Toroidal2dVertexMesh.cpp

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*/
 
#include "Toroidal2dVertexMesh.hpp"
#include "Toroidal2dMesh.hpp"
 
Toroidal2dVertexMesh::Toroidal2dVertexMesh(double width,
                                           double height,
                                           std::vector<Node<2>*> nodes,
                                           std::vector<VertexElement<2, 2>*> vertexElements,
                                           double cellRearrangementThreshold,
                                           double t2Threshold)
    : MutableVertexMesh<2,2>(nodes, vertexElements, cellRearrangementThreshold, t2Threshold),
      mWidth(width),
      mHeight(height),
      mpMeshForVtk(nullptr)
{
    // Call ReMesh() to remove any deleted nodes and relabel
    ReMesh();
}
 
Toroidal2dVertexMesh::Toroidal2dVertexMesh(Toroidal2dMesh& rMesh, bool isBounded)
    : mWidth(rMesh.GetWidth(0)),
      mHeight(rMesh.GetWidth(1)),
      mpMeshForVtk(nullptr)
{
    mpDelaunayMesh = &rMesh;
 
    // Reset member variables and clear mNodes, mFaces and mElements
    Clear();
 
    if (!isBounded)
    {
        unsigned num_elements = mpDelaunayMesh->GetNumAllNodes();
        unsigned num_nodes = mpDelaunayMesh->GetNumAllElements();
 
        // Allocate memory for mNodes and mElements
        this->mNodes.reserve(num_nodes);
 
        // Create as many elements as there are nodes in the mesh
        mElements.reserve(num_elements);
 
        for (unsigned elem_index=0; elem_index<num_elements; elem_index++)
        {
            VertexElement<2,2>* p_element = new VertexElement<2,2>(elem_index);
            mElements.push_back(p_element);
        }
 
        // Populate mNodes
        GenerateVerticesFromElementCircumcentres(rMesh);
 
        // Loop over all generated nodes and check they're not outside [0,mWidth]x[0,mHeight]
        for (unsigned i=0; i<num_nodes; i++)
        {
            CheckNodeLocation(mNodes[i]);
        }
 
        // Loop over elements of the Delaunay mesh (which are nodes/vertices of this mesh)
        for (unsigned i=0; i<num_nodes; i++)
        {
            // Loop over nodes owned by this triangular element in the Delaunay mesh
            // Add this node/vertex to each of the 3 vertex elements
            for (unsigned local_index=0; local_index<3; local_index++)
            {
                unsigned elem_index = mpDelaunayMesh->GetElement(i)->GetNodeGlobalIndex(local_index);
                unsigned num_nodes_in_elem = mElements[elem_index]->GetNumNodes();
                unsigned end_index = num_nodes_in_elem>0 ? num_nodes_in_elem-1 : 0;
 
                mElements[elem_index]->AddNode(this->mNodes[i], end_index);
            }
        }
    }
    else // Is Bounded
    {
        // First create an extended mesh to include points extended from the boundary
        std::vector<Node<2> *> nodes;
        for (typename TetrahedralMesh<2,2>::NodeIterator node_iter = mpDelaunayMesh->GetNodeIteratorBegin();
            node_iter != mpDelaunayMesh->GetNodeIteratorEnd();
            ++node_iter)
        {
            nodes.push_back(new Node<2>(node_iter->GetIndex(), node_iter->rGetLocation(),node_iter->IsBoundaryNode()));
        }
 
        // Add new nodes
        unsigned new_node_index = mpDelaunayMesh->GetNumNodes();
        for (TetrahedralMesh<2,2>::ElementIterator elem_iter = mpDelaunayMesh->GetElementIteratorBegin();
            elem_iter != mpDelaunayMesh->GetElementIteratorEnd();
            ++elem_iter)
        {
            bool bad_element = false;
            double edge_threshold = 1.5; //TODO Make settable variable!
 
