MutableMesh.cpp

/*

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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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*/

#include <map>
#include <cstring>

#include "MutableMesh.hpp"
#include "OutputFileHandler.hpp"

//Jonathan Shewchuk's triangle and Hang Si's tetgen
#define REAL double
#define VOID void
#include "triangle.h"
#include "tetgen.h"
#undef REAL
#undef VOID


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
MutableMesh<ELEMENT_DIM, SPACE_DIM>::MutableMesh()
    : mAddedNodes(false)
{
    this->mMeshChangesDuringSimulation = true;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
MutableMesh<ELEMENT_DIM, SPACE_DIM>::MutableMesh(std::vector<Node<SPACE_DIM> *> nodes)
{
    this->mMeshChangesDuringSimulation = true;
    Clear();
    for (unsigned index=0; index<nodes.size(); index++)
    {
        Node<SPACE_DIM>* p_temp_node = nodes[index];
        this->mNodes.push_back(p_temp_node);
    }
    mAddedNodes = true;
    NodeMap node_map(nodes.size());
    ReMesh(node_map);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
MutableMesh<ELEMENT_DIM, SPACE_DIM>::~MutableMesh()
{
    Clear();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::AddNode(Node<SPACE_DIM>* pNewNode)
{
    if (mDeletedNodeIndices.empty())
    {
        pNewNode->SetIndex(this->mNodes.size());
        this->mNodes.push_back(pNewNode);
    }
    else
    {
        unsigned index = mDeletedNodeIndices.back();
        pNewNode->SetIndex(index);
        mDeletedNodeIndices.pop_back();
        delete this->mNodes[index];
        this->mNodes[index] = pNewNode;
    }
    mAddedNodes = true;
    return pNewNode->GetIndex();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::AddElement(Element<ELEMENT_DIM,SPACE_DIM>* pNewElement)
{
    unsigned new_elt_index;

    if (mDeletedElementIndices.empty())
    {
        new_elt_index = this->mElements.size();
        this->mElements.push_back(pNewElement);
        pNewElement->ResetIndex(new_elt_index);
    }
    else
    {
        unsigned index = mDeletedElementIndices.back();
        pNewElement->ResetIndex(index);
        mDeletedElementIndices.pop_back();
        delete this->mElements[index];
        this->mElements[index] = pNewElement;
    }

    return pNewElement->GetIndex();
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::Clear()
{
    mDeletedElementIndices.clear();
    mDeletedBoundaryElementIndices.clear();
    mDeletedNodeIndices.clear();
    mAddedNodes = false;

    TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::Clear();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::GetNumBoundaryElements() const
{
    return this->mBoundaryElements.size() - mDeletedBoundaryElementIndices.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::GetNumElements() const
{
    return this->mElements.size() - mDeletedElementIndices.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::GetNumNodes() const
{
    return this->mNodes.size() - mDeletedNodeIndices.size();
}

template<>
void MutableMesh<1, 1>::RescaleMeshFromBoundaryNode(ChastePoint<1> updatedPoint, unsigned boundaryNodeIndex)
{
    assert(this->GetNode(boundaryNodeIndex)->IsBoundaryNode());
    double scaleFactor = updatedPoint[0] / this->GetNode(boundaryNodeIndex)->GetPoint()[0];
    double temp;
    for (unsigned i=0; i < boundaryNodeIndex+1; i++)
    {
        temp = scaleFactor * this->mNodes[i]->GetPoint()[0];
        ChastePoint<1> newPoint(temp);
        this->mNodes[i]->SetPoint(newPoint);
    }
    this->RefreshMesh();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::SetNode(unsigned index,
        ChastePoint<SPACE_DIM> point,
        bool concreteMove)
{
    this->mNodes[index]->SetPoint(point);

    if (concreteMove)
    {
        for (typename Node<SPACE_DIM>::ContainingBoundaryElementIterator it = this->mNodes[index]->ContainingBoundaryElementsBegin();
             it != this->mNodes[index]->ContainingBoundaryElementsEnd();
             ++it)
        {
            try
            {
                this->GetBoundaryElement(*it)->CalculateWeightedDirection(this->mBoundaryElementWeightedDirections[ (*it) ],
                                                                    this->mBoundaryElementJacobianDeterminants[ (*it) ]);
            }
            catch (Exception&)
            {
                EXCEPTION("Moving node caused a boundary element to have a non-positive Jacobian determinant");
            }
        }
        for (typename Node<SPACE_DIM>::ContainingElementIterator it = this->mNodes[index]->ContainingElementsBegin();
             it != this->mNodes[index]->ContainingElementsEnd();
             ++it)
        {
            if (ELEMENT_DIM == SPACE_DIM)
            {
                try
                {
                    this->GetElement(*it)->CalculateInverseJacobian(this->mElementJacobians[ (*it) ],
                                                              this->mElementJacobianDeterminants[ (*it) ],
                                                              this->mElementInverseJacobians[ (*it) ]);
                }
                catch (Exception&)
                {
                        EXCEPTION("Moving node caused an element to have a non-positive Jacobian determinant");
                }
            }
            else
            {
                c_vector<double,SPACE_DIM> previous_direction = this->mElementWeightedDirections[ (*it) ];

                this->GetElement(*it)->CalculateWeightedDirection(this->mElementWeightedDirections[ (*it) ],
                                                            this->mElementJacobianDeterminants[ (*it) ]);

                if (inner_prod(previous_direction, this->mElementWeightedDirections[ (*it) ]) < 0)
                {
                    EXCEPTION("Moving node caused an subspace element to change direction");
                }

