void Gl1_L3Geom::draw(const shared_ptr<IGeom>& ig, bool isL6Geom, const Real& phiScale){
const L3Geom& g(ig->cast<L3Geom>());
glTranslatev(g.contactPoint);
#ifdef L3_TRSF_QUATERNION
//glMultMatrixd(Eigen::Affine3d(Matrix3r(g.trsf).transpose()).data());
glMultMatrix(Eigen::Transform<Real,3,Eigen::Affine>(Matrix3r(g.trsf).transpose()).data());
#else
//glMultMatrixd(Eigen::Affine3d(g.trsf.transpose()).data());
glMultMatrix(Eigen::Transform<Real,3,Eigen::Affine>(g.trsf.transpose()).data());
#endif
Real rMin=g.refR1<=0?g.refR2:(g.refR2<=0?g.refR1:min(g.refR1,g.refR2));
if(axesWd>0){
glLineWidth(axesWd);
for(int i=0; i<3; i++){
Vector3r pt=Vector3r::Zero(); pt[i]=.5*rMin*axesScale; Vector3r color=.3*Vector3r::Ones(); color[i]=1;
GLUtils::GLDrawLine(Vector3r::Zero(),pt,color);
if(axesLabels) GLUtils::GLDrawText(string(i==0?"x":(i==1?"y":"z")),pt,color);
}
}
if(uPhiWd>0){
glLineWidth(uPhiWd);
if(uScale!=0) GLUtils::GLDrawLine(Vector3r::Zero(),uScale*g.relU(),Vector3r(0,1,.5));
if(isL6Geom && phiScale>0) GLUtils::GLDrawLine(Vector3r::Zero(),ig->cast<L6Geom>().relPhi()/Mathr::PI*rMin*phiScale,Vector3r(.8,0,1));
}
glLineWidth(1.);
};
void SphereClumpGeom::recompute(int _div, bool failOk, bool fastOnly){
if((centers.empty() && radii.empty()) || centers.size()!=radii.size()){
if(failOk) { makeInvalid(); return;}
throw std::runtime_error("SphereClumpGeom.recompute: centers and radii must have the same length (len(centers)="+to_string(centers.size())+", len(radii)="+to_string(radii.size())+"), and may not be empty.");
}
div=_div;
// one single sphere: simple
if(centers.size()==1){
pos=centers[0];
ori=Quaternionr::Identity();
volume=(4/3.)*M_PI*pow(radii[0],3);
inertia=Vector3r::Constant((2/5.)*volume*pow(radii[0],2));
equivRad=radii[0];
return;
}
volume=0;
Vector3r Sg=Vector3r::Zero();
Matrix3r Ig=Matrix3r::Zero();
if(_div<=0){
// non-intersecting: Steiner's theorem
for(size_t i=0; i<centers.size(); i++){
const Real& r(radii[i]); const Vector3r& x(centers[i]);
Real v=(4/3.)*M_PI*pow(r,3);
volume+=v;
Sg+=v*x;
Ig+=woo::Volumetric::inertiaTensorTranslate(Vector3r::Constant((2/5.)*v*pow(r,2)).asDiagonal(),v,-1.*x);
}
} else {
// intersecting: grid sampling
Real rMin=Inf; AlignedBox3r aabb;
for(size_t i=0; i<centers.size(); i++){
aabb.extend(centers[i]+Vector3r::Constant(radii[i]));
aabb.extend(centers[i]-Vector3r::Constant(radii[i]));
rMin=min(rMin,radii[i]);
}
if(rMin<=0){
if(failOk){ makeInvalid(); return; }
throw std::runtime_error("SphereClumpGeom.recompute: minimum radius must be positive (not "+to_string(rMin)+")");
}
Real dx=rMin/_div; Real dv=pow(dx,3);
long nCellsApprox=(aabb.sizes()/dx).prod();
// don't compute anything, it would take too long
if(fastOnly && nCellsApprox>1e5){ makeInvalid(); return; }
if(nCellsApprox>1e8) LOG_WARN("SphereClumpGeom: space grid has "<<nCellsApprox<<" cells, computing inertia can take a long time.");
Vector3r x;
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(size_t i=0; i<centers.size(); i++){
if((x-centers[i]).squaredNorm()<pow(radii[i],2)){
volume+=dv;
Sg+=dv*x;
Ig+=dv*(x.dot(x)*Matrix3r::Identity()-x*x.transpose())+/*along princial axes of dv; perhaps negligible?*/Matrix3r(Vector3r::Constant(dv*pow(dx,2)/6.).asDiagonal());
break;
}
}
}
}
}
}
woo::Volumetric::computePrincipalAxes(volume,Sg,Ig,pos,ori,inertia);
equivRad=(inertia.array()/volume).sqrt().mean(); // mean of radii of gyration
}
/*
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));
}
};
