// 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();
}
// 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();
}
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);
};
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;
}