TetrahedralMesh.cpp

/*

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*/

#include "TetrahedralMesh.hpp"

#include <iostream>
#include <cassert>
#include <sstream>
#include <map>
#include <limits>

#include "BoundaryElement.hpp"
#include "Element.hpp"
#include "Exception.hpp"
#include "Node.hpp"
#include "OutputFileHandler.hpp"
#include "PetscTools.hpp"
#include "RandomNumberGenerator.hpp"
#include "Warnings.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>
TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::TetrahedralMesh()
{
    Clear();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructFromMeshReader(
    AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader)
{
    assert(rMeshReader.HasNodePermutation() == false);
    this->mMeshFileBaseName = rMeshReader.GetMeshFileBaseName();

    // Record number of corner nodes
    unsigned num_nodes = rMeshReader.GetNumNodes();

    /*
     * Reserve memory for nodes, so we don't have problems with
     * pointers stored in elements becoming invalid.
     */
    this->mNodes.reserve(num_nodes);

    rMeshReader.Reset();

    //typename std::map<std::pair<unsigned,unsigned>,unsigned>::const_iterator iterator;
    //std::map<std::pair<unsigned,unsigned>,unsigned> internal_nodes_map;

    // Add nodes
    std::vector<double> coords;
    for (unsigned node_index=0; node_index < num_nodes; node_index++)
    {
        coords = rMeshReader.GetNextNode();
        Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index, coords, false);

        for (unsigned i=0; i<rMeshReader.GetNodeAttributes().size(); i++)
        {
            double attribute = rMeshReader.GetNodeAttributes()[i];
            p_node->AddNodeAttribute(attribute);

        }
        this->mNodes.push_back(p_node);
    }

    //unsigned new_node_index = mNumCornerNodes;

    rMeshReader.Reset();
    // Add elements
    //new_node_index = mNumCornerNodes;
    this->mElements.reserve(rMeshReader.GetNumElements());

    for (unsigned element_index=0; element_index < (unsigned) rMeshReader.GetNumElements(); element_index++)
    {
        ElementData element_data = rMeshReader.GetNextElementData();
        std::vector<Node<SPACE_DIM>*> nodes;

        /*
         * NOTE: currently just reading element vertices from mesh reader - even if it
         * does contain information about internal nodes (ie for quadratics) this is
         * ignored here and used elsewhere: ie don't do this:
         *   unsigned nodes_size = node_indices.size();
         */
        for (unsigned j=0; j<ELEMENT_DIM+1; j++) // num vertices=ELEMENT_DIM+1, may not be equal to nodes_size.
        {
            assert(element_data.NodeIndices[j] <  this->mNodes.size());
            nodes.push_back(this->mNodes[element_data.NodeIndices[j]]);
        }

        Element<ELEMENT_DIM,SPACE_DIM>* p_element = new Element<ELEMENT_DIM,SPACE_DIM>(element_index, nodes);

        this->mElements.push_back(p_element);

        if (rMeshReader.GetNumElementAttributes() > 0)
        {
            assert(rMeshReader.GetNumElementAttributes() == 1);
            double attribute_value = element_data.AttributeValue;
            p_element->SetAttribute(attribute_value);
        }
    }

    // Add boundary elements and nodes
    for (unsigned face_index=0; face_index<(unsigned)rMeshReader.GetNumFaces(); face_index++)
    {
        ElementData face_data = rMeshReader.GetNextFaceData();
        std::vector<unsigned> node_indices = face_data.NodeIndices;

        /*
         * NOTE: unlike the above where we just read element *vertices* from mesh reader, here we are
         * going to read a quadratic mesh with internal elements.
         * (There are only a few meshes with internals in the face file that we might as well use them.)
         *
         */
        std::vector<Node<SPACE_DIM>*> nodes;
        for (unsigned node_index=0; node_index<node_indices.size(); node_index++)
        {
            assert(node_indices[node_index] < this->mNodes.size());
            // Add Node pointer to list for creating an element
            nodes.push_back(this->mNodes[node_indices[node_index]]);
        }

        // This is a boundary face, so ensure all its nodes are marked as boundary nodes
        for (unsigned j=0; j<nodes.size(); j++)
        {
            if (!nodes[j]->IsBoundaryNode())
            {
                nodes[j]->SetAsBoundaryNode();
                this->mBoundaryNodes.push_back(nodes[j]);
            }

