MutableMesh.cpp

/*
 
Copyright (c) 2005-2024, University of Oxford.
All rights reserved.
 
University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.
 
This file is part of Chaste.
 
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.
 * Neither the name of the University of Oxford nor the names of its
   contributors may be used to endorse or promote products derived from this
   software without specific prior written permission.
 
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
*/
 
#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 = zero_vector<double>(SPACE_DIM+1);
 
    this_circum_centre = pElement->CalculateCircumsphere(this->mElementJacobians[pElement->GetIndex()], this->mElementInverseJacobians[pElement->GetIndex()]);
 
    // Copy the actually circumcentre into a smaller vector
    c_vector<double, ELEMENT_DIM> circum_centre = zero_vector<double>(ELEMENT_DIM);
    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 = this->GetNode(*it)->rGetLocation();
 
        // Calculate vector from circumcenter to node
        node_location -= circum_centre;
 
        // This is to calculate the squared distance between them
        double squared_distance = inner_prod(node_location, node_location);
 
        // If the squared distance 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)