            }
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::DeleteNode(unsigned index)
{
    if (this->mNodes[index]->IsDeleted())
    {
        EXCEPTION("Trying to delete a deleted node");
    }
    unsigned target_index = (unsigned)(-1);
    bool found_target=false;
    for (typename Node<SPACE_DIM>::ContainingElementIterator it = this->mNodes[index]->ContainingElementsBegin();
         !found_target && it != this->mNodes[index]->ContainingElementsEnd();
         ++it)
    {
        Element <ELEMENT_DIM,SPACE_DIM>* p_element = this->GetElement(*it);
        for (unsigned i=0; i<=ELEMENT_DIM && !found_target; i++)
        {
            target_index = p_element->GetNodeGlobalIndex(i);
            try
            {
                MoveMergeNode(index, target_index, false);
                found_target = true;
            }
            catch (Exception&)
            {
                // Just try the next node
            }
        }
    }
    if (!found_target)
    {
        EXCEPTION("Failure to delete node");
    }

    MoveMergeNode(index, target_index);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::DeleteElement(unsigned index)
{
    assert(!this->mElements[index]->IsDeleted());
    this->mElements[index]->MarkAsDeleted();
    mDeletedElementIndices.push_back(index);

    // Delete any nodes that are no longer attached to mesh
    for (unsigned node_index = 0; node_index < this->mElements[index]->GetNumNodes(); ++node_index)
    {
        if (this->mElements[index]->GetNode(node_index)->GetNumContainingElements() == 0u)
        {
            if (this->mElements[index]->GetNode(node_index)->GetNumBoundaryElements() == 0u)
            {
                this->mElements[index]->GetNode(node_index)->MarkAsDeleted();
                mDeletedNodeIndices.push_back(this->mElements[index]->GetNode(node_index)->GetIndex());
            }
            else if (this->mElements[index]->GetNode(node_index)->GetNumBoundaryElements() == 1u && ELEMENT_DIM == 1)
            {
                std::set<unsigned> indices = this->mElements[index]->GetNode(node_index)->rGetContainingBoundaryElementIndices();
                assert(indices.size() == 1u);
                this->mBoundaryElements[*indices.begin()]->MarkAsDeleted();
                mDeletedBoundaryElementIndices.push_back(*indices.begin());

                this->mElements[index]->GetNode(node_index)->MarkAsDeleted();
                mDeletedNodeIndices.push_back(this->mElements[index]->GetNode(node_index)->GetIndex());
            }
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::DeleteNodePriorToReMesh(unsigned index)
{
    this->mNodes[index]->MarkAsDeleted();
    mDeletedNodeIndices.push_back(index);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::MoveMergeNode(unsigned index,
        unsigned targetIndex,
        bool concreteMove)
{
    if (this->mNodes[index]->IsDeleted())
    {
        EXCEPTION("Trying to move a deleted node");
    }

    if (index == targetIndex)
    {
        EXCEPTION("Trying to merge a node with itself");
    }
    if (this->mNodes[index]->IsBoundaryNode())
    {
        if (!this->mNodes[targetIndex]->IsBoundaryNode())
        {
            EXCEPTION("A boundary node can only be moved on to another boundary node");
        }
    }
    std::set<unsigned> unshared_element_indices;
    std::set_difference(this->mNodes[index]->rGetContainingElementIndices().begin(),
                        this->mNodes[index]->rGetContainingElementIndices().end(),
                        this->mNodes[targetIndex]->rGetContainingElementIndices().begin(),
                        this->mNodes[targetIndex]->rGetContainingElementIndices().end(),
                        std::inserter(unshared_element_indices, unshared_element_indices.begin()));


    if (unshared_element_indices.size() == this->mNodes[index]->rGetContainingElementIndices().size())
    {
        EXCEPTION("These nodes cannot be merged since they are not neighbours");
    }

    std::set<unsigned> unshared_boundary_element_indices;
    std::set_difference(this->mNodes[index]->rGetContainingBoundaryElementIndices().begin(),
                        this->mNodes[index]->rGetContainingBoundaryElementIndices().end(),
                        this->mNodes[targetIndex]->rGetContainingBoundaryElementIndices().begin(),
                        this->mNodes[targetIndex]->rGetContainingBoundaryElementIndices().end(),
                        std::inserter(unshared_boundary_element_indices, unshared_boundary_element_indices.begin()));


