model_manager.hh
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model_manager.hh
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	/**
	* @file model_manager.hh
	*
	* @author Alejandro M. Aragón <alejandro.aragon@epfl.ch>
	*
	* @date creation: Mon Jan 07 2013
	* @date last modification: Fri Sep 05 2014
	*
	* @brief higher order object that deals with collections of models
	*
	* @section LICENSE
	*
	* Copyright (©) 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */

	#ifndef __AKANTU_MODEL_MANAGER_HH__
	#define __AKANTU_MODEL_MANAGER_HH__

	#include "aka_common.hh"
	#include "mesh.hh"
	#include "model.hh"
	#include "aka_tree.hh"
	#include "solid_mechanics_model.hh"
	#include "aka_plane.hh"
	#include "aka_geometry.hh"
	#include "solid_mechanics_model_element.hh"
	#include "aka_timer.hh"

	#include <cstring>
	#include <queue>
	#include <unordered_set>
	#include <array/expr.hpp>



	#define DEBUG_MANAGER 1


	__BEGIN_AKANTU__


	typedef array::vector_type<Real> vector_type;
	typedef array::matrix_type<Real> matrix_type;
	using array::transpose;


	enum Discretization_type { Node_to_node, Node_to_segment };


	template <class Model_policy>
	class Model_manager {

	public:

	typedef Model_policy model_type;
	typedef model_type* model_pointer;
	typedef model_type& model_reference;

	typedef std::list<model_type*> model_container;
	typedef typename model_container::iterator model_iterator;
	typedef typename model_container::const_iterator const_model_iterator;

	protected:

	model_container models_; //!< Models


	public:

	//! Default constructor
	Model_manager() : models_() {}

	virtual void add_model(model_reference m)
	{ models_.push_back(&m); }

	virtual void add_model(model_pointer m)
	{ models_.push_back(m); }

	model_iterator models_begin()
	{ return models_.begin(); }

	model_iterator models_end()
	{ return models_.end(); }

	friend std::ostream& operator<<(std::ostream& os, const Model_manager& mm) {

	os<<"Model manager info:"<<endl;
	os<<" models: "<<mm.models_.size()<<endl;
	size_t i=0;
	for (const_model_iterator it = mm.models_.begin(); it != mm.models_.end(); ++it) {
	os<<"\tmodel "<<++i<<" memory address: "<<*it<<endl;
	os<<"\tmodel "<<**it<<endl;
	}

	return os;
	}

	};



	enum Kinematic_type { static_object_t, dynamic_object_t};
	enum Consider_acceleration { Consider_t, Neglect_t };


	template <Consider_acceleration>
	class Kinematic_traits;



	template<>
	class Kinematic_traits<Consider_t> {

	protected:

	typedef Real time_type;

	// check collision considering acceleration
	// the equation to solve is
	//
	// alpha t^4 + beta t^3 + gamma t^2 + delta t + epsilon = 0
	//
	// where alpha = (a.a)/4, beta = (a.v), gamma = a.s + v.v, delta = 2(s.v),
	// epsilon = s.s - r^2, a = a1-a2, v = v1-v2, s = c1-c2, r = r1-r2
	//
	template <class iterator>
	time_type resolve_time(iterator it1, iterator it2) {

	typedef typename iterator::value_type volume_type;
	typedef typename volume_type::point_type point_type;

	const point_type& v1 = it1->velocity_;
	const point_type& v2 = it2->velocity_;

	point_type a1 = it1->acceleration_;
	point_type a2 = it2->acceleration_;

	Real r = it1->radius() + it2->radius();
	point_type s = it2->center() - it1->center();
	point_type v = v2 - v1;
	point_type a = a2 - a1;

	// get coefficients
	Real alpha = (a*a)/4;
	Real beta = a*v;
	Real gamma = as + vv;
	Real delta = 2(sv);
	Real epsilon = ss - rr;

	// obtain roots from quartic equation by calling the function such that
	// the coefficient for the quartic term is equal to one
	std::vector<Real> x(4, inf);


	uint32_t roots = solve_quartic(beta/alpha, gamma/alpha, delta/alpha, epsilon/alpha,
	&x[0], &x[1], &x[2], &x[3]);

	Real tmin = inf;

	// if there are roots, take the first one as an indication of the collision
	if (roots > 0) {

	for (size_t i=0; i<x.size(); ++i)
	tmin = std::min(tmin, x[i]);

	if (tmin > 0) {
	#ifdef DEBUG_MANAGER
	cout<<" Solve quartic with coefficients ";
	cout<<(beta/alpha)<<", "<<(gamma/alpha)<<", "<<(delta/alpha)<<", "<<(epsilon/alpha)<<endl;
	cout<<" Approximate collision time -> tmin = "<<tmin<<" = "<<(tmin)<<endl;
	cout<<" Roots:";
	for (size_t i=0; i<x.size(); ++i)
	cout<<" "<<x[i];
	cout<<endl;
	#endif
	for (size_t i=0; i<x.size(); ++i)
	tmin = std::min(tmin, x[i]);

