PottsBasedCellPopulation.cpp

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*/
 
#include "PottsBasedCellPopulation.hpp"
#include "RandomNumberGenerator.hpp"
#include "AbstractPottsUpdateRule.hpp"
#include "NodesOnlyMesh.hpp"
#include "CellPopulationElementWriter.hpp"
#include "CellIdWriter.hpp"
 
// Needed to convert mesh in order to write nodes to VTK (visualize as glyphs)
#include "VtkMeshWriter.hpp"
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::Validate()
{
    // Check each element has only one cell associated with it
    std::vector<unsigned> validated_element = std::vector<unsigned>(this->GetNumElements(), 0);
 
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        unsigned elem_index = this->GetLocationIndexUsingCell(*cell_iter);
        validated_element[elem_index]++;
    }
 
    for (unsigned i=0; i<validated_element.size(); i++)
    {
        if (validated_element[i] == 0)
        {
            EXCEPTION("At time " << SimulationTime::Instance()->GetTime() << ", Element " << i << " does not appear to have a cell associated with it");
        }
 
        if (validated_element[i] > 1)
        {
            EXCEPTION("At time " << SimulationTime::Instance()->GetTime() << ", Element " << i << " appears to have " << validated_element[i] << " cells associated with it");
        }
    }
}
 
template<unsigned DIM>
PottsBasedCellPopulation<DIM>::PottsBasedCellPopulation(PottsMesh<DIM>& rMesh,
                                                        std::vector<CellPtr>& rCells,
                                                        bool deleteMesh,
                                                        bool validate,
                                                        const std::vector<unsigned> locationIndices)
    : AbstractOnLatticeCellPopulation<DIM>(rMesh, rCells, locationIndices, deleteMesh),
      mpElementTessellation(nullptr),
      mpMutableMesh(nullptr),
      mTemperature(0.1),
      mNumSweepsPerTimestep(1)
{
    mpPottsMesh = static_cast<PottsMesh<DIM>* >(&(this->mrMesh));
    // Check each element has only one cell associated with it
    if (validate)
    {
        Validate();
    }
}
 
template<unsigned DIM>
PottsBasedCellPopulation<DIM>::PottsBasedCellPopulation(PottsMesh<DIM>& rMesh)
    : AbstractOnLatticeCellPopulation<DIM>(rMesh),
      mpElementTessellation(nullptr),
      mpMutableMesh(nullptr),
      mTemperature(0.1),
      mNumSweepsPerTimestep(1)
{
    mpPottsMesh = static_cast<PottsMesh<DIM>* >(&(this->mrMesh));
}
 
template<unsigned DIM>
PottsBasedCellPopulation<DIM>::~PottsBasedCellPopulation()
{
    // This pointer is always null because PottsBasedCellPopulation::CreateElementTessellation
    // is not implemented. See #1666 in the trac ticket archive for more information.
    assert(mpElementTessellation == nullptr);
 
    delete mpMutableMesh;
 
    if (this->mDeleteMesh)
    {
        delete &this->mrMesh;
    }
}
 
template<unsigned DIM>
PottsMesh<DIM>& PottsBasedCellPopulation<DIM>::rGetMesh()
{
    return *mpPottsMesh;
}
 
template<unsigned DIM>
const PottsMesh<DIM>& PottsBasedCellPopulation<DIM>::rGetMesh() const
{
    return *mpPottsMesh;
}
 
template<unsigned DIM>
TetrahedralMesh<DIM, DIM>* PottsBasedCellPopulation<DIM>::GetTetrahedralMeshForPdeModifier()
{
    std::vector<Node<DIM>*> temp_nodes;
 