            for (unsigned j=0; j<3; j++)
            {
                Node<2>* p_node_a = mpDelaunayMesh->GetNode(elem_iter->GetNodeGlobalIndex(j));
                Node<2>* p_node_b = mpDelaunayMesh->GetNode(elem_iter->GetNodeGlobalIndex((j+1)%3));
                if (norm_2(mpDelaunayMesh->GetVectorFromAtoB(p_node_a->rGetLocation(), p_node_b->rGetLocation()))>edge_threshold)
                {
                    bad_element = true;
                    break;
                }
            }
 
            if (bad_element)
            {
                for (unsigned j=0; j<3; j++)
                {
                    Node<2>* p_node_a = mpDelaunayMesh->GetNode(elem_iter->GetNodeGlobalIndex(j));
                    Node<2>* p_node_b = mpDelaunayMesh->GetNode(elem_iter->GetNodeGlobalIndex((j+1)%3));
 
                    c_vector<double,2> edge = mpDelaunayMesh->GetVectorFromAtoB(p_node_a->rGetLocation(), p_node_b->rGetLocation());
                    double edge_length = norm_2(edge);
 
                    // The short edges in these elements are the boundaries of the void
                    if (edge_length<edge_threshold)
                    {
                        // Short Edge so add new node
                        c_vector<double,2> normal_vector;
 
                        // Outward Normal
                        normal_vector[0]= edge[1];
                        normal_vector[1]= -edge[0];
 
                        double dij = norm_2(normal_vector);
                        assert(dij>1e-5); //Sanity check
                        normal_vector /= dij;
 
                        double bound_offset = 0.5; //TODO Make settable variable!
                        c_vector<double,2> new_node_location = -bound_offset*normal_vector + p_node_a->rGetLocation() + 0.5*edge;
 
                        nodes.push_back(new Node<2>(new_node_index, new_node_location));
                        new_node_index++;
 
                        // Now add extra end nodes if appropriate.
                        unsigned num_sections = 1; // I.e. only at ends.
                        for (unsigned section=0; section <= num_sections; section++)
                        {
                            double ratio = (double)section/(double)num_sections;
                            c_vector<double,2> new_node_location = -normal_vector + ratio*p_node_a->rGetLocation() + (1-ratio)*p_node_b->rGetLocation();
 
                            //Check if near other nodes (could be inefficient)
                            bool node_clear = true;
                            double node_clearance = 0.3; // Make settable variable??
 
                            for (unsigned i=0; i<nodes.size(); i++)
                            {
                                double distance = norm_2(mpDelaunayMesh->GetVectorFromAtoB(nodes[i]->rGetLocation(), new_node_location));
                                if (distance < node_clearance)
                                {
                                    node_clear = false;
                                    break;
                                }
                            }
 
                            if (node_clear)
                            {
                                nodes.push_back(new Node<2>(new_node_index, new_node_location));
                                new_node_index++;
                            }
                        }
                    }
                }
            }
        }
 
        // Loop over all nodes and check they're not outside [0,mWidth]x[0,mHeight]
        for (unsigned i=0; i<nodes.size(); i++)
        {
            CheckNodeLocation(nodes[i]);
        }
 
        Toroidal2dMesh extended_mesh(mpDelaunayMesh->GetWidth(0),mpDelaunayMesh->GetWidth(1), nodes);
 
        unsigned num_elements = mpDelaunayMesh->GetNumAllNodes();
        unsigned num_nodes = extended_mesh.GetNumAllElements();
 
        // Allocate memory for mNodes and mElements
        this->mNodes.reserve(num_nodes);
 
        // Create as many elements as there are nodes in the mesh
        mElements.reserve(num_elements);
        for (unsigned elem_index = 0; elem_index < num_elements; elem_index++)
        {
            VertexElement<2, 2>* p_element = new VertexElement<2, 2>(elem_index);
            mElements.push_back(p_element);
        }
 
        // Populate mNodes
        GenerateVerticesFromElementCircumcentres(extended_mesh);
 
        // Loop over all generated nodes and check they're not outside [0,mWidth]x[0,mHeight]
        for (unsigned i=0; i<num_nodes; i++)
        {
            CheckNodeLocation(mNodes[i]);
        }
 
 
        // Loop over elements of the Delaunay mesh (which are nodes/vertices of this mesh)
        for (unsigned i = 0; i < num_nodes; i++)
        {
            // Loop over nodes owned by this triangular element in the Delaunay mesh
            // Add this node/vertex to each of the 3 vertex elements
            for (unsigned local_index = 0; local_index < 3; local_index++)
            {
                unsigned elem_index = extended_mesh.GetElement(i)->GetNodeGlobalIndex(local_index);
 
                if (elem_index < num_elements)
                {
                    unsigned num_nodes_in_elem = mElements[elem_index]->GetNumNodes();
                    unsigned end_index = num_nodes_in_elem > 0 ? num_nodes_in_elem - 1 : 0;
 
                    mElements[elem_index]->AddNode(this->mNodes[i], end_index);
                }
            }
        }
    }
 