	}
	} // if roots
	return tmin > 0 ? tmin : inf;
	}

	private:

	/! \brief Solve quartic equation x^4 + ax^3 + bx^2 + cx + d = 0.
	*
	* Solves the quartic equation. Returns the number of roots
	* found. Roots are filled in ascending order.
	* Code taken from the Ion Beam Simulator, which is distrubuted under
	* the terms of the GNU General Public License as published by the Free
	* Software Foundation; either version 2 of the License, or (at your
	* option) any later version.
	*/
	uint32_t solve_quartic(Real a, Real b, Real c, Real d,
	Real x0, Real x1, Real x2, Real x3 );

	};



	template<>
	class Kinematic_traits<Neglect_t> {

	protected:

	typedef Real time_type;

	// check collision neglecting acceleration
	template <class iterator>
	time_type resolve_time(iterator it1, iterator it2) {

	typedef typename iterator::value_type volume_type;
	typedef typename volume_type::point_type point_type;
	typedef typename point_type::value_type value_type;

	const volume_type& s1 = *it1;
	const volume_type& s2 = *it2;

	const point_type& v1 = s1.velocity_;
	const point_type& v2 = s2.velocity_;

	// vector between spheress
	point_type s = s2.center() - s1.center();
	// relative motion of s1 with respect to stationary s0
	point_type v = v2 - v1;
	// sum of radii
	value_type r = s1.radius() + s2.radius();
	value_type c = ss - rr;

	#ifdef DEBUG_MANAGER
	cout<<"Checking collisiong between:"<<endl;
	cout<<" "<<s1<<", velocity: "<<v1<<endl;
	cout<<" "<<s2<<", velocity: "<<v2<<endl;
	cout<<" Relative velocity: "<<v<<endl;
	#endif

	value_type epsilon = 1e-8;

	// already intersecting
	if (c < -epsilon) {

	#ifdef DEBUG_MANAGER
	cout<<" Intersecting bounding volumes"<<endl;
	#endif
	// should not get to this point
	return time_type();
	}

	value_type a = v*v;
	// if spheres not moving relative to each other
	if (a < epsilon) {
	#ifdef DEBUG_MANAGER
	cout<<" Objects not moving relative to each other"<<endl;
	cout<<" a: "<<a<<endl;
	#endif
	return inf;
	}

	value_type b = v*s;
	// if spheres not moving towards each other
	if (b >= 0.) {
	#ifdef DEBUG_MANAGER
	cout<<" Objects not moving towards each other"<<endl;
	cout<<" b: "<<b<<endl;
	#endif
	return inf;
	}

	value_type d = bb - ac;
	// if no real-valued root (d < 0), spheres do not intersect
	// otherwise add time to timer
	if (d >= 0.) {
	time_type ts = (-b - sqrt(d))/a;
	if (ts > -epsilon) {
	#ifdef DEBUG_MANAGER
	cout<<" Objects intersects at time "<<(ts)<<endl;
	#endif
	return ts;
	}
	#ifdef DEBUG_MANAGER
	else {
	cout<<" ts negative: "<<ts<<endl;
	}
	#endif

	}
	#ifdef DEBUG_MANAGER
	else {
	cout<<" Objects do not intersect"<<endl;
	cout<<" discriminant: "<<d<<endl;
	}
	#endif

	return inf;
	}
	};



	template <class VolumeType, class DataPolicy, template <class> class CostPolicy = Cost_functor>
	class DataTree :
	public Tree<VolumeType, CostPolicy> {

	public:

	typedef DataPolicy data_type;
	typedef VolumeType volume_type;
	typedef CostPolicy<volume_type> cost_functor;
	typedef Tree<volume_type, CostPolicy> tree_type;
	typedef typename tree_type::iterator tree_iterator;
	typedef typename tree_type::const_iterator const_tree_iterator;

	// leaf information
	typedef std::map<tree_iterator, data_type> leaves_data;
	typedef typename leaves_data::iterator leaves_data_iterator;

	bool add_data(tree_iterator it, data_type& data) {
	auto i = data_.insert(std::make_pair(it, data));
	return i.second;
	}

	leaves_data_iterator leaves_data_begin()
	{ return data_.begin(); }

	leaves_data_iterator leaves_data_end()
	{ return data_.end(); }

	leaves_data_iterator find_data(tree_iterator it)
	{ return data_.find(it); }

	private:

	leaves_data data_;