    if (this->mNodes[index]->IsBoundaryNode())
    {
        if (unshared_boundary_element_indices.size()
            == this->mNodes[index]->rGetContainingBoundaryElementIndices().size())
        {
            //May be redundant (only thrown in 1D tests)
            EXCEPTION("These nodes cannot be merged since they are not neighbours on the boundary");
        }
    }

    this->mNodes[index]->rGetModifiableLocation() = this->mNodes[targetIndex]->rGetLocation();

    for (std::set<unsigned>::const_iterator element_iter=unshared_element_indices.begin();
             element_iter != unshared_element_indices.end();
             element_iter++)
    {
        try
        {
            if (SPACE_DIM == ELEMENT_DIM)
            {
                this->GetElement(*element_iter)->CalculateInverseJacobian(this->mElementJacobians[(*element_iter)],
                                                                          this->mElementJacobianDeterminants[(*element_iter)],
                                                                          this->mElementInverseJacobians[ (*element_iter) ]);
            }
            else
            {
                this->GetElement(*element_iter)->CalculateWeightedDirection(this->mElementWeightedDirections[(*element_iter)],
                                                                            this->mElementJacobianDeterminants[(*element_iter)]);
            }

            if (concreteMove)
            {
                this->GetElement(*element_iter)->ReplaceNode(this->mNodes[index], this->mNodes[targetIndex]);
            }

        }
        catch (Exception&)
        {
            EXCEPTION("Moving node caused an element to have a non-positive Jacobian determinant");
        }
    }

    for (std::set<unsigned>::const_iterator boundary_element_iter=
                 unshared_boundary_element_indices.begin();
             boundary_element_iter != unshared_boundary_element_indices.end();
             boundary_element_iter++)
    {

        this->GetBoundaryElement(*boundary_element_iter)->CalculateWeightedDirection(this->mBoundaryElementWeightedDirections[(*boundary_element_iter)],
                                                                                     this->mBoundaryElementJacobianDeterminants[(*boundary_element_iter)]);

        if (concreteMove)
        {
            this->GetBoundaryElement(*boundary_element_iter)->ReplaceNode(this->mNodes[index], this->mNodes[targetIndex]);
        }
    }

    std::set<unsigned> shared_element_indices;
    std::set_intersection(this->mNodes[index]->rGetContainingElementIndices().begin(),
                          this->mNodes[index]->rGetContainingElementIndices().end(),
                          this->mNodes[targetIndex]->rGetContainingElementIndices().begin(),
                          this->mNodes[targetIndex]->rGetContainingElementIndices().end(),
                          std::inserter(shared_element_indices, shared_element_indices.begin()));

    for (std::set<unsigned>::const_iterator element_iter=shared_element_indices.begin();
             element_iter != shared_element_indices.end();
             element_iter++)
    {
        if (concreteMove)
        {
            this->GetElement(*element_iter)->MarkAsDeleted();
            this->mElementJacobianDeterminants[ (*element_iter) ] = 0.0; //This used to be done in MarkAsDeleted
            mDeletedElementIndices.push_back(*element_iter);
        }
        else
        {
            this->mElementJacobianDeterminants[ (*element_iter) ] = 0.0;
        }
    }


    std::set<unsigned> shared_boundary_element_indices;
    std::set_intersection(this->mNodes[index]->rGetContainingBoundaryElementIndices().begin(),
                          this->mNodes[index]->rGetContainingBoundaryElementIndices().end(),
                          this->mNodes[targetIndex]->rGetContainingBoundaryElementIndices().begin(),
                          this->mNodes[targetIndex]->rGetContainingBoundaryElementIndices().end(),
                          std::inserter(shared_boundary_element_indices, shared_boundary_element_indices.begin()));

    for (std::set<unsigned>::const_iterator boundary_element_iter=shared_boundary_element_indices.begin();
             boundary_element_iter != shared_boundary_element_indices.end();
             boundary_element_iter++)
    {
        if (concreteMove)
        {
            this->GetBoundaryElement(*boundary_element_iter)->MarkAsDeleted();
            this->mBoundaryElementJacobianDeterminants[ (*boundary_element_iter) ] = 0.0; //This used to be done in MarkAsDeleted
            mDeletedBoundaryElementIndices.push_back(*boundary_element_iter);
        }
        else
        {
            this->mBoundaryElementJacobianDeterminants[ (*boundary_element_iter) ] = 0.0;
            this->mBoundaryElementWeightedDirections[ (*boundary_element_iter) ] = zero_vector<double>(SPACE_DIM);
        }
    }

    if (concreteMove)
    {
        this->mNodes[index]->MarkAsDeleted();
        mDeletedNodeIndices.push_back(index);
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned MutableMesh<ELEMENT_DIM, SPACE_DIM>::RefineElement(
    Element<ELEMENT_DIM,SPACE_DIM>* pElement,
    ChastePoint<SPACE_DIM> point)
{
    //Check that the point is in the element
    if (pElement->IncludesPoint(point, true) == false)
    {
        EXCEPTION("RefineElement could not be started (point is not in element)");
    }