    // Reorder mNodes anticlockwise
    for (unsigned elem_index=0; elem_index<mElements.size(); elem_index++)
    {
        std::vector<std::pair<double, unsigned> > index_angle_list;
        for (unsigned local_index=0; local_index<mElements[elem_index]->GetNumNodes(); local_index++)
        {
            c_vector<double, 2> vectorA = mpDelaunayMesh->GetNode(elem_index)->rGetLocation();
            c_vector<double, 2> vectorB = mElements[elem_index]->GetNodeLocation(local_index);
            c_vector<double, 2> centre_to_vertex = mpDelaunayMesh->GetVectorFromAtoB(vectorA, vectorB);
 
            double angle = atan2(centre_to_vertex(1), centre_to_vertex(0));
            unsigned global_index = mElements[elem_index]->GetNodeGlobalIndex(local_index);
 
            std::pair<double, unsigned> pair(angle, global_index);
            index_angle_list.push_back(pair);
        }
 
        // Sort the list in order of increasing angle
        sort(index_angle_list.begin(), index_angle_list.end());
 
        // Create a new Voronoi element and pass in the appropriate Nodes, ordered anticlockwise
        VertexElement<2,2>* p_new_element = new VertexElement<2,2>(elem_index);
        for (unsigned count = 0; count < index_angle_list.size(); count++)
        {
            unsigned local_index = count>1 ? count-1 : 0;
            p_new_element->AddNode(mNodes[index_angle_list[count].second], local_index);
        }
 
        // Replace the relevant member of mElements with this Voronoi element
        delete mElements[elem_index];
        mElements[elem_index] = p_new_element;
    }
 
    this->mMeshChangesDuringSimulation = false;
}
 
Toroidal2dVertexMesh::Toroidal2dVertexMesh()
    : mpMeshForVtk(nullptr)
{
}
 
Toroidal2dVertexMesh::~Toroidal2dVertexMesh()
{
    if (mpMeshForVtk != NULL)
    {
         delete mpMeshForVtk;
    }
}
 
c_vector<double, 2> Toroidal2dVertexMesh::GetVectorFromAtoB(const c_vector<double, 2>& rLocation1, const c_vector<double, 2>& rLocation2)
{
    assert(mWidth > 0.0);
    assert(mHeight > 0.0);
 
    c_vector<double, 2> vector = rLocation2 - rLocation1;
    vector[0] = fmod(vector[0], mWidth);
    vector[1] = fmod(vector[1], mHeight);
 
    // If the points are more than halfway across the domain, measure the other way
    if (vector[0] > 0.5*mWidth)
    {
        vector[0] -= mWidth;
    }
    else if (vector[0] < -0.5*mWidth)
    {
        vector[0] += mWidth;
    }
 
    // If the points are more than halfway up the domain, measure the other way
    if (vector[1] > 0.5*mHeight)
    {
        vector[1] -= mHeight;
    }
    else if (vector[1] < -0.5*mHeight)
    {
        vector[1] += mHeight;
    }
    return vector;
}
 
void Toroidal2dVertexMesh::SetNode(unsigned nodeIndex, ChastePoint<2> point)
{
    double x_coord = point.rGetLocation()[0];
    double y_coord = point.rGetLocation()[1];
 
    // Perform a periodic movement if necessary
    if (x_coord >= mWidth)
    {
        // Move point left
        point.SetCoordinate(0, x_coord - mWidth);
    }
    else if (x_coord < 0.0)
    {
        // Move point right
        point.SetCoordinate(0, x_coord + mWidth);
    }
    if (y_coord >= mHeight)
    {
        // Move point down
        point.SetCoordinate(1, y_coord - mHeight);
    }
    else if (y_coord < 0.0)
    {
        // Move point up
        point.SetCoordinate(1, y_coord + mHeight);
    }
 
