C++ Vector3r::norm方法代码示例

bool DihedralConstraint::initConstraint(SimulationModel &model, const unsigned int particle1, const unsigned int particle2,
										const unsigned int particle3, const unsigned int particle4)
{
	m_bodies[0] = particle1;
	m_bodies[1] = particle2;
	m_bodies[2] = particle3;
	m_bodies[3] = particle4;
	ParticleData &pd = model.getParticles();

	const Vector3r &p0 = pd.getPosition0(particle1);
	const Vector3r &p1 = pd.getPosition0(particle2);
	const Vector3r &p2 = pd.getPosition0(particle3);
	const Vector3r &p3 = pd.getPosition0(particle4);

	Vector3r e = p3 - p2;
	Real  elen = e.norm();
	if (elen < 1e-6)
		return false;

	Real invElen = 1.0 / elen;

	Vector3r n1 = (p2 - p0).cross(p3 - p0); n1 /= n1.squaredNorm();
	Vector3r n2 = (p3 - p1).cross(p2 - p1); n2 /= n2.squaredNorm();

	n1.normalize();
	n2.normalize();
	Real dot = n1.dot(n2);

	if (dot < -1.0) dot = -1.0;
	if (dot > 1.0) dot = 1.0;

	m_restAngle = acos(dot);

	return true;
}

// function used to check if the newly broken bond belongs in a cluster or not, if so attach to proper cluster and set appropriate flags
void Law2_ScGeom_JCFpmPhys_JointedCohesiveFrictionalPM::checkForCluster(JCFpmPhys* phys, ScGeom* geom, Body* b1, Body* b2, Interaction* contact){

	const shared_ptr<Shape>& sphere1 = b1->shape;
	const shared_ptr<Shape>& sphere2 = b2->shape;
	const Real sphereRadius1 = static_cast<Sphere*>(sphere1.get())->radius;
	const Real sphereRadius2 = static_cast<Sphere*>(sphere2.get())->radius;
	const Real avgDiameter = (sphereRadius1+sphereRadius2);
	Vector3r& brokenInteractionLocation = geom->contactPoint;
	phys->nearbyFound=0;

	FOREACH(const shared_ptr<Interaction>& I, *scene->interactions){
	//#endif
		JCFpmPhys* nearbyPhys;
		const ScGeom* nearbyGeom;
		if (!I || !I->geom.get() || !I->phys.get()) continue;
		if (I && I->isReal() && JCFpmPhys::getClassIndexStatic()==I->phys->getClassIndex()){
			nearbyPhys = YADE_CAST<JCFpmPhys*>(I->phys.get());
			if (!nearbyPhys) continue;
			if (I->geom.get() /*&& !nearbyPhys->momentBroken*/){
				nearbyGeom = YADE_CAST<ScGeom*> (I->geom.get());
                    		if (!nearbyGeom) continue;
				Vector3r nearbyInteractionLocation = nearbyGeom->contactPoint;
				Vector3r proximityVector = nearbyInteractionLocation-brokenInteractionLocation;
				Real proximity = proximityVector.norm();
				
				// this logic is finding interactions within a radius of the broken one, and identifiying if it is an original event or if it belongs in a cluster
				if (proximity < avgDiameter*momentRadiusFactor && proximity != 0){
					if (nearbyPhys->originalClusterEvent && !nearbyPhys->momentCalculated && !phys->clusteredEvent && clusterMoments) {
						phys->eventNumber = nearbyPhys->eventNumber; 
						phys->clusteredEvent = true;
						phys->originalEvent = I.get();
					} else if (nearbyPhys->clusteredEvent && !phys->clusteredEvent && clusterMoments){
						JCFpmPhys* originalPhys = YADE_CAST<JCFpmPhys*>(nearbyPhys->originalEvent->phys.get());
						if (!originalPhys->momentCalculated){
							phys->eventNumber = nearbyPhys->eventNumber;
							phys->clusteredEvent = true;
							phys->originalEvent = nearbyPhys->originalEvent;
						}
					} 

					if (nearbyPhys->momentBroken) continue;
					phys->nearbyInts.push_back(I.get());
				}
			}
		}
	}
	if (!phys->clusteredEvent) {
		phys->originalClusterEvent = true; // if not clustered, its an original event. We use this interaction as the master for the cluster. Its list of nearbyInts will expand if other ints break nearby. 
		phys->eventBeginTime=scene->time;
		phys->originalEvent = contact;
		eventNumber += 1;
		phys->eventNumber = eventNumber;
	}
	phys->checkedForCluster = true;
}

Vector3r SafetyEval::getDestination(const Vector3r& cur_pos, const Vector3r& velocity) const
{
    //breaking distance at this velocity
    float velocity_mag = velocity.norm();
    float dest_pos_dist = std::max(velocity_mag * vehicle_params_.vel_to_breaking_dist,
        vehicle_params_.min_breaking_dist);

    //calculate dest_pos cur_pos we will be if we had to break suddenly
    return velocity_mag >= vehicle_params_.distance_accuracy ? 
        (cur_pos + (velocity / velocity_mag) * dest_pos_dist) : cur_pos;
}

void SafetyEval::isSafeDestination(const Vector3r& dest_pos, const Vector3r& cur_pos, const Quaternionr& quaternion, SafetyEval::EvalResult& result)
{
    //this function should work even when dest_pos == cur_pos
    result.dest_pos = dest_pos;
    result.cur_pos = cur_pos;

    //is this dest_pos cur_pos within the fence?
    checkFence(dest_pos, cur_pos, result);
 
    if (!(enable_reasons_ & SafetyViolationType_::Obstacle))
        return;

    //transform dest_pos vector to body frame
    const Vector3r cur_dest = dest_pos - cur_pos;
    float cur_dest_norm = cur_dest.norm();    
    
    //check for approx zero vectors to avoid random yaw angles
    if (cur_dest_norm < vehicle_params_.distance_accuracy) {
        //we are hovering
        result.dest_risk_dist = Utils::nan<float>();
        isCurrentSafer(result);
    }
    else { //see if we have obstacle in direction 
        result.cur_dest_body = VectorMath::transformToBodyFrame(cur_dest, quaternion, true);

        //get yaw in body frame, ie, front is always 0 radians
        float point_angle = std::atan2(result.cur_dest_body[1], result.cur_dest_body[0]);

        //yaw to ticks
        int point_tick = obs_xy_ptr_->angleToTick(point_angle);

        //get obstacles in the window at the tick direction around the window
        result.dest_obs = obs_xy_ptr_->hasObstacle(point_tick - vehicle_params_.obs_window, point_tick + vehicle_params_.obs_window);

        //less risk distance is better
        result.dest_risk_dist = cur_dest_norm + adjustClearanceForPrStl(vehicle_params_.obs_clearance, result.dest_obs.confidence) - result.dest_obs.distance;
        if (result.dest_risk_dist >= 0) { //potential collision
            //check obstacles around current position and see if it has lower risk
            isCurrentSafer(result);
        }
        //else obstacle is too far
    }

    //if we detected unsafe condition due to obstacle, find direction to move away to
    if (!result.is_safe && result.reason & SafetyViolationType_::Obstacle) {
        //look for each surrounding tick to see if we have obstacle free angle
        setSuggestedVelocity(result, quaternion);