            // Register the index that this bounday element will have with the node
            nodes[j]->AddBoundaryElement(face_index);
        }

        // The added elements will be deleted in our destructor
        BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>* p_boundary_element = new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(face_index, nodes);
        this->mBoundaryElements.push_back(p_boundary_element);

        if (rMeshReader.GetNumFaceAttributes() > 0)
        {
            assert(rMeshReader.GetNumFaceAttributes() == 1);
            double attribute_value = face_data.AttributeValue;
            p_boundary_element->SetAttribute(attribute_value);
        }
    }

    RefreshJacobianCachedData();

    rMeshReader.Reset();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ReadNodesPerProcessorFile(const std::string& rNodesPerProcessorFile)
{
    std::vector<unsigned> nodes_per_processor_vec;

    std::ifstream file_stream(rNodesPerProcessorFile.c_str());
    if (file_stream.is_open())
    {
        while (file_stream)
        {
            unsigned nodes_per_processor;
            file_stream >> nodes_per_processor;

            if (file_stream)
            {
                nodes_per_processor_vec.push_back(nodes_per_processor);
            }
        }
    }
    else
    {
        EXCEPTION("Unable to read nodes per processor file " + rNodesPerProcessorFile);
    }

    unsigned sum = 0;
    for (unsigned i=0; i<nodes_per_processor_vec.size(); i++)
    {
        sum += nodes_per_processor_vec[i];
    }

    if (sum != this->GetNumNodes())
    {
        EXCEPTION("Sum of nodes per processor, " << sum
                     << ", not equal to number of nodes in mesh, " << this->GetNumNodes());
    }

    unsigned num_owned=nodes_per_processor_vec[PetscTools::GetMyRank()];

    if (nodes_per_processor_vec.size() != PetscTools::GetNumProcs())
    {
        EXCEPTION("Number of processes doesn't match the size of the nodes-per-processor file");
    }
    delete this->mpDistributedVectorFactory;
    this->mpDistributedVectorFactory = new DistributedVectorFactory(this->GetNumNodes(), num_owned);
}
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CheckIsConforming()
{
    /*
     * Each face of each element is a set of node indices.
     * We form a set of these in order to get their parity:
     *   all faces which appear once are inserted into the set;
     *   all faces which appear twice are inserted and then removed from the set;
     *   we're assuming that faces never appear more than twice.
     */
    std::set< std::set<unsigned> > odd_parity_faces;

    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        for (unsigned face_index=0; face_index<=ELEMENT_DIM; face_index++)
        {
            std::set<unsigned> face_info;
            for (unsigned node_index=0; node_index<=ELEMENT_DIM; node_index++)
            {
                // Leave one index out each time
                if (node_index != face_index)
                {
                    face_info.insert(iter->GetNodeGlobalIndex(node_index));
                }
            }
            // Face is now formed - attempt to find it
            std::set< std::set<unsigned> >::iterator find_face=odd_parity_faces.find(face_info);
            if (find_face != odd_parity_faces.end())
            {
                // Face was in set, so it now has even parity.
                // Remove it via the iterator
                odd_parity_faces.erase(find_face);
            }
            else
            {
                // Face is not in set so it now has odd parity. Insert it
                odd_parity_faces.insert(face_info);
            }

        }
    }

    /*
     * At this point the odd parity faces should be the same as the
     * boundary elements. We could check this explicitly or we could
     * just count them.
     */
    return(odd_parity_faces.size() == this->GetNumBoundaryElements());
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetVolume()
{
    double mesh_volume = 0.0;

    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        mesh_volume += iter->GetVolume(mElementJacobianDeterminants[iter->GetIndex()]);
    }

    return mesh_volume;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetSurfaceArea()
{
    // ELEMENT_DIM-1 is the dimension of the boundary element
    assert(ELEMENT_DIM >= 1);
    const unsigned bound_element_dim = ELEMENT_DIM-1;
    assert(bound_element_dim < 3);
    if ( bound_element_dim == 0)
    {
        return 0.0;
    }

    double mesh_surface = 0.0;
    typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::BoundaryElementIterator it = this->GetBoundaryElementIteratorBegin();

    while (it != this->GetBoundaryElementIteratorEnd())
    {
        mesh_surface += mBoundaryElementJacobianDeterminants[(*it)->GetIndex()];
        it++;
    }

    if ( bound_element_dim == 2)
    {
        mesh_surface /= 2.0;
    }

    return mesh_surface;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::PermuteNodes()
{
    // Make a permutation vector of the identity
    RandomNumberGenerator* p_rng = RandomNumberGenerator::Instance();
    std::vector<unsigned> perm;
    p_rng->Shuffle(this->mNodes.size(), perm);