    // Create nodes at the centre of the cells
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
         cell_iter != this->End();
         ++cell_iter)
    {
        unsigned index = this->GetLocationIndexUsingCell(*cell_iter);
        c_vector<double, DIM> location = this->GetLocationOfCellCentre(*cell_iter);
        temp_nodes.push_back(new Node<DIM>(index, location));
    }
 
    return new MutableMesh<DIM, DIM>(temp_nodes);
}
 
template<unsigned DIM>
PottsElement<DIM>* PottsBasedCellPopulation<DIM>::GetElement(unsigned elementIndex)
{
    return mpPottsMesh->GetElement(elementIndex);
}
 
template<unsigned DIM>
unsigned PottsBasedCellPopulation<DIM>::GetNumElements()
{
    return mpPottsMesh->GetNumElements();
}
 
template<unsigned DIM>
Node<DIM>* PottsBasedCellPopulation<DIM>::GetNode(unsigned index)
{
    return this->mrMesh.GetNode(index);
}
 
template<unsigned DIM>
unsigned PottsBasedCellPopulation<DIM>::GetNumNodes()
{
    return this->mrMesh.GetNumNodes();
}
 
template<unsigned DIM>
std::set<unsigned> PottsBasedCellPopulation<DIM>::GetNeighbouringLocationIndices(CellPtr pCell)
{
    unsigned elem_index = this->GetLocationIndexUsingCell(pCell);
    return mpPottsMesh->GetNeighbouringElementIndices(elem_index);
}
 
template<unsigned DIM>
c_vector<double, DIM> PottsBasedCellPopulation<DIM>::GetLocationOfCellCentre(CellPtr pCell)
{
    return mpPottsMesh->GetCentroidOfElement(this->GetLocationIndexUsingCell(pCell));
}
 
template<unsigned DIM>
PottsElement<DIM>* PottsBasedCellPopulation<DIM>::GetElementCorrespondingToCell(CellPtr pCell)
{
    return mpPottsMesh->GetElement(this->GetLocationIndexUsingCell(pCell));
}
 
template<unsigned DIM>
CellPtr PottsBasedCellPopulation<DIM>::AddCell(CellPtr pNewCell, CellPtr pParentCell)
{
    // Get the element associated with this cell
    PottsElement<DIM>* p_element = GetElementCorrespondingToCell(pParentCell);
 
    // Divide the element
    unsigned new_element_index = mpPottsMesh->DivideElement(p_element, true); // new element will be below the existing element
 
    // Associate the new cell with the element
    this->mCells.push_back(pNewCell);
 
    // Update location cell map
    CellPtr p_created_cell = this->mCells.back();
    this->SetCellUsingLocationIndex(new_element_index,p_created_cell);
    return p_created_cell;
}
 
template<unsigned DIM>
unsigned PottsBasedCellPopulation<DIM>::RemoveDeadCells()
{
    unsigned num_removed = 0;
 
    for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
         cell_iter != this->mCells.end();
         )
    {
        if ((*cell_iter)->IsDead())
        {
            // Get the location index corresponding to this cell
            unsigned location_index = this->GetLocationIndexUsingCell(*cell_iter);
 
            // Use this to remove the cell from the population
            mpPottsMesh->DeleteElement(location_index);
 
            // Erase cell and update counter
            cell_iter = this->mCells.erase(cell_iter);
            num_removed++;
        }
        else
        {
            ++cell_iter;
        }
    }
    return num_removed;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::UpdateCellLocations(double dt)
{
    /*
     * This method implements a Monte Carlo method to update the cell population.
     * We sample randomly from all nodes in the mesh. Once we have selected a target
     * node we randomly select a neighbour. The Hamiltonian is evaluated in the
     * current configuration (H_0) and with the target node added to the same
     * element as the neighbour (H_1). Based on the vale of deltaH = H_1 - H_0,
     * the switch is either made or not.
     *
     * For each time step (i.e. each time this method is called) we sample
     * mrMesh.GetNumNodes() nodes. This is known as a Monte Carlo Step (MCS).
     */
 
    RandomNumberGenerator* p_gen = RandomNumberGenerator::Instance();
    unsigned num_nodes = this->mrMesh.GetNumNodes();
 
