MySources/drmsimulationmodel.cpp

#include "drmsimulationmodel.hpp"
#include "linearsimulationmodel.hpp"
#include "simulationhistoryplotter.hpp"
#include <Eigen/Geometry>
#include <algorithm>
#include <chrono>
#include <execution>

#ifdef ENABLE_OPENMP
#include <omp.h>
#endif

void DRMSimulationModel::runUnitTests()
{
    const std::filesystem::path groundOfTruthFolder{
        "/home/iason/Coding/Libraries/MySources/formFinder_unitTestFiles"};

    DRMSimulationModel formFinder;

    // First example of the paper
    VCGEdgeMesh beam;
    //  const size_t spanGridSize = 11;
    //  mesh.createSpanGrid(spanGridSize);
    beam.load(std::filesystem::path(groundOfTruthFolder).append("simpleBeam.ply").string());
    std::unordered_map<VertexIndex, std::unordered_set<DoFType>> fixedVertices;
    fixedVertices[0] = std::unordered_set<DoFType>{0, 1, 2};
    fixedVertices[beam.VN() - 1] = std::unordered_set<DoFType>{1, 2};
    std::unordered_map<VertexIndex, Vector6d> nodalForces{
        {beam.VN() / 2, Vector6d({0, 1000, 1000, 0, 0, 0})}};
    // Forced displacements
    std::unordered_map<size_t, Eigen::Vector3d> nodalForcedDisplacements;
    nodalForcedDisplacements.insert({beam.VN() - 1, Eigen::Vector3d(-0.2, 0, 0)});

    SimulationJob beamSimulationJob{std::make_shared<SimulationMesh>(beam),
                                    "First paper example",
                                    //      SimulationJob::constructFixedVerticesSpanGrid(spanGridSize,
                                    //      mesh.VN()),
                                    fixedVertices,
                                    nodalForces,
                                    nodalForcedDisplacements};
    beamSimulationJob.pMesh->setBeamMaterial(0.3, 200 * 1e9);
    assert(CrossSectionType::name == CylindricalBeamDimensions::name);

    beamSimulationJob.pMesh->setBeamCrossSection(CrossSectionType{0.03, 0.026});
    Settings settings;
    settings.Dtini = 0.1;
    settings.xi = 0.9969;
    settings.maxDRMIterations = 0;
    formFinder.mSettings.totalResidualForcesNormThreshold = 1;
    settings.shouldDraw = false;
    settings.beVerbose = true;
    settings.shouldCreatePlots = true;
    SimulationResults simpleBeam_simulationResults
        = formFinder.executeSimulation(std::make_shared<SimulationJob>(beamSimulationJob), settings);
    simpleBeam_simulationResults.save();
    const std::string simpleBeamGroundOfTruthBinaryFilename
        = std::filesystem::path(groundOfTruthFolder)
              .append("SimpleBeam_displacements.eigenBin")
              .string();
    assert(std::filesystem::exists(std::filesystem::path(simpleBeamGroundOfTruthBinaryFilename)));
    Eigen::MatrixXd simpleBeam_groundOfTruthDisplacements;
    Eigen::read_binary(simpleBeamGroundOfTruthBinaryFilename, simpleBeam_groundOfTruthDisplacements);

    double error;
    if (!simpleBeam_simulationResults.isEqual(simpleBeam_groundOfTruthDisplacements, error)) {
        std::cerr << "Error:Beam simulation produces wrong results. Error:" << error << std::endl;
        //    return;
    }
#ifdef POLYSCOPE_DEFINED
    beam.registerForDrawing();
    simpleBeam_simulationResults.registerForDrawing();
    polyscope::show();
    beam.unregister();
    simpleBeam_simulationResults.unregister();
#endif

    // Second example of the paper
    VCGEdgeMesh shortSpanGrid;
    //  const size_t spanGridSize = 11;
    //  mesh.createSpanGrid(spanGridSize);
    shortSpanGrid.load(
        std::filesystem::path(groundOfTruthFolder).append("shortSpanGridshell.ply").string());

    fixedVertices.clear();
    //// Corner nodes
    fixedVertices[0] = std::unordered_set<DoFType>{2};
    fixedVertices[4] = std::unordered_set<DoFType>{2};
    fixedVertices[16] = std::unordered_set<DoFType>{2};
    fixedVertices[20] = std::unordered_set<DoFType>{2};
    //// Center node
    fixedVertices[10] = std::unordered_set<DoFType>{0, 1, 3, 4, 5};

    nodalForcedDisplacements.clear();
    nodalForcedDisplacements.insert({{0, Eigen::Vector3d(0.1, 0.1, 0)},
                                     {4, Eigen::Vector3d(-0.1, 0.1, 0)},
                                     {16, Eigen::Vector3d(0.1, -0.1, 0)},
                                     {20, Eigen::Vector3d(-0.1, -0.1, 0)}});

    SimulationJob shortSpanGridshellSimulationJob{std::make_shared<SimulationMesh>(shortSpanGrid),
                                                  "Short span gridshell",
                                                  fixedVertices,
                                                  {},
                                                  nodalForcedDisplacements};
    shortSpanGridshellSimulationJob.pMesh->setBeamMaterial(0.3, 200 * 1e9);
    assert(typeid(CrossSectionType) == typeid(CylindricalBeamDimensions));
    shortSpanGridshellSimulationJob.pMesh->setBeamCrossSection(CrossSectionType{0.03, 0.026});
    SimulationResults shortSpanGridshellSimulationResults
        = formFinder.executeSimulation(std::make_shared<SimulationJob>(
                                           shortSpanGridshellSimulationJob),
                                       settings);
    shortSpanGridshellSimulationResults.save();

    const std::string groundOfTruthBinaryFilename
        = std::filesystem::path(groundOfTruthFolder)
              .append("ShortSpanGridshell_displacements.eigenBin")
              .string();
    assert(std::filesystem::exists(std::filesystem::path(groundOfTruthBinaryFilename)));
    Eigen::MatrixXd shortSpanGridshell_groundOfTruthDisplacements;
    Eigen::read_binary(groundOfTruthBinaryFilename, shortSpanGridshell_groundOfTruthDisplacements);
    //  shortSpanGridshellSimulationResults.registerForDrawing(
    //      shortSpanGridshellSimulationJob);
    //  polyscope::show();
    assert(shortSpanGridshellSimulationResults.isEqual(shortSpanGridshell_groundOfTruthDisplacements,
                                                       error));
    if (!shortSpanGridshellSimulationResults.isEqual(shortSpanGridshell_groundOfTruthDisplacements,
                                                     error)) {
        std::cerr << "Error:Short span simulation produces wrong results. Error:" << error
                  << std::endl;
        //        return;
    }
#ifdef POLYSCOPE_DEFINED
    shortSpanGrid.registerForDrawing();
    shortSpanGridshellSimulationResults.registerForDrawing();
    polyscope::show();
    shortSpanGrid.unregister();
    shortSpanGridshellSimulationResults.unregister();
#endif

    // Third example of the paper
    VCGEdgeMesh longSpanGrid;
    longSpanGrid.load(
        std::filesystem::path(groundOfTruthFolder).append("longSpanGridshell.ply").string());
    const size_t spanGridSize = 11;

    fixedVertices.clear();
    for (size_t vi = 0; vi < spanGridSize - 1; vi++) {
        fixedVertices[vi] = {0, 2};
    }
    for (size_t vi = longSpanGrid.VN() - 1 - (spanGridSize - 2); vi < longSpanGrid.VN(); vi++) {
        fixedVertices[vi] = {0, 2};
    }
    for (size_t vi = spanGridSize - 1;
         vi < longSpanGrid.VN() - 1 - (spanGridSize - 2) - spanGridSize + 1;
         vi += spanGridSize + 1) {
        fixedVertices[vi] = {1, 2};
        fixedVertices[vi + spanGridSize] = {1, 2};
    }

    nodalForcedDisplacements.clear();
    const size_t horizontalOffset = std::floor((spanGridSize - 2) / 2);
    nodalForcedDisplacements.insert(
        {{horizontalOffset, Eigen::Vector3d(0, 0.3, 0)},
         {horizontalOffset + 1, Eigen::Vector3d(0, 0.3, 0)},
         {spanGridSize * (spanGridSize + 1) - 2 + horizontalOffset, Eigen::Vector3d(0, -0.3, 0)},
         {spanGridSize * (spanGridSize + 1) - 2 + horizontalOffset + 1, Eigen::Vector3d(0, -0.3, 0)},
         {std::floor(spanGridSize / 2) * (spanGridSize + 1) - 2, Eigen::Vector3d(0.3, 0, 0)},
         {(std::floor(spanGridSize / 2) + 1) * (spanGridSize + 1) - 2, Eigen::Vector3d(0.3, 0, 0)},
         {std::floor(spanGridSize / 2) * (spanGridSize + 1) - 2 + spanGridSize,
          Eigen::Vector3d(-0.3, 0, 0)},
         {(std::floor(spanGridSize / 2) + 1) * (spanGridSize + 1) - 2 + spanGridSize,
          Eigen::Vector3d(-0.3, 0, 0)}});

    SimulationJob longSpanGridshell_simulationJob{std::make_shared<SimulationMesh>(longSpanGrid),
                                                  "long span gridshell",
                                                  fixedVertices,
                                                  {},
                                                  nodalForcedDisplacements};
    longSpanGridshell_simulationJob.pMesh->setBeamMaterial(0.3, 200 * 1e9);
    if (typeid(CrossSectionType) != typeid(CylindricalBeamDimensions)) {
        std::cerr << "A cylindrical cross section is expected for running the "
                     "paper examples."
                  << std::endl;
    }
    longSpanGridshell_simulationJob.pMesh->setBeamCrossSection(CrossSectionType{0.03, 0.026});

    SimulationResults longSpanGridshell_simulationResults
        = formFinder.executeSimulation(std::make_shared<SimulationJob>(
                                           longSpanGridshell_simulationJob),
                                       settings);
    longSpanGridshell_simulationResults.save();

    const std::string longSpan_groundOfTruthBinaryFilename
        = std::filesystem::path(groundOfTruthFolder)
              .append("LongSpanGridshell_displacements.eigenBin")
              .string();
    assert(std::filesystem::exists(std::filesystem::path(longSpan_groundOfTruthBinaryFilename)));
    Eigen::MatrixXd longSpanGridshell_groundOfTruthDisplacements;
    Eigen::read_binary(longSpan_groundOfTruthBinaryFilename,
                       longSpanGridshell_groundOfTruthDisplacements);
    assert(longSpanGridshell_simulationResults.isEqual(longSpanGridshell_groundOfTruthDisplacements,
                                                       error));
    if (!longSpanGridshell_simulationResults.isEqual(longSpanGridshell_groundOfTruthDisplacements,
                                                     error)) {
        std::cerr << "Error:Long span simulation produces wrong results. Error:" << error
                  << std::endl;
        //        return;
    }
#ifdef POLYSCOPE_DEFINED
    longSpanGrid.registerForDrawing();
    longSpanGridshell_simulationResults.registerForDrawing();
    polyscope::show();
    longSpanGrid.unregister();
    longSpanGridshell_simulationResults.unregister();
#endif

    std::cout << "Form finder unit tests succesufully passed." << std::endl;

    //  polyscope::show();
}
void DRMSimulationModel::reset(const std::shared_ptr<SimulationJob> &pJob)
{
    //#ifdef USE_ENSMALLEN
    //    this->pJob = pJob;
    //#endif
    pMesh.reset();
    pMesh = std::make_unique<SimulationMesh>(*pJob->pMesh);
    vcg::tri::UpdateBounding<SimulationMesh>::Box(*pMesh);

    constrainedVertices.clear();
    constrainedVertices = pJob->constrainedVertices;
    if (!pJob->nodalForcedDisplacements.empty()) {
        for (std::pair<VertexIndex, Eigen::Vector3d> viDisplPair : pJob->nodalForcedDisplacements) {
            const VertexIndex vi = viDisplPair.first;
            constrainedVertices[vi].insert({0, 1, 2});
        }
    }
    computeRigidSupports();
    isVertexConstrained.resize(pMesh->VN(), false);
    for (auto fixedVertex : constrainedVertices) {
        isVertexConstrained[fixedVertex.first] = true;
    }
}

void DRMSimulationModel::reset(const std::shared_ptr<SimulationJob> &pJob, const Settings &settings)
{
    mSettings = settings;
    mCurrentSimulationStep = 0;
    history.clear();
    history.label = pJob->pMesh->getLabel() + "_" + pJob->getLabel();
    plotYValues.clear();
    plotHandle.reset();
    checkedForMaximumMoment = false;
    externalMomentsNorm = 0;
    Dt = settings.Dtini;
    numOfDampings = 0;
    shouldTemporarilyDampForces = false;
    externalLoadStep = 1;
    isVertexConstrained.clear();
    minTotalResidualForcesNorm = std::numeric_limits<double>::max();

    reset(pJob);

#ifdef POLYSCOPE_DEFINED
    if (mSettings.shouldDraw || mSettings.debugModeStep.has_value()) {
        PolyscopeInterface::init();
        polyscope::registerCurveNetwork(meshPolyscopeLabel,
                                        pMesh->getEigenVertices(),
                                        pMesh->getEigenEdges());
        polyscope::registerCurveNetwork("Initial_" + meshPolyscopeLabel,
                                        pMesh->getEigenVertices(),
                                        pMesh->getEigenEdges())
            ->setRadius(0.002);
        //    registerWorldAxes();
    }
#endif

    if (!pJob->nodalForcedDisplacements.empty() && pJob->nodalExternalForces.empty()) {
        shouldApplyInitialDistortion = true;
    }
    updateElementalFrames();
}