    // Add a new node from the point that is passed to RefineElement
    unsigned new_node_index = AddNode(new Node<SPACE_DIM>(0, point.rGetLocation()));
    // Note: the first argument is the index of the node, which is going to be
    //       overridden by AddNode, so it can safely be ignored

    // This loop constructs the extra elements which are going to fill the space
    for (unsigned i = 0; i < ELEMENT_DIM; i++)
    {

        // First, make a copy of the current element making sure we update its index
        unsigned new_elt_index;
        if (mDeletedElementIndices.empty())
        {
            new_elt_index = this->mElements.size();
        }
        else
        {
            new_elt_index = mDeletedElementIndices.back();
            mDeletedElementIndices.pop_back();
        }

        Element<ELEMENT_DIM,SPACE_DIM>* p_new_element=
            new Element<ELEMENT_DIM,SPACE_DIM>(*pElement, new_elt_index);

        // Second, update the node in the element with the new one
        p_new_element->UpdateNode(ELEMENT_DIM-1-i, this->mNodes[new_node_index]);

        // Third, add the new element to the set
        if ((unsigned) new_elt_index == this->mElements.size())
        {
            this->mElements.push_back(p_new_element);
        }
        else
        {
            delete this->mElements[new_elt_index];
            this->mElements[new_elt_index] = p_new_element;
        }
    }

    // Lastly, update the last node in the element to be refined
    pElement->UpdateNode(ELEMENT_DIM, this->mNodes[new_node_index]);

    return new_node_index;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::DeleteBoundaryNodeAt(unsigned index)
{
    if (!this->mNodes[index]->IsBoundaryNode() )
    {
        EXCEPTION(" You may only delete a boundary node ");
    }

    this->mNodes[index]->MarkAsDeleted();
    mDeletedNodeIndices.push_back(index);

    // Update the boundary node vector
    typename std::vector<Node<SPACE_DIM>*>::iterator b_node_iter
    = std::find(this->mBoundaryNodes.begin(), this->mBoundaryNodes.end(), this->mNodes[index]);
    this->mBoundaryNodes.erase(b_node_iter);

    // Remove boundary elements containing this node
    std::set<unsigned> boundary_element_indices = this->mNodes[index]->rGetContainingBoundaryElementIndices();
    std::set<unsigned>::const_iterator boundary_element_indices_iterator = boundary_element_indices.begin();
    while (boundary_element_indices_iterator != boundary_element_indices.end())
    {
        BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>* p_boundary_element = this->GetBoundaryElement(*boundary_element_indices_iterator);
        p_boundary_element->MarkAsDeleted();
        mDeletedBoundaryElementIndices.push_back(*boundary_element_indices_iterator);
        boundary_element_indices_iterator++;
    }

    // Remove elements containing this node
    std::set<unsigned> element_indices = this->mNodes[index]->rGetContainingElementIndices();
    std::set<unsigned>::const_iterator element_indices_iterator = element_indices.begin();
    while (element_indices_iterator != element_indices.end())
    {
        Element<ELEMENT_DIM, SPACE_DIM>* p_element = this->GetElement(*element_indices_iterator);
        for (unsigned i=0; i<p_element->GetNumNodes(); i++)
        {
            Node<SPACE_DIM>* p_node = p_element->GetNode(i);
            if (!p_node->IsDeleted())
            {
                p_node->SetAsBoundaryNode();
                // Update the boundary node vector
                this->mBoundaryNodes.push_back(p_node);
            }
        }
        p_element->MarkAsDeleted();
        mDeletedElementIndices.push_back(p_element->GetIndex());
        element_indices_iterator++;
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::ReIndex(NodeMap& map)
{
    assert(!mAddedNodes);
    map.Resize(this->GetNumAllNodes());

    std::vector<Element<ELEMENT_DIM, SPACE_DIM> *> live_elements;

    for (unsigned i=0; i<this->mElements.size(); i++)
    {
        assert(i==this->mElements[i]->GetIndex()); // We need this to be true to be able to reindex the Jacobian cache
        if (this->mElements[i]->IsDeleted())
        {
            delete this->mElements[i];
        }
        else
        {
            live_elements.push_back(this->mElements[i]);