	};

	template <class U, class T>
	std::pair<U, T> minmax(const U& u, const T& t) {
	return u < t ? std::make_pair(u,t) : std::make_pair(t,u);
	}

	template <Discretization_type, class, class>
	class ContactElement;


	template <class point_type, class element_type>
	class ContactElement<Node_to_node, point_type, element_type> {

	public:

	typedef Real time_type;
	typedef typename vector_type::value_type value_type;
	typedef std::tuple<time_type, point_type> impact_tuple;
	typedef typename element_type::model_type model_type;

	struct Comparator {

	bool operator()(const ContactElement c1, const ContactElement c2) const {

	auto p1 = minmax(c1->el1_, c1->el2_);
	auto p2 = minmax(c2->el1_, c2->el2_);

	if (p1.first < p2.first \|\| p1.second < p2.second)
	return true;

	auto i1 = minmax(c1->id1_, c1->id2_);
	auto i2 = minmax(c2->id1_, c2->id2_);

	if (i1.first < i2.first \|\| i1.second < i2.second)
	return true;

	return false;
	}
	};

	typedef Comparator comparator_type;

	//! Parameter constructor
	template <class parameter_type>
	ContactElement(const parameter_type& p) :
	id1_(std::get<0>(p)), id2_(std::get<1>(p)),
	el1_(std::get<2>(p)), el2_(std::get<3>(p)),
	impact_(std::get<4>(p)), m1_(), m2_(), linked_(), release_(true) {}


	//! Resolve impact
	/*! At the moment of impact, obtain velocities after impact from
	* contacting nodes, and join masses (nodes behave as one)
	*/
	void resolve_impact(time_type t, time_type Dt) {

	// if at moment of impact
	if (equal(t, std::get<0>(impact_)) && !linked_) {


	#ifdef DEBUG_MANAGER
	cout<<"Linking nodes"<<endl;
	#endif

	// get models
	model_type &model1 = el1_->model();
	model_type &model2 = el2_->model();

	// get global node ids
	UInt n1 = el1_->node(id1_);
	UInt n2 = el2_->node(id2_);

	// get references to mass and velocity vectors
	Array<Real> &mass1 = model1.getMass();
	Array<Real> &mass2 = model2.getMass();
	Array<Real> &velocity1 = model1.getVelocity();
	Array<Real> &velocity2 = model2.getVelocity();

	// get references to masses and velocities involved in the collision
	Real &m1 = mass1(n1);
	Real &m2 = mass2(n2);
	value_type &v1 = velocity1(n1);
	value_type &v2 = velocity2(n2);

	// set correct velocity
	Real vc = (m1v1 + m2v2) / (m1+m2);
	velocity1(n1) = vc;
	velocity2(n2) = vc;

	// save mass values and add masses to treat them as a single node
	m1_ = m1;
	m2_ = m2;
	mass1(n1) += m2_;
	mass2(n2) += m1_;

	// set link flag
	linked_ = true;
	}
	}

	//! Treat linked nodes
	/*! During the time that the nodes are in contact, treat them as a single
	* node of joint mass and synchronize residual values
	*/
	bool resolve(time_type t, time_type Dt) {

	// get models
	model_type &model1 = el1_->model();
	model_type &model2 = el2_->model();

	// get global node ids
	UInt n1 = el1_->node(id1_);
	UInt n2 = el2_->node(id2_);

	// get references to residual vectors
	Array<Real> & r1 = model1.getResidual();
	Array<Real> & r2 = model2.getResidual();

	// check condition for delinking of nodes
	vector_type vec = el2_->barycenter() - el1_->barycenter();

	if (std::signbit(vec[0]) != std::signbit(r1(n1))) {

	#ifdef DEBUG_MANAGER
	cout<<"Unlinking nodes"<<endl;
	#endif

	if (release_) {

	// get masses
	Array<Real> &mass1 = model1.getMass();
	Array<Real> &mass2 = model2.getMass();

	mass1(id1_) = m1_;
	mass2(id2_) = m2_;

	release_ = false;
	return true;
	}
	}

	// synchronize if necessary
	if (linked_ && release_) {
	Real tmp = r1(n1);

	r1(n1) += r2(n2);
	r2(n2) += tmp;
	}
	return false;
	}

	friend std::ostream& operator<<(std::ostream& os, const ContactElement& ce) {
	cout<<"Contact element info:\n linking elements ("<<ce.el1_<<" - "<<ce.el2_<<")"<<endl;
	cout<<" colliding nodes ("<<ce.id1_<<" - "<<ce.id2_<<")"<<endl;
	cout<<" first impact at location "<<std::get<1>(ce.impact_)<<" at time "<<std::get<0>(ce.impact_)<<endl;
	if (ce.m1_ > 0. && ce.m2_ > 0)
	cout<<" saved masses: ("<<ce.m1_<<","<<ce.m2_<<")"<<endl;
	if (ce.linked_)
	cout<<" linked state (treating contacting nodes as a single node)"<<endl;

	return os;
	}

	private:
	size_t id1_, id2_; //!< Ids of element nodes involved in the collision
	element_type el1_, el2_; //!< Pointers to elements involved in teh collision
	impact_tuple impact_; //!< Impact information, tuple containing the time and point of contact

	value_type m1_, m2_; //!< Mass values stored after linking of the nodes
	bool linked_, release_; //!< Flags used to specify the state of the linking
	};


	template <class Bounding_policy, Discretization_type DT, Consider_acceleration accel = Consider_t, template <class> class Cost_policy = Cost_functor>
	class Contact_model_manager : public Model_manager<SolidMechanicsModel>, public Kinematic_traits<accel> {


	using Kinematic_traits<accel>::resolve_time;

	typedef ctimer chronograph_type;