    // Call the non-random version
    PermuteNodes(perm);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::PermuteNodes(const std::vector<unsigned>& perm)
{
    // Let's not do this if there are any deleted nodes
    assert( this->GetNumAllNodes() == this->GetNumNodes());

    assert(perm.size() == this->mNodes.size());

    // Copy the node pointers
    std::vector< Node<SPACE_DIM>* > copy_m_nodes;
    copy_m_nodes.assign(this->mNodes.begin(), this->mNodes.end());

    for (unsigned original_index=0; original_index<this->mNodes.size(); original_index++)
    {
        assert(perm[original_index] < this->mNodes.size());
        //perm[original_index] holds the new assigned index of that node
        this->mNodes[ perm[original_index] ] = copy_m_nodes[original_index];
    }

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

    // Copy the permutation vector into the mesh
    this->mNodePermutation = perm;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetContainingElementIndexWithInitialGuess(const ChastePoint<SPACE_DIM>& rTestPoint, unsigned startingElementGuess, bool strict)
{
    assert(startingElementGuess<this->GetNumElements());

    /*
     * Let m=startingElementGuess, N=num_elem-1.
     * We search from in this order: m, m+1, m+2, .. , N, 0, 1, .., m-1.
     */
    unsigned i = startingElementGuess;
    bool reached_end = false;

    while (!reached_end)
    {
        if (this->mElements[i]->IncludesPoint(rTestPoint, strict))
        {
            assert(!this->mElements[i]->IsDeleted());
            return i;
        }

        // Increment
        i++;
        if (i==this->GetNumElements())
        {
            i=0;
        }

        // Back to the beginning yet?
        if (i==startingElementGuess)
        {
            reached_end = true;
        }
    }

    // If it's in none of the elements, then throw
    std::stringstream ss;
    ss << "Point [";
    for (unsigned j=0; (int)j<(int)SPACE_DIM-1; j++)
    {
        ss << rTestPoint[j] << ",";
    }
    ss << rTestPoint[SPACE_DIM-1] << "] is not in mesh - all elements tested";
    EXCEPTION(ss.str());
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNearestElementIndex(const ChastePoint<SPACE_DIM>& rTestPoint)
{
    double max_min_weight = -std::numeric_limits<double>::infinity();
    unsigned closest_index = 0;
    for (unsigned i=0; i<this->mElements.size(); i++)
    {
        c_vector<double, ELEMENT_DIM+1> weight=this->mElements[i]->CalculateInterpolationWeights(rTestPoint);
        double neg_weight_sum=0.0;
        for (unsigned j=0; j<=ELEMENT_DIM; j++)
        {
            if (weight[j] < 0.0)
            {
                neg_weight_sum += weight[j];
            }
        }
        if (neg_weight_sum > max_min_weight)
        {
            max_min_weight = neg_weight_sum;
            closest_index = i;
        }
    }
    assert(!this->mElements[closest_index]->IsDeleted());
    return closest_index;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
std::vector<unsigned> TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetContainingElementIndices(const ChastePoint<SPACE_DIM> &rTestPoint)
{
    std::vector<unsigned> element_indices;
    for (unsigned i=0; i<this->mElements.size(); i++)
    {
        if (this->mElements[i]->IncludesPoint(rTestPoint))
        {
            assert(!this->mElements[i]->IsDeleted());
            element_indices.push_back(i);
        }
    }
    return element_indices;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::Clear()
{
    // Three loops, just like the destructor. note we don't delete boundary nodes.
    for (unsigned i=0; i<this->mBoundaryElements.size(); i++)
    {
        delete this->mBoundaryElements[i];
    }
    for (unsigned i=0; i<this->mElements.size(); i++)
    {
        delete this->mElements[i];
    }
    for (unsigned i=0; i<this->mNodes.size(); i++)
    {
        delete this->mNodes[i];
    }

    this->mNodes.clear();
    this->mElements.clear();
    this->mBoundaryElements.clear();
    this->mBoundaryNodes.clear();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
std::set<unsigned> TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateBoundaryOfFlaggedRegion()
{
    // A set of nodes which lie on the face, size 3 in 2D, size 4 in 3D
    typedef std::set<unsigned> FaceNodes;