            unsigned this_element_index = this->mElements[i]->GetIndex();
            if (SPACE_DIM == ELEMENT_DIM)
            {
                this->mElementJacobians[live_elements.size()-1] = this->mElementJacobians[this_element_index];
                this->mElementInverseJacobians[live_elements.size()-1] = this->mElementInverseJacobians[this_element_index];
            }
            else
            {
                this->mElementWeightedDirections[live_elements.size()-1] = this->mElementWeightedDirections[this_element_index];
            }
            this->mElementJacobianDeterminants[live_elements.size()-1] = this->mElementJacobianDeterminants[this_element_index];
        }
    }

    assert(mDeletedElementIndices.size() == this->mElements.size()-live_elements.size());
    mDeletedElementIndices.clear();
    this->mElements = live_elements;
    unsigned num_elements = this->mElements.size();

    if (SPACE_DIM == ELEMENT_DIM)
    {
        this->mElementJacobians.resize(num_elements);
        this->mElementInverseJacobians.resize(num_elements);
    }
    else
    {
        this->mElementWeightedDirections.resize(num_elements);
    }
    this->mElementJacobianDeterminants.resize(num_elements);

    std::vector<Node<SPACE_DIM> *> live_nodes;
    for (unsigned i=0; i<this->mNodes.size(); i++)
    {
        if (this->mNodes[i]->IsDeleted())
        {
            delete this->mNodes[i];
            map.SetDeleted(i);
        }
        else
        {
            live_nodes.push_back(this->mNodes[i]);
            // the nodes will have their index set to be the index into the live_nodes
            // vector further down
            map.SetNewIndex(i, (unsigned)(live_nodes.size()-1));
        }
    }

    assert(mDeletedNodeIndices.size() == this->mNodes.size()-live_nodes.size());
    this->mNodes = live_nodes;
    mDeletedNodeIndices.clear();

    std::vector<BoundaryElement<ELEMENT_DIM-1, SPACE_DIM> *> live_boundary_elements;
    for (unsigned i=0; i<this->mBoundaryElements.size(); i++)
    {
        if (this->mBoundaryElements[i]->IsDeleted())
        {
            delete this->mBoundaryElements[i];
        }
        else
        {
            live_boundary_elements.push_back(this->mBoundaryElements[i]);

            this->mBoundaryElementWeightedDirections[live_boundary_elements.size()-1] = this->mBoundaryElementWeightedDirections[this->mBoundaryElements[i]->GetIndex()];
            this->mBoundaryElementJacobianDeterminants[live_boundary_elements.size()-1] = this->mBoundaryElementJacobianDeterminants[this->mBoundaryElements[i]->GetIndex()];
        }
    }

    assert(mDeletedBoundaryElementIndices.size() == this->mBoundaryElements.size()-live_boundary_elements.size());
    this->mBoundaryElements = live_boundary_elements;
    mDeletedBoundaryElementIndices.clear();

    unsigned num_boundary_elements = this->mBoundaryElements.size();

    this->mBoundaryElementWeightedDirections.resize(num_boundary_elements);
    this->mBoundaryElementJacobianDeterminants.resize(num_boundary_elements);

    for (unsigned i=0; i<this->mNodes.size(); i++)
    {
        this->mNodes[i]->SetIndex(i);
    }

    for (unsigned i=0; i<this->mElements.size(); i++)
    {

        this->mElements[i]->ResetIndex(i);
    }

    for (unsigned i=0; i<this->mBoundaryElements.size(); i++)
    {
        this->mBoundaryElements[i]->ResetIndex(i);
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::ReMesh(NodeMap& map)
{
    // Make sure that we are in the correct dimension - this code will be eliminated at compile time
    assert( ELEMENT_DIM == SPACE_DIM ); // LCOV_EXCL_LINE

    // Avoid some triangle/tetgen errors: need at least four
    // nodes for tetgen, and at least three for triangle
    if (GetNumNodes() <= SPACE_DIM)
    {
        EXCEPTION("The number of nodes must exceed the spatial dimension.");
    }

    // Make sure the map is big enough
    map.Resize(this->GetNumAllNodes());
    if (mAddedNodes || !mDeletedNodeIndices.empty())
    {
        // Size of mesh is about to change
        if (this->mpDistributedVectorFactory)
        {
            delete this->mpDistributedVectorFactory;
            this->mpDistributedVectorFactory = new DistributedVectorFactory(this->GetNumNodes());
        }
    }
    if (SPACE_DIM == 1)
    {
        // Store the node locations
        std::vector<c_vector<double, SPACE_DIM> > old_node_locations;
        unsigned new_index = 0;
        for (unsigned i=0; i<this->GetNumAllNodes(); i++)
        {
            if (this->mNodes[i]->IsDeleted())
            {
                map.SetDeleted(i);
            }
            else
            {
                map.SetNewIndex(i, new_index);
                old_node_locations.push_back(this->mNodes[i]->rGetLocation());
                new_index++;
            }
        }

        // Remove current data
        Clear();