    // Randomly permute mUpdateRuleCollection if specified
    if (this->mIterateRandomlyOverUpdateRuleCollection)
    {
        // Randomly permute mUpdateRuleCollection
        p_gen->Shuffle(this->mUpdateRuleCollection);
    }
 
    for (unsigned i=0; i<num_nodes*mNumSweepsPerTimestep; i++)
    {
        unsigned node_index;
 
        if (this->mUpdateNodesInRandomOrder)
        {
            node_index = p_gen->randMod(num_nodes);
        }
        else
        {
            // Loop over nodes in index order.
            node_index = i%num_nodes;
        }
 
        Node<DIM>* p_node = this->mrMesh.GetNode(node_index);
 
        // Each node in the mesh must be in at most one element
        assert(p_node->GetNumContainingElements() <= 1);
 
        // Find a random available neighbouring node to overwrite current site
        std::set<unsigned> neighbouring_node_indices = mpPottsMesh->GetMooreNeighbouringNodeIndices(node_index);
        unsigned neighbour_location_index;
 
        if (!neighbouring_node_indices.empty())
        {
            unsigned num_neighbours = neighbouring_node_indices.size();
            unsigned chosen_neighbour = p_gen->randMod(num_neighbours);
 
            std::set<unsigned>::iterator neighbour_iter = neighbouring_node_indices.begin();
            for (unsigned j=0; j<chosen_neighbour; j++)
            {
                neighbour_iter++;
            }
 
            neighbour_location_index = *neighbour_iter;
 
            std::set<unsigned> containing_elements = p_node->rGetContainingElementIndices();
            std::set<unsigned> neighbour_containing_elements = GetNode(neighbour_location_index)->rGetContainingElementIndices();
            // Only calculate Hamiltonian and update elements if the nodes are from different elements, or one is from the medium
            if ((!containing_elements.empty() && neighbour_containing_elements.empty())
                || (containing_elements.empty() && !neighbour_containing_elements.empty())
                || (!containing_elements.empty() && !neighbour_containing_elements.empty() && *containing_elements.begin() != *neighbour_containing_elements.begin()))
            {
                double delta_H = 0.0; // This is H_1-H_0.
 
                // Now add contributions to the Hamiltonian from each AbstractPottsUpdateRule
                for (typename std::vector<boost::shared_ptr<AbstractUpdateRule<DIM> > >::iterator iter = this->mUpdateRuleCollection.begin();
                     iter != this->mUpdateRuleCollection.end();
                     ++iter)
                {
                    // This static cast is fine, since we assert the update rule must be a Potts update rule in AddUpdateRule()
                    double dH = (boost::static_pointer_cast<AbstractPottsUpdateRule<DIM> >(*iter))->EvaluateHamiltonianContribution(neighbour_location_index, p_node->GetIndex(), *this);
                    delta_H += dH;
                }
 
                // Generate a uniform random number to do the random motion
                double random_number = p_gen->ranf();
 
                double p = exp(-delta_H/mTemperature);
                if (delta_H <= 0 || random_number < p)
                {
                    // Do swap
 
                    // Remove the current node from any elements containing it (there should be at most one such element)
                    for (std::set<unsigned>::iterator iter = containing_elements.begin();
                         iter != containing_elements.end();
                         ++iter)
                    {
                        GetElement(*iter)->DeleteNode(GetElement(*iter)->GetNodeLocalIndex(node_index));
 
                    }
 
                    // Next add the current node to any elements containing the neighbouring node (there should be at most one such element)
                    for (std::set<unsigned>::iterator iter = neighbour_containing_elements.begin();
                         iter != neighbour_containing_elements.end();
                         ++iter)
                    {
                        GetElement(*iter)->AddNode(this->mrMesh.GetNode(node_index));
                    }
                }
            }
        }
    }
}
 
template<unsigned DIM>
bool PottsBasedCellPopulation<DIM>::IsCellAssociatedWithADeletedLocation(CellPtr pCell)
{
    return GetElementCorrespondingToCell(pCell)->IsDeleted();
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::Update(bool hasHadBirthsOrDeaths)
{
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::OpenWritersFiles(OutputFileHandler& rOutputFileHandler)
{
    if (this->mOutputResultsForChasteVisualizer)
    {
        if (!this-> template HasWriter<CellPopulationElementWriter>())
        {
            this-> template AddPopulationWriter<CellPopulationElementWriter>();
        }
    }
    // Add a CellID writer so that a VTK file will contain IDs for visualisation.  (It will also dump a "loggedcell.dat" file as a side-effect.)
    this-> template AddCellWriter<CellIdWriter>();
 