    /*
     * Face maps to true the first time it is encountered, and false subsequent
     * times. Thus, faces mapping to true at the end are boundary faces.
     */
    std::map<FaceNodes,bool> face_on_boundary;

    // Loop over all elements
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        if (iter->IsFlagged())
        {
            // To get faces, initially start with all nodes
            std::set<unsigned> all_nodes;
            for (unsigned i=0; i<ELEMENT_DIM+1; i++)
            {
                all_nodes.insert(iter->GetNodeGlobalIndex(i));
            }

            // Remove one node in turn to obtain each face
            for (unsigned i=0; i<ELEMENT_DIM+1; i++)
            {
                FaceNodes face_nodes = all_nodes;
                face_nodes.erase(iter->GetNodeGlobalIndex(i));

                // Search the map of faces to see if it contains this face
                std::map<FaceNodes,bool>::iterator it = face_on_boundary.find(face_nodes);

                if (it == face_on_boundary.end())
                {
                    // Face not found, add and assume on boundary
                    face_on_boundary[face_nodes]=true;
                }
                else
                {
                    // Face found in map, so not on boundary
                    it->second = false;
                }
            }
        }
    }

    // Boundary nodes to be returned
    std::set<unsigned> boundary_of_flagged_region;

    // Get all faces in the map
    std::map<FaceNodes,bool>::iterator it=face_on_boundary.begin();
    while (it!=face_on_boundary.end())
    {
        // If the face maps to true it is on the boundary
        if (it->second==true)
        {
            // Get all nodes in the face and put in set to be returned
            boundary_of_flagged_region.insert(it->first.begin(),it->first.end());
        }
        it++;
    }

    return boundary_of_flagged_region;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetAngleBetweenNodes(unsigned indexA, unsigned indexB)
{
    assert(SPACE_DIM == 2);
    assert(SPACE_DIM == ELEMENT_DIM);

    double x_difference = this->mNodes[indexB]->rGetLocation()[0] - this->mNodes[indexA]->rGetLocation()[0];
    double y_difference = this->mNodes[indexB]->rGetLocation()[1] - this->mNodes[indexA]->rGetLocation()[1];

    if (x_difference == 0)
    {
        if (y_difference > 0)
        {
            return M_PI/2.0;
        }
        else if (y_difference < 0)
        {
            return -M_PI/2.0;
        }
        else
        {
            EXCEPTION("Tried to compute polar angle of (0,0)");
        }
    }

    double angle = atan2(y_difference,x_difference);
    return angle;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::UnflagAllElements()
{
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        iter->Unflag();
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::FlagElementsNotContainingNodes(const std::set<unsigned>& rNodes)
{
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        bool found_node = false;

        for (unsigned i=0; i<iter->GetNumNodes(); i++)
        {
            unsigned node_index = iter->GetNodeGlobalIndex(i);

            std::set<unsigned>::iterator set_iter = rNodes.find(node_index);
            if (set_iter != rNodes.end())
            {
                found_node = true;
            }
        }

        if (!found_node)
        {
            iter->Flag();
        }
    }
}

//                          Edge iterator class                             //

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
Node<SPACE_DIM>* TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator::GetNodeA()
{
    assert((*this) != mrMesh.EdgesEnd());
    Element<ELEMENT_DIM,SPACE_DIM>* p_element = mrMesh.GetElement(mElemIndex);
    return p_element->GetNode(mNodeALocalIndex);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
Node<SPACE_DIM>* TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator::GetNodeB()
{
    assert((*this) != mrMesh.EdgesEnd());
    Element<ELEMENT_DIM,SPACE_DIM>* p_element = mrMesh.GetElement(mElemIndex);
    return p_element->GetNode(mNodeBLocalIndex);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator::operator!=(const typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator& rOther)
{
    return (mElemIndex != rOther.mElemIndex ||
            mNodeALocalIndex != rOther.mNodeALocalIndex ||
            mNodeBLocalIndex != rOther.mNodeBLocalIndex);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator& TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator::operator++()
{
    bool already_seen_this_edge;