	// model type
	typedef SolidMechanicsModel model_type;
	typedef model_type* model_pointer;
	typedef model_type& model_reference;

	// geometric types
	typedef Bounding_policy volume_type;
	typedef typename volume_type::point_type point_type;
	typedef typename point_type::value_type value_type;
	typedef typename volume_type::aabb_type aabb_type;

	// element type
	typedef ModelElement<model_type> element_type;
	typedef ContactElement<DT, point_type, element_type> contact_element_type;
	typedef std::set<contact_element_type*, typename contact_element_type::comparator_type > contact_element_container;
	typedef typename contact_element_container::iterator contact_element_iterator;
	typedef typename contact_element_type::time_type time_type;
	typedef typename contact_element_type::impact_tuple impact_tuple;

	// Bounding volume hierarchy related types
	typedef Cost_policy<volume_type> cost_functor;
	typedef DataTree<volume_type, element_type, Cost_policy > tree_type;
	typedef typename tree_type::leaves_data_iterator leaves_data_iterator;
	typedef typename tree_type::leaf_iterator tree_leaf_iterator;
	typedef typename tree_type::iterator tree_iterator;
	typedef typename tree_type::const_iterator const_tree_iterator;
	typedef std::list<tree_type*> forest_container;
	typedef typename forest_container::iterator forest_iterator;
	typedef typename forest_container::const_iterator const_forest_iterator;

	// kinematic types
	typedef point_type velocity_type;
	typedef std::list<velocity_type> velocity_container;
	typedef typename velocity_container::iterator velocity_iterator;

	typedef unsigned long mask_size;

	// timer type
	typedef std::priority_queue<time_type, std::vector<time_type>, std::greater<time_type> > timer_type;

	// tuple type
	typedef std::tuple<time_type, tree_iterator, tree_iterator> tuple_type;

	struct Tuple_compare {
	bool operator()(const tuple_type& t1, const tuple_type& t2) const
	{ return std::get<0>(t1) > std::get<0>(t2); }
	};

	typedef typename std::priority_queue<tuple_type, std::vector<tuple_type>, Tuple_compare> hierarchy_timer;


	//! Structure used to do a postorder update of tree hierarchies
	struct Updater {

	tree_type &t_; //!< Reference to hierarchy

	Updater(tree_type& t) : t_(t) {}

	void operator()(tree_iterator it) {
	if (!it.is_leaf()) {
	volume_type& v = *it;
	volume_type& lv = *it.left();
	volume_type& rv = *it.right();
	v = lv + rv;
	assert(lv.last_time_ == rv.last_time_);
	v.last_time_ = lv.last_time_;
	v.velocity_ = 0.5 * (lv.velocity_ + rv.velocity_);
	v.acceleration_ = 0.5 * (lv.acceleration_ + rv.acceleration_);
	}
	}
	};

	struct Printer {
	void operator()(tree_iterator it)
	{ cout<<*it<<", "; }
	};

	class Time_exception : public std::exception {
	virtual const char* what() const throw()
	{ return "* EXCEPTION * Zero time increment."; }
	};

	struct Continuator : public std::exception {

	tuple_type best_;

	Continuator(const tuple_type& b) : best_(b) {}

	virtual const char* what() const throw()
	{ return "* EXCEPTION * Continue."; }
	};

	struct Contactor : public std::exception {

	impact_tuple data_;

	Contactor(const impact_tuple& c) : data_(c) {}

	virtual const char* what() const throw()
	{ return "* EXCEPTION * Contact."; }
	};

	template <bool flag>
	struct Bool2Type {
	enum { value = flag };
	};

	private:

	forest_container forest_; //!< Bounding volume hierarchies
	hierarchy_timer timer_; //!< Priority queue of times
	mask_size masks_; //!< Variable used for static objects
	tree_iterator null_;
	time_type last_; //!< Keep time of last detection engine reset
	contact_element_container celems_; //!< Contact elements

	public:

	//! Default constructor
	Contact_model_manager()
	: Model_manager(), forest_(), timer_(), masks_(), null_(tree_iterator(nullptr)), last_() {}

	//! Destructor
	~Contact_model_manager() {

	// delete trees
	for (forest_iterator it = forest_.begin(); it != forest_.end(); ++it)
	delete *it;