    AbstractCellPopulation<DIM>::OpenWritersFiles(rOutputFileHandler);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::WriteResultsToFiles(const std::string& rDirectory)
{
    CreateElementTessellation(); // To be used to output to the visualizer
 
    AbstractCellPopulation<DIM>::WriteResultsToFiles(rDirectory);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::AcceptPopulationWriter(boost::shared_ptr<AbstractCellPopulationWriter<DIM, DIM> > pPopulationWriter)
{
    pPopulationWriter->Visit(this);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::AcceptPopulationCountWriter(boost::shared_ptr<AbstractCellPopulationCountWriter<DIM, DIM> > pPopulationCountWriter)
{
    pPopulationCountWriter->Visit(this);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::AcceptPopulationEventWriter(boost::shared_ptr<AbstractCellPopulationEventWriter<DIM, DIM> > pPopulationEventWriter)
{
    pPopulationEventWriter->Visit(this);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::AcceptCellWriter(boost::shared_ptr<AbstractCellWriter<DIM, DIM> > pCellWriter, CellPtr pCell)
{
    pCellWriter->VisitCell(pCell, this);
}
 
template<unsigned DIM>
double PottsBasedCellPopulation<DIM>::GetVolumeOfCell(CellPtr pCell)
{
    // Get element index corresponding to this cell
    unsigned elem_index = this->GetLocationIndexUsingCell(pCell);
 
    // Get volume of this element in the Potts mesh
    double cell_volume = mpPottsMesh->GetVolumeOfElement(elem_index);
 
    return cell_volume;
}
 
template<unsigned DIM>
double PottsBasedCellPopulation<DIM>::GetWidth(const unsigned& rDimension)
{
    // Call GetWidth() on the mesh
    double width = this->mrMesh.GetWidth(rDimension);
 
    return width;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::AddUpdateRule(boost::shared_ptr<AbstractUpdateRule<DIM> > pUpdateRule)
{
    assert(bool(dynamic_cast<AbstractPottsUpdateRule<DIM>*>(pUpdateRule.get())));
    this->mUpdateRuleCollection.push_back(pUpdateRule);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::CreateElementTessellation()
{
//  delete mpElementTessellation;
//
//    ///\todo this code would need to be extended if the domain were required to be periodic
//
//  std::vector<Node<2>*> nodes;
//  for (unsigned node_index=0; node_index<mrMesh.GetNumNodes(); node_index++)
//  {
//      Node<2>* p_temp_node = mrMesh.GetNode(node_index);
//      nodes.push_back(p_temp_node);
//  }
//  MutableMesh<2,2> mesh(nodes);
//    mpElementTessellation = new VertexMesh<2,2>(mesh);
}
 
template<unsigned DIM>
VertexMesh<DIM,DIM>* PottsBasedCellPopulation<DIM>::GetElementTessellation()
{
//    assert(mpElementTessellation != NULL);
    return mpElementTessellation;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::CreateMutableMesh()
{
    delete mpMutableMesh;
 