    unsigned num_elements = mrMesh.GetNumAllElements();
    std::pair<unsigned, unsigned> current_node_pair;
    do
    {
        /*
         * Advance to the next edge in the mesh.
         * Node indices are incremented modulo #nodes_per_elem.
         */
        mNodeBLocalIndex = (mNodeBLocalIndex + 1) % (ELEMENT_DIM+1);
        if (mNodeBLocalIndex == mNodeALocalIndex)
        {
            mNodeALocalIndex = (mNodeALocalIndex + 1) % (ELEMENT_DIM+1);
            mNodeBLocalIndex = (mNodeALocalIndex + 1) % (ELEMENT_DIM+1);
        }

        if (mNodeALocalIndex == 0 && mNodeBLocalIndex == 1) // advance to next element...
        {
            // ...skipping deleted ones
            do
            {
                mElemIndex++;
            }
            while (mElemIndex!=num_elements && mrMesh.GetElement(mElemIndex)->IsDeleted());
        }

        if (mElemIndex != num_elements)
        {
            Element<ELEMENT_DIM, SPACE_DIM>* p_element = mrMesh.GetElement(mElemIndex);
            unsigned node_a_global_index = p_element->GetNodeGlobalIndex(mNodeALocalIndex);
            unsigned node_b_global_index = p_element->GetNodeGlobalIndex(mNodeBLocalIndex);
            if (node_b_global_index < node_a_global_index)
            {
                // Swap them over
                unsigned temp = node_a_global_index;
                node_a_global_index = node_b_global_index;
                node_b_global_index = temp;
            }

            // Check we haven't seen it before
            current_node_pair = std::pair<unsigned, unsigned>(node_a_global_index, node_b_global_index);
            already_seen_this_edge = (mEdgesVisited.count(current_node_pair) != 0);
        }
        else
        {
            already_seen_this_edge = false;
        }
    }

    while (already_seen_this_edge);
    mEdgesVisited.insert(current_node_pair);

    return (*this);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator::EdgeIterator(TetrahedralMesh& rMesh, unsigned elemIndex)
    : mrMesh(rMesh),
      mElemIndex(elemIndex),
      mNodeALocalIndex(0),
      mNodeBLocalIndex(1)
{
    if (elemIndex == mrMesh.GetNumAllElements())
    {
        return;
    }

    mEdgesVisited.clear();

    // Add the current node pair to the store
    unsigned node_a_global_index = mrMesh.GetElement(mElemIndex)->GetNodeGlobalIndex(mNodeALocalIndex);
    unsigned node_b_global_index = mrMesh.GetElement(mElemIndex)->GetNodeGlobalIndex(mNodeBLocalIndex);
    if (node_b_global_index < node_a_global_index)
    {
        // Swap them over
        unsigned temp = node_a_global_index;
        node_a_global_index = node_b_global_index;
        node_b_global_index = temp;
    }

    // Check we haven't seen it before
    std::pair<unsigned, unsigned> current_node_pair = std::pair<unsigned, unsigned>(node_a_global_index, node_b_global_index);
    mEdgesVisited.insert(current_node_pair);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgesBegin()
{
    unsigned first_element_index = 0;
    while (first_element_index!=this->GetNumAllElements() && this->GetElement(first_element_index)->IsDeleted())
    {
        first_element_index++;
    }
    return EdgeIterator(*this, first_element_index);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgeIterator TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::EdgesEnd()
{
    return EdgeIterator(*this, this->GetNumAllElements());
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RefreshMesh()
{
    RefreshJacobianCachedData();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveNodeMapping(unsigned index) const
{
    assert(index < this->mNodes.size() );
    return index;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveElementMapping(unsigned index) const
{
    assert(index < this->mElements.size() );
    return index;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveBoundaryElementMapping(unsigned index) const
{
    assert(index < this->mBoundaryElements.size() );
    return index;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RefreshJacobianCachedData()
{
    unsigned num_elements = this->GetNumAllElements();
    unsigned num_boundary_elements = this->GetNumAllBoundaryElements();

    // Make sure we have enough space
    this->mElementJacobians.resize(num_elements);
    this->mElementInverseJacobians.resize(num_elements);

    if (ELEMENT_DIM < SPACE_DIM)
    {
        this->mElementWeightedDirections.resize(num_elements);
    }

    this->mBoundaryElementWeightedDirections.resize(num_boundary_elements);

    this->mElementJacobianDeterminants.resize(num_elements);
    this->mBoundaryElementJacobianDeterminants.resize(num_boundary_elements);