    // Update the node's location
    MutableVertexMesh<2,2>::SetNode(nodeIndex, point);
}
 
double Toroidal2dVertexMesh::GetWidth(const unsigned& rDimension) const
{
    assert(rDimension==0 || rDimension==1);
 
    double width = mWidth;
    if (rDimension == 1)
    {
        width = mHeight;
    }
 
    return width;
}
 
void Toroidal2dVertexMesh::SetHeight(double height)
{
    assert(height > 0);
    mHeight = height;
}
 
void Toroidal2dVertexMesh::SetWidth(double width)
{
    assert(width > 0);
    mWidth = width;
}
 
unsigned Toroidal2dVertexMesh::AddNode(Node<2>* pNewNode)
{
    // If necessary move it to be back onto the torus
    CheckNodeLocation(pNewNode);
 
    unsigned node_index = MutableVertexMesh<2,2>::AddNode(pNewNode);
 
    return node_index;
}
 
void Toroidal2dVertexMesh::CheckNodeLocation(Node<2>* pNode)
{
    double x_location = pNode->rGetLocation()[0];
    if (x_location < 0)
    {
        pNode->rGetModifiableLocation()[0] = x_location + mWidth;
    }
    else if (x_location > mWidth)
    {
        pNode->rGetModifiableLocation()[0] = x_location - mWidth;
    }
    double y_location = pNode->rGetLocation()[1];
    if (y_location < 0)
    {
        pNode->rGetModifiableLocation()[1] = y_location + mHeight;
    }
    else if (y_location > mHeight)
    {
        pNode->rGetModifiableLocation()[1] = y_location - mHeight;
    }
}
 
VertexMesh<2, 2>* Toroidal2dVertexMesh::GetMeshForVtk()
{
    unsigned num_nodes = GetNumNodes();
 
    std::vector<Node<2>*> temp_nodes;
    std::vector<VertexElement<2, 2>*> elements;
 
    if(!mpDelaunayMesh) // No Delaunay mesh so less copies as all too top right
    {
        temp_nodes.resize(4 * num_nodes);
 
        // Create four copies of each node.
        for (unsigned index = 0; index < num_nodes; index++)
        {
            c_vector<double, 2> location;
            location = GetNode(index)->rGetLocation();
 
            // Node copy at original location
            Node<2>* p_node = new Node<2>(index, false, location[0], location[1]);
            temp_nodes[index] = p_node;
 
            // Node copy shifted right
            p_node = new Node<2>(num_nodes + index, false, location[0] + mWidth, location[1]);
            temp_nodes[num_nodes + index] = p_node;
 
            // Node copy shifted up
            p_node = new Node<2>(2*num_nodes + index, false, location[0], location[1] + mHeight);
            temp_nodes[2*num_nodes + index] = p_node;
 
            // Node copy shifted right and up
            p_node = new Node<2>(3*num_nodes + index, false, location[0] + mWidth, location[1] + mHeight);
            temp_nodes[3*num_nodes + index] = p_node;
        }
 
        // Iterate over elements
        for (VertexMesh<2,2>::VertexElementIterator elem_iter = GetElementIteratorBegin();
            elem_iter != GetElementIteratorEnd();
            ++elem_iter)
        {
            unsigned elem_index = elem_iter->GetIndex();
            unsigned num_nodes_in_elem = elem_iter->GetNumNodes();
 
            std::vector<Node<2>*> elem_nodes;
 
            // Compute whether the element straddles either periodic boundary
            bool element_straddles_left_right_boundary = false;
            bool element_straddles_top_bottom_boundary = false;
 
            const c_vector<double, 2>& r_this_node_location = elem_iter->GetNode(0)->rGetLocation();
            for (unsigned local_index=0; local_index<num_nodes_in_elem; local_index++)
            {
                const c_vector<double, 2>& r_next_node_location = elem_iter->GetNode((local_index+1)%num_nodes_in_elem)->rGetLocation();
                c_vector<double, 2> vector;
                vector = r_next_node_location - r_this_node_location;
 
                if (fabs(vector[0]) > 0.5*mWidth)
                {
                    element_straddles_left_right_boundary = true;
                }
                if (fabs(vector[1]) > 0.5*mHeight)
                {
                    element_straddles_top_bottom_boundary = true;
                }
            }
 
            // Use the above information when duplicating the element
            for (unsigned local_index=0; local_index<num_nodes_in_elem; local_index++)
            {
                unsigned this_node_index = elem_iter->GetNodeGlobalIndex(local_index);
 
