PottsMesh.cpp

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*/
 
#include "PottsMesh.hpp"
#include "RandomNumberGenerator.hpp"
 
 
template<unsigned DIM>
PottsMesh<DIM>::PottsMesh(std::vector<Node<DIM>*> nodes,
                          std::vector<PottsElement<DIM>*> pottsElements,
                          std::vector<std::set<unsigned> > vonNeumannNeighbouringNodeIndices,
                          std::vector<std::set<unsigned> > mooreNeighbouringNodeIndices)
{
    // Reset member variables and clear mNodes, mElements.
    Clear();
 
    // Verify the same size of nodes and neighbour information.
    if ((vonNeumannNeighbouringNodeIndices.size() != nodes.size()) || (mooreNeighbouringNodeIndices.size() != nodes.size()))
    {
        EXCEPTION("Nodes and neighbour information for a Potts mesh need to be the same length.");
    }
    mVonNeumannNeighbouringNodeIndices = vonNeumannNeighbouringNodeIndices;
    mMooreNeighbouringNodeIndices = mooreNeighbouringNodeIndices;
 
    // Populate mNodes and mElements
    for (unsigned node_index=0; node_index<nodes.size(); node_index++)
    {
        Node<DIM>* p_temp_node = nodes[node_index];
        this->mNodes.push_back(p_temp_node);
    }
    for (unsigned elem_index=0; elem_index<pottsElements.size(); elem_index++)
    {
        PottsElement<DIM>* p_temp_element = pottsElements[elem_index];
        mElements.push_back(p_temp_element);
    }
 
    // Register elements with nodes
    for (unsigned index=0; index<mElements.size(); index++)
    {
        PottsElement<DIM>* p_element = mElements[index];
 
        unsigned element_index = p_element->GetIndex();
        unsigned num_nodes_in_element = p_element->GetNumNodes();
 
        for (unsigned node_index=0; node_index<num_nodes_in_element; node_index++)
        {
            p_element->GetNode(node_index)->AddElement(element_index);
        }
    }
 
    this->mMeshChangesDuringSimulation = true;
}
 
template<unsigned DIM>
PottsMesh<DIM>::PottsMesh()
{
    this->mMeshChangesDuringSimulation = true;
    Clear();
}
 
template<unsigned DIM>
PottsMesh<DIM>::~PottsMesh()
{
    Clear();
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::SolveNodeMapping(unsigned index) const
{
    assert(index < this->mNodes.size());
    return index;
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::SolveElementMapping(unsigned index) const
{
    assert(index < this->mElements.size());
    return index;
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::SolveBoundaryElementMapping(unsigned index) const
{
    return index;
}
 
template<unsigned DIM>
void PottsMesh<DIM>::Clear()
{
    // Delete elements
    for (unsigned i=0; i<mElements.size(); i++)
    {
        delete mElements[i];
    }
    mElements.clear();
 
    // Delete nodes
    for (unsigned i=0; i<this->mNodes.size(); i++)
    {
        delete this->mNodes[i];
    }
    this->mNodes.clear();
 
    mDeletedElementIndices.clear();
 
    // Delete neighbour info
    //mVonNeumannNeighbouringNodeIndices.clear();
    //mMooreNeighbouringNodeIndices.clear();
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::GetNumNodes() const
{
    return this->mNodes.size();
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::GetNumElements() const
{
    return mElements.size() - mDeletedElementIndices.size();
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::GetNumAllElements() const
{
    return mElements.size();
}
 
template<unsigned DIM>
PottsElement<DIM>* PottsMesh<DIM>::GetElement(unsigned index) const
{
    assert(index < mElements.size());
    return mElements[index];
}
 
template<unsigned DIM>
c_vector<double, DIM> PottsMesh<DIM>::GetCentroidOfElement(unsigned index)
{
    PottsElement<DIM>* p_element = GetElement(index);
    unsigned num_nodes_in_element = p_element->GetNumNodes();
 
    c_vector<double, DIM> centroid = zero_vector<double>(DIM);
 
    for (unsigned local_index=0; local_index<num_nodes_in_element; local_index++)
    {
        // Find location of current node and add it to the centroid
        centroid += p_element->GetNodeLocation(local_index);
    }
 
    centroid /= num_nodes_in_element;
 
    return centroid;
}
 
template<unsigned DIM>
double PottsMesh<DIM>::GetVolumeOfElement(unsigned index)
{
    PottsElement<DIM>* p_element = GetElement(index);
    double element_volume = (double) p_element->GetNumNodes();
 
    return element_volume;
}
 
template<unsigned DIM>
double PottsMesh<DIM>::GetSurfaceAreaOfElement(unsigned index)
{
    assert(DIM==2 || DIM==3); // LCOV_EXCL_LINE
 