    // Update caches
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        unsigned index = iter->GetIndex();
        iter->CalculateInverseJacobian(this->mElementJacobians[index], this->mElementJacobianDeterminants[index], this->mElementInverseJacobians[index]);
    }

    if (ELEMENT_DIM < SPACE_DIM)
    {
        for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
             iter != this->GetElementIteratorEnd();
             ++iter)
        {
             unsigned index = iter->GetIndex();
             iter->CalculateWeightedDirection(this->mElementWeightedDirections[index], this->mElementJacobianDeterminants[index]);
        }
    }

    for ( typename TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::BoundaryElementIterator itb = this->GetBoundaryElementIteratorBegin();
          itb != this->GetBoundaryElementIteratorEnd();
          itb++)
    {
        unsigned index = (*itb)->GetIndex();
        (*itb)->CalculateWeightedDirection(this->mBoundaryElementWeightedDirections[index], this->mBoundaryElementJacobianDeterminants[index]);
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetJacobianForElement(unsigned elementIndex, c_matrix<double, SPACE_DIM, SPACE_DIM>& rJacobian, double& rJacobianDeterminant) const
{
    assert(ELEMENT_DIM <= SPACE_DIM);
    assert(elementIndex < this->mElementJacobians.size());
    rJacobian = this->mElementJacobians[elementIndex];
    rJacobianDeterminant = this->mElementJacobianDeterminants[elementIndex];
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetInverseJacobianForElement(unsigned elementIndex, c_matrix<double, SPACE_DIM, ELEMENT_DIM>& rJacobian, double& rJacobianDeterminant, c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian) const
{
    assert(ELEMENT_DIM <= SPACE_DIM);
    assert(elementIndex < this->mElementInverseJacobians.size());
    rInverseJacobian = this->mElementInverseJacobians[elementIndex];
    rJacobian = this->mElementJacobians[elementIndex];
    rJacobianDeterminant = this->mElementJacobianDeterminants[elementIndex];
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetWeightedDirectionForElement(unsigned elementIndex, c_vector<double, SPACE_DIM>& rWeightedDirection, double& rJacobianDeterminant) const
{
    assert(ELEMENT_DIM < SPACE_DIM);
    assert(elementIndex < this->mElementWeightedDirections.size());
    rWeightedDirection = this->mElementWeightedDirections[elementIndex];
    rJacobianDeterminant = this->mElementJacobianDeterminants[elementIndex];
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetWeightedDirectionForBoundaryElement(unsigned elementIndex, c_vector<double, SPACE_DIM>& rWeightedDirection, double& rJacobianDeterminant) const
{
    assert(elementIndex < this->mBoundaryElementWeightedDirections.size());
    rWeightedDirection = this->mBoundaryElementWeightedDirections[elementIndex];
    rJacobianDeterminant = this->mBoundaryElementJacobianDeterminants[elementIndex];
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::InitialiseTriangulateIo(triangulateio& mesherIo)
{
    mesherIo.numberofpoints = 0;
    mesherIo.pointlist = NULL;
    mesherIo.numberofpointattributes = 0;
    mesherIo.pointattributelist = (double *) NULL;
    mesherIo.pointmarkerlist = (int *) NULL;
    mesherIo.numberofsegments = 0;
    mesherIo.numberofholes = 0;
    mesherIo.numberofregions = 0;
    mesherIo.trianglelist = (int *) NULL;
    mesherIo.triangleattributelist = (double *) NULL;
    mesherIo.numberoftriangleattributes = 0;
    mesherIo.edgelist = (int *) NULL;
    mesherIo.edgemarkerlist = (int *) NULL;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::FreeTriangulateIo(triangulateio& mesherIo)
{
    if (mesherIo.numberofpoints != 0)
    {
        mesherIo.numberofpoints=0;
        free(mesherIo.pointlist);
    }