VectorType DRMSimulationModel::computeDisplacementDifferenceDerivative(
    const EdgeType &e, const DifferentiateWithRespectTo &dui) const
{
    VectorType displacementDiffDeriv(0, 0, 0);
    const DoFType &dofi = dui.dofi;
    const bool differentiateWithRespectToANonEdgeNode = e.cV(0) != &dui.v && e.cV(1) != &dui.v;
    if (differentiateWithRespectToANonEdgeNode || dofi > 2) {
        return displacementDiffDeriv;
    }

    if (e.cV(0) == &dui.v) {
        displacementDiffDeriv[dofi] = -1;
    } else if (e.cV(1) == &dui.v) {
        displacementDiffDeriv[dofi] = 1;
    }

    return displacementDiffDeriv;
}

VectorType DRMSimulationModel::computeDerivativeOfNormal(const VertexType &v,
                                                         const DifferentiateWithRespectTo &dui) const
{
    const size_t vi = pMesh->getIndex(v);
    VectorType normalDerivative(0, 0, 0);
    if (&dui.v != &v || (dui.dofi == 0 || dui.dofi == 1 || dui.dofi == 2 || dui.dofi == 5)) {
        return normalDerivative;
    }
    const VectorType &n = v.cN();
    const double &nx = n[0], ny = n[1];
    const double nxnyMagnitude = std::pow(nx, 2) + std::pow(ny, 2);

    if (dui.dofi == 3) {
        if (nxnyMagnitude + 1e-5 >= 1) {
            const double normalDerivativeX = 1 / sqrt(nxnyMagnitude)
                                             - std::pow(nx, 2) / std::pow(nxnyMagnitude, 1.5);
            const double normalDerivativeY = -nx * ny / std::pow(nxnyMagnitude, 1.5);
            const double normalDerivativeZ = 0;
            normalDerivative = VectorType(normalDerivativeX, normalDerivativeY, normalDerivativeZ);
        } else {
            const double normalDerivativeX = 1;
            const double normalDerivativeY = 0;
            const double normalDerivativeZ = -nx / std::sqrt(1 - nxnyMagnitude);
            normalDerivative = VectorType(normalDerivativeX, normalDerivativeY, normalDerivativeZ);
        }
    } else if (dui.dofi == 4) {
        if (nxnyMagnitude + 1e-5 >= 1) {
            const double normalDerivativeX = -nx * ny / std::pow(nxnyMagnitude, 1.5);
            const double normalDerivativeY = 1 / sqrt(nxnyMagnitude)
                                             - std::pow(ny, 2) / std::pow(nxnyMagnitude, 1.5);
            const double normalDerivativeZ = 0;
            normalDerivative = VectorType(normalDerivativeX, normalDerivativeY, normalDerivativeZ);
        } else {
            const double normalDerivativeX = 0;
            const double normalDerivativeY = 1;
            const double normalDerivativeZ = -ny / std::sqrt(1 - nxnyMagnitude);
            normalDerivative = VectorType(normalDerivativeX, normalDerivativeY, normalDerivativeZ);
        }
    }

    const bool normalDerivativeIsFinite = std::isfinite(normalDerivative[0])
                                          && std::isfinite(normalDerivative[1])
                                          && std::isfinite(normalDerivative[2]);
    assert(normalDerivativeIsFinite);
    const bool shouldBreak = mCurrentSimulationStep == 118 && vi == 1 && dui.dofi == 3;

    return normalDerivative;
}

double DRMSimulationModel::computeDerivativeElementLength(
    const EdgeType &e, const DifferentiateWithRespectTo &dui) const
{
    if (e.cV(0) != &dui.v && e.cV(1) != &dui.v) {
        return 0;
    }

    const VectorType &X_j = e.cP(0);
    const VectorType &X_jplus1 = e.cP(1);
    const VectorType positionVectorDiff = X_jplus1 - X_j;
    const VectorType displacementDiffDeriv = computeDisplacementDifferenceDerivative(e, dui);
    const double edgeLength = pMesh->elements[e].length;
    const double L_kDeriv = positionVectorDiff * displacementDiffDeriv / edgeLength;
    return L_kDeriv;
}

double DRMSimulationModel::computeDerivativeOfNorm(const VectorType &x,
                                                   const VectorType &derivativeOfX)
{
    return x.dot(derivativeOfX) / x.Norm();
}

VectorType DRMSimulationModel::computeDerivativeOfCrossProduct(const VectorType &a,
                                                               const VectorType &derivativeOfA,
                                                               const VectorType &b,
                                                               const VectorType &derivativeOfB)
{
    const auto firstTerm = Cross(derivativeOfA, b);
    const auto secondTerm = Cross(a, derivativeOfB);
    return firstTerm + secondTerm;
}

VectorType DRMSimulationModel::computeDerivativeOfR(const EdgeType &e,
                                                    const DifferentiateWithRespectTo &dui) const
{
    const VertexType &v_j = *e.cV(0);
    const VertexType &v_jplus1 = *e.cV(1);
    const VectorType normal_j = v_j.cN();
    const VectorType normal_jplus1 = v_jplus1.cN();
    const VectorType derivativeOfNormal_j = &v_j == &dui.v && dui.dofi > 2
                                                ? pMesh->nodes[v_j].derivativeOfNormal[dui.dofi]
                                                : VectorType(0, 0, 0);
    const VectorType derivativeOfNormal_jplus1
        = &v_jplus1 == &dui.v && dui.dofi > 2 ? pMesh->nodes[v_jplus1].derivativeOfNormal[dui.dofi]
                                              : VectorType(0, 0, 0);

    const VectorType derivativeOfSumOfNormals = derivativeOfNormal_j + derivativeOfNormal_jplus1;
    const VectorType sumOfNormals = normal_j + normal_jplus1;
    const double normOfSumOfNormals = sumOfNormals.Norm();
    assert(normOfSumOfNormals != 0);
    const double derivativeOfNormOfSumOfNormals = computeDerivativeOfNorm(sumOfNormals,
                                                                          derivativeOfSumOfNormals);

    const VectorType derivativeOfR_firstTerm = -sumOfNormals * derivativeOfNormOfSumOfNormals
                                               / std::pow(normOfSumOfNormals, 2);
    const VectorType derivativeOfR_secondTerm = derivativeOfSumOfNormals / normOfSumOfNormals;
    const VectorType derivativeOfR = derivativeOfR_firstTerm + derivativeOfR_secondTerm;

    assert(std::isfinite(derivativeOfR[0]) && std::isfinite(derivativeOfR[1])
           && std::isfinite(derivativeOfR[2]));

    return derivativeOfR;
}

VectorType DRMSimulationModel::computeDerivativeT1(const EdgeType &e,
                                                   const DifferentiateWithRespectTo &dui) const
{
    const VectorType &X_j = e.cP(0);
    const VectorType &X_jplus1 = e.cP(1);
    const VectorType edgeVector = X_jplus1 - X_j;
    const double L_kDerivative = computeDerivativeElementLength(e, dui);
    const double edgeLength = pMesh->elements[e].length;
    const VectorType firstTerm = -edgeVector * L_kDerivative / std::pow(edgeLength, 2);
    const VectorType secondTerm = computeDisplacementDifferenceDerivative(e, dui) / edgeLength;
    const VectorType t1Derivative = firstTerm + secondTerm;

    return t1Derivative;
}

VectorType DRMSimulationModel::computeDerivativeT2(const EdgeType &e,
                                                   const DifferentiateWithRespectTo &dui) const
{
    const DoFType dofi = dui.dofi;

    const VertexType &v_j = *e.cV(0);
    const size_t vi_j = pMesh->getIndex(v_j);
    const VertexType &v_jplus1 = *e.cV(1);
    const size_t vi_jplus1 = pMesh->getIndex(v_jplus1);

    const VectorType r = (v_j.cN() + v_jplus1.cN()).Normalize();
    const VectorType derivativeR_j = dofi > 2 && &v_j == &dui.v
                                         ? pMesh->elements[e].derivativeR_j[dui.dofi]
                                         : VectorType(0, 0, 0);
    const VectorType derivativeR_jplus1 = dofi > 2 && &v_jplus1 == &dui.v
                                              ? pMesh->elements[e].derivativeR_jplus1[dui.dofi]
                                              : VectorType(0, 0, 0);
    const VectorType derivativeR = derivativeR_j + derivativeR_jplus1;

    const VectorType &t1 = pMesh->elements[e].frame.t1;
    const VectorType derivativeT1_j = dofi < 3 && &v_j == &dui.v
                                          ? pMesh->elements[e].derivativeT1_j[dui.dofi]
                                          : VectorType(0, 0, 0);
    const VectorType derivativeT1_jplus1 = dofi < 3 && &v_jplus1 == &dui.v
                                               ? pMesh->elements[e].derivativeT1_jplus1[dui.dofi]
                                               : VectorType(0, 0, 0);
    const VectorType derivativeT1 = derivativeT1_j + derivativeT1_jplus1;

    const VectorType derivativeOfRCrossT1 = computeDerivativeOfCrossProduct(r,
                                                                            derivativeR,
                                                                            t1,
                                                                            derivativeT1);
    const VectorType rCrossT1 = Cross(r, t1);
    const double normOfRCrossT1 = rCrossT1.Norm();
    const double derivativeNormRCrossT1 = computeDerivativeOfNorm(rCrossT1, derivativeOfRCrossT1);

    const VectorType t2Deriv_firstTerm = -(rCrossT1 * derivativeNormRCrossT1)
                                         / std::pow(normOfRCrossT1, 2);
    const VectorType t2Deriv_secondTerm = derivativeOfRCrossT1 / normOfRCrossT1;
    const VectorType t2Deriv = t2Deriv_firstTerm + t2Deriv_secondTerm;

    const double t2DerivNorm = t2Deriv.Norm();
    assert(std::isfinite(t2DerivNorm));
    const bool shouldBreak = mCurrentSimulationStep == 118 && (vi_jplus1 == 1 || vi_j == 1)
                             && dofi == 3;
    return t2Deriv;
}

VectorType DRMSimulationModel::computeDerivativeT3(const EdgeType &e,
                                                   const DifferentiateWithRespectTo &dui) const
{
    const Element &element = pMesh->elements[e];
    const VectorType &t1 = element.frame.t1;
    const VectorType &t2 = element.frame.t2;
    const VectorType t1CrossT2 = Cross(t1, t2);
    const VertexType &v_j = *e.cV(0);
    const size_t vi_j = pMesh->getIndex(v_j);
    const VertexType &v_jplus1 = *e.cV(1);
    const size_t vi_jplus1 = pMesh->getIndex(v_jplus1);
    const VectorType derivativeT1_j = dui.dofi < 3 && &v_j == &dui.v
                                          ? pMesh->elements[e].derivativeT1_j[dui.dofi]
                                          : VectorType(0, 0, 0);
    const VectorType derivativeT1_jplus1 = dui.dofi < 3 && &v_jplus1 == &dui.v
                                               ? pMesh->elements[e].derivativeT1_jplus1[dui.dofi]
                                               : VectorType(0, 0, 0);
    const VectorType derivativeT1 = derivativeT1_j + derivativeT1_jplus1;

    //  const VectorType derivativeOfT2 = computeDerivativeT2(e, dui);
    //  const VectorType derivativeT2_j =
    //      &v_j == &dui.v
    //          ? mesh->elements[e].derivativeT2_j[dui.dofi]
    //          : VectorType(0, 0, 0);
    //  const VectorType derivativeT2_jplus1 =
    //       &v_jplus1 == &dui.v
    //          ? mesh->elements[e].derivativeT2_jplus1[dui.dofi]
    //          : VectorType(0, 0, 0);
    VectorType derivativeT2(0, 0, 0);
    if (&v_j == &dui.v) {
        derivativeT2 = pMesh->elements[e].derivativeT2_j[dui.dofi];
    } else if (&v_jplus1 == &dui.v) {
        derivativeT2 = pMesh->elements[e].derivativeT2_jplus1[dui.dofi];
    }

    const VectorType derivativeT1CrossT2 = computeDerivativeOfCrossProduct(t1,
                                                                           derivativeT1,
                                                                           t2,
                                                                           derivativeT2);
    const double derivativeOfNormT1CrossT2 = computeDerivativeOfNorm(t1CrossT2, derivativeT1CrossT2);
    const double normT1CrossT2 = t1CrossT2.Norm();

    const VectorType t3Deriv_firstTerm = -(t1CrossT2 * derivativeOfNormT1CrossT2)
                                         / std::pow(normT1CrossT2, 2);
    const VectorType t3Deriv_secondTerm = derivativeT1CrossT2 / normT1CrossT2;
    const VectorType t3Deriv = t3Deriv_firstTerm + t3Deriv_secondTerm;

    assert(std::isfinite(t3Deriv[0]) && std::isfinite(t3Deriv[1]) && std::isfinite(t3Deriv[2]));
    return t3Deriv;
}

double DRMSimulationModel::computeDerivativeTheta1(const EdgeType &e,
                                                   const VertexIndex &evi,
                                                   const VertexIndex &dwrt_evi,
                                                   const DoFType &dwrt_dofi) const
{
    const VertexType &v = *e.cV(evi);
    const size_t vi = pMesh->getIndex(v);
    const Element &element = pMesh->elements[e];
    const VectorType derivativeT1 = element.derivativeT1[dwrt_evi][dwrt_dofi];
    const VectorType derivativeT3 = element.derivativeT3[dwrt_evi][dwrt_dofi];
    const VectorType nDerivative = evi != dwrt_evi ? VectorType(0, 0, 0)
                                                   : pMesh->nodes[v].derivativeOfNormal[dwrt_dofi];
    const VectorType n = v.cN();
    const VectorType &t1 = element.frame.t1;
    const VectorType &t3 = element.frame.t3;
    const double theta1Derivative = derivativeT1 * Cross(t3, n)
                                    + t1 * (Cross(derivativeT3, n) + Cross(t3, nDerivative));
    const bool shouldBreak = mCurrentSimulationStep == 118 && vi == 1 && dwrt_dofi == 3;

    return theta1Derivative;
}

double DRMSimulationModel::computeDerivativeTheta2(const EdgeType &e,
                                                   const VertexIndex &evi,
                                                   const VertexIndex &dwrt_evi,
                                                   const DoFType &dwrt_dofi) const
{
    const VertexType &v = *e.cV(evi);

    const Element &element = pMesh->elements[e];
    const VectorType derivativeT2 = element.derivativeT2[dwrt_evi][dwrt_dofi];
    const VectorType derivativeT3 = element.derivativeT3[dwrt_evi][dwrt_dofi];

    const VectorType n = v.cN();
    const VectorType &t2 = element.frame.t2;
    const VectorType &t3 = element.frame.t3;
    const VectorType nDerivative = dwrt_evi == evi ? pMesh->nodes[v].derivativeOfNormal[dwrt_dofi]
                                                   : VectorType(0, 0, 0);
    const double theta2Derivative = derivativeT2 * Cross(t3, n)
                                    + t2 * (Cross(derivativeT3, n) + Cross(t3, nDerivative));

    return theta2Derivative;
}

double DRMSimulationModel::computeTheta3(const EdgeType &e, const VertexType &v)
{
    const VertexIndex &vi = pMesh->nodes[v].vi;
    //  assert(e.cV(0) == &v || e.cV(1) == &v);

    const Element &elem = pMesh->elements[e];
    const EdgeIndex &ei = elem.ei;
    const Element::LocalFrame &ef = elem.frame;
    const VectorType &t1 = ef.t1;
    const VectorType &n = v.cN();
    const Node &node = pMesh->nodes[v];
    const double &nR = node.nR; // TODO: This makes the function non-const.
                                // Should be refactored in the future

    double theta3;
    const bool shouldBreak = mCurrentSimulationStep == 12970;
    if (&e == node.referenceElement) {
        // Use nR as theta3 only for the first star edge
        return nR;
    }
    //    std::vector<int> incidentElementsIndices(node.incidentElements.size());
    //    for (int iei = 0; iei < incidentElementsIndices.size(); iei++) {
    //        incidentElementsIndices[iei] = pMesh->getIndex(node.incidentElements[iei]);
    //    }
    assert(pMesh->getIndex(e) == ei);
    //    assert(node.alphaAngles.contains(ei));
    const double alphaAngle = std::find_if(node.alphaAngles.begin(),
                                           node.alphaAngles.end(),
                                           [&](const std::pair<EdgeIndex, double> &p) {
                                               return elem.ei == p.first;
                                           })
                                  ->second;
    const EdgeType &refElem = *node.referenceElement;
    const double rotationAngle = nR + alphaAngle;

    //    const VectorType &t1_k = computeT1Vector(refElem);
    const VectorType &t1_k = pMesh->elements[refElem].frame.t1;
    const VectorType f1 = (t1_k - (n * (t1_k * n))).Normalize();
    vcg::Matrix44<double> rotationMatrix;
    rotationMatrix.SetRotateRad(rotationAngle, n);
    const double cosRotationAngle = cos(rotationAngle);
    const double sinRotationAngle = sin(rotationAngle);
    const VectorType f2 = (f1 * cosRotationAngle + Cross(n, f1) * sinRotationAngle).Normalize();
    const VectorType &t1Current = t1;
    const VectorType f3 = Cross(t1Current, f2);