	// delete contact element
	for (contact_element_iterator it = celems_.begin(); it != celems_.end(); ++it)
	delete *it;
	}

	virtual void add_model(model_pointer m, Kinematic_type k = dynamic_object_t) {

	m->initializeUpdateResidualData();
	models_.push_back(m);

	if (models_.size() > 8*sizeof(mask_size)) {
	cout<<"* ERROR * Type used for masks is too small to handle all models."<<endl;
	cout<<"Aborting..."<<endl;
	exit(1);
	}

	// create tree
	tree_type* tp = construct_tree_bottom_up<tree_type, model_type, element_type>(*m);
	forest_.push_back(tp);


	#ifdef DEBUG_MANAGER
	cout<<"tree "<<*tp<<endl;
	// print_mathematica(*tp);
	#endif

	// mask model as dynamic or static
	masks_ \|= (k << (models_.size()-1));
	}


	void update_forest(time_type t) {

	int k = 0;
	for (forest_iterator fit = forest_.begin(); fit != forest_.end(); ++fit) {

	// check if the object is dynamic to update
	if (!(masks_ & (1 << k++)))
	continue;

	// loop over leaves
	for (leaves_data_iterator lit = (*fit)->leaves_data_begin();
	lit != (*fit)->leaves_data_end(); ++lit) {

	Real t_old = lit->first->last_time_;

	std::vector<const Real*> c = lit->second.coordinates();
	volume_type v = Volume_creator<volume_type>::create(c);

	// get positions
	const point_type& p0 = lit->first->center();
	const point_type& p1 = v.center();

	// get velocities
	const point_type& v0 = lit->first->velocity_;
	const point_type& v1 = v.velocity_;

	// new velocity and acceleration
	v.velocity_ = 1/(t - t_old) * (p1-p0);
	v.acceleration_ = 1/(t - t_old) * (v1-v0);

	v.last_time_ = t;

	// set new volume
	*lit->first = v;
	}

	tree_type &t = **fit;
	Updater u(t);
	postorder(t.root(),u);
	}
	}


	void reset() {

	// clear queue
	while (!timer_.empty())
	timer_.pop();

	timer_.push(std::make_tuple(last_, null_, null_));
	timer_.push(std::make_tuple(inf, null_, null_));
	}

	void resolve(time_type t, time_type Dt) {

	// loop over contact elements
	contact_element_iterator elit = celems_.begin();
	while (elit != celems_.end()) {

	cout<<**elit<<endl;
	if ((*elit)->resolve(t, Dt)) {
	celems_.erase(elit++);

	last_ = t + Dt;

	} else
	++elit;
	}
	}


	template <class queue_type>
	void print_queue(queue_type copy) {

	cout<<"Printing queue values:";
	while (!copy.empty()) {
	const tuple_type& tuple = copy.top();
	cout<<" "<<std::get<0>(tuple);
	copy.pop();
	}
	cout<<endl;
	}



	/*! \param t - Current elapsed time
	* \param Dt - Time step
	*/
	void intersect(time_type t, time_type& Dt) {

	#ifdef DEBUG_MANAGER
	cout<<"t = "<<t<<", Dt = "<<Dt<<", timer:";

	hierarchy_timer copy = timer_;
	while (!copy.empty()) {
	const tuple_type& tuple = copy.top();
	cout<<" "<<std::get<0>(tuple);
	copy.pop();
	}
	cout<<endl;

	#endif

	static time_type Dt1 = Dt;

	// reset if first enter the function
	if (t == last_ \|\| t == Dt1) {
	Dt = Dt1;
	reset();
	}

	const tuple_type& tuple = timer_.top();
	time_type top = std::get<0>(tuple);

	// update hierarchies and get positions
	// note that the updating starts before the next intetersection check
	if (models_.size() > 1 && top <= t + 3*Dt1) {
	update_forest(t);
	#ifdef DEBUG_MANAGER
	cout<<"Updating forest"<<endl;
	#endif
	}

	// check if detection is shut off
	if (t + Dt < top)
	return;

	// get iterators from priority element
	tree_iterator it1 = std::get<1>(tuple);
	tree_iterator it2 = std::get<2>(tuple);

	// remove time from timer
	timer_.pop();

	// check for intersection becase:
	// 1. there are enough models
	// 2. intersection happens before the next increment
	if (models_.size() > 1 && top <= t + Dt1) {

	// if first step, add next time to timer and return because there
	// is not enough information for the computation of intersection times
	if (t <= last_ + (accel == Consider_t ? 2 : 1)*Dt) {
	// remove time from timer
	timer_.push(std::make_tuple(t, null_, null_));
	#ifdef DEBUG_MANAGER
	cout<<"Early out"<<endl;
	#endif
	return;
	}

	// check if iterators are null to compute O(n^2) collision times
	if (it1 == null_ \|\| it2 == null_) {