    // These (and the above) should actually be safe since we explicity set to NULL above
    free(mesherIo.pointattributelist);
    free(mesherIo.pointmarkerlist);
    free(mesherIo.trianglelist);
    free(mesherIo.triangleattributelist);
    free(mesherIo.edgelist);
    free(mesherIo.edgemarkerlist);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
template <class MESHER_IO>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ExportToMesher(NodeMap& map, MESHER_IO& mesherInput, int *elementList)
{
    if (SPACE_DIM == 2)
    {
        mesherInput.pointlist = (double *) malloc(this->GetNumNodes() * SPACE_DIM * sizeof(double));
    }
    else
    {
        mesherInput.pointlist = new double[this->GetNumNodes() * SPACE_DIM];
    }

    mesherInput.numberofpoints = this->GetNumNodes();
    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);
            for (unsigned j=0; j<SPACE_DIM; j++)
            {
                mesherInput.pointlist[SPACE_DIM*new_index + j] = this->mNodes[i]->rGetLocation()[j];
            }
            new_index++;
        }
    }
    if (elementList != NULL)
    {
        unsigned element_index = 0;

        // Assume there is enough space for this
        mesherInput.numberofcorners=ELEMENT_DIM+1;
        for (typename TetrahedralMesh<ELEMENT_DIM,SPACE_DIM>::ElementIterator elem_iter = this->GetElementIteratorBegin();
             elem_iter != this->GetElementIteratorEnd();
             ++elem_iter)
        {

            for (unsigned j=0; j<=ELEMENT_DIM; j++)
            {
                elementList[element_index*(ELEMENT_DIM+1) + j] = (*elem_iter).GetNodeGlobalIndex(j);
            }
            element_index++;
        }
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
template <class MESHER_IO>
void TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ImportFromMesher(MESHER_IO& mesherOutput, unsigned numberOfElements, int *elementList, unsigned numberOfFaces, int *faceList, int *edgeMarkerList)
{
    unsigned nodes_per_element = mesherOutput.numberofcorners;

    assert( nodes_per_element == ELEMENT_DIM+1 || nodes_per_element == (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2 );

    Clear();

    // Construct the nodes
    for (unsigned node_index=0; node_index<(unsigned)mesherOutput.numberofpoints; node_index++)
    {
        this->mNodes.push_back(new Node<SPACE_DIM>(node_index, &mesherOutput.pointlist[node_index * SPACE_DIM], false));
    }

    // Construct the elements
    this->mElements.reserve(numberOfElements);

    unsigned real_element_index=0;
    for (unsigned element_index=0; element_index<numberOfElements; element_index++)
    {
        std::vector<Node<SPACE_DIM>*> nodes;
        for (unsigned j=0; j<ELEMENT_DIM+1; j++)
        {
            unsigned global_node_index = elementList[element_index*(nodes_per_element) + j];
            assert(global_node_index < this->mNodes.size());
            nodes.push_back(this->mNodes[global_node_index]);

        }

        /*
         * For some reason, tetgen in library mode makes its initial Delaunay mesh
         * with very thin slivers. Hence we expect to ignore some of the elements!
         */
        Element<ELEMENT_DIM, SPACE_DIM>* p_element;
        try
        {
            p_element = new Element<ELEMENT_DIM, SPACE_DIM>(real_element_index, nodes);

            // Shouldn't throw after this point
            this->mElements.push_back(p_element);

            // Add the internals to quadratics
            for (unsigned j=ELEMENT_DIM+1; j<nodes_per_element; j++)
            {
                unsigned global_node_index = elementList[element_index*nodes_per_element + j];
                assert(global_node_index < this->mNodes.size());
                this->mElements[real_element_index]->AddNode( this->mNodes[global_node_index] );
                this->mNodes[global_node_index]->AddElement(real_element_index);
                this->mNodes[global_node_index]->MarkAsInternal();
            }
            real_element_index++;
        }
        catch (Exception &)
        {
            if (SPACE_DIM == 2)
            {
                WARNING("Triangle has produced a zero area (collinear) element");
            }
            else
            {
                WARNING("Tetgen has produced a zero volume (coplanar) element");
            }
        }
    }

    // Construct the BoundaryElements (and mark boundary nodes)
    unsigned next_boundary_element_index = 0;
    for (unsigned boundary_element_index=0; boundary_element_index<numberOfFaces; boundary_element_index++)
    {
        /*
         * Tetgen produces only boundary faces (set edgeMarkerList to NULL).
         * Triangle marks which edges are on the boundary.
         */
        if (edgeMarkerList == NULL || edgeMarkerList[boundary_element_index] == 1)
        {
            std::vector<Node<SPACE_DIM>*> nodes;
            for (unsigned j=0; j<ELEMENT_DIM; j++)
            {
                unsigned global_node_index = faceList[boundary_element_index*ELEMENT_DIM + j];
                assert(global_node_index < this->mNodes.size());
                nodes.push_back(this->mNodes[global_node_index]);
                if (!nodes[j]->IsBoundaryNode())
                {
                    nodes[j]->SetAsBoundaryNode();
                    this->mBoundaryNodes.push_back(nodes[j]);
                }
            }