        Utils::log(Utils::stringf("isSafeDestination: cur_dest_norm=%f, result=%s, quaternion=%s", 
            cur_dest_norm, result.toString().c_str(), VectorMath::toString(quaternion, true).c_str()));
    }
    //else no suggestions required
}

//!			O/
bool Ig2_Sphere_GridConnection_ScGridCoGeom::go(	const shared_ptr<Shape>& cm1,
						const shared_ptr<Shape>& cm2,
						const State& state1, const State& state2, const Vector3r& shift2, const bool& force,
						const shared_ptr<Interaction>& c)
{	// Useful variables :
	const State*    sphereSt  = YADE_CAST<const State*>(&state1);
	//const State*    gridCoSt  = YADE_CAST<const State*>(&state2);
	Sphere*         sphere    = YADE_CAST<Sphere*>(cm1.get());
	GridConnection* gridCo    = YADE_CAST<GridConnection*>(cm2.get());
	//GridNode*       gridNo1   = YADE_CAST<GridNode*>(gridCo->node1->shape.get());
	//GridNode*       gridNo2   = YADE_CAST<GridNode*>(gridCo->node2->shape.get());
	State*          gridNo1St = YADE_CAST<State*>(gridCo->node1->state.get());
	State*          gridNo2St = YADE_CAST<State*>(gridCo->node2->state.get());
	bool isNew = !c->geom;
	shared_ptr<ScGridCoGeom> scm;
	if (!isNew) scm = YADE_PTR_CAST<ScGridCoGeom>(c->geom);
	Vector3r segt = gridCo->getSegment();
	float len = gridCo->getLength();
	Vector3r branch = sphereSt->pos - gridNo1St->pos;
	float relPos = branch.dot(segt)/(len*len);
	Vector3r fictiousPos=gridNo1St->pos+relPos*segt;
	Vector3r branchP = fictiousPos - sphereSt->pos;
 	float dist = branchP.norm();
	
	if(isNew){
		if(dist > (sphere->radius + gridCo->radius)) return false;
		else {scm=shared_ptr<ScGridCoGeom>(new ScGridCoGeom()); c->geom=scm;}
	}
	if(dist <= (sphere->radius + gridCo->radius)){
		scm->refR1=sphere->radius;	//FIXME don't know why I have to do that ...
		scm->refR2=gridCo->radius;
		scm->id3=gridCo->node1->getId();
 		scm->id4=gridCo->node2->getId();
		scm->relPos=relPos;
		Vector3r normal=branchP/dist;
		scm->penetrationDepth=sphere->radius+gridCo->radius-dist;
		scm->fictiousState.pos = gridNo1St->pos+segt*relPos;
		scm->fictiousState.vel = (1-relPos)*gridNo1St->vel + relPos*gridNo2St->vel;
		scm->fictiousState.angVel =
			((1-relPos)*gridNo1St->angVel + relPos*gridNo2St->angVel).dot(segt/len)*segt/len //twist part : interpolated
			+ segt.cross(gridNo2St->vel - gridNo1St->vel);// non-twist part : defined from nodes velocities
		scm->contactPoint = sphereSt->pos+normal*(sphere->radius-0.5*scm->penetrationDepth);
		scm->precompute(state1,scm->fictiousState,scene,c,normal,isNew,shift2,true);//use sphere-sphere precompute (with a virtual sphere)
	}
	return true;
}

	void Gl1_PolyhedraPhys::go(const shared_ptr<IPhys>& ip, const shared_ptr<Interaction>& i, const shared_ptr<Body>& b1, const shared_ptr<Body>& b2, bool wireFrame){
		if(!gluQuadric){ gluQuadric=gluNewQuadric(); if(!gluQuadric) throw runtime_error("Gl1_PolyhedraPhys::go unable to allocate new GLUquadric object (out of memory?)."); }
		PolyhedraPhys* np=static_cast<PolyhedraPhys*>(ip.get());
		shared_ptr<IGeom> ig(i->geom); if(!ig) return; // changed meanwhile?
		PolyhedraGeom* geom=YADE_CAST<PolyhedraGeom*>(ig.get());
		Real fnNorm=np->normalForce.dot(geom->normal);
		if((signFilter>0 && fnNorm<0) || (signFilter<0 && fnNorm>0)) return;
		int fnSign=fnNorm>0?1:-1;
		fnNorm=std::abs(fnNorm);
		Real radiusScale=1.;
		maxFn=max(fnNorm,maxFn);
		Real realMaxRadius;
		if(maxRadius<0){
			refRadius=min(0.03,refRadius);
			realMaxRadius=refRadius;
		}
		else realMaxRadius=maxRadius;
		Real radius=radiusScale*realMaxRadius*(fnNorm/maxFn); 
		if (radius<=0.) radius = 1E-8;
		Vector3r color=Shop::scalarOnColorScale(fnNorm*fnSign,-maxFn,maxFn);
		
		Vector3r p1=b1->state->pos, p2=b2->state->pos;
		Vector3r relPos;
		relPos=p2-p1;
		Real dist=relPos.norm();
				
		glDisable(GL_CULL_FACE); 
		glPushMatrix();
			glTranslatef(p1[0],p1[1],p1[2]);
			Quaternionr q(Quaternionr().setFromTwoVectors(Vector3r(0,0,1),relPos/dist /* normalized */));
			// using Transform with OpenGL: http://eigen.tuxfamily.org/dox/TutorialGeometry.html
			//glMultMatrixd(Eigen::Affine3d(q).data());
			glMultMatrix(Eigen::Transform<Real,3,Eigen::Affine>(q).data());
			glColor3v(color);
			gluCylinder(gluQuadric,radius,radius,dist,slices,stacks);
		glPopMatrix();
	}

bool Law2_ScGeom_MindlinPhys_Mindlin::go(shared_ptr<IGeom>& ig, shared_ptr<IPhys>& ip, Interaction* contact){
	const Real& dt = scene->dt; // get time step
	
	Body::id_t id1 = contact->getId1(); // get id body 1
 	Body::id_t id2 = contact->getId2(); // get id body 2

	State* de1 = Body::byId(id1,scene)->state.get();
	State* de2 = Body::byId(id2,scene)->state.get();	

	ScGeom* scg = static_cast<ScGeom*>(ig.get());
	MindlinPhys* phys = static_cast<MindlinPhys*>(ip.get());	

	const shared_ptr<Body>& b1=Body::byId(id1,scene); 
	const shared_ptr<Body>& b2=Body::byId(id2,scene); 

	bool useDamping=(phys->betan!=0. || phys->betas!=0. || phys->alpha!=0.);
	bool LinDamp=true;
	if (phys->alpha!=0.) {LinDamp=false;} // use non linear damping

	// tangential and normal stiffness coefficients, recomputed from betan,betas at every step
	Real cn=0, cs=0;