	// do O(n^2) operation to obtain next time of intersections
	for (forest_iterator it1 = forest_.begin(); it1 != --forest_.end(); ++it1) {

	forest_iterator it2 = it1;
	for (++it2; it2 != forest_.end(); ++it2) {

	// get collision time
	#ifdef DEBUG_MANAGER
	cout<<"Calling check_collision in O(n^2) branch"<<endl;
	#endif
	time_type tstar = resolve_time((it1)->root(), (it2)->root());
	if (tstar != inf)
	timer_.push(std::make_tuple(t+tstar, (it1)->root(), (it2)->root()));
	#ifdef DEBUG_MANAGER
	else
	cout<<"* INFO * Objects do not intersect:\n "<<(it1)->root()<<"\n "<<(it2)->root()<<endl;
	#endif
	} // inner hierarchy loop
	} // outer hierarchy loop

	}

	// else use collision information previously computed (avoids O(n^2) operation above)
	else {

	#ifdef DEBUG_MANAGER
	cout<<"Calling check_collision in non-O(n^2) branch"<<endl;
	#endif

	// temporary queue for tree traversal
	hierarchy_timer pq;
	pq.push(std::make_tuple(top, it1, it2));

	try {

	// enter infinite loop
	while (true) {

	#ifdef DEBUG_MANAGER
	cout<<"______________________________________________"<<endl;
	print_queue(pq);
	#endif

	const tuple_type& tuple = pq.top();

	time_type tstar = std::get<0>(tuple);
	tree_iterator left = std::get<1>(tuple);
	tree_iterator right = std::get<2>(tuple);

	#ifdef DEBUG_MANAGER
	cout<<"Queue time "<<tstar<<", items: "<<left<<", "<<right<<endl;
	#endif

	pq.pop();

	check_collision(t, left, right, pq);

	} // infinite loop

	}
	catch (Continuator& e) {

	tuple_type& best = e.best_;
	time_type& best_time = std::get<0>(best);
	Dt = best_time;
	best_time += t;

	// clean hierarchy timer until best time
	while (std::get<0>(timer_.top()) <= best_time)
	timer_.pop();

	timer_.push(best);
	timer_.push(best);

	try {
	// set time step if required
	cout<<"calling set_time_set in Continuator"<<endl;

	set_time_step(t, Dt, Dt1);
	} catch (Time_exception& e) {
	cout<<"catching inner Time_exception"<<endl;

	}


	}
	catch (Contactor& c) {

	// get collision impact
	Dt = std::get<0>(c.data_);

	try {

	cout<<"calling set_time_set in Contactor"<<endl;

	// set time step if required
	set_time_step(t, Dt, Dt1);
	// last_ = t + Dt;

	} catch (Time_exception& e) {
	// if too small a time step, do nothing, next time step
	// will carry out DCR

	cout<<"catching outter Time_exception"<<endl;

	// last_ = t + Dt;

	Dt = Dt1;
	}
	cout<<"last -> "<<last_<<endl;
	}
	}

	} // if statement on enough models
	// else do nothing as there are not enough models to carry out intersection
	// or the check engine is shut down until the next time in timer


	// resolve collision if necessary
	for (contact_element_iterator elit = celems_.begin(); elit != celems_.end(); ++elit)
	(*elit)->resolve_impact(t, Dt);


	}


	private:

	void set_time_step(time_type t, time_type& Dt, time_type Dt1) {

	if (Dt > Dt1)
	Dt = Dt1;

	if (Dt < 1e-10) {
	cout<<"* INFO * New time step is too small. Throwing exception..."<<endl;
	throw Time_exception();
	}
	#ifdef DEBUG_MANAGER
	cout<<" Leaves found that collide at time "<<(t + Dt)<<endl;
	cout<<" Setting new time step: "<<Dt<<endl;
	#endif
	for (model_iterator mit = models_.begin(); mit != models_.end(); ++mit)
	(*mit)->setTimeStep(Dt);
	}

	// check time of collision between points
	impact_tuple check_points(time_type t, leaves_data_iterator it1, leaves_data_iterator it2) {

	const volume_type& v1 = *it1->first;
	const volume_type& v2 = *it2->first;

	std::vector<const Real*> c1 = it1->second.coordinates();
	std::vector<const Real*> c2 = it2->second.coordinates();

	// compute intersection
	volume_type vint = v1 && v2;

	// get indices of colliding nodes
	size_t ii=0, jj=0;
	for (size_t i=1; i<c1.size(); ++i) {

	if (vint & point_type(c1[i]))
	ii = i;
	if (vint & point_type(c2[i]))
	jj = i;
	}

	impact_tuple impact =
	moving_point_against_point(point_type(c1[ii]), point_type(c2[jj]), it1->first->velocity_, it2->first->velocity_);

	time_type &timpact = std::get<0>(impact);
	timpact += t;

	celems_.insert(new contact_element_type(std::make_tuple(ii, jj, &it1->second, &it2->second, impact)));

	return impact;

	}

	// check time of collision between 2D segments
	impact_tuple check_2D_sides(time_type t, leaves_data_iterator it1, leaves_data_iterator it2) {

	typedef Point<3> test_point;


	const volume_type& v1 = *it1->first;
	const volume_type& v2 = *it2->first;

	std::vector<const Real*> c1 = it1->second.coordinates();
	std::vector<const Real*> c2 = it2->second.coordinates();