        // Construct the nodes and boundary nodes
        for (unsigned node_index=0; node_index<old_node_locations.size(); node_index++)
        {
            // As we're in 1D, the boundary nodes are simply at either end of the mesh
            bool is_boundary_node = (node_index==0 || node_index==old_node_locations.size()-1);

            Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index, old_node_locations[node_index], is_boundary_node);
            this->mNodes.push_back(p_node);

            if (is_boundary_node)
            {
                this->mBoundaryNodes.push_back(p_node);
            }
        }

        // Create a map between node indices and node locations
        std::map<double, unsigned> location_index_map;
        for (unsigned i=0; i<this->mNodes.size(); i++)
        {
            location_index_map[this->mNodes[i]->rGetLocation()[0]] = this->mNodes[i]->GetIndex();
        }

        // Use this map to generate a vector of node indices that are ordered spatially
        std::vector<unsigned> node_indices_ordered_spatially;
        for (std::map<double, unsigned>::iterator iter = location_index_map.begin();
             iter != location_index_map.end();
             ++iter)
        {
            node_indices_ordered_spatially.push_back(iter->second);
        }

        // Construct the elements
        this->mElements.reserve(old_node_locations.size()-1);
        for (unsigned element_index=0; element_index<old_node_locations.size()-1; element_index++)
        {
            std::vector<Node<SPACE_DIM>*> nodes;
            for (unsigned j=0; j<2; j++)
            {
                unsigned global_node_index = node_indices_ordered_spatially[element_index + j];
                assert(global_node_index < this->mNodes.size());
                nodes.push_back(this->mNodes[global_node_index]);
            }
            this->mElements.push_back(new Element<ELEMENT_DIM, SPACE_DIM>(element_index, nodes));
        }

        // Construct the two boundary elements - as we're in 1D, these are simply at either end of the mesh
        std::vector<Node<SPACE_DIM>*> nodes;
        nodes.push_back(this->mNodes[0]);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>(0, nodes));

        nodes.clear();
        nodes.push_back(this->mNodes[old_node_locations.size()-1]);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>(1, nodes));

        this->RefreshJacobianCachedData();
    }
    else if (SPACE_DIM==2)  // In 2D, remesh using triangle via library calls
    {
        struct triangulateio mesher_input, mesher_output;
        this->InitialiseTriangulateIo(mesher_input);
        this->InitialiseTriangulateIo(mesher_output);

        this->ExportToMesher(map, mesher_input);

        // Library call
        triangulate((char*)"Qze", &mesher_input, &mesher_output, nullptr);

        this->ImportFromMesher(mesher_output, mesher_output.numberoftriangles, mesher_output.trianglelist, mesher_output.numberofedges, mesher_output.edgelist, mesher_output.edgemarkerlist);

        //Tidy up triangle
        this->FreeTriangulateIo(mesher_input);
        this->FreeTriangulateIo(mesher_output);
    }
    else // in 3D, remesh using tetgen
    {

        class tetgen::tetgenio mesher_input, mesher_output;

        this->ExportToMesher(map, mesher_input);

        // Library call
        tetgen::tetrahedralize((char*)"Qz", &mesher_input, &mesher_output);

        this->ImportFromMesher(mesher_output, mesher_output.numberoftetrahedra, mesher_output.tetrahedronlist, mesher_output.numberoftrifaces, mesher_output.trifacelist, nullptr);
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void MutableMesh<ELEMENT_DIM, SPACE_DIM>::ReMesh()
{
    NodeMap map(GetNumNodes());
    ReMesh(map);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
std::vector<c_vector<unsigned, 5> > MutableMesh<ELEMENT_DIM, SPACE_DIM>::SplitLongEdges(double cutoffLength)
{
    assert(ELEMENT_DIM == 2);     // LCOV_EXCL_LINE
    assert(SPACE_DIM == 3);     // LCOV_EXCL_LINE

    std::vector<c_vector<unsigned, 5> > history;

    bool long_edge_exists = true;

    while (long_edge_exists)
    {
        std::set<std::pair<unsigned, unsigned> > long_edges;

        // Loop over elements to check for Long edges
        for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator elem_iter = this->GetElementIteratorBegin();
             elem_iter != this->GetElementIteratorEnd();
             ++elem_iter)
        {
            unsigned num_nodes = ELEMENT_DIM+1;

            // Loop over element vertices
            for (unsigned local_index=0; local_index<num_nodes; local_index++)
            {
                // Find locations of current node (node a) and anticlockwise node (node b)
                Node<SPACE_DIM>* p_node_a = elem_iter->GetNode(local_index);
                unsigned local_index_plus_one = (local_index+1)%num_nodes; 
                Node<SPACE_DIM>* p_node_b = elem_iter->GetNode(local_index_plus_one);

