};
void Cell::integrateAndUpdate(Real dt){
//incremental displacement gradient
_trsfInc=dt*gradV;
// total transformation; M = (Id+G).M = F.M
trsf+=_trsfInc*trsf;
_invTrsf=trsf.inverse();
if(trsfUpperTriangular) checkTrsfUpperTriangular();
// hSize contains colums with updated base vectors
Matrix3r prevHsize=hSize; // remember old value
if(homoDeform==HOMO_GRADV2) hSize=(Matrix3r::Identity()-gradV*dt/2.).inverse()*(Matrix3r::Identity()+gradV*dt/2.)*hSize;
else hSize+=_trsfInc*hSize;
pprevHsize=.5*(prevHsize+hSize); // average of previous and current value
if(hSize.determinant()==0){ throw std::runtime_error("Cell is degenerate (zero volume)."); }
// lengths of transformed cell vectors, skew cosines
Matrix3r Hnorm; // normalized transformed base vectors
for(int i=0; i<3; i++){
Vector3r base(hSize.col(i));
_size[i]=base.norm(); base/=_size[i]; //base is normalized now
Hnorm(0,i)=base[0]; Hnorm(1,i)=base[1]; Hnorm(2,i)=base[2];
};
// skew cosines
for(int i=0; i<3; i++){
int i1=(i+1)%3, i2=(i+2)%3;
// sin between axes is cos of skew
_cos[i]=(Hnorm.col(i1).cross(Hnorm.col(i2))).squaredNorm();
}
// pure shear trsf: ones on diagonal
_shearTrsf=Hnorm;
// pure unshear transformation
_unshearTrsf=_shearTrsf.inverse();
// some parts can branch depending on presence/absence of shear
_hasShear=(hSize(0,1)!=0 || hSize(0,2)!=0 || hSize(1,0)!=0 || hSize(1,2)!=0 || hSize(2,0)!=0 || hSize(2,1)!=0);
// OpenGL shear matrix (used frequently)
fillGlShearTrsfMatrix(_glShearTrsfMatrix);
if(!(homoDeform==HOMO_NONE || homoDeform==HOMO_POS || homoDeform==HOMO_VEL || homoDeform==HOMO_VEL_2ND || homoDeform==HOMO_GRADV2)) throw std::invalid_argument("Cell.homoDeform must be in {0,1,2,3,4}.");
}
bool PositionBasedElasticRod::ComputeDarbouxVector(const Matrix3r& dA, const Matrix3r& dB, const float mid_edge_length, Vector3r& darboux_vector)
{
float factor = 1.0f + dA.col(0).dot(dB.col(0)) + dA.col(1).dot(dB.col(1)) + dA.col(2).dot(dB.col(2));
factor = 2.0f / (mid_edge_length * factor);
for (int c = 0; c < 3; ++c)
{
const int i = permutation[c][0];
const int j = permutation[c][1];
const int k = permutation[c][2];
darboux_vector[i] = dA.col(j).dot(dB.col(k)) - dA.col(k).dot(dB.col(j));
}
darboux_vector *= factor;
return true;
}
// ----------------------------------------------------------------------------------------------
bool PositionBasedElasticRod::ComputeMaterialFrame(
const Vector3r& pA,
const Vector3r& pB,
const Vector3r& pG,
Matrix3r& frame)
{
frame.col(2) = (pB - pA);
frame.col(2).normalize();
frame.col(1) = (frame.col(2).cross(pG - pA));
frame.col(1).normalize();
frame.col(0) = frame.col(1).cross(frame.col(2));
// frame.col(0).normalize();