	/****************/
	/* NORMAL FORCE */
	/****************/
	
	Real uN = scg->penetrationDepth; // get overlapping 
	if (uN<0) {
		if (neverErase) {phys->shearForce = phys->normalForce = Vector3r::Zero(); phys->kn=phys->ks=0; return true;}
		else return false;
	}
	/* Hertz-Mindlin's formulation (PFC) 
	Note that the normal stiffness here is a secant value (so as it is cannot be used in the GSTS)
	In the first place we get the normal force and then we store kn to be passed to the GSTS */
	Real Fn = phys->kno*std::pow(uN,1.5); // normal Force (scalar)
	if (includeAdhesion) {
			Fn -= phys->adhesionForce; // include adhesion force to account for the effect of Van der Waals interactions
			phys->isAdhesive = (Fn<0); // set true the bool to count the number of adhesive contacts
			}
	phys->normalForce = Fn*scg->normal; // normal Force (vector)

	if (calcEnergy){
		Real R=scg->radius1*scg->radius2/(scg->radius1+scg->radius2);
		phys->radius=pow((Fn+(includeAdhesion?phys->adhesionForce:0.))*pow(R,3/2.)/phys->kno,1/3.); // attribute not used anywhere, we do not need it
	}

	/*******************************/
	/* TANGENTIAL NORMAL STIFFNESS */
	/*******************************/
	
	phys->kn = 3./2.*phys->kno*std::pow(uN,0.5); // here we store the value of kn to compute the time step
	
	/******************************/
	/* TANGENTIAL SHEAR STIFFNESS */
	/******************************/
	
	phys->ks = phys->kso*std::pow(uN,0.5); // get tangential stiffness (this is a tangent value, so we can pass it to the GSTS)

	/************************/
	/* DAMPING COEFFICIENTS */
	/************************/
	
	// Inclusion of local damping if requested
	// viscous damping is defined for both linear and non-linear elastic case 
	if (useDamping && LinDamp){
		Real mbar = (!b1->isDynamic() && b2->isDynamic()) ? de2->mass : ((!b2->isDynamic() && b1->isDynamic()) ? de1->mass : (de1->mass*de2->mass / (de1->mass + de2->mass))); // get equivalent mass if both bodies are dynamic, if not set it equal to the one of the dynamic body
		//Real mbar = de1->mass*de2->mass / (de1->mass + de2->mass); // equivalent mass
		Real Cn_crit = 2.*sqrt(mbar*phys->kn); // Critical damping coefficient (normal direction)
		Real Cs_crit = 2.*sqrt(mbar*phys->ks); // Critical damping coefficient (shear direction)
		// Note: to compare with the analytical solution you provide cn and cs directly (since here we used a different method to define c_crit)
		cn = Cn_crit*phys->betan; // Damping normal coefficient
		cs = Cs_crit*phys->betas; // Damping tangential coefficient
		if(phys->kn<0 || phys->ks<0){ cerr<<"Negative stiffness kn="<<phys->kn<<" ks="<<phys->ks<<" for ##"<<b1->getId()<<"+"<<b2->getId()<<", step "<<scene->iter<<endl; }
	}
	else if (useDamping){ // (see Tsuji, 1992)
		Real mbar = (!b1->isDynamic() && b2->isDynamic()) ? de2->mass : ((!b2->isDynamic() && b1->isDynamic()) ? de1->mass : (de1->mass*de2->mass / (de1->mass + de2->mass))); // get equivalent mass if both bodies are dynamic, if not set it equal to the one of the dynamic body
		cn = phys->alpha*sqrt(mbar)*pow(uN,0.25); // normal viscous coefficient, see also [Antypov2011] eq. 10
		cs = cn; // same value for shear viscous coefficient
	}

	/***************/
	/* SHEAR FORCE */
	/***************/
	
	Vector3r& shearElastic = phys->shearElastic; // reference for shearElastic force
	// Define shifts to handle periodicity
	const Vector3r shift2 = scene->isPeriodic ? scene->cell->intrShiftPos(contact->cellDist): Vector3r::Zero(); 
	const Vector3r shiftVel = scene->isPeriodic ? scene->cell->intrShiftVel(contact->cellDist): Vector3r::Zero(); 
	// 1. Rotate shear force
	shearElastic = scg->rotate(shearElastic);
	Vector3r prev_FsElastic = shearElastic; // save shear force at previous time step
	// 2. Get incident velocity, get shear and normal components
	Vector3r incidentV = scg->getIncidentVel(de1, de2, dt, shift2, shiftVel, preventGranularRatcheting);	
	Vector3r incidentVn = scg->normal.dot(incidentV)*scg->normal; // contact normal velocity
	Vector3r incidentVs = incidentV - incidentVn; // contact shear velocity
	// 3. Get shear force (incrementally)
	shearElastic = shearElastic - phys->ks*(incidentVs*dt);

	/**************************************/
	/* VISCOUS DAMPING (Normal direction) */
//.........这里部分代码省略.........

void Law2_ScGeom_CFpmPhys_CohesiveFrictionalPM::go(shared_ptr<IGeom>& ig, shared_ptr<IPhys>& ip, Interaction* contact){
	ScGeom* geom = static_cast<ScGeom*>(ig.get()); 
	CFpmPhys* phys = static_cast<CFpmPhys*>(ip.get());
	const int &id1 = contact->getId1();
	const int &id2 = contact->getId2();
	Body* b1 = Body::byId(id1,scene).get();
	Body* b2 = Body::byId(id2,scene).get();
	
	Real displN = geom->penetrationDepth; // NOTE: the sign for penetrationdepth is different from ScGeom and Dem3DofGeom: geom->penetrationDepth>0 when spheres interpenetrate
	Real Dtensile=phys->FnMax/phys->kn;
	Real Dsoftening = phys->strengthSoftening*Dtensile; 
	
	/*to set the equilibrium distance between all cohesive elements when they first meet -> allows one to work with initial stress-free assembly*/
	if ( contact->isFresh(scene) ) { phys->initD = displN; phys->normalForce = Vector3r::Zero(); phys->shearForce = Vector3r::Zero();}
	Real D = displN - phys->initD; // interparticular distance is computed depending on the equilibrium distance

	/* Determination of interaction */
	if (D < 0){ //spheres do not touch 
	  if (!phys->isCohesive){ scene->interactions->requestErase(contact); return; } // destroy the interaction before calculation
	  if ((phys->isCohesive) && (abs(D) > (Dtensile + Dsoftening))) { // spheres are bonded and the interacting distance is greater than the one allowed ny the defined cohesion
	    phys->isCohesive=false; 
	    // update body state with the number of broken bonds
	    CFpmState* st1=dynamic_cast<CFpmState*>(b1->state.get());
	    CFpmState* st2=dynamic_cast<CFpmState*>(b2->state.get());
	    st1->numBrokenCohesive+=1;
	    st2->numBrokenCohesive+=1;
	    //// the same thing but from ConcretePM
	    //const shared_ptr<Body>& body1=Body::byId(contact->getId1(),scene), body2=Body::byId(contact->getId2(),scene); assert(body1); assert(body2);
	    //const shared_ptr<CFpmState>& st1=YADE_PTR_CAST<CFpmState>(body1->state), st2=YADE_PTR_CAST<CFpmState>(body2->state);
	    //{ boost::mutex::scoped_lock lock(st1->updateMutex); st1->numBrokenCohesive+=1; }
	    //{ boost::mutex::scoped_lock lock(st2->updateMutex); st2->numBrokenCohesive+=1; }
	    // end of update
	    scene->interactions->requestErase(contact); return;
	  }
	}	  
	