            /*
             * For some reason, tetgen in library mode makes its initial Delaunay mesh
             * with very thin slivers. Hence we expect to ignore some of the elements!
             */
            BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>* p_b_element;
            try
            {
                p_b_element = new BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>(next_boundary_element_index, nodes);
                this->mBoundaryElements.push_back(p_b_element);
                next_boundary_element_index++;
            }
            catch (Exception &)
            {
                // Tetgen is feeding us lies  //Watch this space for coverage
                assert(SPACE_DIM == 3);
            }
        }
    }

    this->RefreshJacobianCachedData();
}

// Explicit instantiation

template class TetrahedralMesh<1,1>;
template class TetrahedralMesh<1,2>;
template class TetrahedralMesh<1,3>;
template class TetrahedralMesh<2,2>;
template class TetrahedralMesh<2,3>;
template class TetrahedralMesh<3,3>;

template void TetrahedralMesh<2,2>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<2,2>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);

template void TetrahedralMesh<3,3>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
template void TetrahedralMesh<3,3>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned, int *, unsigned, int *, int *);

//The following don't ever need to be instantiated, but are needed to keep some compilers happy
template void TetrahedralMesh<1,2>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1,2>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);

template void TetrahedralMesh<1,3>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
template void TetrahedralMesh<1,3>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned, int *, unsigned, int *, int *);
template void TetrahedralMesh<2,3>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
template void TetrahedralMesh<2,3>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned, int *, unsigned, int *, int *);

//Intel compilation with IPO thinks that it's missing some bizarre instantiations
template void TetrahedralMesh<3u, 3u>::ImportFromMesher<triangulateio>(triangulateio&, unsigned int, int*, unsigned int, int*, int*);
template void TetrahedralMesh<1u, 1u>::ImportFromMesher<triangulateio>(triangulateio&, unsigned int, int*, unsigned int, int*, int*);
template void TetrahedralMesh<1u, 1u>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned int, int*, unsigned int, int*, int*);
template void TetrahedralMesh<2u, 2u>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned int, int*, unsigned int, int*, int*);
template void TetrahedralMesh<1u, 1u>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);

// Compiler on ARC cluser HAL requires the following
template void TetrahedralMesh<3u, 3u>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1u, 1u>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<2u, 2u>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);

// Intel v11 compilation thinks that it's missing even more bizarre instantiations
//template void TetrahedralMesh<2,2>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
//template void TetrahedralMesh<3,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
//template void TetrahedralMesh<1,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
//template void TetrahedralMesh<1,1>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
//template void TetrahedralMesh<1,2>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
//template void TetrahedralMesh<2,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
//template void TetrahedralMesh<1,3>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);
//template void TetrahedralMesh<2,3>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);
//template void TetrahedralMesh<1,2>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned, int *, unsigned, int *, int *);
#ifdef _MSC_VER
//MSVC requires these
template void TetrahedralMesh<2,2>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
template void TetrahedralMesh<3,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1,1>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1,2>::ExportToMesher<tetgen::tetgenio>(NodeMap&, tetgen::tetgenio&, int*);
template void TetrahedralMesh<2,3>::ExportToMesher<triangulateio>(NodeMap&, triangulateio&, int*);
template void TetrahedralMesh<1,3>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);
template void TetrahedralMesh<2,3>::ImportFromMesher<triangulateio>(triangulateio&, unsigned, int *, unsigned, int *, int *);
template void TetrahedralMesh<1,2>::ImportFromMesher<tetgen::tetgenio>(tetgen::tetgenio&, unsigned, int *, unsigned, int *, int *);
#endif

// Serialization for Boost >= 1.36
#define CHASTE_SERIALIZATION_CPP
#include "SerializationExportWrapper.hpp"
EXPORT_TEMPLATE_CLASS_ALL_DIMS(TetrahedralMesh)