return true;
}
void Membrane::setRefConf(){
if(!node) node=make_shared<Node>();
// set initial node position and orientation
node->pos=this->getCentroid();
// for orientation, there is a few choices which one to pick
enum {INI_CS_SIMPLE=0,INI_CS_NODE0_AT_X};
const int ini_cs=INI_CS_NODE0_AT_X;
//const int ini_cs=INI_CS_SIMPLE;
switch(ini_cs){
case INI_CS_SIMPLE:
node->ori.setFromTwoVectors(Vector3r::UnitZ(),this->getNormal());
break;
case INI_CS_NODE0_AT_X:{
Matrix3r T;
T.col(0)=(nodes[0]->pos-node->pos).normalized(); // QQQ: row->col
T.col(2)=this->getNormal();
T.col(1)=T.col(2).cross(T.col(0));
assert(T.col(0).dot(T.col(2))<1e-12);
node->ori=Quaternionr(T);
break;
}
};
// reference nodal positions
for(int i:{0,1,2}){
// Vector3r nl=node->ori.conjugate()*(nodes[i]->pos-node->pos); // QQQ
Vector3r nl=node->glob2loc(nodes[i]->pos);
assert(nl[2]<1e-6*(max(abs(nl[0]),abs(nl[1])))); // z-coord should be zero
refPos.segment<2>(2*i)=nl.head<2>();
}
// reference nodal rotations
refRot.resize(3);
for(int i:{0,1,2}){
// facet node orientation minus vertex node orientation, in local frame (read backwards)
/// QQQ: refRot[i]=node->ori*nodes[i]->ori.conjugate();
refRot[i]=nodes[i]->ori.conjugate()*node->ori;
//LOG_WARN("refRot["<<i<<"]="<<AngleAxisr(refRot[i]).angle()<<"/"<<AngleAxisr(refRot[i]).axis().transpose());
};
// set displacements to zero
uXy=phiXy=Vector6r::Zero();
#ifdef MEMBRANE_DEBUG_ROT
drill=Vector3r::Zero();
currRot.resize(3);
#endif
// delete stiffness matrices to force their re-creating
KKcst.resize(0,0);
KKdkt.resize(0,0);
};
void Gl1_Membrane::go(const shared_ptr<Shape>& sh, const Vector3r& shift, bool wire2, const GLViewInfo& viewInfo){
Gl1_Facet::go(sh,shift,/*don't force wire rendering*/ wire2,viewInfo);
if(Renderer::fastDraw) return;
Membrane& ff=sh->cast<Membrane>();
if(!ff.hasRefConf()) return;
if(node){
Renderer::setNodeGlData(ff.node,false/*set refPos only for the first time*/);
Renderer::renderRawNode(ff.node);
if(ff.node->rep) ff.node->rep->render(ff.node,&viewInfo);
#ifdef MEMBRANE_DEBUG_ROT
// show what Membrane thinks the orientation of nodes is - render those midway
if(ff.currRot.size()==3){
for(int i:{0,1,2}){
shared_ptr<Node> n=make_shared<Node>();
n->pos=ff.node->pos+.5*(ff.nodes[i]->pos-ff.node->pos);
n->ori=(ff.currRot[i]*ff.node->ori.conjugate()).conjugate();
Renderer::renderRawNode(n);
}
}
#endif
}
// draw everything in in local coords now
glPushMatrix();
if(!Renderer::scaleOn){
// without displacement scaling, local orientation is easy
GLUtils::setLocalCoords(ff.node->pos,ff.node->ori);
} else {
/* otherwise compute scaled orientation such that
* +x points to the same point on the triangle (in terms of angle)