                // Find distance between nodes
                double distance_between_nodes = this->GetDistanceBetweenNodes(p_node_a->GetIndex(), p_node_b->GetIndex());

                if (distance_between_nodes > cutoffLength)
                {
                    if (p_node_a->GetIndex() < p_node_b->GetIndex())
                    {
                        std::pair<unsigned, unsigned> long_edge(p_node_a->GetIndex(),p_node_b->GetIndex());
                        long_edges.insert(long_edge);
                    }
                    else
                    {
                        std::pair<unsigned, unsigned> long_edge(p_node_b->GetIndex(),p_node_a->GetIndex());
                        long_edges.insert(long_edge);
                    }
                }
            }
        }

        if (long_edges.size() > 0) //Split the edges in decreasing order.
        {
            while (long_edges.size() > 0)
            {
                double longest_edge = 0.0;
                std::set<std::pair<unsigned, unsigned> >::iterator longest_edge_iter;

                //Find the longest edge in the set and split it
                for (std::set<std::pair<unsigned, unsigned> >::iterator edge_iter = long_edges.begin();
                         edge_iter != long_edges.end();
                         ++edge_iter)
                {
                    unsigned node_a_global_index = edge_iter->first;
                    unsigned node_b_global_index = edge_iter->second;

                    double distance_between_nodes = this->GetDistanceBetweenNodes(node_a_global_index, node_b_global_index);

                    if (distance_between_nodes > longest_edge)
                    {
                        longest_edge = distance_between_nodes;
                        longest_edge_iter = edge_iter;
                    }
                }
                assert(longest_edge >0);

                c_vector<unsigned, 3> new_node_index = SplitEdge(this->GetNode(longest_edge_iter->first), this->GetNode(longest_edge_iter->second));

                c_vector<unsigned, 5> node_set;
                node_set(0) = new_node_index[0];
                node_set(1) = longest_edge_iter->first;
                node_set(2) = longest_edge_iter->second;
                node_set(3) = new_node_index[1];
                node_set(4) = new_node_index[2];
                history.push_back(node_set);

                // Delete pair from set
                long_edges.erase(*longest_edge_iter);
            }
        }
        else
        {
            long_edge_exists = false;
        }
    }

    return history;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<unsigned, 3> MutableMesh<ELEMENT_DIM, SPACE_DIM>::SplitEdge(Node<SPACE_DIM>* pNodeA, Node<SPACE_DIM>* pNodeB)
{
    c_vector<unsigned, 3> new_node_index_vector;

    std::set<unsigned> elements_of_node_a = pNodeA->rGetContainingElementIndices();
    std::set<unsigned> elements_of_node_b = pNodeB->rGetContainingElementIndices();

    std::set<unsigned> intersection_elements;
    std::set_intersection(elements_of_node_a.begin(), elements_of_node_a.end(),
                          elements_of_node_b.begin(), elements_of_node_b.end(),
                          std::inserter(intersection_elements, intersection_elements.begin()));

    // Create the new node
    c_vector<double, SPACE_DIM> new_node_location = pNodeA->rGetLocation() + 0.5*this->GetVectorFromAtoB(pNodeA->rGetLocation(), pNodeB->rGetLocation());

    bool is_boundary_node =  intersection_elements.size() == 1; // If only in one element then its on the boundary

    Node<SPACE_DIM>* p_new_node = new Node<SPACE_DIM>(0u,new_node_location,is_boundary_node); // Index is rewritten once added to mesh

    unsigned new_node_index = this->AddNode(p_new_node);

    new_node_index_vector[0] = new_node_index;

    unsigned counter = 1;

    for (std::set<unsigned>::const_iterator it = intersection_elements.begin(); it != intersection_elements.end(); ++it)
    {
        unsigned elementIndex = *it;

        Element<ELEMENT_DIM,SPACE_DIM>* p_original_element = this->GetElement(elementIndex);

        // First, make a copy of the current element and assign an unused index
        Element<ELEMENT_DIM,SPACE_DIM>* p_new_element = new Element<ELEMENT_DIM,SPACE_DIM>(*p_original_element, UINT_MAX);

        // Second, add the new element to the set of existing elements. This method will assign a proper index to the element.
        AddElement(p_new_element);

        // Third, update node a in the element with the new one
        p_new_element->ReplaceNode(pNodeA, this->mNodes[new_node_index]);

        // Last, update node b in the original element with the new one
        p_original_element->ReplaceNode(pNodeB, this->mNodes[new_node_index]);