                // If the element straddles the left/right periodic boundary...
                if (element_straddles_left_right_boundary)
                {
                    // ...and this node is located to the left of the centre of the mesh...
                    bool node_is_right_of_centre = (elem_iter->GetNode(local_index)->rGetLocation()[0] - 0.5*mWidth > 0);
                    if (!node_is_right_of_centre)
                    {
                        // ...then choose the equivalent node to the right
                        this_node_index += num_nodes;
                    }
                }
 
                // If the element straddles the top/bottom periodic boundary...
                if (element_straddles_top_bottom_boundary)
                {
                    // ...and this node is located below the centre of the mesh...
                    bool node_is_above_centre = (elem_iter->GetNode(local_index)->rGetLocation()[1] - 0.5*mHeight > 0);
                    if (!node_is_above_centre)
                    {
                        // ...then choose the equivalent node above
                        this_node_index += 2*num_nodes;
                    }
                }
 
                elem_nodes.push_back(temp_nodes[this_node_index]);
            }
 
            VertexElement<2,2>* p_element = new VertexElement<2,2>(elem_index, elem_nodes);
            elements.push_back(p_element);
        }
    }
    else // Has Delaunay mesh so match elements to centres
    {
        temp_nodes.resize(9*num_nodes);
 
        // Create nine copies of each node.
        for (unsigned index=0; index<num_nodes; index++)
        {
            c_vector<double, 2> location;
            location = GetNode(index)->rGetLocation();
 
            // Node copy at original location
            Node<2>* p_node = new Node<2>(index, false, location[0], location[1]);
            temp_nodes[index] = p_node;
 
            // Node copy shifted right
            p_node = new Node<2>(num_nodes + index, false, location[0] + mWidth, location[1]);
            temp_nodes[num_nodes + index] = p_node;
 
            // Node copy shifted up and right
            p_node = new Node<2>(2*num_nodes + index, false, location[0] + mWidth, location[1] + mHeight);
            temp_nodes[2*num_nodes + index] = p_node;
 
            // Node copy shifted up
            p_node = new Node<2>(3*num_nodes + index, false, location[0], location[1] + mHeight);
            temp_nodes[3*num_nodes + index] = p_node;
 
            // Node copy shifted up and left
            p_node = new Node<2>(4*num_nodes + index, false, location[0] - mWidth, location[1] + mHeight);
            temp_nodes[4*num_nodes + index] = p_node;
 
            // Node copy shifted left
            p_node = new Node<2>(5*num_nodes + index, false, location[0] - mWidth, location[1]);
            temp_nodes[5*num_nodes + index] = p_node;
 
            // Node copy shifted left and down
            p_node = new Node<2>(6*num_nodes + index, false, location[0] - mWidth, location[1] - mHeight);
            temp_nodes[6*num_nodes + index] = p_node;
 
            // Node copy shifted down
            p_node = new Node<2>(7*num_nodes + index, false, location[0], location[1] - mHeight);
            temp_nodes[7*num_nodes + index] = p_node;
 
            // Node copy shifted down and right
            p_node = new Node<2>(8*num_nodes + index, false, location[0] + mWidth, location[1] - mHeight);
            temp_nodes[8*num_nodes + index] = p_node;
        }
 
        // Iterate over elements
        for (VertexMesh<2,2>::VertexElementIterator elem_iter = GetElementIteratorBegin();
            elem_iter != GetElementIteratorEnd();
            ++elem_iter)
        {
            unsigned elem_index = elem_iter->GetIndex();
            unsigned num_nodes_in_elem = elem_iter->GetNumNodes();
 
            std::vector<Node<2>*> elem_nodes;
 