	// create plane from second container node
	// THIS WON'T WORK, SIDES HAVE ONLY TWO NODES, CONTINUE DEVELOPING FROM HERE
	assert(c2.size() == 3);

	// form plane from three points
	test_point o,p,q;

	for (size_t j=0; j<point_type::dim(); ++j) {
	o[j] = c2[0][j];
	p[j] = c2[1][j];
	q[j] = c2[2][j];
	}

	// point_type o(c2[0]);
	// point_type p(c2[1]);
	// point_type q(c2[2]);

	Plane pi(o,p,q);

	// loop over the nodes of the container
	for (size_t i=0; i<c1.size(); ++i) {

	test_point v;
	point_type v2d = v1.velocity_ - v2.velocity_;

	// create 3D point, used to check for plane intersection
	test_point x;
	for (size_t j=0; j<point_type::dim(); ++j) {
	x[j] = c1[i][j];
	v[j] = v2d[j];
	}

	cout<<"x -> "<<x<<endl;

	cout<<"v -> "<<v<<endl;


	std::tuple<time_type, test_point> impact =
	moving_point_against_plane(x, v, pi);



	}

	exit(1);

	//// impact_tuple impact =
	//// moving_point_against_point(point_type(c1[ii]), point_type(c2[jj]), it1->first->velocity_, it2->first->velocity_);
	////
	//// time_type &timpact = std::get<0>(impact);
	//// timpact += t;
	////
	//// celems_.insert(new contact_element_type(std::make_tuple(ii, jj, &it1->second, &it2->second, impact)));
	////
	// return impact;

	}


	// check time of collision between triangles
	impact_tuple check_triangles(leaves_data_iterator it1, leaves_data_iterator it2) {

	std::vector<const Real*> c1 = it1->second.coordinates();
	std::vector<const Real*> c2 = it2->second.coordinates();

	assert(c1.size() == 3);
	assert(c1.size() == c2.size());
	impact_tuple min = std::make_tuple(inf,point_type());

	for (size_t i=0; i<c1.size(); ++i) {

	point_type r(c1[i]);

	// form plane from three points
	point_type o(c2[0]);
	point_type p(c2[1]);
	point_type q(c2[2]);

	Plane pi(o,p,q);

	// relative velocity
	point_type v = it1->first->velocity_ - it2->first->velocity_;

	// intersect point r with velocity v with plane pi
	// the function returns collision time and point of contact
	impact_tuple impact = moving_point_against_plane(r, v, pi);

	// make sure intersection point lies within the triangle
	if (is_point_in_triangle(std::get<1>(impact), o, p, q))
	if (std::get<0>(impact) < std::get<0>(min))
	min = impact;
	}
	return min;
	}

	impact_tuple fine_collision_time(time_type t, leaves_data_iterator it1, leaves_data_iterator it2, Int2Type<1>) {

	// check nodes of first segment against second segment
	return check_points(t, it1, it2);
	}

	impact_tuple fine_collision_time(time_type t, leaves_data_iterator it1, leaves_data_iterator it2, Int2Type<2>) {

	// check sides of the colliding elements
	return check_2D_sides(t, it1, it2);
	}

	impact_tuple fine_collision_time(time_type t, leaves_data_iterator it1, leaves_data_iterator it2, Int2Type<3>) {

	// check nodes of first triangle against second triangle
	impact_tuple impact1 = check_triangles(it1, it2);
	impact_tuple impact2 = check_triangles(it2, it1);

	// check nodes of second triangle against first triangle
	return std::get<0>(impact1) < std::get<0>(impact2) ? impact1 : impact2;
	}

	template <class iterator>
	void traverse_right(iterator it1, iterator it2, hierarchy_timer& pq) {

	#ifdef DEBUG_MANAGER
	cout<<" traversing right hierarchy"<<endl;
	#endif

	iterator lit = it2.left();
	iterator rit = it2.right();
	assert(lit != null_);
	assert(rit != null_);

	time_type tstar1 = resolve_time(it1, lit);
	if (tstar1 != inf) {
	#ifdef DEBUG_MANAGER
	cout<<" Adding queue time "<<tstar1<<endl;
	#endif
	pq.push(std::make_tuple(tstar1, it1, lit));
	}
	time_type tstar2 = resolve_time(it1, rit);
	if (tstar2 != inf) {
	#ifdef DEBUG_MANAGER
	cout<<" Adding queue time "<<tstar2<<endl;
	#endif
	pq.push(std::make_tuple(tstar2, it1, rit));
	}
	}

	template <class iterator>
	void traverse_left(iterator it1, iterator it2, hierarchy_timer& pq) {