    // Helper variables
    PottsElement<DIM>* p_element = GetElement(index);
    unsigned num_nodes = p_element->GetNumNodes();
 
    double surface_area = 0.0;
    for (unsigned node_index=0; node_index<num_nodes; node_index++)
    {
        std::set<unsigned> neighbouring_node_indices = GetVonNeumannNeighbouringNodeIndices(p_element->GetNode(node_index)->GetIndex());
        unsigned local_edges = 2*DIM;
        for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
             iter != neighbouring_node_indices.end();
             iter++)
        {
            std::set<unsigned> neighbouring_node_element_indices = this->mNodes[*iter]->rGetContainingElementIndices();
 
            if (!(neighbouring_node_element_indices.empty()) && (local_edges!=0))
            {
                unsigned neighbouring_node_element_index = *(neighbouring_node_element_indices.begin());
                if (neighbouring_node_element_index == index)
                {
                    local_edges--;
                }
            }
        }
        surface_area += local_edges;
    }
    return surface_area;
}
 
template<unsigned DIM>
std::set<unsigned> PottsMesh<DIM>::GetMooreNeighbouringNodeIndices(unsigned nodeIndex)
{
    return mMooreNeighbouringNodeIndices[nodeIndex];
}
 
template<unsigned DIM>
std::set<unsigned> PottsMesh<DIM>::GetVonNeumannNeighbouringNodeIndices(unsigned nodeIndex)
{
    return mVonNeumannNeighbouringNodeIndices[nodeIndex];
}
 
template<unsigned DIM>
void PottsMesh<DIM>::DeleteElement(unsigned index)
{
    // Mark this element as deleted; this also updates the nodes containing element indices
    this->mElements[index]->MarkAsDeleted();
    mDeletedElementIndices.push_back(index);
}
 
template<unsigned DIM>
void PottsMesh<DIM>::RemoveDeletedElements()
{
    // Remove any elements that have been removed and re-order the remaining ones
    unsigned num_deleted_elements = mDeletedElementIndices.size();
 
    for (unsigned index = num_deleted_elements; index>0; index--)
    {
        unsigned deleted_elem_index = mDeletedElementIndices[index-1];
        delete mElements[deleted_elem_index];
        mElements.erase(mElements.begin()+deleted_elem_index);
        for (unsigned elem_index=deleted_elem_index; elem_index<mElements.size(); elem_index++)
        {
            mElements[elem_index]->ResetIndex(elem_index);
        }
    }
    mDeletedElementIndices.clear();
}
 
template<unsigned DIM>
void PottsMesh<DIM>::DeleteNode(unsigned index)
{
    //Mark node as deleted so we don't consider it when iterating over nodes
    this->mNodes[index]->MarkAsDeleted();
 
    //Remove from Elements
    std::set<unsigned> containing_element_indices = this->mNodes[index]->rGetContainingElementIndices();
 
    for (std::set<unsigned>::iterator iter = containing_element_indices.begin();
         iter != containing_element_indices.end();
         iter++)
    {
        assert(mElements[*iter]->GetNumNodes() > 0);
        if (mElements[*iter]->GetNumNodes() == 1)
        {
            DeleteElement(*iter);
        }
        else
        {
            this->mElements[*iter]->DeleteNode(this->mElements[*iter]->GetNodeLocalIndex(index));
        }
    }
 
    // Remove from connectivity
    mVonNeumannNeighbouringNodeIndices[index].clear();
    mMooreNeighbouringNodeIndices[index].clear();
 
    assert(mVonNeumannNeighbouringNodeIndices.size()==mMooreNeighbouringNodeIndices.size());
    for (unsigned node_index = 0;
         node_index < mVonNeumannNeighbouringNodeIndices.size();
         node_index++)
    {
        // Remove node "index" from the Von Neuman neighbourhood of node "node_index".
        mVonNeumannNeighbouringNodeIndices[node_index].erase(index);
        mMooreNeighbouringNodeIndices[node_index].erase(index);
 
        // Check there's still connectivity for the other non-deleted nodes
        if (!this->mNodes[node_index]->IsDeleted())
        {
            assert(!mVonNeumannNeighbouringNodeIndices[node_index].empty());
            assert(!mMooreNeighbouringNodeIndices[node_index].empty());
        }
    }
 
    // Remove node from mNodes and renumber all the elements and nodes
    delete this->mNodes[index];
    this->mNodes.erase(this->mNodes.begin()+index);
    unsigned num_nodes = GetNumNodes();
    mVonNeumannNeighbouringNodeIndices.erase(mVonNeumannNeighbouringNodeIndices.begin()+index);
    mMooreNeighbouringNodeIndices.erase(mMooreNeighbouringNodeIndices.begin()+index);
 
    assert(mVonNeumannNeighbouringNodeIndices.size()==num_nodes);
    assert(mMooreNeighbouringNodeIndices.size()==num_nodes);
 
    for (unsigned node_index = 0; node_index < num_nodes; node_index++)
    {
        // Reduce the index of all nodes greater than  node "index"
        if (node_index >= index)
        {
            assert(this->mNodes[node_index]->GetIndex() == node_index+1);
            this->mNodes[node_index]->SetIndex(node_index);
        }
        assert(this->mNodes[node_index]->GetIndex() == node_index);
 