    Element &element = pMesh->elements[e];
    // Save for computing theta3Derivative
    if (&v == e.cV(0)) {
        element.f1_j = f1;
        element.f2_j = f2;
        element.f3_j = f3;
        element.cosRotationAngle_j = cosRotationAngle;
        element.sinRotationAngle_j = sinRotationAngle;
    } else {
        element.f1_jplus1 = f1;
        element.f2_jplus1 = f2;
        element.f3_jplus1 = f3;
        element.cosRotationAngle_jplus1 = cosRotationAngle;
        element.sinRotationAngle_jplus1 = sinRotationAngle;
    }
    theta3 = f3.dot(n);

    return theta3;
}

double DRMSimulationModel::computeDerivativeTheta3(const EdgeType &e,
                                                   const VertexType &v,
                                                   const DifferentiateWithRespectTo &dui) const
{
    const Node &node = pMesh->nodes[v];
    const VertexIndex &vi = pMesh->nodes[v].vi;
    if (&e == node.referenceElement && !isRigidSupport[vi]) {
        if (dui.dofi == DoF::Nr && &dui.v == &v) {
            return 1;
        } else {
            return 0;
        }
    }
    //  assert(e.cV(0) == &v || e.cV(1) == &v);

    const Element &element = pMesh->elements[e];
    const Element::LocalFrame &ef = element.frame;
    const VectorType &t1 = ef.t1;
    const VectorType &n = v.cN();
    const DoFType &dofi = dui.dofi;
    const VertexPointer &vp_j = e.cV(0);
    const VertexPointer &vp_jplus1 = e.cV(1);

    double derivativeTheta3_dofi = 0;
    if (isRigidSupport[vi]) {
        const VectorType &t1Initial = computeT1Vector(pMesh->nodes[vp_j].initialLocation,
                                                      pMesh->nodes[vp_jplus1].initialLocation);
        VectorType g1 = Cross(t1, t1Initial);

        const VectorType derivativeInitialT1_dofi(0, 0, 0);
        const VectorType derivativeT1_j = dui.dofi < 3 && vp_j == &dui.v
                                              ? element.derivativeT1_j[dui.dofi]
                                              : VectorType(0, 0, 0);
        const VectorType derivativeT1_jplus1 = dui.dofi < 3 && vp_jplus1 == &dui.v
                                                   ? element.derivativeT1_jplus1[dui.dofi]
                                                   : VectorType(0, 0, 0);
        const VectorType derivativeT1_dofi = derivativeT1_j + derivativeT1_jplus1;
        //    VectorType derivativeT1_dofi(0, 0, 0);
        //    if (dui.dofi < 3) {
        //      if (&v_j == &dui.v) {
        //        derivativeT1_dofi = mesh->elements[e].derivativeT1_j[dui.dofi];
        //      } else if (&v_jplus1 == &dui.v) {
        //        derivativeT1_dofi =
        //        mesh->elements[e].derivativeT1_jplus1[dui.dofi];
        //      }
        //    }

        const VectorType derivativeG1_firstTerm = Cross(derivativeT1_dofi, t1Initial);
        const VectorType derivativeG1_secondTerm = Cross(t1, derivativeInitialT1_dofi);
        const VectorType derivativeG1 = derivativeG1_firstTerm + derivativeG1_secondTerm;
        const VectorType derivativeNormal = &v == &dui.v && dui.dofi > 2
                                                ? node.derivativeOfNormal[dui.dofi]
                                                : VectorType(0, 0, 0);
        derivativeTheta3_dofi = derivativeG1 * n + g1 * derivativeNormal;
        if (std::isnan(derivativeTheta3_dofi)) {
            std::cerr << "nan derivative theta3 rigid" << std::endl;
        }
        return derivativeTheta3_dofi;
    }
    EdgeType &refElem = *node.referenceElement;
    const VectorType &t1_k = pMesh->elements[refElem].frame.t1;
    VectorType f1, f2, f3;
    double cosRotationAngle, sinRotationAngle;
    if (e.cV(0) == &v) {
        f1 = element.f1_j;
        cosRotationAngle = element.cosRotationAngle_j;
        sinRotationAngle = element.sinRotationAngle_j;
        f2 = element.f2_j;
        f3 = element.f3_j;
    } else {
        f1 = element.f1_jplus1;
        cosRotationAngle = element.cosRotationAngle_jplus1;
        sinRotationAngle = element.sinRotationAngle_jplus1;
        f2 = element.f2_jplus1;
        f3 = element.f3_jplus1;
    }
    const VectorType &t1_kplus1 = t1;
    const VectorType f1Normalized = f1 / f1.Norm();

    VectorType derivativeF1(0, 0, 0);
    VectorType derivativeF2(0, 0, 0);
    VectorType derivativeF3(0, 0, 0);
    if (dui.dofi < 3) {
        const VectorType derivativeT1_kplus1_j = vp_j == &dui.v ? element.derivativeT1_j[dui.dofi]
                                                                : VectorType(0, 0, 0);
        const VectorType derivativeT1_kplus1_jplus1 = vp_jplus1 == &dui.v
                                                          ? element.derivativeT1_jplus1[dui.dofi]
                                                          : VectorType(0, 0, 0);
        const VectorType derivativeT1_kplus1 = derivativeT1_kplus1_j + derivativeT1_kplus1_jplus1;

        const VectorType derivativeT1_k_j = refElem.cV(0) == &dui.v
                                                ? pMesh->elements[refElem].derivativeT1_j[dui.dofi]
                                                : VectorType(0, 0, 0);
        const VectorType derivativeT1_k_jplus1
            = refElem.cV(1) == &dui.v ? pMesh->elements[refElem].derivativeT1_jplus1[dui.dofi]
                                      : VectorType(0, 0, 0);
        const VectorType derivativeT1_k = derivativeT1_k_j + derivativeT1_k_jplus1;

        derivativeF1 = derivativeT1_k - (n * (derivativeT1_k * n));

        const double f1Norm = f1.Norm();
        const double derivativeF1Norm = f1 * derivativeF1 / f1Norm;
        const VectorType derivativeF1Normalized = -f1 * derivativeF1Norm / (f1Norm * f1Norm)
                                                  + derivativeF1 / f1Norm;

        derivativeF2 = derivativeF1Normalized * cosRotationAngle
                       + Cross(n, derivativeF1Normalized) * sinRotationAngle;
        const VectorType derivativeF3_firstTerm = Cross(derivativeT1_kplus1, f2);
        const VectorType derivativeF3_secondTerm = Cross(t1_kplus1, derivativeF2);
        derivativeF3 = derivativeF3_firstTerm + derivativeF3_secondTerm;
        derivativeTheta3_dofi = derivativeF3 * n;

    } else if (dui.dofi == DoF::Nr && &dui.v == &v) {
        derivativeF2 = f1Normalized * (-sinRotationAngle)
                       + Cross(n, f1Normalized) * cosRotationAngle;
        derivativeF3 = Cross(t1_kplus1, derivativeF2);
        derivativeTheta3_dofi = derivativeF3 * n;
    } else { // 2<dofi<5
        if (&v == &dui.v) {
            const VectorType &derivativeOfNormal = node.derivativeOfNormal[dofi];
            derivativeF1 = -(n * (t1_k * derivativeOfNormal) + derivativeOfNormal * (t1_k * n));
            const double f1Norm = f1.Norm();
            const double derivativeF1Norm = f1 * derivativeF1 / f1Norm;
            const VectorType derivativeF1Normalized = -f1 * derivativeF1Norm / (f1Norm * f1Norm)
                                                      + derivativeF1 / f1Norm;

            derivativeF2 = derivativeF1Normalized * cosRotationAngle +

                           (Cross(derivativeOfNormal, f1Normalized)
                            + Cross(n, derivativeF1Normalized))
                               * sinRotationAngle;
            derivativeF3 = Cross(t1_kplus1, derivativeF2);
            derivativeTheta3_dofi = derivativeF3 * n + f3 * derivativeOfNormal;
        }
    }
    if (std::isnan(derivativeTheta3_dofi)) {
        std::cerr << "nan derivative theta3" << std::endl;
    }
    return derivativeTheta3_dofi;
}

double DRMSimulationModel::computeTotalInternalPotentialEnergy()
{
    double totalInternalPotentialEnergy = 0;
    for (const SimulationMesh::EdgeType &e : pMesh->edge) {
        const Element &element = pMesh->elements[e];
        const SimulationMesh::VertexType &ev_j = *e.cV(0);
        const SimulationMesh::VertexType &ev_jplus1 = *e.cV(1);
        const Element::LocalFrame &ef = element.frame;
        const VectorType t3CrossN_j = Cross(ef.t3, ev_j.cN());
        const VectorType t3CrossN_jplus1 = Cross(ef.t3, ev_jplus1.cN());
        const double theta1_j = ef.t1.dot(t3CrossN_j);
        const double theta1_jplus1 = ef.t1.dot(t3CrossN_jplus1);
        const double theta2_j = ef.t2.dot(t3CrossN_j);
        const double theta2_jplus1 = ef.t2.dot(t3CrossN_jplus1);
        const double theta3_j = computeTheta3(e, ev_j);
        const double theta3_jplus1 = computeTheta3(e, ev_jplus1);

        const EdgeIndex ei = pMesh->getIndex(e);
        const double e_k = element.length - element.initialLength;
        const double axialPE = pow(e_k, 2) * element.material.youngsModulus * element.dimensions.A
                               / (2 * element.initialLength);
        const double theta1Diff = theta1_jplus1 - theta1_j;
        const double torsionalPE = element.material.G * element.dimensions.inertia.J
                                   * pow(theta1Diff, 2) / (2 * element.initialLength);
        const double firstBendingPE_inBracketsTerm = 4 * pow(theta2_j, 2)
                                                     + 4 * theta2_j * theta2_jplus1
                                                     + 4 * pow(theta2_jplus1, 2);
        const double firstBendingPE = firstBendingPE_inBracketsTerm * element.material.youngsModulus
                                      * element.dimensions.inertia.I2 / (2 * element.initialLength);
        const double secondBendingPE_inBracketsTerm = 4 * pow(theta3_j, 2)
                                                      + 4 * theta3_j * theta3_jplus1
                                                      + 4 * pow(theta3_jplus1, 2);
        const double secondBendingPE = secondBendingPE_inBracketsTerm
                                       * element.material.youngsModulus * element.dimensions.inertia.I3
                                       / (2 * element.initialLength);

        totalInternalPotentialEnergy += axialPE + torsionalPE + firstBendingPE + secondBendingPE;
        int i = 0;
        i++;
    }

    return totalInternalPotentialEnergy;
}

double DRMSimulationModel::computeTotalPotentialEnergy()
{
    double totalExternalPotentialEnergy = 0;
    for (const SimulationMesh::VertexType &v : pMesh->vert) {
        const Node &node = pMesh->nodes[v];
        if (!node.force.hasExternalForce()) {
            continue;
        }
        const auto nodeDisplacement = v.cP() - node.initialLocation;
        const SimulationMesh::CoordType externalForce(node.force.external[0],
                                                      node.force.external[1],
                                                      node.force.external[2]);
        totalExternalPotentialEnergy += externalForce.dot(nodeDisplacement);
    }

    const double totalInternalPotentialEnergy = computeTotalInternalPotentialEnergy();

    return totalInternalPotentialEnergy - totalExternalPotentialEnergy;
}

void DRMSimulationModel::updateResidualForcesOnTheFly(
    const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    //  std::vector<Vector6d> internalForcesParallel(mesh->vert.size());

    std::vector<std::vector<std::pair<int, Vector6d>>> internalForcesContributionsFromEachEdge(
        pMesh->EN(), std::vector<std::pair<int, Vector6d>>(4, {-1, Vector6d()}));
    //  omp_lock_t writelock;
    //  omp_init_lock(&writelock);
    //#ifdef ENABLE_OPENMP
    //#pragma omp parallel for schedule(static) num_threads(5)
    //#endif
    std::for_each(
#ifdef ENABLE_PARALLEL_DRM
        std::execution::par_unseq,
#endif
        pMesh->edge.begin(),
        pMesh->edge.end(),
        [&](const EdgeType &e)
        //    for (int ei = 0; ei < pMesh->EN(); ei++)
        {
            const int ei = pMesh->getIndex(e);
            //        const EdgeType &e = pMesh->edge[ei];
            const SimulationMesh::VertexType &ev_j = *e.cV(0);
            const SimulationMesh::VertexType &ev_jplus1 = *e.cV(1);
            const Element &element = pMesh->elements[e];
            const Element::LocalFrame &ef = element.frame;
            const VectorType t3CrossN_j = Cross(ef.t3, ev_j.cN());
            const VectorType t3CrossN_jplus1 = Cross(ef.t3, ev_jplus1.cN());
            const double theta1_j = ef.t1.dot(t3CrossN_j);
            const double theta1_jplus1 = ef.t1.dot(t3CrossN_jplus1);
            const double theta2_j = ef.t2.dot(t3CrossN_j);
            const double theta2_jplus1 = ef.t2.dot(t3CrossN_jplus1);
            const double theta3_j = computeTheta3(e, ev_j);
            const double theta3_jplus1 = computeTheta3(e, ev_jplus1);
            //    element.rotationalDisplacements_j.theta1 = theta1_j;
            //    element.rotationalDisplacements_jplus1.theta1 = theta1_jplus1;
            //    element.rotationalDisplacements_j.theta2 = theta2_j;
            //    element.rotationalDisplacements_jplus1.theta2 = theta2_jplus1;
            //    element.rotationalDisplacements_j.theta3 = theta3_j;
            //    element.rotationalDisplacements_jplus1.theta3 = theta3_jplus1;
            std::vector<std::pair<int, Vector6d>>
                internalForcesContributionFromThisEdge(4, {-1, Vector6d()});
            for (VertexIndex evi = 0; evi < 2; evi++) {
                const SimulationMesh::VertexType &ev = *e.cV(evi);
                const Node &edgeNode = pMesh->nodes[ev];
                internalForcesContributionFromThisEdge[evi].first = edgeNode.vi;

                const VertexPointer &rev_j = edgeNode.referenceElement->cV(0);
                const VertexPointer &rev_jplus1 = edgeNode.referenceElement->cV(1);
                // refElemOtherVertex can be precomputed
                const VertexPointer &refElemOtherVertex = rev_j == &ev ? rev_jplus1 : rev_j;
                const Node &refElemOtherVertexNode = pMesh->nodes[refElemOtherVertex];
                if (edgeNode.referenceElement != &e) {
                    internalForcesContributionFromThisEdge[evi + 2].first = refElemOtherVertexNode.vi;
                }
                const size_t vi = edgeNode.vi;
                //      #pragma omp parallel for schedule(static) num_threads(6)
                for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
                    const bool isDofConstrainedFor_ev = isVertexConstrained[edgeNode.vi]
                                                        && fixedVertices.at(edgeNode.vi)
                                                               .contains(dofi);
                    if (!isDofConstrainedFor_ev) {
                        DifferentiateWithRespectTo dui{ev, dofi};
                        // Axial force computation
                        const double e_k = element.length - element.initialLength;
                        const double e_kDeriv = computeDerivativeElementLength(e, dui);
                        const double axialForce_dofi = e_kDeriv * e_k * element.rigidity.axial;

#ifdef POLYSCOPE_DEFINED
                        if (std::isnan(axialForce_dofi)) {
                            std::cerr << "nan in axial" << evi << std::endl;
                        }
#endif