    // Get the nodes of the PottsMesh
    std::vector<Node<DIM>*> nodes;
    for (unsigned node_index=0; node_index<this->mrMesh.GetNumNodes(); node_index++)
    {
      const c_vector<double, DIM>& r_location = this->mrMesh.GetNode(node_index)->rGetLocation();
      nodes.push_back(new Node<DIM>(node_index, r_location));
    }
 
    mpMutableMesh = new MutableMesh<DIM,DIM>(nodes);
}
 
template<unsigned DIM>
MutableMesh<DIM,DIM>* PottsBasedCellPopulation<DIM>::GetMutableMesh()
{
    assert(mpMutableMesh);
    return mpMutableMesh;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::OutputCellPopulationParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t<Temperature>" << mTemperature << "</Temperature>\n";
    *rParamsFile << "\t\t<NumSweepsPerTimestep>" << mNumSweepsPerTimestep << "</NumSweepsPerTimestep>\n";
 
    // Call method on direct parent class
    AbstractOnLatticeCellPopulation<DIM>::OutputCellPopulationParameters(rParamsFile);
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::SetTemperature(double temperature)
{
    mTemperature = temperature;
}
 
template<unsigned DIM>
double PottsBasedCellPopulation<DIM>::GetTemperature()
{
    return mTemperature;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::SetNumSweepsPerTimestep(unsigned numSweepsPerTimestep)
{
    mNumSweepsPerTimestep = numSweepsPerTimestep;
}
 
template<unsigned DIM>
unsigned PottsBasedCellPopulation<DIM>::GetNumSweepsPerTimestep()
{
    return mNumSweepsPerTimestep;
}
 
template<unsigned DIM>
void PottsBasedCellPopulation<DIM>::WriteVtkResultsToFile(const std::string& rDirectory)
{
    unsigned num_timesteps = SimulationTime::Instance()->GetTimeStepsElapsed();
    std::stringstream time;
    time << num_timesteps;
 
    // Create mesh writer for VTK output
    VtkMeshWriter<DIM, DIM> mesh_writer(rDirectory, "results_"+time.str(), false);
 
    // Iterate over any cell writers that are present
    unsigned num_nodes = GetNumNodes();
    for (typename std::vector<boost::shared_ptr<AbstractCellWriter<DIM, DIM> > >::iterator cell_writer_iter = this->mCellWriters.begin();
         cell_writer_iter != this->mCellWriters.end();
         ++cell_writer_iter)
    {
        // Create vector to store VTK cell data
        std::vector<double> vtk_cell_data(num_nodes);
 
        // Iterate over nodes in the mesh
        for (typename AbstractMesh<DIM,DIM>::NodeIterator iter = mpPottsMesh->GetNodeIteratorBegin();
             iter != mpPottsMesh->GetNodeIteratorEnd();
             ++iter)
        {
            // Get the index of this node in the mesh and those elements (i.e. cells) that contain this node
            unsigned node_index = iter->GetIndex();
            std::set<unsigned> element_indices = iter->rGetContainingElementIndices();
 
            // If there are no elements associated with this node, then we set the value of any VTK cell data to be -1 at this node...
            if (element_indices.empty())
            {
                // Populate the vector of VTK cell data
                vtk_cell_data[node_index] = -1.0;
            }
            else
            {
                // ... otherwise there should be exactly one element (i.e. cell) containing this node
                assert(element_indices.size() == 1);
                unsigned elem_index = *(element_indices.begin());
                CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
 
                // Populate the vector of VTK cell data
                vtk_cell_data[node_index] = (*cell_writer_iter)->GetCellDataForVtkOutput(p_cell, this);
            }
        }
 
        mesh_writer.AddPointData((*cell_writer_iter)->GetVtkCellDataName(), vtk_cell_data);
    }
 
    // When outputting any CellData, we assume that the first cell is representative of all cells
    unsigned num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
    std::vector<std::string> cell_data_names = this->Begin()->GetCellData()->GetKeys();
 
    std::vector<std::vector<double> > cell_data;
    for (unsigned var=0; var<num_cell_data_items; var++)
    {
        std::vector<double> cell_data_var(num_nodes);
        cell_data.push_back(cell_data_var);
    }
 
    for (typename AbstractMesh<DIM,DIM>::NodeIterator iter = mpPottsMesh->GetNodeIteratorBegin();
         iter != mpPottsMesh->GetNodeIteratorEnd();
         ++iter)
    {
        // Get the index of this node in the mesh and those elements (i.e. cells) that contain this node
        unsigned node_index = iter->GetIndex();
        std::set<unsigned> element_indices = iter->rGetContainingElementIndices();
 