	/*NormalForce*/
	Real Fn=0, Dsoft=0;
		
	if ((D < 0) && (abs(D) > Dtensile)) { //to take into account strength softening
	  Dsoft = D+Dtensile; // Dsoft<0 for a negative value of Fn (attractive force)
	  Fn = -(phys->FnMax+(phys->kn/phys->strengthSoftening)*Dsoft); // computes FnMax - FnSoftening
	}
	else {
	  Fn = phys->kn*D;
	}
	phys->normalForce = Fn*geom->normal;  // NOTE normal is position2-position1 - It is directed from particle1 to particle2
	        
	/*ShearForce*/
	Vector3r& shearForce = phys->shearForce; 
		
	// using scGeom function rotateAndGetShear	
	State* st1 = Body::byId(id1,scene)->state.get();
	State* st2 = Body::byId(id2,scene)->state.get();

	geom->rotate(phys->shearForce);
	const Vector3r& dus = geom->shearIncrement();
	
	//Linear elasticity giving "trial" shear force
	shearForce -= phys->ks*dus;
	// needed for the next timestep
	phys->prevNormal = geom->normal;
		
	/* Morh-Coulomb criterion */
	Real maxFs = phys->FsMax + Fn*phys->tanFrictionAngle;

	if (shearForce.squaredNorm() > maxFs*maxFs){ 
	  shearForce*=maxFs/shearForce.norm(); // to fix the shear force to its yielding value
	}
	
	/* Apply forces */
	Vector3r f = phys->normalForce + shearForce;
	// these lines to adapt to periodic boundary conditions (NOTE applyForceAtContactPoint computes torque induced by normal and shear force too)
	if (!scene->isPeriodic)  
	applyForceAtContactPoint(f , geom->contactPoint , id2, st2->se3.position, id1, st1->se3.position);
	else { // in scg we do not wrap particles positions, hence "applyForceAtContactPoint" cannot be used when scene is periodic
		scene->forces.addForce(id1,-f);
		scene->forces.addForce(id2,f);
		scene->forces.addTorque(id1,(geom->radius1-0.5*geom->penetrationDepth)* geom->normal.cross(-f));
		scene->forces.addTorque(id2,(geom->radius2-0.5*geom->penetrationDepth)* geom->normal.cross(-f));
	}
	
	/* Moment Rotation Law */
	// NOTE this part could probably be computed in ScGeom to avoid copy/paste multiplication !!!
	Quaternionr delta( b1->state->ori * phys->initialOrientation1.conjugate() *phys->initialOrientation2 * b2->state->ori.conjugate()); delta.normalize(); //relative orientation
	AngleAxisr aa(delta); // axis of rotation - this is the Moment direction UNIT vector; angle represents the power of resistant ELASTIC moment
	if(aa.angle() > Mathr::PI) aa.angle() -= Mathr::TWO_PI; // angle is between 0 and 2*pi, but should be between -pi and pi 
	  
	phys->cumulativeRotation = aa.angle();
	  
	//Find angle*axis. That's all.  But first find angle about contact normal. Result is scalar. Axis is contact normal.
	Real angle_twist(aa.angle() * aa.axis().dot(geom->normal) ); //rotation about normal
	Vector3r axis_twist(angle_twist * geom->normal);
	Vector3r moment_twist(axis_twist * phys->kr);
	  
	Vector3r axis_bending(aa.angle()*aa.axis() - axis_twist); //total rotation minus rotation about normal
	Vector3r moment_bending(axis_bending * phys->kr);
	Vector3r moment = moment_twist + moment_bending;
	
	Real MomentMax = phys->maxBend*std::fabs(phys->normalForce.norm());
//.........这里部分代码省略.........

bool Ig2_Facet_Sphere_ScGeom::go(const shared_ptr<Shape>& cm1,
							const shared_ptr<Shape>& cm2,
							const State& state1,
							const State& state2,
							const Vector3r& shift2,
							const bool& force,
							const shared_ptr<Interaction>& c)
{
	TIMING_DELTAS_START();
	const Se3r& se31=state1.se3; const Se3r& se32=state2.se3;
	Facet*   facet = static_cast<Facet*>(cm1.get());
	/* could be written as (needs to be tested):
	 * Vector3r cl=se31.orientation.Conjugate()*(se32.position-se31.position);
	 */
	Matrix3r facetAxisT=se31.orientation.toRotationMatrix(); 
	Matrix3r facetAxis = facetAxisT.transpose();
	// local orientation
	Vector3r cl = facetAxis*(se32.position + shift2 - se31.position);  // "contact line" in facet-local coords

	//
	// BEGIN everything in facet-local coordinates
	//

	Vector3r normal = facet->normal;
	Real L = normal.dot(cl);
	if (L<0) {normal=-normal; L=-L; }

	Real sphereRadius = static_cast<Sphere*>(cm2.get())->radius;
	if (L>sphereRadius && !c->isReal() && !force) { // no contact, but only if there was no previous contact; ortherwise, the constitutive law is responsible for setting Interaction::isReal=false
		TIMING_DELTAS_CHECKPOINT("Ig2_Facet_Sphere_ScGeom");
		return false;
	}

	Vector3r cp = cl - L*normal;
	const Vector3r* ne = facet->ne;
	
	Real penetrationDepth=0;
	
	Real bm = ne[0].dot(cp);
	int m=0;
	for (int i=1; i<3; ++i)
	{
		Real b=ne[i].dot(cp);
		if (bm<b) {bm=b; m=i;}
	}

	Real sh = sphereRadius*shrinkFactor;
	Real icr = facet->icr-sh;

	if (icr<0)
	{
		LOG_WARN("a radius of a facet's inscribed circle less than zero! So, shrinkFactor is too large and would be reduced to zero.");
		shrinkFactor=0;
		icr = facet->icr;
		sh = 0;
	}


	if (bm<icr) // contact with facet's surface
	{
		penetrationDepth = sphereRadius - L;
		normal.normalize();
	}
	else
	{
		cp = cp + ne[m]*(icr-bm);
		if (cp.dot(ne[(m-1<0)?2:m-1])>icr) // contact with vertex m
//			cp = facet->vertices[m];
			cp = facet->vu[m]*(facet->vl[m]-sh);
		else if (cp.dot(ne[m=(m+1>2)?0:m+1])>icr) // contact with vertex m+1
//			cp = facet->vertices[(m+1>2)?0:m+1];
			cp = facet->vu[m]*(facet->vl[m]-sh);
		normal = cl-cp;
		Real norm=normal.norm(); normal/=norm;
		penetrationDepth = sphereRadius - norm;
	}

	//
	// END everything in facet-local coordinates
	//

	if (penetrationDepth>0 || c->isReal())
	{
		shared_ptr<ScGeom> scm;
		bool isNew = !c->geom;
		if (c->geom)
			scm = YADE_PTR_CAST<ScGeom>(c->geom);
		else
			scm = shared_ptr<ScGeom>(new ScGeom());
	  
		normal = facetAxisT*normal; // in global orientation
		scm->contactPoint = se32.position + shift2 - (sphereRadius-0.5*penetrationDepth)*normal;
		scm->penetrationDepth = penetrationDepth;
		scm->radius1 = 2*sphereRadius;
		scm->radius2 = sphereRadius;
		if (isNew) c->geom = scm;
		scm->precompute(state1,state2,scene,c,normal,isNew,shift2,false/*avoidGranularRatcheting only for sphere-sphere*/);
		TIMING_DELTAS_CHECKPOINT("Ig2_Facet_Sphere_ScGeom");
		return true;
	}
//.........这里部分代码省略.........