        // Reduce the index of all nodes greater than  node "index"
        // in the Moore and Von Neuman neighbourhoods.
        std::set<unsigned> von_neuman = mVonNeumannNeighbouringNodeIndices[node_index];
        mVonNeumannNeighbouringNodeIndices[node_index].clear();
        for (std::set<unsigned>::iterator iter = von_neuman.begin();
             iter != von_neuman.end();
             iter++)
        {
            if (*iter >= index)
            {
                mVonNeumannNeighbouringNodeIndices[node_index].insert(*iter-1);
            }
            else
            {
                mVonNeumannNeighbouringNodeIndices[node_index].insert(*iter);
            }
        }
        std::set<unsigned> moore = mMooreNeighbouringNodeIndices[node_index];
        mMooreNeighbouringNodeIndices[node_index].clear();
        for (std::set<unsigned>::iterator iter = moore.begin();
             iter != moore.end();
             iter++)
        {
            if (*iter >= index)
            {
                mMooreNeighbouringNodeIndices[node_index].insert(*iter-1);
            }
            else
            {
                mMooreNeighbouringNodeIndices[node_index].insert(*iter);
            }
        }
    }
    // Finally remove any elements that have been removed
    assert(mDeletedElementIndices.size() <= 1); // Should have at most one element to remove
    if (mDeletedElementIndices.size() == 1)
    {
        unsigned deleted_elem_index = mDeletedElementIndices[0];
        delete mElements[deleted_elem_index];
        mElements.erase(mElements.begin()+deleted_elem_index);
        mDeletedElementIndices.clear();
 
        for (unsigned elem_index=deleted_elem_index; elem_index<GetNumElements(); elem_index++)
        {
            mElements[elem_index]->ResetIndex(elem_index);
        }
    }
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::DivideElement(PottsElement<DIM>* pElement,
                                       bool placeOriginalElementBelow)
{
    assert(DIM==2 || DIM==3); // LCOV_EXCL_LINE
 
    // Store the number of nodes in the element (this changes when nodes are deleted from the element)
    unsigned num_nodes = pElement->GetNumNodes();
 
    if (num_nodes < 2)
    {
        EXCEPTION("Tried to divide a Potts element with only one node. Cell dividing too often given dynamic parameters.");
    }
 
    // Copy the nodes in this element
    std::vector<Node<DIM>*> nodes_elem;
    for (unsigned i=0; i<num_nodes; i++)
    {
        nodes_elem.push_back(pElement->GetNode(i));
    }
 
    // Get the index of the new element
    unsigned new_element_index;
    if (mDeletedElementIndices.empty())
    {
        new_element_index = this->mElements.size();
    }
    else
    {
        new_element_index = mDeletedElementIndices.back();
        mDeletedElementIndices.pop_back();
        delete this->mElements[new_element_index];
    }
 
    // Add the new element to the mesh
    AddElement(new PottsElement<DIM>(new_element_index, nodes_elem));
 
    unsigned half_num_nodes = num_nodes/2; // This will round down
    assert(half_num_nodes > 0);
    assert(half_num_nodes < num_nodes);
 
    // Find lowest element
    double height_midpoint_1 = 0.0;
    double height_midpoint_2 = 0.0;
    unsigned counter_1 = 0;
    unsigned counter_2 = 0;
 
    for (unsigned i=0; i<num_nodes; i++)
    {
        if (i<half_num_nodes)
        {
            height_midpoint_1 += pElement->GetNode(i)->rGetLocation()[DIM - 1];
            counter_1++;
        }
        else
        {
            height_midpoint_2 += pElement->GetNode(i)->rGetLocation()[DIM -1];
            counter_2++;
        }
    }
    height_midpoint_1 /= (double)counter_1;
    height_midpoint_2 /= (double)counter_2;
 