        // If there are no elements associated with this node, then we set the value of any VTK cell data to be -1 at this node...
        if (element_indices.empty())
        {
            for (unsigned var=0; var<num_cell_data_items; var++)
            {
                cell_data[var][node_index] = -1.0;
            }
        }
        else
        {
            // ... otherwise there should be exactly one element (i.e. cell) containing this node
            assert(element_indices.size() == 1);
            unsigned elem_index = *(element_indices.begin());
            CellPtr p_cell = this->GetCellUsingLocationIndex(elem_index);
 
            for (unsigned var=0; var<num_cell_data_items; var++)
            {
                cell_data[var][node_index] = p_cell->GetCellData()->GetItem(cell_data_names[var]);
            }
        }
    }
    for (unsigned var=0; var<cell_data.size(); var++)
    {
        mesh_writer.AddPointData(cell_data_names[var], cell_data[var]);
    }
 
    /*
     * At present, the VTK writer can only write things which inherit from AbstractTetrahedralMeshWriter.
     * For now, we do an explicit conversion to NodesOnlyMesh. This can be written to VTK, then visualized
     * as glyphs in Paraview.
     */
    NodesOnlyMesh<DIM> temp_mesh;
    temp_mesh.ConstructNodesWithoutMesh(*mpPottsMesh, 1.5); // This cut-off is arbitrary, as node connectivity is not used here
    mesh_writer.WriteFilesUsingMesh(temp_mesh);
 
    *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << "\" group=\"\" part=\"0\" file=\"results_";
    *(this->mpVtkMetaFile) << num_timesteps;
    *(this->mpVtkMetaFile) << ".vtu\"/>\n";
 
    // Extra part to output the outlines of cells
    if (DIM ==2)
    {
        std::vector<Node<2>*> outline_nodes;
        std::vector<VertexElement<2,2>*>  outline_elements;
 
        unsigned outline_node_index = 0;
        unsigned outline_element_index = 0;
        for (typename AbstractMesh<DIM,DIM>::NodeIterator iter = mpPottsMesh->GetNodeIteratorBegin();
             iter != mpPottsMesh->GetNodeIteratorEnd();
             ++iter)
        {
            // Get the index of this node in the mesh and those elements (i.e. cells) that contain this node
            unsigned node_index = iter->GetIndex();
            std::set<unsigned> element_indices = iter->rGetContainingElementIndices();
 
            std::set<unsigned> target_neighbouring_node_indices = this->rGetMesh().GetVonNeumannNeighbouringNodeIndices(node_index);
 
            for (std::set<unsigned>::iterator neighbour_iter = target_neighbouring_node_indices.begin();
                 neighbour_iter != target_neighbouring_node_indices.end();
                 ++neighbour_iter)
            {
                std::set<unsigned> neighbouring_element_indices = this->rGetMesh().GetNode(*neighbour_iter)->rGetContainingElementIndices();
 
                // If different cells add a line
                if (element_indices != neighbouring_element_indices)
                {
                    std::vector<Node<2>*> element_nodes;
 
                    const c_vector<double, 2>& r_node_location = this->mrMesh.GetNode(node_index)->rGetLocation();
                    const c_vector<double, 2>& r_neighbour_node_location = this->mrMesh.GetNode(*neighbour_iter)->rGetLocation();
 
                    c_vector<double, 2> unit_tangent = r_neighbour_node_location - r_node_location;
 
                    if (norm_2(unit_tangent) > 1.0) // It's a periodic neighbour
                    {
                        c_vector<double, 2> mid_point = 0.5*(r_node_location + r_neighbour_node_location);
                        if (unit_tangent(0) == 0)
                        {
                            if (r_node_location(1) < r_neighbour_node_location(1))
                            {
                                mid_point(1) = r_node_location(1) - 0.5;
                            }
                            else
                            {
                                mid_point(1) = r_node_location(1) + 0.5;
                            }
                        }
                        else
                        {
                            assert(unit_tangent(1) == 0);
 