string FlowAnalysis::vtkExportFractions(const string& out, /*copy, since we may modify locally*/ vector<size_t> fractions){ 
	if(timeSpan==0.) throw std::runtime_error("FlowAnalysis.timeSpan==0, no data was ever collected.");
	if(nFractions<=0) throw std::runtime_error("FlowAnalysis.nFractions<=0?!!");
	auto grid=vtkMakeGrid();
	auto flow=vtkMakeArray(grid,"flow (momentum density)",3);
	auto flowNorm=vtkMakeArray(grid,"|flow|",1);
	auto ek=vtkMakeArray(grid,"Ek density",1);
	auto hitRate=vtkMakeArray(grid,"hit rate",1);
	auto sumWeight=vtkMakeArray(grid,"sum weight",1);

	auto diam=vtkMakeArray(grid,"avg. diameter",1);
	auto solid=vtkMakeArray(grid,"avg. solid ratio",1);
	auto vel=vtkMakeArray(grid,"avg. velocity",3);
	// no fractions given, export all of them together
	if(fractions.empty()){ for(size_t i=0; i<(size_t)nFractions; i++) fractions.push_back(i); }

	for(size_t fraction: fractions){
		if((int)fraction>=nFractions) throw std::runtime_error("FlowAnalysis.vtkExportFraction: fraction="+to_string(fraction)+" out of range 0.."+to_string(nFractions-1));
		// traverse the grid now
		for(int i=0; i<boxCells[0]; i++){
			for(int j=0; j<boxCells[1]; j++){
				for(int k=0; k<boxCells[2]; k++){
					int ijk[]={i,j,k};
					vtkIdType dataId;
					if(cellData) dataId=grid->ComputeCellId(ijk);
					else dataId=grid->ComputePointId(ijk);
					const auto ptData(data[fraction][i][j][k]);
					/* quantities SUMMED over fractions */
					// flow vector
					Vector3r f;
					flow->GetTupleValue(dataId,f.data());
					flow->SetTupleValue(dataId,(f+Vector3r(ptData[PT_FLOW_X],ptData[PT_FLOW_Y],ptData[PT_FLOW_Z])/timeSpan).eval().data());
					// scalars
					*(ek->GetPointer(dataId))+=ptData[PT_EK]/timeSpan;
					*(hitRate->GetPointer(dataId))+=ptData[PT_SUM_WEIGHT]/timeSpan;
					*(sumWeight->GetPointer(dataId))+=ptData[PT_SUM_WEIGHT];

					/* quantities AVERAGED over fractions (summed here and divided by summary weight in the next loop) */
					*(diam ->GetPointer(dataId))+=ptData[PT_SUM_DIAM];
					*(solid->GetPointer(dataId))+=ptData[PT_SUM_SOLID_RATIO];
					Vector3r v;
					vel->GetTupleValue(dataId,v.data());
					vel->SetTupleValue(dataId,(v+Vector3r(ptData[PT_VEL_X],ptData[PT_VEL_Y],ptData[PT_VEL_Z])).eval().data());
				}
			}
		}
	}
	// extra loop to fill the |flow|
	// (cannot be done incrementally above, as sum or norms does not equal norm of sums)
	for(int i=0; i<boxCells[0]; i++){
		for(int j=0; j<boxCells[1]; j++){
			for(int k=0; k<boxCells[2]; k++){
				int ijk[]={i,j,k};
				vtkIdType dataId;
				if(cellData) dataId=grid->ComputeCellId(ijk);
				else dataId=grid->ComputePointId(ijk);
				Vector3r f;
				flow->GetTupleValue(dataId,f.data());
				flowNorm->SetValue(dataId,f.norm());
				// averages over all fractions
				Real wAll=0.;
				for(size_t fraction: fractions) wAll+=data[fraction][i][j][k][PT_SUM_WEIGHT];
				if(wAll!=0){
					*(diam ->GetPointer(dataId))/=wAll;
					*(solid->GetPointer(dataId))/=wAll;
					Vector3r v; vel->GetTupleValue(dataId,v.data()); vel->SetTupleValue(dataId,(v/wAll).eval().data());
				} else {
					*(diam ->GetPointer(dataId))=NaN;
					*(solid->GetPointer(dataId))=0;
					vel->SetTupleValue(dataId,Vector3r::Zero().eval().data());
				}