                        // Torsional force computation
                        const double theta1_j_deriv = computeDerivativeTheta1(e, 0, evi, dofi);
                        const double theta1_jplus1_deriv = computeDerivativeTheta1(e, 1, evi, dofi);
                        const double theta1Diff = theta1_jplus1 - theta1_j;
                        const double theta1DiffDerivative = theta1_jplus1_deriv - theta1_j_deriv;
                        const double torsionalForce_dofi = theta1DiffDerivative * theta1Diff
                                                           * element.rigidity.torsional;
#ifdef POLYSCOPE_DEFINED
                        if (std::isnan(torsionalForce_dofi)) {
                            std::cerr << "nan in torsional" << evi << std::endl;
                        }
#endif

                        // First bending force computation
                        ////theta2_j derivative
                        const double theta2_j_deriv = computeDerivativeTheta2(e, 0, evi, dofi);
                        ////theta2_jplus1 derivative
                        const double theta2_jplus1_deriv = computeDerivativeTheta2(e, 1, evi, dofi);
                        ////1st in bracket term
                        const double firstBendingForce_inBracketsTerm_0 = theta2_j_deriv * 2
                                                                          * theta2_j;
                        ////2nd in bracket term
                        const double firstBendingForce_inBracketsTerm_1 = theta2_jplus1_deriv
                                                                          * theta2_j;
                        ////3rd in bracket term
                        const double firstBendingForce_inBracketsTerm_2 = theta2_j_deriv
                                                                          * theta2_jplus1;
                        ////4th in bracket term
                        const double firstBendingForce_inBracketsTerm_3 = 2 * theta2_jplus1_deriv
                                                                          * theta2_jplus1;
                        // 3rd term computation
                        const double firstBendingForce_inBracketsTerm
                            = firstBendingForce_inBracketsTerm_0
                              + firstBendingForce_inBracketsTerm_1
                              + firstBendingForce_inBracketsTerm_2
                              + firstBendingForce_inBracketsTerm_3;
                        const double firstBendingForce_dofi = firstBendingForce_inBracketsTerm
                                                              * element.rigidity.firstBending;

                        // Second bending force computation
                        ////theta2_j derivative
                        const double theta3_j_deriv = computeDerivativeTheta3(e, ev_j, dui);
                        ////theta2_jplus1 derivative
                        const double theta3_jplus1_deriv = computeDerivativeTheta3(e,
                                                                                   ev_jplus1,
                                                                                   dui);
                        ////1st in bracket term
                        const double secondBendingForce_inBracketsTerm_0 = theta3_j_deriv * 2
                                                                           * theta3_j;
                        ////2nd in bracket term
                        const double secondBendingForce_inBracketsTerm_1 = theta3_jplus1_deriv
                                                                           * theta3_j;
                        ////3rd in bracket term
                        const double secondBendingForce_inBracketsTerm_2 = theta3_j_deriv
                                                                           * theta3_jplus1;
                        ////4th in bracket term
                        const double secondBendingForce_inBracketsTerm_3 = theta3_jplus1_deriv * 2
                                                                           * theta3_jplus1;
                        // 3rd term computation
                        const double secondBendingForce_inBracketsTerm
                            = secondBendingForce_inBracketsTerm_0
                              + secondBendingForce_inBracketsTerm_1
                              + secondBendingForce_inBracketsTerm_2
                              + secondBendingForce_inBracketsTerm_3;
                        double secondBendingForce_dofi = secondBendingForce_inBracketsTerm
                                                         * element.rigidity.secondBending;
                        internalForcesContributionFromThisEdge[evi].second[dofi]
                            = axialForce_dofi + firstBendingForce_dofi + secondBendingForce_dofi
                              + torsionalForce_dofi;
                    }
                    if (edgeNode.referenceElement != &e) {
                        const bool isDofConstrainedFor_refElemOtherVertex
                            = isVertexConstrained[refElemOtherVertexNode.vi]
                              && fixedVertices.at(refElemOtherVertexNode.vi).contains(dofi);
                        if (!isDofConstrainedFor_refElemOtherVertex) {
                            DifferentiateWithRespectTo dui{*refElemOtherVertex, dofi};
                            ////theta3_j derivative
                            const double theta3_j_deriv = computeDerivativeTheta3(e, ev_j, dui);
                            ////theta3_jplus1 derivative
                            const double theta3_jplus1_deriv = computeDerivativeTheta3(e,
                                                                                       ev_jplus1,
                                                                                       dui);
                            ////1st in bracket term
                            const double secondBendingForce_inBracketsTerm_0 = theta3_j_deriv * 2
                                                                               * theta3_j;
                            ////2nd in bracket term
                            const double secondBendingForce_inBracketsTerm_1 = theta3_jplus1_deriv
                                                                               * theta3_j;
                            ////3rd in bracket term
                            const double secondBendingForce_inBracketsTerm_2 = theta3_j_deriv
                                                                               * theta3_jplus1;
                            ////4th in bracket term
                            const double secondBendingForce_inBracketsTerm_3 = theta3_jplus1_deriv
                                                                               * 2 * theta3_jplus1;

                            // 4th term computation
                            const double secondBendingForce_inBracketsTerm
                                = secondBendingForce_inBracketsTerm_0
                                  + secondBendingForce_inBracketsTerm_1
                                  + secondBendingForce_inBracketsTerm_2
                                  + secondBendingForce_inBracketsTerm_3;
                            const double secondBendingForce_dofi = secondBendingForce_inBracketsTerm
                                                                   * element.rigidity.secondBending;
                            internalForcesContributionFromThisEdge[evi + 2].second[dofi]
                                = secondBendingForce_dofi;
                        }
                    }
                }
            }
            internalForcesContributionsFromEachEdge[ei] = internalForcesContributionFromThisEdge;
        });

    //#pragma omp parallel for schedule(static) num_threads(8)

    for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        Node::Forces &force = pMesh->nodes[vi].force;
        //        Vector6d ext = force.external;
        //        if (mCurrentSimulationStep <= 100) {
        //        ext[3] = 0;
        //        ext[4] = 0;
        //        }
        force.residual = force.external;
        force.internal = 0;
    }
    for (size_t ei = 0; ei < pMesh->EN(); ei++) {
        for (int i = 0; i < 4; i++) {
            std::pair<int, Vector6d> internalForcePair
                = internalForcesContributionsFromEachEdge[ei][i];
            int vi = internalForcePair.first;
            if (i > 1 && vi == -1) {
                continue;
            }
            Node::Forces &force = pMesh->nodes[vi].force;
            force.internal = force.internal + internalForcePair.second;
            force.residual = force.residual + (internalForcePair.second * -1);
#ifdef POLYSCOPE_DEFINED
            if (std::isnan(internalForcePair.second.norm())) {
                std::cerr << "nan on edge" << ei << std::endl;
            }
#endif
        }
    }
    double totalResidualForcesNorm = 0;
    Vector6d sumOfResidualForces(0);
    for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        Node::Forces &force = pMesh->nodes[vi].force;
        const Vector6d &nodeResidualForce = force.residual;
        sumOfResidualForces = sumOfResidualForces + nodeResidualForce;
        const double residualForceNorm = nodeResidualForce.norm();
        //        const double residualForceNorm = nodeResidualForce.getTranslation().norm();
        totalResidualForcesNorm += residualForceNorm;
#ifdef POLYSCOPE_DEFINED
        if (std::isnan(force.residual.norm())) {
            std::cout << "residual " << vi << ":" << force.residual.toString() << std::endl;
        }
#endif
    }
    pMesh->totalResidualForcesNorm = totalResidualForcesNorm;
    pMesh->averageResidualForcesNorm = totalResidualForcesNorm / pMesh->VN();
    //    pMesh->averageResidualForcesNorm = sumOfResidualForces.norm() / pMesh->VN();

    //  plotYValues.push_back(totalResidualForcesNorm);
    //  auto xPlot = matplot::linspace(0, plotYValues.size(), plotYValues.size());
    //  plotHandle = matplot::scatter(xPlot, plotYValues);
}

void DRMSimulationModel::updateNodalExternalForces(
    const std::unordered_map<VertexIndex, Vector6d> &nodalForces,
    const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    externalMomentsNorm = 0;
    double totalExternalForcesNorm = 0;
    for (const std::pair<VertexIndex, Vector6d> &nodalForce : nodalForces) {
        const VertexIndex nodeIndex = nodalForce.first;
        const bool isNodeConstrained = fixedVertices.contains(nodeIndex);
        Node &node = pMesh->nodes[nodeIndex];
        Vector6d nodalExternalForce(0);
        for (DoFType dofi = 0; dofi < 6; dofi++) {
            const bool isDofConstrained = isNodeConstrained
                                          && fixedVertices.at(nodeIndex).contains(dofi);
            if (isDofConstrained) {
                continue;
            }
            nodalExternalForce[dofi] = nodalForce.second[dofi];
        }
        externalMomentsNorm += std::sqrt(pow(nodalExternalForce[3], 2)
                                         + pow(nodalExternalForce[4], 2)
                                         + pow(nodalExternalForce[5], 2));

        /*
     * The external moments are given as a rotation around an axis.
     * In this implementation we model moments as rotation of the normal vector
     * and because of that we need to transform the moments.
     */

        if (externalMomentsNorm != 0) {
            VectorType momentAxis(nodalExternalForce[3],
                                  nodalExternalForce[4],
                                  nodalExternalForce[5]); // rotation around this vector
            VectorType transformedVector = vcg::RotationMatrix(VectorType(0, 0, 1),
                                                               vcg::math::ToRad(-90.0))
                                           * momentAxis;
            nodalExternalForce[3] = transformedVector[0];
            nodalExternalForce[4] = transformedVector[1];
            nodalExternalForce[5] = transformedVector[2];
            //            node.nR = transformedVector[2];
        }

        node.force.external = nodalExternalForce;
        totalExternalForcesNorm += node.force.external.norm();
    }

    pMesh->totalExternalForcesNorm = totalExternalForcesNorm;
}

void DRMSimulationModel::updateResidualForces()
{
    pMesh->totalResidualForcesNorm = 0;
    for (const VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        node.force.residual = node.force.external - node.force.internal;
        const double residualForceNorm = (node.force.residual).norm();
        pMesh->totalResidualForcesNorm += residualForceNorm;
    }
}

void DRMSimulationModel::computeRigidSupports()
{
    isRigidSupport.clear();
    isRigidSupport.resize(pMesh->VN(), false);
    for (const VertexType &v : pMesh->vert) {
        const VertexIndex vi = pMesh->nodes[v].vi;
        const bool isVertexConstrained = constrainedVertices.contains(vi);
        if (isVertexConstrained) {
            auto constrainedDoFType = constrainedVertices.at(vi);
            const bool hasAllDoFTypeConstrained = constrainedDoFType.contains(DoF::Ux)
                                                  && constrainedDoFType.contains(DoF::Uy)
                                                  && constrainedDoFType.contains(DoF::Uz)
                                                  && constrainedDoFType.contains(DoF::Nx)
                                                  && constrainedDoFType.contains(DoF::Ny)
                                                  && constrainedDoFType.contains(DoF::Nr);
            if (hasAllDoFTypeConstrained) {
                isRigidSupport[vi] = true;
            }
        }
    }
}

void DRMSimulationModel::updateNormalDerivatives()
{
    for (const VertexType &v : pMesh->vert) {
        for (DoFType dofi = DoF::Nx; dofi < DoF::NumDoF; dofi++) {
            DifferentiateWithRespectTo dui{v, dofi};
            pMesh->nodes[v].derivativeOfNormal[dofi] = computeDerivativeOfNormal(v, dui);
        }
    }
}

void DRMSimulationModel::updateT1Derivatives()
{
    for (const EdgeType &e : pMesh->edge) {
        for (DoFType dofi = DoF::Ux; dofi < DoF::Nx; dofi++) {
            DifferentiateWithRespectTo dui_v0{*e.cV(0), dofi};
            Element &element = pMesh->elements[e];
            element.derivativeT1_j[dofi] = computeDerivativeT1(e, dui_v0);
            DifferentiateWithRespectTo dui_v1{*e.cV(1), dofi};
            element.derivativeT1_jplus1[dofi] = computeDerivativeT1(e, dui_v1);

            element.derivativeT1[0][dofi] = element.derivativeT1_j[dofi];
            element.derivativeT1[1][dofi] = element.derivativeT1_jplus1[dofi];
        }
    }
}

void DRMSimulationModel::updateT2Derivatives()
{
    for (const EdgeType &e : pMesh->edge) {
        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
            DifferentiateWithRespectTo dui_v0{*e.cV(0), dofi};
            pMesh->elements[e].derivativeT2_j[dofi] = computeDerivativeT2(e, dui_v0);
            DifferentiateWithRespectTo dui_v1{*e.cV(1), dofi};
            pMesh->elements[e].derivativeT2_jplus1[dofi] = computeDerivativeT2(e, dui_v1);

            Element &element = pMesh->elements[e];
            element.derivativeT2[0][dofi] = element.derivativeT2_j[dofi];
            element.derivativeT2[1][dofi] = element.derivativeT2_jplus1[dofi];
        }
    }
}

void DRMSimulationModel::updateT3Derivatives()
{
    for (const EdgeType &e : pMesh->edge) {
        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
            DifferentiateWithRespectTo dui_v0{*e.cV(0), dofi};
            Element &element = pMesh->elements[e];
            element.derivativeT3_j[dofi] = computeDerivativeT3(e, dui_v0);
            DifferentiateWithRespectTo dui_v1{*e.cV(1), dofi};
            element.derivativeT3_jplus1[dofi] = computeDerivativeT3(e, dui_v1);

            element.derivativeT3[0][dofi] = element.derivativeT3_j[dofi];
            element.derivativeT3[1][dofi] = element.derivativeT3_jplus1[dofi];
        }
    }
}

void DRMSimulationModel::updateRDerivatives()
{
    for (const EdgeType &e : pMesh->edge) {
        for (DoFType dofi = DoF::Nx; dofi < DoF::NumDoF; dofi++) {
            DifferentiateWithRespectTo dui_v0{*e.cV(0), dofi};
            pMesh->elements[e].derivativeR_j[dofi] = computeDerivativeOfR(e, dui_v0);
            DifferentiateWithRespectTo dui_v1{*e.cV(1), dofi};
            pMesh->elements[e].derivativeR_jplus1[dofi] = computeDerivativeOfR(e, dui_v1);
        }
    }
}

void DRMSimulationModel::updateElementalLengths()
{
    pMesh->updateElementalLengths();
}