                            if (r_node_location(0) < r_neighbour_node_location(0))
                            {
                                mid_point(0) = r_node_location(0) - 0.5;
                            }
                            else
                            {
                                mid_point(0) = r_node_location(0) + 0.5;
                            }
                        }
                        assert(norm_2(unit_tangent) > 0);
                        unit_tangent = unit_tangent/norm_2(unit_tangent);
 
                        c_vector<double, DIM> unit_normal;
                        unit_normal(0) = -unit_tangent(1);
                        unit_normal(1) = unit_tangent(0);
 
                        std::vector<Node<2>*> element_nodes;
 
                        // Need at least three points to visualise in Paraview
                        Node<2>* p_node_1 = new Node<2>(outline_node_index, mid_point - 0.5*unit_normal);
                        outline_nodes.push_back(p_node_1);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        Node<2>* p_node_2 = new Node<2>(outline_node_index, mid_point);
                        outline_nodes.push_back(p_node_2);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        Node<2>* p_node_3 = new Node<2>(outline_node_index, mid_point + 0.5*unit_normal);
                        outline_nodes.push_back(p_node_3);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        VertexElement<2,2>* p_element = new VertexElement<2,2>(outline_element_index, element_nodes);
                        outline_elements.push_back(p_element);
                        outline_element_index++;
 
                    }
                    else // Standard Neighbour
                    {
                        c_vector<double, 2> mid_point = 0.5*(r_node_location + r_neighbour_node_location);
 
                        assert(norm_2(unit_tangent) > 0);
                        unit_tangent = unit_tangent/norm_2(unit_tangent);
 
                        c_vector<double, 2> unit_normal;
                        unit_normal(0) = -unit_tangent(1);
                        unit_normal(1) = unit_tangent(0);
 
                        std::vector<Node<2>*> element_nodes;
 
                        // Need at least three points to visualise in Paraview
                        Node<2>* p_node_1 = new Node<2>(outline_node_index, mid_point - 0.5*unit_normal);
                        outline_nodes.push_back(p_node_1);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        Node<2>* p_node_2 = new Node<2>(outline_node_index, mid_point);
                        outline_nodes.push_back(p_node_2);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        Node<2>* p_node_3 = new Node<2>(outline_node_index, mid_point + 0.5*unit_normal);
                        outline_nodes.push_back(p_node_3);
                        element_nodes.push_back(outline_nodes[outline_node_index]);
                        outline_node_index++;
 
                        VertexElement<2,2>* p_element = new VertexElement<2,2>(outline_element_index, element_nodes);
                        outline_elements.push_back(p_element);
                        outline_element_index++;
                    }
                }
            }
        }
        VertexMesh<2,2> cell_outline_mesh(outline_nodes,outline_elements);
 
        VertexMeshWriter<2, 2> outline_mesh_writer(rDirectory, "outlines", false);
        outline_mesh_writer.WriteVtkUsingMesh(cell_outline_mesh, time.str());
        outline_mesh_writer.WriteFilesUsingMesh(cell_outline_mesh);
    }
}
 
template<unsigned DIM>
double PottsBasedCellPopulation<DIM>::GetCellDataItemAtPdeNode(
    unsigned pdeNodeIndex,
    std::string& rVariableName,
    bool dirichletBoundaryConditionApplies,
    double dirichletBoundaryValue)
{
    CellPtr p_cell = this->GetCellUsingLocationIndex(pdeNodeIndex);
    double value = p_cell->GetCellData()->GetItem(rVariableName);
    return value;
}
 
// Explicit instantiation
template class PottsBasedCellPopulation<1>;
template class PottsBasedCellPopulation<2>;
template class PottsBasedCellPopulation<3>;
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(PottsBasedCellPopulation)