        //Add node in both of these elements to new_node_index_vector (this enables us to add a new spring in the MeshBasedCellPopulation
        unsigned other_node_index = UNSIGNED_UNSET;

        if ((p_original_element->GetNodeGlobalIndex(0) != new_node_index) &&
            (p_original_element->GetNodeGlobalIndex(0) != pNodeA->GetIndex()))
        {
            other_node_index = p_original_element->GetNodeGlobalIndex(0);
        }
        else if ((p_original_element->GetNodeGlobalIndex(1) != new_node_index) &&
                 (p_original_element->GetNodeGlobalIndex(1) != pNodeA->GetIndex()))
        {
            other_node_index = p_original_element->GetNodeGlobalIndex(1);
        }
        else if ((p_original_element->GetNodeGlobalIndex(2) != new_node_index) &&
                 (p_original_element->GetNodeGlobalIndex(2) != pNodeA->GetIndex()))
        {
            other_node_index = p_original_element->GetNodeGlobalIndex(2);
        }
        else
        {
            NEVER_REACHED;
        }
        new_node_index_vector[counter] = other_node_index;
        counter++;
    }

    assert(counter < 4);
    assert(counter > 1);// need to be in at least one element

    if (counter == 2) // only one new element
    {
        new_node_index_vector[2] = UNSIGNED_UNSET;
    }

    return new_node_index_vector;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool MutableMesh<ELEMENT_DIM, SPACE_DIM>::CheckIsVoronoi(Element<ELEMENT_DIM, SPACE_DIM>* pElement, double maxPenetration)
{
    assert(ELEMENT_DIM == SPACE_DIM);     // LCOV_EXCL_LINE
    unsigned num_nodes = pElement->GetNumNodes();
    std::set<unsigned> neighbouring_elements_indices;
    std::set< Element<ELEMENT_DIM,SPACE_DIM> *> neighbouring_elements;
    std::set<unsigned> neighbouring_nodes_indices;

    // Form a set of neighbouring elements via the nodes
    for (unsigned i=0; i<num_nodes; i++)
    {
        Node<SPACE_DIM>* p_node = pElement->GetNode(i);
        neighbouring_elements_indices = p_node->rGetContainingElementIndices();
        for (std::set<unsigned>::const_iterator it = neighbouring_elements_indices.begin();
             it != neighbouring_elements_indices.end();
             ++it)
        {
            neighbouring_elements.insert(this->GetElement(*it));
        }
    }
    neighbouring_elements.erase(pElement);

    // For each neighbouring element find the supporting nodes
    typedef typename std::set<Element<ELEMENT_DIM,SPACE_DIM> *>::const_iterator ElementIterator;

    for (ElementIterator it = neighbouring_elements.begin();
         it != neighbouring_elements.end();
         ++it)
    {
        for (unsigned i=0; i<num_nodes; i++)
        {
            neighbouring_nodes_indices.insert((*it)->GetNodeGlobalIndex(i));
        }
    }

    // Remove the nodes that support this element
    for (unsigned i = 0; i < num_nodes; i++)
    {
        neighbouring_nodes_indices.erase(pElement->GetNodeGlobalIndex(i));
    }

    // Get the circumsphere information
    c_vector<double, SPACE_DIM+1> this_circum_centre;

    this_circum_centre = pElement->CalculateCircumsphere(this->mElementJacobians[pElement->GetIndex()], this->mElementInverseJacobians[pElement->GetIndex()]);

    // Copy the actualy circumcentre into a smaller vector
    c_vector<double, ELEMENT_DIM> circum_centre;
    for (unsigned i=0; i<ELEMENT_DIM; i++)
    {
        circum_centre[i] = this_circum_centre[i];
    }

    for (std::set<unsigned>::const_iterator it = neighbouring_nodes_indices.begin();
         it != neighbouring_nodes_indices.end();
         ++it)
    {
        c_vector<double, ELEMENT_DIM> node_location;
        node_location = this->GetNode(*it)->rGetLocation();

        // Calculate vector from circumcenter to node
        node_location -= circum_centre;

        // This is to calculate the squared distance betweeen them
        double squared_distance = inner_prod(node_location, node_location);

        // If the squared idstance is less than the elements circum-radius(squared),
        // then the Voronoi property is violated.
        if (squared_distance < this_circum_centre[ELEMENT_DIM])
        {
            // We know the node is inside the circumsphere, but we don't know how far
            double radius = sqrt(this_circum_centre[ELEMENT_DIM]);
            double distance = radius - sqrt(squared_distance);

            // If the node penetration is greater than supplied maximum penetration factor
            if (distance/radius > maxPenetration)
            {
                return false;
            }
        }
    }
    return true;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool MutableMesh<ELEMENT_DIM, SPACE_DIM>::CheckIsVoronoi(double maxPenetration)
{
    // Looping through all the elements in the mesh
    for (unsigned i=0; i<this->mElements.size(); i++)
    {
        // Check if the element is not deleted
        if (!this->mElements[i]->IsDeleted())
        {
            // Checking the Voronoi of the Element
            if (CheckIsVoronoi(this->mElements[i], maxPenetration) == false)
            {
                return false;
            }
        }
    }
    return true;
}

// Explicit instantiation
template class MutableMesh<1,1>;
template class MutableMesh<1,2>;
template class MutableMesh<1,3>;
template class MutableMesh<2,2>;
template class MutableMesh<2,3>;
template class MutableMesh<3,3>;

// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_ALL_DIMS(MutableMesh)