DRMSimulationModel::DRMSimulationModel() {}

void DRMSimulationModel::updateNodalMasses()
{
    double gamma = mSettings.gamma;
    const size_t untilStep = 4000;
    if (shouldTemporarilyDampForces && mCurrentSimulationStep < untilStep) {
        gamma *= 1e6 * (1 - static_cast<double>(mCurrentSimulationStep) / untilStep);
    }
    //    if (mCurrentSimulationStep == static_cast<size_t>(1.4 * untilStep)
    //        && shouldTemporarilyDampForces) {
    //        Dt = mSettings.Dtini;
    //    }
    for (VertexType &v : pMesh->vert) {
        const size_t vi = pMesh->getIndex(v);
        double translationalSumSk = 0;
        double rotationalSumSk_I2 = 0;
        double rotationalSumSk_I3 = 0;
        double rotationalSumSk_J = 0;
        for (const EdgePointer &ep : pMesh->nodes[v].incidentElements) {
            const size_t ei = pMesh->getIndex(ep);
            const Element &elem = pMesh->elements[ep];
            const double SkTranslational = elem.material.youngsModulus * elem.dimensions.A
                                           / elem.length;
            translationalSumSk += SkTranslational;
            const double lengthToThe3 = std::pow(elem.length, 3);
            const long double SkRotational_I2 = elem.material.youngsModulus * elem.dimensions.inertia.I2
                                                / lengthToThe3;
            const long double SkRotational_I3 = elem.material.youngsModulus * elem.dimensions.inertia.I3
                                                / lengthToThe3;
            const long double SkRotational_J = elem.material.youngsModulus * elem.dimensions.inertia.J
                                               / lengthToThe3;
            rotationalSumSk_I2 += SkRotational_I2;
            rotationalSumSk_I3 += SkRotational_I3;
            rotationalSumSk_J += SkRotational_J;
            assert(rotationalSumSk_I2 != 0);
            assert(rotationalSumSk_I3 != 0);
            assert(rotationalSumSk_J != 0);
        }
        pMesh->nodes[v].mass.translational = gamma * pow(mSettings.Dtini, 2) * 2
                                             * translationalSumSk;
        pMesh->nodes[v].mass.rotationalI2 = gamma * pow(mSettings.Dtini, 2) * 8
                                            * rotationalSumSk_I2;
        pMesh->nodes[v].mass.rotationalI3 = gamma * pow(mSettings.Dtini, 2) * 8
                                            * rotationalSumSk_I3;
        pMesh->nodes[v].mass.rotationalJ = gamma * pow(mSettings.Dtini, 2) * 8 * rotationalSumSk_J;

        //fill 6d mass vector
        pMesh->nodes[v].mass_6d[DoF::Ux] = pMesh->nodes[v].mass.translational;
        pMesh->nodes[v].mass_6d[DoF::Uy] = pMesh->nodes[v].mass.translational;
        pMesh->nodes[v].mass_6d[DoF::Uz] = pMesh->nodes[v].mass.translational;
        pMesh->nodes[v].mass_6d[DoF::Nx] = pMesh->nodes[v].mass.rotationalJ;
        pMesh->nodes[v].mass_6d[DoF::Ny] = pMesh->nodes[v].mass.rotationalI3;
        pMesh->nodes[v].mass_6d[DoF::Nr] = pMesh->nodes[v].mass.rotationalI2;
        if (mSettings.viscousDampingFactor.has_value()) {
            //fill 6d damping vector
            const double translationalDampingFactor
                = 2 * std::sqrt(translationalSumSk * pMesh->nodes[v].mass.translational);
            pMesh->nodes[v].damping_6d[DoF::Ux] = translationalDampingFactor;
            pMesh->nodes[v].damping_6d[DoF::Uy] = translationalDampingFactor;
            pMesh->nodes[v].damping_6d[DoF::Uz] = translationalDampingFactor;
            pMesh->nodes[v].damping_6d[DoF::Nx] = 2
                                                  * std::sqrt(rotationalSumSk_J
                                                              * pMesh->nodes[v].mass_6d[DoF::Nx]);
            pMesh->nodes[v].damping_6d[DoF::Ny] = 2
                                                  * std::sqrt(rotationalSumSk_I3
                                                              * pMesh->nodes[v].mass_6d[DoF::Ny]);
            pMesh->nodes[v].damping_6d[DoF::Nr] = 2
                                                  * std::sqrt(rotationalSumSk_I2
                                                              * pMesh->nodes[v].mass_6d[DoF::Nr]);
            pMesh->nodes[v].damping_6d = pMesh->nodes[v].damping_6d
                                         * mSettings.viscousDampingFactor.value();
        }
        assert(std::pow(mSettings.Dtini, 2.0) * translationalSumSk
                   / pMesh->nodes[v].mass.translational
               < 2);
        assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_I2
                   / pMesh->nodes[v].mass.rotationalI2
               < 2);
        assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_I3
                   / pMesh->nodes[v].mass.rotationalI3
               < 2);
        assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_J / pMesh->nodes[v].mass.rotationalJ
               < 2);
    }
}

void DRMSimulationModel::updateNodalAccelerations()
{
    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        const VertexIndex vi = pMesh->getIndex(v);
        node.acceleration = node.force.residual / node.mass_6d;
#ifdef POLYSCOPE_DEFINED
        if (std::isnan(node.acceleration.norm())) {
            std::cout << "acceleration " << vi << ":" << node.acceleration.toString() << std::endl;
        }
#endif
        //        if (vi == 10) {
        //            std::cout << "Acceleration:" << node.acceleration[0] << " " << node.acceleration[1]
        //                      << " " << node.acceleration[2] << std::endl;
        //        }

        //        if (shouldTemporarilyDampForces && mCurrentSimulationStep < 700) {
        //            node.acceleration = node.acceleration * 1e-2;
        //        }
    }
}

void DRMSimulationModel::updateNodalVelocities()
{
    for (VertexType &v : pMesh->vert) {
        const VertexIndex vi = pMesh->getIndex(v);
        Node &node = pMesh->nodes[v];
        if (mSettings.viscousDampingFactor.has_value()) {
            const Vector6d massOverDt = node.mass_6d / Dt;
            //            const Vector6d visciousDampingFactor(viscuousDampingConstant / 2);
            const Vector6d &visciousDampingFactor = node.damping_6d;
            const Vector6d denominator = massOverDt + visciousDampingFactor / 2;
            const Vector6d firstTermNominator = massOverDt - visciousDampingFactor / 2;
            const Vector6d firstTerm = node.velocity * firstTermNominator / denominator;
            const Vector6d secondTerm = node.force.residual / denominator;
            node.velocity = firstTerm + secondTerm;
        } else {
            node.velocity = node.velocity + node.acceleration * Dt;
        }
#ifdef POLYSCOPE_DEFINED
        if (std::isnan(node.velocity.norm())) {
            std::cout << "Velocity " << vi << ":" << node.velocity.toString() << std::endl;
        }
#endif
    }
    updateKineticEnergy();
}

void DRMSimulationModel::updateNodalDisplacements()
{
    //    const bool shouldCapDisplacements = mSettings.displacementCap.has_value();
    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        Vector6d stepDisplacement = node.velocity * Dt;
        //        if (shouldCapDisplacements
        //            && stepDisplacement.getTranslation().norm() > mSettings.displacementCap) {
        //            stepDisplacement = stepDisplacement
        //                               * (*mSettings.displacementCap
        //                                  / stepDisplacement.getTranslation().norm());
        //            std::cout << "Displacement capped" << std::endl;
        //        }
        node.displacements = node.displacements + stepDisplacement;
        //        if (mSettings.isDebugMode && mSettings.beVerbose && pMesh->getIndex(v) == 40) {
        //            std::cout << "Node " << node.vi << ":" << endl;
        //            std::cout << node.displacements[0] << " " << node.displacements[0] << " "
        //                      << node.displacements[1] << " " << node.displacements[2] << " "
        //                      << node.displacements[3] << " " << node.displacements[4] << " "
        //                      << node.displacements[5] << std::endl;
        //        }
    }
}

void DRMSimulationModel::updateNodePosition(
    VertexType &v, const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    Node &node = pMesh->nodes[v];
    const VertexIndex &vi = pMesh->nodes[v].vi;

    VectorType displacementVector(0, 0, 0);
    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(0)) {
        displacementVector += VectorType(node.displacements[0], 0, 0);
    }
    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(1)) {
        displacementVector += VectorType(0, node.displacements[1], 0);
    }
    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(2)) {
        displacementVector += VectorType(0, 0, node.displacements[2]);
    }
    v.P() = node.initialLocation + displacementVector;
    if (shouldApplyInitialDistortion && mCurrentSimulationStep < 100) {
        //TODO:The initial displacement should depend on the model and should only be applied if the forced displacements applied are out of plane
        VectorType desiredInitialDisplacement(0.0015, 0.0015, 0.0015);
        v.P() = v.P() + desiredInitialDisplacement;
    }
}

void DRMSimulationModel::updateNodeNr(VertexType &v)
{
    const VertexIndex &vi = pMesh->nodes[v].vi;
    Node &node = pMesh->nodes[v];
    if (!isRigidSupport[vi]) {
        node.nR = node.displacements[5];
    } else {
        const EdgePointer &refElem = node.referenceElement;
        const VectorType &refT1 = pMesh->elements[refElem].frame.t1;

        const VectorType &t1Initial = computeT1Vector(pMesh->nodes[refElem->cV(0)].initialLocation,
                                                      pMesh->nodes[refElem->cV(1)].initialLocation);
        VectorType g1 = Cross(refT1, t1Initial);
        node.nR = g1.dot(v.cN());
    }
}

void DRMSimulationModel::updateNodeNormal(
    VertexType &v, const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    Node &node = pMesh->nodes[v];
    const VertexIndex &vi = node.vi;
    //  if (vi == 1) {
    //    std::cout << "PRE:" << mesh->vert[1].N()[0] << " " <<
    //    mesh->vert[1].N()[1]
    //              << " " << mesh->vert[1].N()[2] << std::endl;
    //  }
    VectorType normalDisplacementVector(0, 0, 0);
    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(3)) {
        normalDisplacementVector += VectorType(node.displacements[3], 0, 0);
    }
    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(4)) {
        normalDisplacementVector += VectorType(0, node.displacements[4], 0);
    }
    const double nxnyMagnitudePre = std::pow(v.N()[0], 2) + std::pow(v.N()[1], 2);
    v.N() = node.initialNormal + normalDisplacementVector;
    const double &nx = v.N()[0], ny = v.N()[1], nz = v.N()[2];
    const double nxnyMagnitude = std::pow(nx, 2) + std::pow(ny, 2);
    VectorType n = v.N();
    const bool shouldBreak = mCurrentSimulationStep == 118 && vi == 3;
    if (nxnyMagnitude > 1) {
        VectorType newNormal(nx / std::sqrt(nxnyMagnitude), ny / std::sqrt(nxnyMagnitude), 0);
        v.N() = newNormal;

        /*If an external moment caused the normal to lay on the xy plane this means
     * that in order to disable its effect a greater internal force is needed
     * than what is possible (the constraint on the z of the normals imposes a
     * constraint on the maximum internal force). Because of that the
     * totalResidualForcesNorm can't drop below the magnitude of external moment
     * applied on vertex vi. In order to allow termination of the simulation
     * when the described phenomenon happens we allow the termination of the
     * algorithm if the kinetic energy of the system drops below the set
     * threshold.
     * */
        const bool viHasMoments = node.force.external[3] != 0 || node.force.external[4] != 0;
        if (!checkedForMaximumMoment && viHasMoments) {
            mSettings.totalTranslationalKineticEnergyThreshold = 1e-8;
#ifdef POLYSCOPE_DEFINED
            std::cout << "Maximum moment reached.The Kinetic energy of the system will "
                         "be used as a convergence criterion"
                      << std::endl;
#endif
            checkedForMaximumMoment = true;
        }

    } else {
        const double nzSquared = 1.0 - nxnyMagnitude;
        const double nz = std::sqrt(nzSquared);
        VectorType newNormal(nx, ny, nz);
        v.N() = newNormal;
    }

    //    if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(DoF::Nr)) {
    //  if (vi == 1) {
    //    std::cout << "AFTER:" << mesh->vert[1].N()[0] << " " <<
    //    mesh->vert[1].N()[1]
    //              << " " << mesh->vert[1].N()[2] << std::endl;
    //  }
}

void DRMSimulationModel::applyDisplacements(
    const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    for (VertexType &v : pMesh->vert) {
        updateNodePosition(v, fixedVertices);
        updateNodeNormal(v, fixedVertices);
        updateNodeNr(v);
    }
    updateElementalFrames();
    if (mSettings.shouldDraw) {
        pMesh->updateEigenEdgeAndVertices();
    }
}

void DRMSimulationModel::updateElementalFrames()
{
    for (const EdgeType &e : pMesh->edge) {
        const VectorType elementNormal = (e.cV(0)->cN() + e.cV(1)->cN()).Normalize();
        pMesh->elements[e].frame = computeElementFrame(e.cP(0), e.cP(1), elementNormal);
    }
}

void DRMSimulationModel::applyForcedDisplacements(
    const std::unordered_map<VertexIndex, Eigen::Vector3d> &nodalForcedDisplacements)
{
    for (const std::pair<VertexIndex, Eigen::Vector3d> vertexIndexDisplacementPair :
         nodalForcedDisplacements) {
        const VertexIndex vi = vertexIndexDisplacementPair.first;
        const Eigen::Vector3d vertexDisplacement = vertexIndexDisplacementPair.second;
        Node &node = pMesh->nodes[vi];
        VectorType displacementVector(vertexDisplacement(0),
                                      vertexDisplacement(1),
                                      vertexDisplacement(2));
        if (mCurrentSimulationStep < mSettings.gradualForcedDisplacementSteps) {
            displacementVector *= mCurrentSimulationStep
                                  / static_cast<double>(mSettings.gradualForcedDisplacementSteps);
        }
        pMesh->vert[vi].P() = node.initialLocation + displacementVector;
        node.displacements = Vector6d({displacementVector[0],
                                       displacementVector[1],
                                       displacementVector[2],
                                       node.displacements[3],
                                       node.displacements[4],
                                       node.displacements[5]});
    }

    if (mSettings.shouldDraw) {
        pMesh->updateEigenEdgeAndVertices();
    }
}

void DRMSimulationModel::applyForcedNormals(
    const std::unordered_map<VertexIndex, VectorType> nodalForcedRotations)
{
    for (const std::pair<VertexIndex, VectorType> vertexIndexDesiredNormalPair :
         nodalForcedRotations) {
        const VertexIndex vi = vertexIndexDesiredNormalPair.first;

        Node &node = pMesh->nodes[vi];
        pMesh->vert[vi].N() = vertexIndexDesiredNormalPair.second;
        node.displacements = Vector6d(
            {node.displacements[0],
             node.displacements[1],
             node.displacements[2],
             vertexIndexDesiredNormalPair.second[0] - node.initialNormal[0],
             vertexIndexDesiredNormalPair.second[1] - node.initialNormal[1],
             node.displacements[5]});
    }
}