			}
		}
	}
	return vtkWriteGrid(out,grid);
}

bool Ig2_ChainedCylinder_ChainedCylinder_ScGeom6D::go(	const shared_ptr<Shape>& cm1,
							const shared_ptr<Shape>& cm2,
							const State& state1, const State& state2, const Vector3r& shift2, const bool& force,
							const shared_ptr<Interaction>& c)
{
	const ChainedState *pChain1, *pChain2;
	pChain1=YADE_CAST<const ChainedState*>(&state1);
	pChain2=YADE_CAST<const ChainedState*>(&state2);
	unsigned int sizeChain1=pChain1->chains[pChain1->chainNumber].size();
	unsigned int sizeChain2=pChain2->chains[pChain2->chainNumber].size();
	if (!pChain1 || !pChain2) {
		cerr <<"cast failed8567"<<endl;
	}
	const bool revert = ((int) pChain2->rank- (int) pChain1->rank == -1);
	const ChainedState& bchain1 = revert? *pChain2 : *YADE_CAST<const ChainedState*>(&state1);
	const ChainedState& bchain2 = revert? *pChain1 : *pChain2;
	ChainedCylinder *bs1=static_cast<ChainedCylinder*>(revert? cm2.get():cm1.get());
	bool isLast = bchain1.chains[bchain1.chainNumber].size()==(bchain1.rank+1) || bchain2.chains[bchain2.chainNumber].size()==(bchain2.rank+1);
	bool isNew = !c->geom;
	if (pChain2->chainNumber!=pChain1->chainNumber) {
		shared_ptr<ChCylGeom6D> scm;
		if(isLast){ return false; }
		shared_ptr<Body> cylinderNext1=Body::byId(pChain1->chains[pChain1->chainNumber][pChain1->rank+1],scene);
		shared_ptr<Body> cylinderNext2=Body::byId(pChain2->chains[pChain2->chainNumber][pChain2->rank+1],scene);
		//cout<<c->id1<<"  "<<c->id2<<endl;
		bool colinearVectors=0, insideCyl1=1, insideCyl2=1;	//insideCyl1&2 are used to determine whether the contact is inside each cylinder's segment
		Real dist=NaN,k=0,m=0;	//k and m are the parameters of the fictious states on the cylinders.
		Vector3r A=pChain1->pos, a=cylinderNext1->state->pos-A , B=pChain2->pos , b=cylinderNext2->state->pos-B;
		Vector3r N=a.cross(b);
		Vector3r normal;
		if(N.norm()>1e-14){
			dist=std::abs(N.dot(B-A)/(N.norm()));	//distance between the two LINES.
			//But we need to check that the intersection point is inside the two SEGMENTS ...
			//Projection of B to have a common plan between the two segments.
			Vector3r projB1=B+dist*(N/(N.norm())) , projB2=B-dist*(N/(N.norm()));
			Real distB1A=(projB1-A).norm() , distB2A=(projB2-A).norm() ;
			Vector3r projB=(distB1A<=distB2A)*projB1 + (distB1A>distB2A)*projB2;
			int b1=0, b2=1; //base vectors used to compute the segment intersection (if N is aligned with an axis, we can't use this axis)
			if(std::abs(N[1])<1e-14 && std::abs(N[2])<1e-14){b1=1;b2=2;}
			if(std::abs(N[0])<1e-14 && std::abs(N[2])<1e-14){b1=0;b2=2;}
			Real det=a[b1]*b[b2]-a[b2]*b[b1];
			if(std::abs(det)>1e-14){	//Check if the two segments are intersected (using k and m)
				k = (b[b2]*(projB[b1]-A[b1])+b[b1]*(A[b2]-projB[b2]))/det;
				m = (a[b1]*(-projB[b2]+A[b2])+a[b2]*(projB[b1]-A[b1]))/det;
				if( k<0.0 || k>=1.0 || m<0.0 || m>=1.0 ) {	//so they are not intersected
					dist=NaN;
					if(k>=1){k=1;
						if(!(pChain1->rank>=sizeChain1-2))insideCyl1=0;
					}
					if(k<0){k=0;
						if(!(pChain1->rank==0))insideCyl1=0;
					}
					if(m>=1){m=1;
						if(!(pChain2->rank>=sizeChain2-2))insideCyl2=0;
					}
					if(m<0){m=0;
						if(!(pChain2->rank==0))insideCyl2=0;
					}
				}
			}
			else cout<<"Error in Ig2_ChainedCylinder_ChainedCylinder_ScGeom6D : det==0 !!!"<<endl;//should not happen
		}
		else {
			//Special case for parallel cylinders.
			//FIXME : this is an approximation, but it seems very complicated to do something else.
			//FIXME : contact following have to be done for parallel cylinders.
			colinearVectors=1;
			insideCyl1=1 ; insideCyl2=1;
			Real PA=(A-B).dot(b)/(b.norm()*b.norm()); PA=min((Real)1.0,max((Real)0.0,PA));
			Real Pa=(A+a-B).dot(b)/(b.norm()*b.norm()); Pa=min((Real)1.0,max((Real)0.0,Pa));
			Real PB=(B-A).dot(a)/(a.norm()*a.norm()); PB=min((Real)1.0,max((Real)0.0,PB));
			Real Pb=(B+b-A).dot(a)/(a.norm()*a.norm()); Pb=min((Real)1.0,max((Real)0.0,Pb));
			
			Real h1=(A+0.5*a-B).dot(b)/(b.norm()*b.norm());	//Projection parameter of center of a on b
			Real h2=(B+0.5*b-A).dot(a)/(a.norm()*a.norm());	//Projection parameter of center of b on a
			k=(PB+Pb)/2. ; m=(PA+Pa)/2.; dist= (A+k*a - (B+m*b)).norm();
			bool edgeEdgeContact = (h1>1 && pChain2->rank>=sizeChain2-2) || (h1<0 && pChain2->rank==0) || (h2>1 && pChain1->rank>=sizeChain1-2) || (h2<0 && pChain1->rank==0);
			if(edgeEdgeContact)colinearVectors=0;
			if( (0<=h1 and 1>h1) or (0<=h2 and 1>h2) or edgeEdgeContact){;	//Do a perfectly flat contact
			}
			else return false;//Parallel lines but edge-edge contact
		}
		
		ChainedCylinder *cc1=static_cast<ChainedCylinder*>(cm1.get());
		ChainedCylinder *cc2=static_cast<ChainedCylinder*>(cm2.get());
		if(isnan(dist)){ //now if we didn't found a suitable distance because the segments don't cross each other, we try to find a sphere-cylinder distance.
			Vector3r pointsToCheck[4]={A,A+a,B,B+b}; Real resultDist=dist, resultProj=dist ; int whichCaseIsCloser=-1 ;
			for (int i=0;i<4;i++){  //loop on the 4 cylinder's extremities and look at the extremity-cylinder distance
				Vector3r S=pointsToCheck[i], C=(i<2)?B:A, vec=(i<2)?b:a; Vector3r CS=S-C;
				Real d=CS.dot(vec)/(vec.norm());
				if(d<0.) resultDist=CS.norm();
				else if(d>vec.norm()) resultDist=(C+vec-S).norm();
				else resultDist=(CS.cross(vec)).norm()/(vec.norm());
				if(dist>resultDist or isnan(dist)){dist=resultDist ; whichCaseIsCloser=i; resultProj=d;}
			}
			//we know which extremity may be in contact (i), so k and m are computed to generate the right fictiousStates.
			insideCyl1=1 ; insideCyl2=1;
			
			//FIXME:NATCHOS ! this should be reformulated
			if(whichCaseIsCloser==0 || whichCaseIsCloser==1){
//.........这里部分代码省略.........

	void Gl1_NormPhys::go(const shared_ptr<IPhys>& ip, const shared_ptr<Interaction>& i, const shared_ptr<Body>& b1, const shared_ptr<Body>& b2, bool wireFrame){
		if(!gluQuadric){ gluQuadric=gluNewQuadric(); if(!gluQuadric) throw runtime_error("Gl1_NormPhys::go unable to allocate new GLUquadric object (out of memory?)."); }
		NormPhys* np=static_cast<NormPhys*>(ip.get());
		shared_ptr<IGeom> ig(i->geom); if(!ig) return; // changed meanwhile?
		GenericSpheresContact* geom=YADE_CAST<GenericSpheresContact*>(ig.get());
		//if(!geom) cerr<<"Gl1_NormPhys: IGeom is not a GenericSpheresContact, but a "<<ig->getClassName()<<endl;
		Real fnNorm=np->normalForce.dot(geom->normal);
		if((signFilter>0 && fnNorm<0) || (signFilter<0 && fnNorm>0)) return;
		int fnSign=fnNorm>0?1:-1;
		fnNorm=abs(fnNorm);
		Real radiusScale=1.;
		// weak/strong fabric, only used if maxWeakFn is set
		if(!isnan(maxWeakFn)){
			if(fnNorm*fnSign<maxWeakFn){ // weak fabric
				if(weakFilter>0) return;
				radiusScale=weakScale;
			} else { // strong fabric
				if(weakFilter<0) return;
			}
		}