* +z is normal to the facet in the GL space
*/
Real phi0=atan2(ff.refPos[1],ff.refPos[0]);
Vector3r C=ff.getGlCentroid();
Matrix3r rot;
rot.row(2)=ff.getGlNormal();
rot.row(0)=(ff.getGlVertex(0)-C).normalized();
rot.row(1)=rot.row(2).cross(rot.row(0));
Quaternionr ori=AngleAxisr(phi0,Vector3r::UnitZ())*Quaternionr(rot);
GLUtils::setLocalCoords(C,ori.conjugate());
}
if(refConf){
glColor3v(refColor);
glLineWidth(refWd);
glBegin(GL_LINE_LOOP);
for(int i:{0,1,2}) glVertex3v(Vector3r(ff.refPos[2*i],ff.refPos[2*i+1],0));
glEnd();
}
if(uScale!=0){
glLineWidth(uWd);
for(int i:{0,1,2}) drawLocalDisplacement(ff.refPos.segment<2>(2*i),uScale*ff.uXy.segment<2>(2*i),uRange,uSplit,arrows?1:0,uWd);
}
if(relPhi!=0 && ff.hasBending()){
glLineWidth(phiWd);
for(int i:{0,1,2}) drawLocalDisplacement(ff.refPos.segment<2>(2*i),relPhi*viewInfo.sceneRadius*ff.phiXy.segment<2>(2*i),phiRange,phiSplit,arrows?2:0,phiWd
#ifdef MEMBRANE_DEBUG_ROT
, relPhi*viewInfo.sceneRadius*ff.drill[i] /* show the out-of-plane component */
#endif
);
}
glPopMatrix();
}
Matrix3r inertiaRotate(const Matrix3r& I, const Matrix3r& T){
return T.transpose()*I*T;
}
bool PositionBasedElasticRod::ComputeDarbouxGradient(
const Vector3r& darboux_vector, const float length,
const Matrix3r& da, const Matrix3r& db,
//const Matrix3r(*dajpi)[3], const Matrix3r(*dbjpi)[3],
const Matrix3r dajpi[3][3], const Matrix3r dbjpi[3][3],
const Vector3r& bendAndTwistKs,
Matrix3r& omega_pa, Matrix3r& omega_pb, Matrix3r& omega_pc, Matrix3r& omega_pd, Matrix3r& omega_pe
)
{
//float x = 1.0f + da[0] * db[0] + da[1] * db[1] + da[2] * db[2];
float x = 1.0f + da.col(0).dot(db.col(0)) + da.col(1).dot(db.col(1)) + da.col(2).dot(db.col(2));
x = 2.0f / (length * x);
for (int c = 0; c < 3; ++c)
{
const int i = permutation[c][0];
const int j = permutation[c][1];
const int k = permutation[c][2];
// pa
{
Vector3r term1(0,0,0);
Vector3r term2(0,0,0);
Vector3r tmp(0,0,0);
// first term
//dj::MulVecMatrix3x3<real>(db[k](), (real(*)[3]) &dajpi[j][0], term1());
//dj::MulVecMatrix3x3<real>(db[j](), (real(*)[3]) &dajpi[k][0], tmp());
//DOUBLE CHECK !!!
term1 = dajpi[j][0].transpose() * db.col(k);
tmp = dajpi[k][0].transpose() * db.col(j);
term1 = term1 - tmp;
// second term
for (int n = 0; n < 3; ++n)
{
//dj::MulVecMatrix3x3<real>(db[n](), (real(*)[3]) &dajpi[n][0], tmp());
//DOUBLE CHECK !!!
tmp = dajpi[n][0].transpose() * db.col(n);
term2 = term2 + tmp;
}
omega_pa.col(i) = (term1)-(0.5f * darboux_vector[i] * length) * (term2);
omega_pa.col(i) *= (x * bendAndTwistKs[i]);
}
// pb
{
Vector3r term1(0, 0, 0);
Vector3r term2(0, 0, 0);
Vector3r tmp(0, 0, 0);
// first term
//dj::MulVecMatrix3x3<real>(db[k](), (real(*)[3]) &dajpi[j][1], term1());