// NOTE: Is this correct? Should the kinetic energy be computed like that?
void DRMSimulationModel::updateKineticEnergy()
{
    pMesh->previousTotalKineticEnergy = pMesh->currentTotalKineticEnergy;
    pMesh->currentTotalKineticEnergy = 0;
    pMesh->currentTotalTranslationalKineticEnergy = 0;
    for (const VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        node.kineticEnergy = 0;

        const double translationalVelocityNorm = std::sqrt(std::pow(node.velocity[0], 2)
                                                           + std::pow(node.velocity[1], 2)
                                                           + std::pow(node.velocity[2], 2));
        const double nodeTranslationalKineticEnergy = 0.5 * node.mass.translational
                                                      * pow(translationalVelocityNorm, 2);

        const double nodeRotationalKineticEnergy
            = 0.5
              * (node.mass.rotationalJ * pow(node.velocity[3], 2)
                 + node.mass.rotationalI3 * pow(node.velocity[4], 2)
                 + node.mass.rotationalI2 * pow(node.velocity[5], 2));

        node.kineticEnergy = nodeTranslationalKineticEnergy + nodeRotationalKineticEnergy;
        assert(node.kineticEnergy < 1e15);

        pMesh->currentTotalKineticEnergy += node.kineticEnergy;
        pMesh->currentTotalTranslationalKineticEnergy += nodeTranslationalKineticEnergy;
    }
    //  assert(mesh->currentTotalKineticEnergy < 100000000000000);
}

void DRMSimulationModel::resetVelocities()
{
    for (const VertexType &v : pMesh->vert) {
        pMesh->nodes[v].velocity =
            //        pMesh->nodes[v].acceleration * Dt
            //                                   * 0.5; // NOTE: Do I reset the previous
            //                                          //            velocity?
            //                                          //        reset
            //                                          // current to 0 or this?
            0;
    }
    updateKineticEnergy();
}

void DRMSimulationModel::updatePositionsOnTheFly(
    const std::unordered_map<VertexIndex, std::unordered_set<DoFType>> &fixedVertices)
{
    const double gamma = 0.8;
    for (VertexType &v : pMesh->vert) {
        double translationalSumSk = 0;
        double rotationalSumSk_I2 = 0;
        double rotationalSumSk_I3 = 0;
        double rotationalSumSk_J = 0;
        for (const EdgePointer &ep : pMesh->nodes[v].incidentElements) {
            const Element &elem = pMesh->elements[ep];
            const double SkTranslational = elem.material.youngsModulus * elem.dimensions.A
                                           / elem.length;
            translationalSumSk += SkTranslational;
            const double lengthToThe3 = std::pow(elem.length, 3);
            const double SkRotational_I2 = elem.material.youngsModulus * elem.dimensions.inertia.I2
                                           / lengthToThe3; // TODO: I2->t2,I3->t3,t1->polar inertia
            const double SkRotational_I3 = elem.material.youngsModulus * elem.dimensions.inertia.I3
                                           / lengthToThe3; // TODO: I2->t2,I3->t3,t1->polar inertia
            const double SkRotational_J = elem.material.youngsModulus * elem.dimensions.inertia.J
                                          / lengthToThe3; // TODO: I2->t2,I3->t3,t1->polar inertia
            rotationalSumSk_I2 += SkRotational_I2;
            rotationalSumSk_I3 += SkRotational_I3;
            rotationalSumSk_J += SkRotational_J;
            //      assert(rotationalSumSk_I2 != 0);
            //      assert(rotationalSumSk_I3 != 0);
            //      assert(rotationalSumSk_J != 0);
        }
        pMesh->nodes[v].mass.translational = gamma * pow(mSettings.Dtini, 2) * 2
                                             * translationalSumSk;
        pMesh->nodes[v].mass.rotationalI2 = gamma * pow(mSettings.Dtini, 2) * 8
                                            * rotationalSumSk_I2;
        pMesh->nodes[v].mass.rotationalI3 = gamma * pow(mSettings.Dtini, 2) * 8
                                            * rotationalSumSk_I3;
        pMesh->nodes[v].mass.rotationalJ = gamma * pow(mSettings.Dtini, 2) * 8 * rotationalSumSk_J;

        //    assert(std::pow(mSettings.Dtini, 2.0) * translationalSumSk /
        //               mesh->nodes[v].translationalMass <
        //           2);
        //    assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_I2 /
        //               mesh->nodes[v].rotationalMass_I2 <
        //           2);
        //    assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_I3 /
        //               mesh->nodes[v].rotationalMass_I3 <
        //           2);
        //    assert(std::pow(mSettings.Dtini, 2.0) * rotationalSumSk_J /
        //               mesh->nodes[v].rotationalMass_J <
        //           2);
    }

    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
            if (dofi == DoF::Ux || dofi == DoF::Uy || dofi == DoF::Uz) {
                node.acceleration[dofi] = node.force.residual[dofi] / node.mass.translational;
            } else if (dofi == DoF::Nx) {
                node.acceleration[dofi] = node.force.residual[dofi] / node.mass.rotationalJ;
            } else if (dofi == DoF::Ny) {
                node.acceleration[dofi] = node.force.residual[dofi] / node.mass.rotationalI3;
            } else if (dofi == DoF::Nr) {
                node.acceleration[dofi] = node.force.residual[dofi] / node.mass.rotationalI2;
            }
        }
    }

    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        node.velocity = node.velocity + node.acceleration * Dt;
    }
    updateKineticEnergy();

    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        node.displacements = node.displacements + node.velocity * Dt;
    }

    for (VertexType &v : pMesh->vert) {
        updateNodePosition(v, fixedVertices);
        Node &node = pMesh->nodes[v];
        const VertexIndex &vi = node.vi;
        VectorType normalDisplacementVector(0, 0, 0);
        if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(3)) {
            normalDisplacementVector += VectorType(node.displacements[3], 0, 0);
        }
        if (!fixedVertices.contains(vi) || !fixedVertices.at(vi).contains(4)) {
            normalDisplacementVector += VectorType(0, node.displacements[4], 0);
        }
        v.N() = node.initialNormal + normalDisplacementVector;
        const double &nx = v.N()[0], ny = v.N()[1];
        const double nxnyMagnitude = std::pow(nx, 2) + std::pow(ny, 2);
        if (nxnyMagnitude > 1) {
            v.N() = VectorType(nx / std::sqrt(nxnyMagnitude), ny / std::sqrt(nxnyMagnitude), 0);
        } else {
            const double nzSquared = 1.0 - nxnyMagnitude;
            const double nz = std::sqrt(nzSquared);
            VectorType newNormal(nx, ny, nz);
            v.N() = newNormal;
        }
        if (!isRigidSupport[vi]) {
            node.nR = node.displacements[5];
        } else {
        }
    }
    updateElementalFrames();
}

SimulationResults DRMSimulationModel::computeResults(const std::shared_ptr<SimulationJob> &pJob)
{
    std::vector<Vector6d> displacements(pMesh->VN());
    for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        displacements[vi] = pMesh->nodes[vi].displacements;
    }
    history.numberOfSteps = mCurrentSimulationStep;
    SimulationResults results;
    results.converged = true;
    results.pJob = pJob;
    results.history = history;
    results.displacements = displacements;
    results.setLabelPrefix("DRM");

    if (mSettings.maxDRMIterations.has_value()
        && mCurrentSimulationStep == mSettings.maxDRMIterations && mCurrentSimulationStep != 0) {
        if (mSettings.beVerbose) {
            std::cout << "Did not reach equilibrium before reaching the maximum number "
                         "of DRM steps ("
                      << mSettings.maxDRMIterations.value() << "). Breaking simulation"
                      << std::endl;
        }
        results.converged = false;
    } else if (std::isnan(pMesh->currentTotalKineticEnergy)) {
        if (mSettings.beVerbose) {
            std::cerr << "Simulation did not converge due to infinite kinetic energy." << std::endl;
        }
        results.converged = false;
    }
    //    mesh.printVertexCoordinates(mesh.VN() / 2);
#ifdef POLYSCOPE_DEFINED
    if (mSettings.shouldDraw && !mSettings.debugModeStep.has_value()) {
        draw();
    }
#endif
    if (!std::isnan(pMesh->currentTotalKineticEnergy)) {
        results.debug_drmDisplacements = results.displacements;
        results.internalPotentialEnergy = computeTotalInternalPotentialEnergy();

        results.rotationalDisplacementQuaternion.resize(pMesh->VN());
        results.debug_q_f1.resize(pMesh->VN());
        results.debug_q_normal.resize(pMesh->VN());
        results.debug_q_nr.resize(pMesh->VN());
        for (int vi = 0; vi < pMesh->VN(); vi++) {
            const Node &node = pMesh->nodes[vi];
            const Eigen::Vector3d nInitial_eigen = node.initialNormal
                                                       .ToEigenVector<Eigen::Vector3d>();
            const Eigen::Vector3d nDeformed_eigen
                = pMesh->vert[vi].cN().ToEigenVector<Eigen::Vector3d>();

            Eigen::Quaternion<double> q_normal;
            q_normal.setFromTwoVectors(nInitial_eigen, nDeformed_eigen);
            Eigen::Quaternion<double> q_nr_nDeformed;
            q_nr_nDeformed = Eigen::AngleAxis<double>(pMesh->nodes[vi].nR, nDeformed_eigen);
            Eigen::Quaternion<double> q_nr_nInit;
            q_nr_nInit = Eigen::AngleAxis<double>(pMesh->nodes[vi].nR, nInitial_eigen);
            const auto w = q_nr_nDeformed.w();
            const auto theta = 2 * acos(q_nr_nDeformed.w());
            const auto nr = pMesh->nodes[vi].nR;
            Eigen::Vector3d deformedNormal_debug(q_nr_nDeformed.x() * sin(theta / 2),
                                                 q_nr_nDeformed.y() * sin(theta / 2),
                                                 q_nr_nDeformed.z() * sin(theta / 2));
            deformedNormal_debug.normalize();
            //        const double nr = nr_0To2pi <= M_PI ? nr_0To2pi : (nr_0To2pi - 2 * M_PI);
            const double nr_debug = deformedNormal_debug.dot(nDeformed_eigen) > 0 ? theta : -theta;
            assert(pMesh->nodes[vi].nR - nr_debug < 1e-6);
            VectorType referenceT1_deformed = pMesh->elements[node.referenceElement].frame.t1;
            const VectorType &nDeformed = pMesh->vert[vi].cN();
            const VectorType referenceF1_deformed
                = (referenceT1_deformed
                   - (node.initialNormal * (referenceT1_deformed * node.initialNormal)))
                      .Normalize();

            const VectorType referenceT1_initial
                = computeT1Vector(pMesh->nodes[node.referenceElement->cV(0)].initialLocation,
                                  pMesh->nodes[node.referenceElement->cV(1)].initialLocation);
            //          const VectorType &n_initial = node.initialNormal;
            const VectorType referenceF1_initial = (referenceT1_initial
                                                    - (node.initialNormal
                                                       * (referenceT1_initial * node.initialNormal)))
                                                       .Normalize();
            Eigen::Quaternion<double> q_f1_nInit; //nr is with respect to f1
            q_f1_nInit.setFromTwoVectors(referenceF1_initial.ToEigenVector<Eigen::Vector3d>(),
                                         referenceF1_deformed.ToEigenVector<Eigen::Vector3d>());

            Eigen::Quaternion<double> q_f1_nDeformed; //nr is with respect to f1
            //          const VectorType &n_initial = node.initialNormal;
            const VectorType referenceF1_initial_def
                = (referenceT1_initial - (nDeformed * (referenceT1_initial * nDeformed))).Normalize();
            const VectorType referenceF1_deformed_def = (referenceT1_deformed
                                                         - (nDeformed
                                                            * (referenceT1_deformed * nDeformed)))
                                                            .Normalize();
            q_f1_nDeformed
                .setFromTwoVectors(referenceF1_initial_def.ToEigenVector<Eigen::Vector3d>(),
                                   referenceF1_deformed_def.ToEigenVector<Eigen::Vector3d>());
            const auto debug_qf1_nDef = (q_f1_nDeformed * q_nr_nDeformed) * nDeformed_eigen;
            const auto debug_qf1_nInit = (q_f1_nInit * q_nr_nInit) * nInitial_eigen;
            const auto debug_deformedNormal_f1Init = (q_normal * (q_f1_nInit * q_nr_nInit))
                                                     * nInitial_eigen;
            const auto debug_deformedNormal_f1Def = ((q_nr_nDeformed * q_f1_nDeformed) * q_normal)
                                                    * nInitial_eigen;
            //          Eigen::Quaternion<double> q_t1;
            //          q_t1.setFromTwoVectors(referenceT1_initial.ToEigenVector<Eigen::Vector3d>(),
            //                                 referenceT1_deformed.ToEigenVector<Eigen::Vector3d>());

            results.debug_q_f1[vi] = q_f1_nInit;
            results.debug_q_normal[vi] = q_normal;
            results.debug_q_nr[vi] = q_nr_nInit;
            results.rotationalDisplacementQuaternion[vi]
                //Eigen::Quaterniond R
                = (q_normal
                   * (q_f1_nInit * q_nr_nInit)); //q_f1_nDeformed * q_nr_nDeformed * q_normal;
            //Update the displacement vector to contain the euler angles
            const Eigen::Vector3d eulerAngles = results
                                                    .rotationalDisplacementQuaternion[vi]
                                                    //            R
                                                    .toRotationMatrix()
                                                    .eulerAngles(0, 1, 2);
            results.displacements[vi][3] = eulerAngles[0];
            results.displacements[vi][4] = eulerAngles[1];
            results.displacements[vi][5] = eulerAngles[2];

            //          Eigen::Quaterniond q_test = Eigen::AngleAxisd(eulerAngles[0], Eigen::Vector3d::UnitX())
            //                                      * Eigen::AngleAxisd(eulerAngles[1], Eigen::Vector3d::UnitY())
            //                                      * Eigen::AngleAxisd(eulerAngles[2], Eigen::Vector3d::UnitZ());

            //          const double dot_test = results.rotationalDisplacementQuaternion[vi].dot(q_test);
            //          assert(dot_test > 1 - 1e5);

            int i = 0;
            i++;
        }
    }

    return results;
}

void DRMSimulationModel::printCurrentState() const
{
    std::cout << "Simulation steps executed:" << mCurrentSimulationStep << std::endl;
    std::cout << "Residual forces norm: " << pMesh->totalResidualForcesNorm << std::endl;
    std::cout << "Average Residual forces norm/extForcesNorm: "
              << pMesh->totalResidualForcesNorm / pMesh->VN() / pMesh->totalExternalForcesNorm
              << std::endl;
    std::cout << "Moving average residual forces:" << pMesh->residualForcesMovingAverage
              << std::endl;
    std::cout << "Kinetic energy:" << pMesh->currentTotalKineticEnergy << std::endl;
    static std::chrono::steady_clock::time_point begin = std::chrono::steady_clock::now();
    const double timePerNodePerIteration = std::chrono::duration_cast<std::chrono::microseconds>(
                                               std::chrono::steady_clock::now() - begin)
                                               .count()
                                           * 1e-6
                                           / (static_cast<double>(mCurrentSimulationStep)
                                              * pMesh->VN());
    std::cout << "Total potential:" << pMesh->currentTotalPotentialEnergykN << " kNm" << std::endl;
    std::cout << "time(s)/(iterations*node) = " << timePerNodePerIteration << std::endl;
    std::cout << "Mov aver deriv norm:" << pMesh->residualForcesMovingAverageDerivativeNorm
              << std::endl;
    std::cout << "xi:" << mSettings.xi << std::endl;
    std::cout << "Dt:" << Dt << std::endl;
}

void DRMSimulationModel::printDebugInfo() const
{
    std::cout << pMesh->elements[0].rigidity.toString() << std::endl;
    std::cout << "Number of dampings:" << numOfDampings << std::endl;
    printCurrentState();
}

#ifdef POLYSCOPE_DEFINED
void DRMSimulationModel::draw(const std::string &screenshotsFolder)
{
    // update positions
    //  polyscope::getCurveNetwork("Undeformed edge mesh")->setEnabled(false);
    polyscope::CurveNetwork *meshPolyscopeHandle = polyscope::getCurveNetwork(meshPolyscopeLabel);
    meshPolyscopeHandle->updateNodePositions(pMesh->getEigenVertices());