    for (unsigned i=num_nodes; i>0; i--)
    {
        if (i-1 >= half_num_nodes)
        {
            if (height_midpoint_1 < height_midpoint_2)
            {
                if (placeOriginalElementBelow)
                {
                    pElement->DeleteNode(i-1);
                }
                else
                {
                    this->mElements[new_element_index]->DeleteNode(i-1);
                }
            }
            else
            {
                if (placeOriginalElementBelow)
                {
                    this->mElements[new_element_index]->DeleteNode(i-1);
                }
                else
                {
                    pElement->DeleteNode(i-1);
                }
            }
        }
        else // i-1 < half_num_nodes
        {
            if (height_midpoint_1 < height_midpoint_2)
            {
                if (placeOriginalElementBelow)
                {
                    this->mElements[new_element_index]->DeleteNode(i-1);
                }
                else
                {
                    pElement->DeleteNode(i-1);
                }
            }
            else
            {
                if (placeOriginalElementBelow)
                {
                    pElement->DeleteNode(i-1);
                }
                else
                {
                    this->mElements[new_element_index]->DeleteNode(i-1);
                }
            }
        }
    }
 
    return new_element_index;
}
 
template<unsigned DIM>
unsigned PottsMesh<DIM>::AddElement(PottsElement<DIM>* pNewElement)
{
    unsigned new_element_index = pNewElement->GetIndex();
 
    if (new_element_index == this->mElements.size())
    {
        this->mElements.push_back(pNewElement);
    }
    else
    {
        this->mElements[new_element_index] = pNewElement;
    }
    pNewElement->RegisterWithNodes();
    return pNewElement->GetIndex();
}
 
template<unsigned DIM>
std::set<unsigned> PottsMesh<DIM>::GetNeighbouringElementIndices(unsigned elementIndex)
{
    // Helper variables
    PottsElement<DIM>* p_element = this->GetElement(elementIndex);
    unsigned num_nodes = p_element->GetNumNodes();
 
    // Create a set of neighbouring element indices
    std::set<unsigned> neighbouring_element_indices;
 
    // Loop over nodes owned by this element
    for (unsigned local_index=0; local_index<num_nodes; local_index++)
    {
        // Get a pointer to this node
        Node<DIM>* p_node = p_element->GetNode(local_index);
 
        // Find the indices of the elements owned by neighbours of this node
 
        // Loop over neighbouring nodes. Only want Von Neuman neighbours (i.e N,S,E,W) as need to share an edge
        std::set<unsigned> neighbouring_node_indices = GetVonNeumannNeighbouringNodeIndices(p_node->GetIndex());
 
         // Iterate over these neighbouring nodes
         for (std::set<unsigned>::iterator neighbour_iter = neighbouring_node_indices.begin();
              neighbour_iter != neighbouring_node_indices.end();
              ++neighbour_iter)
         {
             std::set<unsigned> neighbouring_node_containing_elem_indices = this->GetNode(*neighbour_iter)->rGetContainingElementIndices();
 
             assert(neighbouring_node_containing_elem_indices.size()<2); // Either in element or in medium
 
             if (neighbouring_node_containing_elem_indices.size()==1) // Node is in an element
             {
                 // Add this element to the neighbouring elements set
                 neighbouring_element_indices.insert(*(neighbouring_node_containing_elem_indices.begin()));
             }
         }
    }
 
    // Lastly remove this element's index from the set of neighbouring element indices
    neighbouring_element_indices.erase(elementIndex);
 
    return neighbouring_element_indices;
}
 
template<unsigned DIM>
void PottsMesh<DIM>::ConstructFromMeshReader(AbstractMeshReader<DIM, DIM>& rMeshReader)
{
    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 i=0; i<num_nodes; i++)
    {
        node_data = rMeshReader.GetNextNode();
        unsigned is_boundary_node = (bool) node_data[DIM];
        node_data.pop_back();
        this->mNodes.push_back(new Node<DIM>(i, node_data, is_boundary_node));
    }
 
    rMeshReader.Reset();
 
    // Reserve memory for nodes
    mElements.reserve(rMeshReader.GetNumElements());
 
    // Add elements
    for (unsigned elem_index=0; elem_index<num_elements; elem_index++)
    {
        // Get the data for this element
        ElementData element_data = rMeshReader.GetNextElementData();
 
        // Get the nodes owned by this element
        std::vector<Node<DIM>*> 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
        PottsElement<DIM>* p_element = new PottsElement<DIM>(elem_index, nodes);
        mElements.push_back(p_element);
 
        if (rMeshReader.GetNumElementAttributes() > 0)
        {
            assert(rMeshReader.GetNumElementAttributes() == 1);
            double attribute_value = element_data.AttributeValue;
            p_element->SetAttribute(attribute_value);
        }
    }
 
    // If we are just using a mesh reader, then there is no neighbour information (see #1932)
    if (mVonNeumannNeighbouringNodeIndices.empty())
    {
        mVonNeumannNeighbouringNodeIndices.resize(num_nodes);
    }
    if (mMooreNeighbouringNodeIndices.empty())
    {
        mMooreNeighbouringNodeIndices.resize(num_nodes);
    }
}
 
// Explicit instantiation
template class PottsMesh<1>;
template class PottsMesh<2>;
template class PottsMesh<3>;
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(PottsMesh)