	#ifdef DEBUG_MANAGER
	cout<<" traversing left hierarchy"<<endl;
	#endif

	iterator lit = it1.left();
	iterator rit = it1.right();
	assert(lit != null_);
	assert(rit != null_);

	time_type tstar1 = resolve_time(lit, it2);
	if (tstar1 != inf) {
	#ifdef DEBUG_MANAGER
	cout<<" Adding queue time "<<tstar1<<endl;
	#endif
	pq.push(std::make_tuple(tstar1, lit, it2));
	}
	time_type tstar2 = resolve_time(rit, it2);
	if (tstar2 != inf) {
	#ifdef DEBUG_MANAGER
	cout<<" Adding queue time "<<tstar2<<endl;
	#endif
	pq.push(std::make_tuple(tstar2, rit, it2));
	}
	}


	template <class iterator>
	void check_collision(time_type t, iterator it1, iterator it2, hierarchy_timer& pq) {

	// if volumes are leaves, change the timer and time step
	if (it1.is_leaf() && it2.is_leaf()) {

	cout<<"* FOUND LEAVES *"<<endl;

	// case where objects intersect
	if (it1 & it2) {

	cout<<"* BOUNDING SPHERE INTERSECTION *"<<endl;

	// add leaves to carry out penetration tests
	leaves_data_iterator lit1(nullptr), lit2(nullptr);

	for (forest_iterator it = forest_.begin(); it != forest_.end(); ++it) {

	leaves_data_iterator lit = (*it)->find_data(it1);
	if (lit != (*it)->leaves_data_end())
	lit1 = lit;

	lit = (*it)->find_data(it2);
	if (lit != (*it)->leaves_data_end())
	lit2 = lit;

	}

	assert (lit1 != leaves_data_iterator(nullptr));
	assert (lit2 != leaves_data_iterator(nullptr));

	// determine collision time at the lowest level of detection
	impact_tuple impact = fine_collision_time(t, lit1, lit2, Int2Type<volume_type::dim()>());

	#ifdef DEBUG_MANAGER
	cout<<" Fine intersection time: "<<std::get<0>(impact)<<endl;
	#endif
	throw Contactor(impact);
	}
	else
	cout<<"* NO INTERSECTION BETWEEN BOUNDING SPHERES *"<<endl;


	time_type tstar = resolve_time(it1, it2);

	#ifdef DEBUG_MANAGER

	if (tstar == inf)
	cout<<" Leaves found that DO NOT collide"<<endl;
	else {
	cout<<" Leaves found that collide at time "<<(tstar)<<endl;
	cout<<" Modifying timer and time step..."<<endl;
	}
	#endif

	if (tstar == inf) {
	cout<<" Leaves found that DO NOT collide"<<endl;
	return;
	}
	throw Continuator(std::make_tuple(tstar, it1, it2));
	}

	// found left leaf, traverse right hierarchy
	else if (it1.is_leaf() && !it2.is_leaf()) {

	#ifdef DEBUG_MANAGER
	cout<<" s1 is leaf"<<endl;
	#endif
	traverse_right(it1, it2, pq);
	}

	// found right leaf, traverse left hierarchy
	else if (!it1.is_leaf() && it2.is_leaf()) {

	#ifdef DEBUG_MANAGER
	cout<<" s2 is leaf"<<endl;
	#endif
	traverse_left(it1, it2, pq);
	}

	// else non-leaf case found, check volume sizes
	else {

	value_type m1 = it1->measure();
	value_type m2 = it2->measure();

	// volumes are equal to numerical error, traverse both hierarchies
	if (equal(m1, m2)) {

	#ifdef DEBUG_MANAGER
	cout<<" "<<m1<<" == "<<m2<<endl;
	#endif
	traverse_right(it1, it2, pq);
	traverse_left(it1, it2, pq);
	}
	// left volume is bigger, traverse right hierarchy
	else if (m1 > m2) {

	#ifdef DEBUG_MANAGER
	cout<<" "<<m1<<" > "<<m2<<endl;
	#endif
	traverse_left(it1, it2, pq);
	}
	// right volume is bigger, traverse left hierarchy
	else if (m1 < m2) {

	#ifdef DEBUG_MANAGER
	cout<<" "<<m1<<" < "<<m2<<endl;
	#endif
	traverse_right(it1, it2, pq);
	}
	} // non-leaf case
	}


	friend std::ostream& operator<<(std::ostream& os, const Contact_model_manager& mm) {

	os<<"Contact model manager info:"<<endl;
	os<<" models: "<<mm.models_.size()<<endl;
	size_t i=0;
	const_forest_iterator tit = mm.forest_.begin();
	for (const_model_iterator it = mm.models_.begin(); it != mm.models_.end(); ++it) {
	os<<"\tmodel "<<++i<<" memory address: "<<*it<<endl;
	os<<"\tmodel: "<<**it<<endl;
	os<<"\ttree: ";
	print_mathematica(**tit++);
	}
	return os;
	}
	};

	__END_AKANTU__

	#endif /* __AKANTU_MODEL_MANAGER_HH__ */

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