    // Vertex quantities
    std::vector<double> kineticEnergies(pMesh->VN());
    std::vector<std::array<double, 3>> nodeNormals(pMesh->VN());
    std::vector<std::array<double, 3>> internalForces(pMesh->VN());
    std::vector<std::array<double, 3>> externalForces(pMesh->VN());
    std::vector<std::array<double, 3>> externalMoments(pMesh->VN());
    std::vector<double> internalForcesNorm(pMesh->VN());
    std::vector<std::array<double, 3>> internalAxialForces(pMesh->VN());
    std::vector<std::array<double, 3>> internalFirstBendingTranslationForces(
        pMesh->VN());
    std::vector<std::array<double, 3>> internalFirstBendingRotationForces(
        pMesh->VN());
    std::vector<std::array<double, 3>> internalSecondBendingTranslationForces(
        pMesh->VN());
    std::vector<std::array<double, 3>> internalSecondBendingRotationForces(
        pMesh->VN());
    std::vector<double> nRs(pMesh->VN());
    std::vector<double> theta2(pMesh->VN());
    std::vector<double> theta3(pMesh->VN());
    std::vector<std::array<double, 3>> residualForces(pMesh->VN());
    std::vector<double> residualForcesNorm(pMesh->VN());
    std::vector<double> accelerationX(pMesh->VN());
    for (const VertexType &v : pMesh->vert) {
        kineticEnergies[pMesh->getIndex(v)] = pMesh->nodes[v].kineticEnergy;
        const VectorType n = v.cN();
        nodeNormals[pMesh->getIndex(v)] = {n[0], n[1], n[2]};
        // per node internal forces
        const Vector6d nodeforce = pMesh->nodes[v].force.internal * (-1);
        internalForces[pMesh->getIndex(v)] = {nodeforce[0], nodeforce[1],
                                              nodeforce[2]};
        internalForcesNorm[pMesh->getIndex(v)] = nodeforce.norm();
        // External force
        const Vector6d nodeExternalForce = pMesh->nodes[v].force.external;
        externalForces[pMesh->getIndex(v)] = {
            nodeExternalForce[0], nodeExternalForce[1], nodeExternalForce[2]};
        externalMoments[pMesh->getIndex(v)] = {nodeExternalForce[3],
                                               nodeExternalForce[4], 0};
        internalAxialForces[pMesh->getIndex(v)] = {nodeforce[0], nodeforce[1],
                                                   nodeforce[2]};
        const Node &node = pMesh->nodes[v];
        const Vector6d nodeForceFirst = node.force.internalFirstBending * (-1);
        internalFirstBendingTranslationForces[pMesh->getIndex(v)] = {
            nodeForceFirst[0], nodeForceFirst[1], nodeForceFirst[2]};
        internalFirstBendingRotationForces[pMesh->getIndex(v)] = {
            nodeForceFirst[3], nodeForceFirst[4], 0};

        const Vector6d nodeForceSecond = node.force.internalSecondBending * (-1);
        internalSecondBendingTranslationForces[pMesh->getIndex(v)] = {
            nodeForceSecond[0], nodeForceSecond[1], nodeForceSecond[2]};
        internalSecondBendingRotationForces[pMesh->getIndex(v)] = {
            nodeForceSecond[3], nodeForceSecond[4], 0};
        nRs[pMesh->getIndex(v)] = node.nR;
        const Vector6d nodeResidualForce = pMesh->nodes[v].force.residual;
        residualForces[pMesh->getIndex(v)] = {
            nodeResidualForce[0], nodeResidualForce[1], nodeResidualForce[2]};
        residualForcesNorm[pMesh->getIndex(v)] = nodeResidualForce.norm();
        accelerationX[pMesh->getIndex(v)] = pMesh->nodes[v].acceleration[0];
    }
    meshPolyscopeHandle->addNodeScalarQuantity("Kinetic Energy", kineticEnergies)->setEnabled(false);
    meshPolyscopeHandle->addNodeVectorQuantity("Node normals", nodeNormals)->setEnabled(true);
    meshPolyscopeHandle->addNodeVectorQuantity("Internal force", internalForces)->setEnabled(false);
    meshPolyscopeHandle->addNodeVectorQuantity("External force", externalForces)->setEnabled(false);
    meshPolyscopeHandle->addNodeVectorQuantity("External Moments", externalMoments)->setEnabled(true);
    meshPolyscopeHandle->addNodeScalarQuantity("Internal force norm", internalForcesNorm)
        ->setEnabled(true);
    meshPolyscopeHandle->setRadius(0.002);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeVectorQuantity("Internal Axial force", internalAxialForces)
    //      ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeVectorQuantity("First bending force-Translation",
    //                              internalFirstBendingTranslationForces)
    //      ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeVectorQuantity("First bending force-Rotation",
    //                              internalFirstBendingRotationForces)
    //      ->setEnabled(false);

    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeVectorQuantity("Second bending force-Translation",
    //                              internalSecondBendingTranslationForces)
    //      ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeVectorQuantity("Second bending force-Rotation",
    //                              internalSecondBendingRotationForces)
    //      ->setEnabled(false);
    polyscope::getCurveNetwork(meshPolyscopeLabel)
        ->addNodeScalarQuantity("nR", nRs)
        ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeScalarQuantity("theta3", theta3)
    //      ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeScalarQuantity("theta2", theta2)
    //      ->setEnabled(false);
    polyscope::getCurveNetwork(meshPolyscopeLabel)
        ->addNodeVectorQuantity("Residual force", residualForces)
        ->setEnabled(false);
    polyscope::getCurveNetwork(meshPolyscopeLabel)
        ->addNodeScalarQuantity("Residual force norm", residualForcesNorm)
        ->setEnabled(false);
    //  polyscope::getCurveNetwork(meshPolyscopeLabel)
    //      ->addNodeScalarQuantity("Node acceleration x", accelerationX);

    // Edge quantities
    std::vector<double> A(pMesh->EN());
    std::vector<double> J(pMesh->EN());
    std::vector<double> I2(pMesh->EN());
    std::vector<double> I3(pMesh->EN());
    for (const EdgeType &e : pMesh->edge) {
        const size_t ei = pMesh->getIndex(e);
        A[ei] = pMesh->elements[e].dimensions.A;
        J[ei] = pMesh->elements[e].dimensions.inertia.J;
        I2[ei] = pMesh->elements[e].dimensions.inertia.I2;
        I3[ei] = pMesh->elements[e].dimensions.inertia.I3;
    }

    polyscope::getCurveNetwork(meshPolyscopeLabel)->addEdgeScalarQuantity("A", A);
    polyscope::getCurveNetwork(meshPolyscopeLabel)->addEdgeScalarQuantity("J", J);
    polyscope::getCurveNetwork(meshPolyscopeLabel)
        ->addEdgeScalarQuantity("I2", I2);
    polyscope::getCurveNetwork(meshPolyscopeLabel)->addEdgeScalarQuantity("I3", I3);

    // Specify the callback
    static bool calledOnce = false;
    if (!calledOnce) {
        PolyscopeInterface::addUserCallback([&]() {
            // Since options::openImGuiWindowForUserCallback == true by default,
            // we can immediately start using ImGui commands to build a UI

            ImGui::PushItemWidth(100); // Make ui elements 100 pixels wide,
                // instead of full width. Must have
                // matching PopItemWidth() below.

            static int debugModeStep = mSettings.debugModeStep.has_value()
                                           ? mSettings.debugModeStep.value()
                                           : 0;
            if (ImGui::InputInt("Simulation debug step",
                                &debugModeStep)) { // set a int variable
                if (debugModeStep != 0) {
                    *mSettings.debugModeStep = debugModeStep;
                }
            }
            //            mSettings.drawingStep = mSettings.debugModeStep;
            ImGui::Checkbox("Enable drawing",
                            &mSettings.shouldDraw); // set a int variable
            ImGui::Text("Number of simulation steps: %zu", mCurrentSimulationStep);

            ImGui::PopItemWidth();
        });
        calledOnce = true;
    }

    if (!screenshotsFolder.empty()) {
        static bool firstDraw = true;
        if (firstDraw) {
            for (const auto &entry :
                 std::filesystem::directory_iterator(screenshotsFolder))
                std::filesystem::remove_all(entry.path());
            //      polyscope::view::processZoom(5);
            firstDraw = false;
        }
        polyscope::screenshot(
            std::filesystem::path(screenshotsFolder)
                .append(std::to_string(mCurrentSimulationStep) + ".png")
                .string(),
            false);
    }
    polyscope::show();
}
#endif

void DRMSimulationModel::applySolutionGuess(const SimulationResults &solutionGuess,
                                            const std::shared_ptr<SimulationJob> &pJob)
{
    assert(solutionGuess.displacements.size() == pMesh->VN()
           && solutionGuess.rotationalDisplacementQuaternion.size() == pMesh->VN());

    for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        Node &node = pMesh->nodes[vi];
        Eigen::Vector3d translationalDisplacements(solutionGuess.displacements[vi].getTranslation());
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(0)) {
            node.displacements[0] = translationalDisplacements[0];
        }
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(1)) {
            node.displacements[1] = translationalDisplacements[1];
        }
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(2)) {
            node.displacements[2] = translationalDisplacements[2];
        }

        updateNodePosition(pMesh->vert[vi], pJob->constrainedVertices);
    }

    for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        Node &node = pMesh->nodes[vi];
        const Eigen::Vector3d nInitial_eigen = node.initialNormal.ToEigenVector<Eigen::Vector3d>();
        Eigen::Quaternion<double> q;
        Eigen::Vector3d eulerAngles = solutionGuess.displacements[vi].getRotation();
        q = Eigen::AngleAxisd(eulerAngles[0], Eigen::Vector3d::UnitX())
            * Eigen::AngleAxisd(eulerAngles[1], Eigen::Vector3d::UnitY())
            * Eigen::AngleAxisd(eulerAngles[2], Eigen::Vector3d::UnitZ());

        Eigen::Vector3d nDeformed_eigen = (q * nInitial_eigen) /*.normalized()*/;
        nDeformed_eigen.normalized();
        //        Eigen::Vector3d n_groundOfTruth = solutionGuess.debug_q_normal[vi] * nInitial_eigen;
        //        n_groundOfTruth.normalized();
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(3)) {
            node.displacements[3] = (nDeformed_eigen - nInitial_eigen)[0];
        }
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(4)) {
            node.displacements[4] = (nDeformed_eigen - nInitial_eigen)[1];
        }
        updateNodeNormal(pMesh->vert[vi], pJob->constrainedVertices);
        //        const auto debug_rightNy = solutionGuess.debug_drmDisplacements[vi][4];

        Eigen::Vector3d referenceT1_deformed = computeT1Vector(node.referenceElement->cP(0),
                                                               node.referenceElement->cP(1))
                                                   .ToEigenVector<Eigen::Vector3d>();
        const Eigen::Vector3d referenceF1_deformed
            = (referenceT1_deformed - (nInitial_eigen * (referenceT1_deformed.dot(nInitial_eigen))))
                  .normalized();

        const Eigen::Vector3d referenceT1_initial
            = computeT1Vector(pMesh->nodes[node.referenceElement->cV(0)].initialLocation,
                              pMesh->nodes[node.referenceElement->cV(1)].initialLocation)
                  .ToEigenVector<Eigen::Vector3d>();
        //          const VectorType &n_initial = node.initialNormal;
        const Eigen::Vector3d referenceF1_initial
            = (referenceT1_initial - (nInitial_eigen * (referenceT1_initial.dot(nInitial_eigen))))
                  .normalized();
        Eigen::Quaternion<double> q_f1; //nr is with respect to f1
        q_f1.setFromTwoVectors(referenceF1_initial, referenceF1_deformed);
        Eigen::Quaternion<double> q_normal;
        q_normal.setFromTwoVectors(nInitial_eigen, nDeformed_eigen);
        Eigen::Quaternion<double> q_nr = q_f1.inverse() * q_normal.inverse() * q;
        q_nr.w() = q_nr.w() >= 1 ? 1 : q_nr.w();
        q_nr.w() = q_nr.w() <= -1 ? -1 : q_nr.w();

        const double nr_0To2pi_pos = 2 * std::acos(q_nr.w());
        //        const double nr_0To2pi_groundOfTruth = 2 * std::acos(solutionGuess.debug_q_nr[vi].w());
        const double nr_0To2pi = nr_0To2pi_pos <= M_PI ? nr_0To2pi_pos : (nr_0To2pi_pos - 2 * M_PI);
        Eigen::Vector3d deformedNormal_debug(q_nr.x() * sin(nr_0To2pi_pos / 2),
                                             q_nr.y() * sin(nr_0To2pi_pos / 2),
                                             q_nr.z() * sin(nr_0To2pi_pos / 2));
        /*deformedNormal_debug =*/deformedNormal_debug.normalize();
#ifdef POLYSCOPE_DEFINED
        if (std::isnan(deformedNormal_debug.norm())) {
            std::cerr << "nr_0To2pi_pos:" << nr_0To2pi_pos << std::endl;
            std::cerr << "q_nrx:" << q_nr.x() << std::endl;
            std::cerr << "q_nry:" << q_nr.y() << std::endl;
            std::cerr << "q_nrz:" << q_nr.z() << std::endl;
            std::cerr << "q_nrw:" << q_nr.w() << std::endl;
            std::cerr << "nan deformedNormal in guess" << std::endl;
        }
#endif
        const double nr = deformedNormal_debug.dot(nDeformed_eigen) > 0 ? nr_0To2pi : -nr_0To2pi;
        if (!pJob->constrainedVertices.contains(vi)
            || !pJob->constrainedVertices.at(vi).contains(5)) {
            node.displacements[5] = nr;
        }
        //        const double nr_asin = q_nr.x()
        if (isRigidSupport[vi]) {
            const EdgePointer &refElem = node.referenceElement;
            const VectorType &refT1 = computeT1Vector(refElem->cP(0), refElem->cP(1));

            const VectorType &t1Initial
                = computeT1Vector(pMesh->nodes[refElem->cV(0)].initialLocation,
                                  pMesh->nodes[refElem->cV(1)].initialLocation);
            VectorType g1 = Cross(refT1, t1Initial);
            node.nR = g1.dot(pMesh->vert[vi].cN());

        } else {
            node.displacements[5] = nr;
        }
    }
    updateElementalFrames();

    applyDisplacements(constrainedVertices);
    if (!pJob->nodalForcedDisplacements.empty()) {
        applyForcedDisplacements(
            pJob->nodalForcedDisplacements);
    }
    updateElementalLengths();

    //    //    registerWorldAxes();
    //    Eigen::MatrixX3d framesX(pMesh->VN(), 3);
    //    Eigen::MatrixX3d framesY(pMesh->VN(), 3);
    //    Eigen::MatrixX3d framesZ(pMesh->VN(), 3);
    //    for (VertexIndex vi = 0; vi < pMesh->VN(); vi++) {
    //        Node &node = pMesh->nodes[vi];
    //        Eigen::Vector3d translationalDisplacements(solutionGuess.displacements[vi].getTranslation());
    //        node.displacements[0] = translationalDisplacements[0];
    //        node.displacements[1] = translationalDisplacements[1];
    //        node.displacements[2] = translationalDisplacements[2];
    //        Eigen::Quaternion<double> q;
    //        Eigen::Vector3d eulerAngles = solutionGuess.displacements[vi].getRotation();
    //        q = Eigen::AngleAxisd(eulerAngles[0], Eigen::Vector3d::UnitX())
    //            * Eigen::AngleAxisd(eulerAngles[1], Eigen::Vector3d::UnitY())
    //            * Eigen::AngleAxisd(eulerAngles[2], Eigen::Vector3d::UnitZ());