            // Compute whether the element straddles either periodic boundary
            bool element_straddles_left_right_boundary = false;
            bool element_straddles_top_bottom_boundary = false;
 
            const c_vector<double, 2>& r_this_node_location = elem_iter->GetNode(0)->rGetLocation();
            for (unsigned local_index=0; local_index<num_nodes_in_elem; local_index++)
            {
                const c_vector<double, 2>& r_next_node_location = elem_iter->GetNode((local_index+1)%num_nodes_in_elem)->rGetLocation();
                c_vector<double, 2> vector;
                vector = r_next_node_location - r_this_node_location;
 
                if (fabs(vector[0]) > 0.5*mWidth)
                {
                    element_straddles_left_right_boundary = true;
                }
                if (fabs(vector[1]) > 0.5*mHeight)
                {
                    element_straddles_top_bottom_boundary = true;
                }
            }
            /* If this is a voronoi tesselation make sure the elements contain
            * the original Delaunay node
            */
            bool element_centre_on_right = true;
            bool element_centre_on_top = true;
 
            unsigned delaunay_index = this->GetDelaunayNodeIndexCorrespondingToVoronoiElementIndex(elem_index);
            double element_centre_x_location = this->mpDelaunayMesh->GetNode(delaunay_index)->rGetLocation()[0];
            double element_centre_y_location = this->mpDelaunayMesh->GetNode(delaunay_index)->rGetLocation()[1];
 
            if (element_centre_x_location < 0.5*mWidth)
            {
                element_centre_on_right = false;
            }
            if (element_centre_y_location < 0.5*mHeight)
            {
                element_centre_on_top = false;
            }
 
            // Use the above information when duplicating the element
            for (unsigned local_index=0; local_index<num_nodes_in_elem; local_index++)
            {
                unsigned this_node_index = elem_iter->GetNodeGlobalIndex(local_index);
 
                // If the element straddles the left/right periodic boundary...
                if (element_straddles_left_right_boundary && !element_straddles_top_bottom_boundary)
                {
                    // ...and this node is located to the left of the centre of the mesh...
                    bool node_is_right_of_centre = (elem_iter->GetNode(local_index)->rGetLocation()[0] - 0.5*mWidth > 0);
                    if (!node_is_right_of_centre && element_centre_on_right)
                    {
                        // ...then choose the equivalent node to the right
                        this_node_index += num_nodes;
                    }
                    else if (node_is_right_of_centre && !element_centre_on_right)
                    {
                        // ...then choose the equivalent node to the left
                        this_node_index += 5*num_nodes;
                    }
                }
                else if (!element_straddles_left_right_boundary && element_straddles_top_bottom_boundary)
                {
                    // ...and this node is located to the bottom of the centre of the mesh...
                    bool node_is_top_of_centre = (elem_iter->GetNode(local_index)->rGetLocation()[1] - 0.5*mHeight > 0);
                    if (!node_is_top_of_centre && element_centre_on_top)
                    {
                        // ...then choose the equivalent node to the top
                        this_node_index += 3*num_nodes;
                    }
                    else if (node_is_top_of_centre && !element_centre_on_top)
                    {
                        // ...then choose the equivalent node to the bottom
                        this_node_index += 7*num_nodes;
                    }
                }
                else if (element_straddles_left_right_boundary && element_straddles_top_bottom_boundary)
                {
                    bool node_is_right_of_centre = (elem_iter->GetNode(local_index)->rGetLocation()[0] - 0.5*mWidth > 0);
                    bool node_is_top_of_centre = (elem_iter->GetNode(local_index)->rGetLocation()[1] - 0.5*mHeight > 0);
 
                    if (!node_is_top_of_centre && element_centre_on_top)
                    {
                        if (!node_is_right_of_centre && element_centre_on_right)
                        {
                            this_node_index += 2*num_nodes;
                        }
                        else if (node_is_right_of_centre && !element_centre_on_right)
                        {
                            this_node_index += 4*num_nodes;
                        }
                        else
                        {
                            this_node_index += 3*num_nodes;
                        }
                    }
                    else if (node_is_top_of_centre && !element_centre_on_top)
                    {
                        if (!node_is_right_of_centre && element_centre_on_right)
                        {
                            this_node_index += 8*num_nodes;
                        }
                        else if (node_is_right_of_centre && !element_centre_on_right)
                        {
                            this_node_index += 6*num_nodes;
                        }
                        else
                        {
                            this_node_index += 7*num_nodes;
                        }
                    }
                    else
                    {
                        if (!node_is_right_of_centre && element_centre_on_right)
                        {
                            this_node_index += num_nodes;
                        }
                        else if (node_is_right_of_centre && !element_centre_on_right)
                        {
                            this_node_index += 5*num_nodes;
                        }
                    }
                }
 