//dj::MulVecMatrix3x3<real>(db[j](), (real(*)[3]) &dajpi[k][1], tmp());
term1 = dajpi[j][1].transpose() * db.col(k);
tmp = dajpi[k][1].transpose() * db.col(j);
term1 = term1 - tmp;
// third term
//dj::MulVecMatrix3x3<real>(da[k](), (real(*)[3]) &dbjpi[j][0], tmp());
tmp = dbjpi[j][0].transpose() * da.col(k);
term1 = term1 - tmp;
//dj::MulVecMatrix3x3<real>(da[j](), (real(*)[3]) &dbjpi[k][0], tmp());
tmp = dbjpi[k][0].transpose() * da.col(j);
term1 = term1 + tmp;
// second term
for (int n = 0; n < 3; ++n)
{
//dj::MulVecMatrix3x3<real>(db[n](), (real(*)[3]) &dajpi[n][1], tmp());
tmp = dajpi[n][1].transpose() * db.col(n);
term2 = term2 + tmp;
//dj::MulVecMatrix3x3<real>(da[n](), (real(*)[3]) &dbjpi[n][0], tmp());
tmp = dbjpi[n][0].transpose() * da.col(n);
term2 = term2 + tmp;
}
omega_pb.col(i) = (term1)-(0.5f * darboux_vector[i] * length) * (term2);
omega_pb.col(i) *= (x * bendAndTwistKs[i]);
}
// pc
{
Vector3r term1(0, 0, 0);
Vector3r term2(0, 0, 0);
Vector3r tmp(0, 0, 0);
// first term
//dj::MulVecMatrix3x3<real>(da[k](), (real(*)[3]) &dbjpi[j][1], term1());
//dj::MulVecMatrix3x3<real>(da[j](), (real(*)[3]) &dbjpi[k][1], tmp());
term1 = dbjpi[j][1].transpose() * da.col(k);
tmp = dbjpi[k][1].transpose() * da.col(j);
term1 = term1 - tmp;
// second term
for (int n = 0; n < 3; ++n)
{
//dj::MulVecMatrix3x3<real>(da[n](), (real(*)[3]) &dbjpi[n][1], tmp());
tmp = dbjpi[n][1].transpose() * da.col(n);
term2 = term2 + tmp;
}
omega_pc.col(i) = (term1)+(0.5f * darboux_vector[i] * length) * (term2);
omega_pc.col(i) *= (-x * bendAndTwistKs[i]);
}
// pd
{
Vector3r term1(0, 0, 0);
Vector3r term2(0, 0, 0);
Vector3r tmp(0, 0, 0);
// first term
//dj::MulVecMatrix3x3<real>(db[k](), (real(*)[3]) &dajpi[j][2], term1());
//dj::MulVecMatrix3x3<real>(db[j](), (real(*)[3]) &dajpi[k][2], tmp());
term1 = dajpi[j][2].transpose() * db.col(k);
tmp = dajpi[k][2].transpose() * db.col(j);
term1 = term1 - tmp;
// second term
for (int n = 0; n < 3; ++n) {
//dj::MulVecMatrix3x3<real>(db[n](), (real(*)[3]) &dajpi[n][2], tmp());
tmp = dajpi[n][2].transpose() * db.col(n);
term2 = term2 + tmp;
}
omega_pd.col(i) = (term1)-(0.5f * darboux_vector[i] * length) * (term2);
omega_pd.col(i) *= (x * bendAndTwistKs[i]);
}
// pe
{
Vector3r term1(0, 0, 0);
Vector3r term2(0, 0, 0);
Vector3r tmp(0, 0, 0);
// first term
//dj::MulVecMatrix3x3<real>(da[k](), (real(*)[3]) &dbjpi[j][2], term1());
//dj::MulVecMatrix3x3<real>(da[j](), (real(*)[3]) &dbjpi[k][2], tmp());
term1 = dbjpi[j][2].transpose() * da.col(k);
tmp = dbjpi[k][2].transpose() * da.col(j);
term1 -= tmp;
// second term
for (int n = 0; n < 3; ++n)
{ //WARNING!!! &dbjpi[n][2][0][0] ???