		maxFn=max(fnNorm,maxFn);
		Real realMaxRadius;
		if(maxRadius<0){
			if(geom->refR1>0) refRadius=min(geom->refR1,refRadius);
			if(geom->refR2>0) refRadius=min(geom->refR2,refRadius);
			realMaxRadius=refRadius;
		}
		else realMaxRadius=maxRadius;
		Real radius=radiusScale*realMaxRadius*(fnNorm/maxFn); // use logarithmic scale here?
		Vector3r color=Shop::scalarOnColorScale(fnNorm*fnSign,-maxFn,maxFn);
		# if 0
			// get endpoints from body positions
			Vector3r p1=b1->state->pos, p2=b2->state->pos;
			Vector3r relPos;
			if(scene->isPeriodic){
				relPos=p2+scene->cell->Hsize*i->cellDist.cast<Real>()-p1;
				p1=scene->cell->wrapShearedPt(p1);
				p2=p1+relPos;
			} else {
				relPos=p2-p1;
			}
			Real dist=relPos.norm();
		#else
			// get endpoints from geom
			// max(r,0) handles r<0 which is the case for "radius" of the facet in Dem3DofGeom_FacetSphere
			Vector3r cp=scene->isPeriodic? scene->cell->wrapShearedPt(geom->contactPoint) : geom->contactPoint;
			Vector3r p1=cp-max(geom->refR1,(Real)0.)*geom->normal;
			Vector3r p2=cp+max(geom->refR2,(Real)0.)*geom->normal;
			const Vector3r& dispScale=scene->renderer ? scene->renderer->dispScale : Vector3r::Ones(); 
			if(dispScale!=Vector3r::Ones()){
				// move p1 and p2 by the same amounts as particles themselves would be moved
				p1+=dispScale.cwiseProduct(Vector3r(b1->state->pos-b1->state->refPos));
				p2+=dispScale.cwiseProduct(Vector3r(b2->state->pos-b2->state->refPos));
			}
			Vector3r relPos=p2-p1;
			Real dist=relPos.norm(); //max(geom->refR1,0.)+max(geom->refR2,0.);
	#endif


	glDisable(GL_CULL_FACE); 
	glPushMatrix();
		glTranslatef(p1[0],p1[1],p1[2]);
		Quaternionr q(Quaternionr().setFromTwoVectors(Vector3r(0,0,1),relPos/dist /* normalized */));
		// using Transform with OpenGL: http://eigen.tuxfamily.org/dox/TutorialGeometry.html
		//glMultMatrixd(Eigen::Affine3d(q).data());
		glMultMatrix(Eigen::Transform<Real,3,Eigen::Affine>(q).data());
		glColor3v(color);
		gluCylinder(gluQuadric,radius,radius,dist,slices,stacks);
	glPopMatrix();
}

void RockLiningGlobal::action(){
	const double PI = 3.14159;
	if (openingCreated == true && installed == false){
		
		double angleInterval = 2.0*PI/static_cast<double>(totalNodes);
		for (int n=0; n<totalNodes;n++){
			double currentAngle = 0.0 + n*angleInterval; /* from 0 degrees east */
			double unitX = cos(currentAngle);
			double unitY = sin(currentAngle);
			Vector3r searchDir(unitX,0,unitY);

			vector<double> distanceFrOpening; vector<int> IDs;
			double outerRadius = openingRad + 1.0;
			FOREACH(const shared_ptr<Body>& b, *scene->bodies){
				if (!b) continue;
				if (b->isClump() == true) continue;
				PotentialBlock* pb=static_cast<PotentialBlock*>(b->shape.get()); 
				if(!pb) continue;
				if(pb->isBoundary == true || pb->erase== true || pb->isLining==true){continue;}	
				State* state1 = b->state.get();				
				Vector3r intersectionPt(0,0,0);
				if ( installLining(pb,  state1, startingPoint, searchDir, outerRadius, intersectionPt )){
					IDs.push_back(b->id);
					distanceFrOpening.push_back((intersectionPt-startingPoint).norm());
					//std::cout<<"currentAngle: "<<currentAngle<<", b->id: "<<b->id<<", dist: "<<(intersectionPt-startingPoint).norm()<<endl;
				}
			}

			/* find closest block */
			int totalBlocks = IDs.size(); 
			double closestDistance = 100000.0; 
			int closestID=0;
			for (int i=0; i<totalBlocks; i++){
				if ( distanceFrOpening[i] < closestDistance){
					closestID = IDs[i];
					closestDistance = distanceFrOpening[i];
				}			
			}
			stickIDs.push_back(closestID);
			IDs.clear();distanceFrOpening.clear();
//std::cout<<"closestID: "<<closestID<<endl;
	
			/* find intersection with edges of polygon */
			Vector3r jointIntersection (0,0,0); 
			State* state1 = Body::byId(closestID,scene)->state.get();
			Shape* shape1 = Body::byId(closestID,scene)->shape.get();
			PotentialBlock *pb=static_cast<PotentialBlock*>(shape1);
			int totalPlanes = pb->a.size();
			int intersectNo = 0;
			Vector3r nodeLocalPos(0,0,0); Vector3r nodeGlobalPos(0,0,0);
//std::cout<<"totalPlanes: "<<totalPlanes<<endl;
			double closestPlaneDist = 1000000;
			for (int i=0; i<totalPlanes; i++){						
					Vector3r plane = state1->ori*Vector3r(pb->a[i], pb->b[i], pb->c[i]); double planeD = plane.dot(state1->pos) + pb->d[i] +pb->r;
					if ( intersectPlane(pb, state1,startingPoint,searchDir, outerRadius, jointIntersection, plane, planeD)){
						double distance = jointIntersection.norm();
						if (distance < closestPlaneDist){
							closestPlaneDist = distance;
							nodeLocalPos = state1->ori.conjugate()*(jointIntersection-state1->pos);
							nodeGlobalPos=jointIntersection;
						}
						
					}
			}
			if(nodeGlobalPos.norm() > 1.03*openingRad){ nodeGlobalPos=1.03*openingRad*searchDir;} 
			//if(nodeGlobalPos.norm() < 0.98*openingRad){ continue;} 
			//initOverlap = interfaceTension/interfaceStiffness;
			nodeGlobalPos = nodeGlobalPos + searchDir*initOverlap;
			localCoordinates.push_back(nodeLocalPos);
			refPos.push_back(nodeGlobalPos);
			int nodeID = insertNode(nodeGlobalPos, lumpedMass, contactLength);
			blockIDs.push_back(nodeID); //(nodeID); //(closestID);
			refOri.push_back(Quaternionr::Identity()); //(state1->ori);
			installed = true;
			
			axialForces.push_back(0.0);
			shearForces.push_back(0.0);
			moment.push_back(0.0);
			sigmaMax.push_back(0.0);
			sigmaMin.push_back(0.0);
			displacement.push_back(0.0);
			radialDisplacement.push_back(0.0);
		}
		totalNodes=blockIDs.size();

	
		/* Assembling global stiffness matrix */
		for (int n=0; n<totalNodes;n++){
			int nextID = n+1;
			if(nextID==totalNodes){nextID=0;}
			double Length = (refPos[nextID]-refPos[n]).norm();
			lengthNode.push_back(Length);
			
			Vector3r localDir = refPos[nextID]-refPos[n];
			localDir.normalize(); refDir.push_back(localDir);
			double angle = acos(localDir.dot(Vector3r(1,0,0)));
			Vector3r signAngle =  Vector3r(1,0.0,0).cross(localDir); 

			if (signAngle.dot(Vector3r(0,-1.0,0)) < 0.0){angle =2.0*PI - angle;}			
			refAngle.push_back(angle);
//.........这里部分代码省略.........