                // If the element straddles the top/bottom periodic boundary...
                // if (element_straddles_top_bottom_boundary)
                // {
                //     // ...and this node is located below the centre of the mesh...
                //     bool node_is_above_centre = (elem_iter->GetNode(local_index)->rGetLocation()[1] - 0.5*mHeight > 0);
                //     if (!node_is_above_centre)
                //     {
                //         // ...then choose the equivalent node above
                //         this_node_index += 2*num_nodes;
                //     }
                // }
 
                elem_nodes.push_back(temp_nodes[this_node_index]);
            }
 
            VertexElement<2,2>* p_element = new VertexElement<2,2>(elem_index, elem_nodes);
            elements.push_back(p_element);
        }
    }
 
    // Now delete any nodes from the mesh for VTK that are not contained in any elements
    std::vector<Node<2>*> nodes;
    unsigned count = 0;
    for (unsigned index=0; index<temp_nodes.size(); index++)
    {
        unsigned num_elems_containing_this_node = temp_nodes[index]->rGetContainingElementIndices().size();
 
        if (num_elems_containing_this_node == 0)
        {
            // Avoid memory leak
            delete temp_nodes[index];
        }
        else
        {
            temp_nodes[index]->SetIndex(count);
            nodes.push_back(temp_nodes[index]);
            count++;
        }
    }
 
    if (mpMeshForVtk != nullptr)
    {
        delete mpMeshForVtk;
    }
 
    mpMeshForVtk = new VertexMesh<2,2>(nodes, elements);
    return mpMeshForVtk;
}
 
void Toroidal2dVertexMesh::ConstructFromMeshReader(AbstractMeshReader<2,2>& rMeshReader, double width, double height)
{
    assert(rMeshReader.HasNodePermutation() == false);
 
    // Store numbers of nodes and elements
    unsigned num_nodes = rMeshReader.GetNumNodes();
    unsigned num_elements = rMeshReader.GetNumElements();
 
    // Reserve memory for nodes
    this->mNodes.reserve(num_nodes);
 
    rMeshReader.Reset();
 
    // Add nodes
    std::vector<double> node_data;
    for (unsigned node_idx = 0 ; node_idx < num_nodes ; node_idx++)
    {
        node_data = rMeshReader.GetNextNode();
        node_data.pop_back();
        this->mNodes.push_back(new Node<2>(node_idx, node_data, false));
    }
 
    rMeshReader.Reset();
 
    // Reserve memory for elements
    mElements.reserve(rMeshReader.GetNumElements());
 
    // Add elements
    for (unsigned elem_idx = 0 ; elem_idx < num_elements ; elem_idx++)
    {
        // Get the data for this element
        ElementData element_data = rMeshReader.GetNextElementData();
 
        // Get the nodes owned by this element
        std::vector<Node<2>*> nodes;
        unsigned num_nodes_in_element = element_data.NodeIndices.size();
        for (unsigned j=0; j<num_nodes_in_element; j++)
        {
            assert(element_data.NodeIndices[j] < this->mNodes.size());
            nodes.push_back(this->mNodes[element_data.NodeIndices[j]]);
        }
 
        // Use nodes and index to construct this element
        VertexElement<2,2>* p_element = new VertexElement<2,2>(elem_idx, nodes);
        mElements.push_back(p_element);
 
        if (rMeshReader.GetNumElementAttributes() > 0)
        {
            assert(rMeshReader.GetNumElementAttributes() == 1);
            unsigned attribute_value = (unsigned) element_data.AttributeValue;
            p_element->SetAttribute(attribute_value);
        }
    }
 
    /*
     * Set width and height from function arguments, and validate by checking area is correct
     */
    this->mWidth = width;
    this->mHeight = height;
 
    double total_surface_area = 0.0;
    for (unsigned elem_idx = 0 ; elem_idx < num_elements ; elem_idx++)
    {
        total_surface_area += this->GetVolumeOfElement(elem_idx);
    }
 
    if (fabs(mWidth * mHeight - total_surface_area) > 1e-6)
    {
        EXCEPTION("Mesh width and height do not match sheet surface area.");
    }
 
    // Set default parameter values
    this->mCellRearrangementRatio = 1.5;
    this->mCellRearrangementThreshold = 0.01;
    this->mT2Threshold = 0.001;
    this->mMeshChangesDuringSimulation = true;
    this->mpMeshForVtk = nullptr;
}
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(Toroidal2dVertexMesh)