//dj::MulVecMatrix3x3<real>(da[n](), (real(*)[3]) &dbjpi[n][2][0][0], tmp());
tmp = dbjpi[n][2].transpose() * da.col(n);
term2 += tmp;
}
omega_pe.col(i) = (term1)+(0.5f * darboux_vector[i] * length) * (term2);
omega_pe.col(i) *= (-x * bendAndTwistKs[i]);
}
}
return true;
}
bool PositionBasedElasticRod::ComputeMaterialFrameDerivative(
const Vector3r& p0, const Vector3r& p1, const Vector3r& p2, const Matrix3r& d,
Matrix3r& d1p0, Matrix3r& d1p1, Matrix3r& d1p2,
Matrix3r& d2p0, Matrix3r& d2p1, Matrix3r& d2p2,
Matrix3r& d3p0, Matrix3r& d3p1, Matrix3r& d3p2)
{
// d3pi
Vector3r p01 = p1 - p0;
float length_p01 = p01.norm();
d3p0.col(0) = d.col(2)[0] * d.col(2);
d3p0.col(1) = d.col(2)[1] * d.col(2);
d3p0.col(2) = d.col(2)[2] * d.col(2);
d3p0.col(0)[0] -= 1.0f;
d3p0.col(1)[1] -= 1.0f;
d3p0.col(2)[2] -= 1.0f;
d3p0.col(0) *= (1.0f / length_p01);
d3p0.col(1) *= (1.0f / length_p01);
d3p0.col(2) *= (1.0f / length_p01);
d3p1.col(0) = -d3p0.col(0);
d3p1.col(1) = -d3p0.col(1);
d3p1.col(2) = -d3p0.col(2);
d3p2.col(0).setZero();
d3p2.col(1).setZero();
d3p2.col(2).setZero();
////>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
//// d2pi
Vector3r p02 = p2 - p0;
Vector3r p01_cross_p02 = p01.cross(p02);
float length_cross = p01_cross_p02.norm();
Matrix3r mat;
mat.col(0) = d.col(1)[0] * d.col(1);
mat.col(1) = d.col(1)[1] * d.col(1);
mat.col(2) = d.col(1)[2] * d.col(1);
mat.col(0)[0] -= 1.0f;
mat.col(1)[1] -= 1.0f;
mat.col(2)[2] -= 1.0f;
mat.col(0) *= (-1.0f / length_cross);
mat.col(1) *= (-1.0f / length_cross);
mat.col(2) *= (-1.0f / length_cross);
Matrix3r product_matrix;
MathFunctions::crossProductMatrix(p2 - p1, product_matrix);
d2p0 = mat * product_matrix;
MathFunctions::crossProductMatrix(p0 - p2, product_matrix);
d2p1 = mat * product_matrix;
MathFunctions::crossProductMatrix(p1 - p0, product_matrix);
d2p2 = mat * product_matrix;
////>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
//// d1pi
Matrix3r product_mat_d3;
Matrix3r product_mat_d2;
Matrix3r m1, m2;
MathFunctions::crossProductMatrix(d.col(2), product_mat_d3);
MathFunctions::crossProductMatrix(d.col(1), product_mat_d2);
//dj::MulMatrix3x3<real>(&product_mat_d3[0][0], &d2p0[0][0], &m1[0][0]);
//dj::MulMatrix3x3<real>(&product_mat_d2[0][0], &d3p0[0][0], &m2[0][0]);
d1p0 = product_mat_d2 * d3p0 - product_mat_d3 * d2p0;
//dj::MulMatrix3x3<real>(&product_mat_d3[0][0], &d2p1[0][0], &m1[0][0]);
//dj::MulMatrix3x3<real>(&product_mat_d2[0][0], &d3p1[0][0], &m2[0][0]);
d1p1 = product_mat_d2 * d3p1 - product_mat_d3 * d2p1;
/*dj::MulMatrix3x3<real>(&product_mat_d3[0][0], &d2p2[0][0], &d1p2[0][0]);*/
d1p2 = product_mat_d3 * d2p2;
d1p2.col(0) *= -1.0f;
d1p2.col(1) *= -1.0f;
d1p2.col(2) *= -1.0f;
return true;
}
/*! @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 woo::Volumetric::inertiaTensorRotate(const Matrix3r& I,const Matrix3r& T){
/* [http://www.kwon3d.com/theory/moi/triten.html] */
return T.transpose()*I*T;
}
/*
Generic function to compute L3Geom (with colinear points), used for {sphere,facet,wall}+sphere contacts now
*/
void Ig2_Sphere_Sphere_L3Geom::handleSpheresLikeContact(const shared_ptr<Interaction>& I, const State& state1, const State& state2, const Vector3r& shift2, bool is6Dof, const Vector3r& normal, const Vector3r& contPt, Real uN, Real r1, Real r2){
// create geometry
if(!I->geom){
if(is6Dof) I->geom=shared_ptr<L6Geom>(new L6Geom);
else I->geom=shared_ptr<L3Geom>(new L3Geom);
L3Geom& g(I->geom->cast<L3Geom>());
g.contactPoint=contPt;
g.refR1=r1; g.refR2=r2;
g.normal=normal;
// g.trsf.setFromTwoVectors(Vector3r::UnitX(),g.normal); // quaternion just from the X-axis; does not seem to work for some reason?!