	inHyperboloid(const Vector3r& _c1, const Vector3r& _c2, Real _R, Real _r){
		c1=_c1; c2=_c2; R=_R; a=_r;
		c12=c2-c1; ht=c12.norm();
		Real uMax=sqrt(pow(R/a,2)-1); c=ht/(2*uMax);
	}

//!			O/
bool Ig2_Sphere_GridConnection_ScGridCoGeom::go(	const shared_ptr<Shape>& cm1,
						const shared_ptr<Shape>& cm2,
						const State& state1, const State& state2, const Vector3r& shift2, const bool& force,
						const shared_ptr<Interaction>& c)
{	// Useful variables :
	const State*    sphereSt  = YADE_CAST<const State*>(&state1);
	//const State*    gridCoSt  = YADE_CAST<const State*>(&state2);
	Sphere*         sphere    = YADE_CAST<Sphere*>(cm1.get());
	GridConnection* gridCo    = YADE_CAST<GridConnection*>(cm2.get());
	GridNode*       gridNo1   = YADE_CAST<GridNode*>(gridCo->node1->shape.get());
	GridNode*       gridNo2   = YADE_CAST<GridNode*>(gridCo->node2->shape.get());
	State*          gridNo1St = YADE_CAST<State*>(gridCo->node1->state.get());
	State*          gridNo2St = YADE_CAST<State*>(gridCo->node2->state.get());
	bool isNew = !c->geom;
	shared_ptr<ScGridCoGeom> scm;
	if (!isNew) scm = YADE_PTR_CAST<ScGridCoGeom>(c->geom);
	else {scm = shared_ptr<ScGridCoGeom>(new ScGridCoGeom());}
	Vector3r segt = gridCo->getSegment();
	Real len = gridCo->getLength();
	Vector3r spherePos = sphereSt->pos - shift2;
	Vector3r branch = spherePos - gridNo1St->pos;
	Vector3r branchN = spherePos - gridNo2St->pos;
	for(int i=0;i<3;i++){
		if(abs(branch[i])<1e-14) branch[i]=0.0;
		if(abs(branchN[i])<1e-14) branchN[i]=0.0;
	}
	Real relPos = branch.dot(segt)/(len*len);
	if(scm->isDuplicate==2 && scm->trueInt!=c->id2)return true;	//the contact will be deleted into the Law.
	scm->isDuplicate=0;
	scm->trueInt=-1;
	
	if(relPos<=0){	// if the sphere projection is BEFORE the segment ...
		if(gridNo1->ConnList.size()>1){//	if the node is not an extremity of the Grid (only one connection)
			for(int unsigned i=0;i<gridNo1->ConnList.size();i++){	// ... loop on all the Connections of the same Node ...
				GridConnection* GC = (GridConnection*)gridNo1->ConnList[i]->shape.get();
				if(GC==gridCo)continue;//	self comparison.
				Vector3r segtCandidate1 = GC->node1->state->pos - gridNo1St->pos; // (be sure of the direction of segtPrev to compare relPosPrev.)
				Vector3r segtCandidate2 = GC->node2->state->pos - gridNo1St->pos;
				Vector3r segtPrev = segtCandidate1.norm()>segtCandidate2.norm() ? segtCandidate1:segtCandidate2;
				for(int j=0;j<3;j++){
					if(abs(segtPrev[j])<1e-14) segtPrev[j]=0.0;
				}
				Real relPosPrev = (branch.dot(segtPrev))/(segtPrev.norm()*segtPrev.norm());
				// ... and check whether the sphere projection is before the neighbours connections too.
				const shared_ptr<Interaction> intr = scene->interactions->find(c->id1,gridNo1->ConnList[i]->getId());
				if(relPosPrev<=0){ //if the sphere projection is outside both the current Connection AND this neighbouring connection, then create the interaction if the neighbour did not already do it before.
					if(intr && intr->isReal() && isNew) return false;
					if(intr && intr->isReal() && !isNew) {scm->isDuplicate=1;/*cout<<"Declare "<<c->id1<<"-"<<c->id2<<" as duplicated."<<endl;*/}
				}
				else{//the sphere projection is outside the current Connection but inside the previous neighbour. The contact has to be handled by the Prev GridConnection, not here.
					if (isNew)return false;
					else {
						//cout<<"The contact "<<c->id1<<"-"<<c->id2<<" HAVE to be copied and deleted NOW."<<endl ;
						scm->isDuplicate=1;
						scm->trueInt=-1;
						return true;}
				}
			}
		}
	}
	
	//Exactly the same but in the case the sphere projection is AFTER the segment.
	else if(relPos>=1){
		if(gridNo2->ConnList.size()>1){
			for(int unsigned i=0;i<gridNo2->ConnList.size();i++){
				GridConnection* GC = (GridConnection*)gridNo2->ConnList[i]->shape.get();
				if(GC==gridCo)continue;//	self comparison.
				Vector3r segtCandidate1 = GC->node1->state->pos - gridNo2St->pos;
				Vector3r segtCandidate2 = GC->node2->state->pos - gridNo2St->pos;
				Vector3r segtNext = segtCandidate1.norm()>segtCandidate2.norm() ? segtCandidate1:segtCandidate2;
				for(int j=0;j<3;j++){
					if(abs(segtNext[j])<1e-14) segtNext[j]=0.0;
				}
				Real relPosNext = (branchN.dot(segtNext))/(segtNext.norm()*segtNext.norm());
				const shared_ptr<Interaction> intr = scene->interactions->find(c->id1,gridNo2->ConnList[i]->getId());
				if(relPosNext<=0){ //if the sphere projection is outside both the current Connection AND this neighbouring connection, then create the interaction if the neighbour did not already do it before.
					if(intr && intr->isReal() && isNew) return false;
					if(intr && intr->isReal() && !isNew) {scm->isDuplicate=1;/*cout<<"Declare "<<c->id1<<"-"<<c->id2<<" as duplicated."<<endl;*/}
				}
				else{//the sphere projection is outside the current Connection but inside the previous neighbour. The contact has to be handled by the Prev GridConnection, not here.
					if (isNew)return false;
					else {//cout<<"The contact "<<c->id1<<"-"<<c->id2<<" HAVE to be copied and deleted NOW."<<endl ;
						scm->isDuplicate=1 ;
						scm->trueInt=-1 ;
						return true;}
				}
			}
		}
	}
	
	else if (isNew && relPos<=0.5){
		if(gridNo1->ConnList.size()>1){//	if the node is not an extremity of the Grid (only one connection)
			for(int unsigned i=0;i<gridNo1->ConnList.size();i++){	// ... loop on all the Connections of the same Node ...
				GridConnection* GC = (GridConnection*)gridNo1->ConnList[i]->shape.get();
				if(GC==gridCo)continue;//	self comparison.
				Vector3r segtCandidate1 = GC->node1->state->pos - gridNo1St->pos; // (be sure of the direction of segtPrev to compare relPosPrev.)
				Vector3r segtCandidate2 = GC->node2->state->pos - gridNo1St->pos;
				Vector3r segtPrev = segtCandidate1.norm()>segtCandidate2.norm() ? segtCandidate1:segtCandidate2;
				for(int j=0;j<3;j++){
//.........这里部分代码省略.........