const Vector3r& locX(g.normal);
// initial local y-axis orientation, in the xz or xy plane, depending on which component is larger to avoid singularities
Vector3r locY=normal.cross(abs(normal[1])<abs(normal[2])?Vector3r::UnitY():Vector3r::UnitZ()); locY-=locX*locY.dot(locX); locY.normalize();
Vector3r locZ=normal.cross(locY);
#ifdef L3_TRSF_QUATERNION
Matrix3r trsf; trsf.row(0)=locX; trsf.row(1)=locY; trsf.row(2)=locZ;
g.trsf=Quaternionr(trsf); // from transformation matrix
#else
g.trsf.row(0)=locX; g.trsf.row(1)=locY; g.trsf.row(2)=locZ;
#endif
g.u=Vector3r(uN,0,0); // zero shear displacement
if(distFactor<0) g.u0[0]=uN;
// L6Geom::phi is initialized to Vector3r::Zero() automatically
//cerr<<"Init trsf=\n"<<g.trsf<<endl<<"locX="<<locX<<", locY="<<locY<<", locZ="<<locZ<<endl;
return;
}
// update geometry
/* motion of the conctact consists in rigid motion (normRotVec, normTwistVec) and mutual motion (relShearDu);
they are used to update trsf and u
*/
L3Geom& g(I->geom->cast<L3Geom>());
const Vector3r& currNormal(normal); const Vector3r& prevNormal(g.normal);
// normal rotation vector, between last steps
Vector3r normRotVec=prevNormal.cross(currNormal);
// contrary to what ScGeom::precompute does now (r2486), we take average normal, i.e. .5*(prevNormal+currNormal),
// so that all terms in the equation are in the previous mid-step
// the re-normalization might not be necessary for very small increments, but better do it
Vector3r avgNormal=(approxMask&APPROX_NO_MID_NORMAL) ? prevNormal : .5*(prevNormal+currNormal);
if(!(approxMask&APPROX_NO_RENORM_MID_NORMAL) && !(approxMask&APPROX_NO_MID_NORMAL)) avgNormal.normalize(); // normalize only if used and if requested via approxMask
// twist vector of the normal from the last step
Vector3r normTwistVec=avgNormal*scene->dt*.5*avgNormal.dot(state1.angVel+state2.angVel);
// compute relative velocity
// noRatch: take radius or current distance as the branch vector; see discussion in ScGeom::precompute (avoidGranularRatcheting)
Vector3r c1x=((noRatch && !r1>0) ? ( r1*normal).eval() : (contPt-state1.pos).eval()); // used only for sphere-sphere
Vector3r c2x=(noRatch ? (-r2*normal).eval() : (contPt-state2.pos+shift2).eval());
//Vector3r state2velCorrected=state2.vel+(scene->isPeriodic?scene->cell->intrShiftVel(I->cellDist):Vector3r::Zero()); // velocity of the second particle, corrected with meanfield velocity if necessary
//cerr<<"correction "<<(scene->isPeriodic?scene->cell->intrShiftVel(I->cellDist):Vector3r::Zero())<<endl;
Vector3r relShearVel=(state2.vel+state2.angVel.cross(c2x))-(state1.vel+state1.angVel.cross(c1x));
// account for relative velocity of particles in different cell periods
if(scene->isPeriodic) relShearVel+=scene->cell->intrShiftVel(I->cellDist);
relShearVel-=avgNormal.dot(relShearVel)*avgNormal;
Vector3r relShearDu=relShearVel*scene->dt;
/* Update of quantities in global coords consists in adding 3 increments we have computed; in global coords (a is any vector)
1. +relShearVel*scene->dt; // mutual motion of the contact
2. -a.cross(normRotVec); // rigid rotation perpendicular to the normal
3. -a.cross(normTwistVec); // rigid rotation parallel to the normal
*/
// compute current transformation, by updating previous axes
// the X axis can be prescribed directly (copy of normal)
// the mutual motion on the contact does not change transformation
#ifdef L3_TRSF_QUATERNION
const Matrix3r prevTrsf(g.trsf.toRotationMatrix());
Quaternionr prevTrsfQ(g.trsf);
#else
const Matrix3r prevTrsf(g.trsf); // could be reference perhaps, but we need it to compute midTrsf (if applicable)
#endif
Matrix3r currTrsf; currTrsf.row(0)=currNormal;
for(int i=1; i<3; i++){
currTrsf.row(i)=prevTrsf.row(i)-prevTrsf.row(i).cross(normRotVec)-prevTrsf.row(i).cross(normTwistVec);
}
#ifdef L3_TRSF_QUATERNION
Quaternionr currTrsfQ(currTrsf);
if((scene->iter % trsfRenorm)==0 && trsfRenorm>0) currTrsfQ.normalize();
#else
if((scene->iter % trsfRenorm)==0 && trsfRenorm>0){
#if 1
currTrsf.row(0).normalize();
currTrsf.row(1)-=currTrsf.row(0)*currTrsf.row(1).dot(currTrsf.row(0)); // take away y projected on x, to stabilize numerically
currTrsf.row(1).normalize();
currTrsf.row(2)=currTrsf.row(0).cross(currTrsf.row(1));
currTrsf.row(2).normalize();
#else
currTrsf=Matrix3r(Quaternionr(currTrsf).normalized());
#endif
#ifdef YADE_DEBUG
if(abs(currTrsf.determinant()-1)>.05){
LOG_ERROR("##"<<I->getId1()<<"+"<<I->getId2()<<", |trsf|="<<currTrsf.determinant());
g.trsf=currTrsf;
throw runtime_error("Transformation matrix far from orthonormal.");
}
#endif
}
#endif
/* Previous local trsf u'⁻ must be updated to current u'⁰. We have transformation T⁻ and T⁰,
δ(a) denotes increment of a as defined above. Two possibilities:
1. convert to global, update, convert back: T⁰(T⁻*(u'⁻)+δ(T⁻*(u'⁻))). Quite heavy.
2. update u'⁻ straight, using relShearVel in local coords; since relShearVel is computed
at (t-Δt/2), we would have to find intermediary transformation (same axis, half angle;
the same as slerp at t=.5 between the two).
This could be perhaps simplified by using T⁰ or T⁻ since they will not differ much,
but it would have to be verified somehow.
*/
// if requested via approxMask, just use prevTrsf
#ifdef L3_TRSF_QUATERNION
Quaternionr midTrsf=(approxMask&APPROX_NO_MID_TRSF) ? prevTrsfQ : prevTrsfQ.slerp(.5,currTrsfQ);
#else
Quaternionr midTrsf=(approxMask&APPROX_NO_MID_TRSF) ? Quaternionr(prevTrsf) : Quaternionr(prevTrsf).slerp(.5,Quaternionr(currTrsf));
#endif
//cerr<<"prevTrsf=\n"<<prevTrsf<<", currTrsf=\n"<<currTrsf<<", midTrsf=\n"<<Matrix3r(midTrsf)<<endl;
// updates of geom here
// midTrsf*relShearVel should have the 0-th component (approximately) zero -- to be checked
g.u+=midTrsf*relShearDu;
//cerr<<"midTrsf=\n"<<midTrsf<<",relShearDu="<<relShearDu<<", transformed "<<midTrsf*relShearDu<<endl;
g.u[0]=uN; // this does not have to be computed incrementally
#ifdef L3_TRSF_QUATERNION
g.trsf=currTrsfQ;
#else
g.trsf=currTrsf;
#endif
// GenericSpheresContact
g.refR1=r1; g.refR2=r2;
g.normal=currNormal;
g.contactPoint=contPt;
if(is6Dof){
// update phi, from the difference of angular velocities
// the difference is transformed to local coord using the midTrsf transformation
// perhaps not consistent when spheres have different radii (depends how bending moment is computed)
I->geom->cast<L6Geom>().phi+=midTrsf*(scene->dt*(state2.angVel-state1.angVel));
}
};