    //        auto deformedNormal = q * Eigen::Vector3d(0, 0, 1);
    //        auto deformedFrameY = q * Eigen::Vector3d(0, 1, 0);
    //        auto deformedFrameX = q * Eigen::Vector3d(1, 0, 0);
    //        framesX.row(vi) = Eigen::Vector3d(deformedFrameX[0], deformedFrameX[1], deformedFrameX[2]);
    //        framesY.row(vi) = Eigen::Vector3d(deformedFrameY[0], deformedFrameY[1], deformedFrameY[2]);
    //        framesZ.row(vi) = Eigen::Vector3d(deformedNormal[0], deformedNormal[1], deformedNormal[2]);
    //    }
    //    polyscope::CurveNetwork *meshPolyscopeHandle = polyscope::getCurveNetwork(meshPolyscopeLabel);
    //    meshPolyscopeHandle->updateNodePositions(pMesh->getEigenVertices());

    //    //if(showFramesOn.contains(vi)){
    //    auto polyscopeHandle_frameX = meshPolyscopeHandle->addNodeVectorQuantity("FrameX", framesX);
    //    polyscopeHandle_frameX->setVectorLengthScale(0.01);
    //    polyscopeHandle_frameX->setVectorRadius(0.01);
    //    polyscopeHandle_frameX->setVectorColor(
    //        /*polyscope::getNextUniqueColor()*/ glm::vec3(1, 0, 0));
    //    auto polyscopeHandle_frameY = meshPolyscopeHandle->addNodeVectorQuantity("FrameY", framesY);
    //    polyscopeHandle_frameY->setVectorLengthScale(0.01);
    //    polyscopeHandle_frameY->setVectorRadius(0.01);
    //    polyscopeHandle_frameY->setVectorColor(
    //        /*polyscope::getNextUniqueColor()*/ glm::vec3(0, 1, 0));
    //    auto polyscopeHandle_frameZ = meshPolyscopeHandle->addNodeVectorQuantity("FrameZ", framesZ);
    //    polyscopeHandle_frameZ->setVectorLengthScale(0.01);
    //    polyscopeHandle_frameZ->setVectorRadius(0.01);
    //    polyscopeHandle_frameZ->setVectorColor(
    //        /*polyscope::getNextUniqueColor()*/ glm::vec3(0, 0, 1));
    //    //}
    //    polyscope::show();
}
void DRMSimulationModel::applyKineticDamping(const std::shared_ptr<SimulationJob> &pJob)
{
    //    if (!mSettings.viscousDampingFactor.has_value()) {
    //            const bool shouldCapDisplacements = mSettings.displacementCap.has_value();
    for (VertexType &v : pMesh->vert) {
        Node &node = pMesh->nodes[v];
        Vector6d stepDisplacement = node.velocity * 0.5 * Dt;
        //                if (shouldCapDisplacements
        //                    && stepDisplacement.getTranslation().norm() > mSettings.displacementCap) {
        //                    stepDisplacement = stepDisplacement
        //                                       * (*mSettings.displacementCap
        //                                          / stepDisplacement.getTranslation().norm());
        //                }
        node.displacements = node.displacements - stepDisplacement;
    }
    applyDisplacements(constrainedVertices);
    if (!pJob->nodalForcedDisplacements.empty()) {
        applyForcedDisplacements(

            pJob->nodalForcedDisplacements);
    }
    updateElementalLengths();
    //    }
    //            const double triggerPercentage = 0.01;
    //            const double xi_min = 0.55;
    //            const double xi_init = 0.9969;
    //            if (mSettings.totalResidualForcesNormThreshold / pMesh->totalResidualForcesNorm
    //                > triggerPercentage) {
    //                mSettings.xi = ((xi_min - xi_init)
    //                                    * (mSettings.totalResidualForcesNormThreshold
    //                                       / pMesh->totalResidualForcesNorm)
    //                                + xi_init - triggerPercentage * xi_min)
    //                               / (1 - triggerPercentage);
    //            }
    resetVelocities();
    ++numOfDampings;
}

SimulationResults DRMSimulationModel::executeSimulation(const std::shared_ptr<SimulationJob> &pJob)
{
    auto beginTime = std::chrono::high_resolution_clock::now();
    updateNodalMasses();
    //    std::unordered_map<VertexIndex, Vector6d> nodalExternalForces = pJob->nodalExternalForces;
    //    double totalExternalForcesNorm = 0;
    //    Vector6d sumOfExternalForces(0);
    //    for (auto &nodalForce : nodalExternalForces) {
    //        const double percentageOfExternalLoads = double(externalLoadStep)
    //                                                 / mSettings.desiredGradualExternalLoadsSteps;
    //        nodalForce.second = nodalForce.second * percentageOfExternalLoads;
    //        totalExternalForcesNorm += nodalForce.second.norm();
    //        //        sumOfExternalForces = sumOfExternalForces + nodalForce.second;
    //    }
    updateNodalExternalForces(pJob->nodalExternalForces, constrainedVertices);
    if (!pJob->nodalExternalForces.empty()) {
        mSettings.totalResidualForcesNormThreshold
            = mSettings.totalExternalForcesNormPercentageTermination
              * pMesh->totalExternalForcesNorm;
    } else {
        mSettings.totalResidualForcesNormThreshold = 1e-3;
        std::cout << "No forces setted default residual forces norm threshold" << std::endl;
    }
    if (mSettings.beVerbose) {
        std::cout << "totalResidualForcesNormThreshold:"
                  << mSettings.totalResidualForcesNormThreshold << std::endl;
        if (mSettings.averageResidualForcesCriterionThreshold.has_value()) {
            std::cout << "average/extNorm threshold:"
                      << *mSettings.averageResidualForcesCriterionThreshold << std::endl;
        }
    }

    if (mSettings.beVerbose) {
        std::cout << "Executing simulation for mesh with:" << pMesh->VN() << " nodes and "
                  << pMesh->EN() << " elements." << std::endl;
    }

    const size_t movingAverageSampleSize = 200;
    std::queue<double> residualForcesMovingAverageHistorySample;
    std::vector<double> percentageOfConvergence;
    //    double residualForcesMovingAverageDerivativeMax = 0;
    while (!mSettings.maxDRMIterations.has_value()
           || mCurrentSimulationStep < mSettings.maxDRMIterations.value()) {
        if ((mSettings.debugModeStep.has_value() && mCurrentSimulationStep == 50000)) {
            //            std::filesystem::create_directory("./PatternOptimizationNonConv");
            //            pJob->save("./PatternOptimizationNonConv");
            //            Dt = mSettings.Dtini;
        }
        //        if (mCurrentSimulationStep == 500 && shouldTemporarilyDampForces) {
        //            Dt = mSettings.Dtini;
        //        }
        //  while (true) {
        updateNormalDerivatives();
        updateT1Derivatives();
        updateRDerivatives();
        updateT2Derivatives();
        updateT3Derivatives();
        const bool shouldBreak = mCurrentSimulationStep == 12970;
        updateResidualForcesOnTheFly(constrainedVertices);

        // TODO: write parallel function for updating positions
        // TODO: Make a single function out of updateResidualForcesOnTheFly
        // updatePositionsOnTheFly
        //    updatePositionsOnTheFly(constrainedVertices);
        updateNodalMasses();
        updateNodalAccelerations();
        updateNodalVelocities();
        updateNodalDisplacements();
        applyDisplacements(constrainedVertices);
        if (!pJob->nodalForcedDisplacements.empty()) {
            applyForcedDisplacements(

                pJob->nodalForcedDisplacements);
        }
        //    if (!pJob->nodalForcedNormals.empty()) {
        //      applyForcedNormals(pJob->nodalForcedNormals);
        //    }
        updateElementalLengths();
        mCurrentSimulationStep++;
        if (std::isnan(pMesh->currentTotalKineticEnergy)) {
            std::cout << pMesh->currentTotalKineticEnergy << std::endl;
            if (mSettings.beVerbose) {
                std::cerr << "Infinite kinetic energy at step " << mCurrentSimulationStep
                          << ". Exiting.." << std::endl;
            }
            break;
        }

        if (minTotalResidualForcesNorm > pMesh->totalResidualForcesNorm) {
            minTotalResidualForcesNorm = pMesh->totalResidualForcesNorm;
            static int lastSavedStep = mCurrentSimulationStep;
            if (mSettings.saveIntermediateBestStates.has_value()
                && mSettings.saveIntermediateBestStates.value()
                && mCurrentSimulationStep - lastSavedStep > 20000) {
                lastSavedStep = mCurrentSimulationStep;
                computeResults(pJob).save("./IntermediateResults_" + pJob->getLabel());
            }
        }

        //normalized sum of displacements
        //        double sumOfDisplacementsNorm = 0;
        //        for (size_t vi = 0; vi < pMesh->VN(); vi++) {
        //            sumOfDisplacementsNorm += pMesh->nodes[vi].displacements.getTranslation().norm();
        //        }
        //        sumOfDisplacementsNorm /= pMesh->bbox.Diag();
        //        pMesh->sumOfNormalizedDisplacementNorms = sumOfDisplacementsNorm;

        //moving average
        //        //      pMesh->residualForcesMovingAverage = (pMesh->totalResidualForcesNorm
        //        //                                            + mCurrentSimulationStep
        //        //                                                  * pMesh->residualForcesMovingAverage)
        //        //                                           / (1 + mCurrentSimulationStep);
        pMesh->residualForcesMovingAverage += pMesh->totalResidualForcesNorm
                                              / movingAverageSampleSize;
        residualForcesMovingAverageHistorySample.push(pMesh->residualForcesMovingAverage);
        if (movingAverageSampleSize < residualForcesMovingAverageHistorySample.size()) {
            const double firstElementValue = residualForcesMovingAverageHistorySample.front();
            pMesh->residualForcesMovingAverage -= firstElementValue / movingAverageSampleSize;
            residualForcesMovingAverageHistorySample.pop();

            //            pMesh->residualForcesMovingAverageDerivativeNorm
            //                = std::abs((residualForcesMovingAverageHistorySample.back()
            //                            - residualForcesMovingAverageHistorySample.front()))
            //                  / (movingAverageSampleSize);
            //            residualForcesMovingAverageDerivativeMax
            //                = std::max(pMesh->residualForcesMovingAverageDerivativeNorm,
            //                           residualForcesMovingAverageDerivativeMax);
            //            pMesh->residualForcesMovingAverageDerivativeNorm
            //                /= residualForcesMovingAverageDerivativeMax;
            //            //          std::cout << "Normalized derivative:"
            //            //                    << residualForcesMovingAverageDerivativeNorm
            //            //                    << std::endl;
        }

        //    pMesh->previousTotalPotentialEnergykN =
        //        pMesh->currentTotalPotentialEnergykN;
        //    pMesh->currentTotalPotentialEnergykN = computeTotalPotentialEnergy() / 1000;
        //    timePerNodePerIterationHistor.push_back(timePerNodePerIteration);
        if (mSettings.beVerbose && mSettings.debugModeStep.has_value()
            && mCurrentSimulationStep % mSettings.debugModeStep.value() == 0) {
            printCurrentState();

            //            auto t2 = std::chrono::high_resolution_clock::now();
            //            const double executionTime_min
            //                = std::chrono::duration_cast<std::chrono::minutes>(t2 - beginTime).count();
            //            std::cout << "Execution time(min):" << executionTime_min << std::endl;
            if (mSettings.averageResidualForcesCriterionThreshold.has_value()) {
                std::cout << "Best percentage of target (average):"
                          << 100 * mSettings.averageResidualForcesCriterionThreshold.value()
                                 * pMesh->totalExternalForcesNorm * pMesh->VN()
                                 / minTotalResidualForcesNorm
                          << "%" << std::endl;
            } else {
                std::cout << "Best percentage of target:"
                          << 100 * mSettings.totalExternalForcesNormPercentageTermination
                                 * pMesh->totalExternalForcesNorm / minTotalResidualForcesNorm
                          << "%" << std::endl;
            }
            //            SimulationResultsReporter::createPlot("Number of Steps",
            //                                                  "Residual Forces mov aver",
            //                                                  history.residualForcesMovingAverage);
            //          SimulationResultsReporter::createPlot("Number of Steps",
            //                                                "Residual Forces mov aver deriv",
            //                                                movingAveragesDerivatives);
            //          draw();
            //        SimulationResulnodalForcedDisplacementstsReporter::createPlot("Number of Steps",
            //                                              "Time/(#nodes*#iterations)",
            //                                              timePerNodePerIterationHistory);
        }

        if ((mSettings.shouldCreatePlots || mSettings.debugModeStep.has_value())
            && mCurrentSimulationStep != 0) {
            history.stepPulse(*pMesh);
            percentageOfConvergence.push_back(100 * mSettings.totalResidualForcesNormThreshold
                                              / pMesh->totalResidualForcesNorm);
        }

        if (mSettings.shouldCreatePlots && mSettings.debugModeStep.has_value()
            && mCurrentSimulationStep % mSettings.debugModeStep.value() == 0) {
            //            SimulationResultsReporter::createPlot("Number of Steps",
            //                                                  "Residual Forces mov aver deriv",
            //                                                  movingAveragesDerivatives_norm);
            //            SimulationResultsReporter::createPlot("Number of Steps",
            //                                                  "Residual Forces mov aver",
            //                                                  history.residualForcesMovingAverage,
            //                                                  {},
            //                                                  history.redMarks);
            SimulationResultsReporter::createPlot("Number of Steps",
                                                  "Log of Residual Forces",
                                                  history.logResidualForces,
                                                  {},
                                                  history.redMarks);
            //            SimulationResultsReporter::createPlot("Number of Steps",
            //                                                  "Log of Kinetic energy",
            //                                                  history.kineticEnergy,
            //                                                  {},
            //                                                  history.redMarks);
            //            SimulationResultsReporter reporter;
            //            reporter.reportHistory(history, "IntermediateResults", pJob->pMesh->getLabel());
            //            SimulationResultsReporter::createPlot("Number of Iterations",
            //                                                  "Sum of normalized displacement norms",
            //                                                  history.sumOfNormalizedDisplacementNorms /*,
            //                               std::filesystem::path("./")
            //                                   .append("SumOfNormalizedDisplacementNorms_" + graphSuffix + ".png")
            //                                   .string()*/
            //                                                  ,
            //                                                  {},
            //                                                  history.redMarks);
            //          SimulationResultsReporter::createPlot("Number of Steps",
            //                                                "Percentage of convergence",
            //                                                percentageOfConvergence,
            //                                                {},
            //                                                history.redMarks);
        }

#ifdef POLYSCOPE_DEFINED
        if (mSettings.shouldDraw && mSettings.debugModeStep.has_value()
            && mCurrentSimulationStep % mSettings.debugModeStep.value() == 0) /* &&
          
currentSimulationStep > maxDRMIterations*/
        {
            //      std::string saveTo = std::filesystem::current_path()
            //                               .append("Debugging_files")
            //                               .append("Screenshots")
            //                               .string();
            draw();
            //      yValues = history.kineticEnergy;
            //      plotHandle = matplot::scatter(xPlot, yValues);
            //      label = "Log of Kinetic energy";
            //      plotHandle->legend_string(label);

            //      shouldUseKineticEnergyThreshold = true;
        }
#endif

        //    t = t + Dt;
        //    std::cout << "Kinetic energy:" << mesh.currentTotalKineticEnergy
        //              << std::endl;
        //    std::cout << "Residual forces norm:" << mesh.totalResidualForcesNorm
        //              << std::endl;
        const bool fullfillsResidualForcesNormTerminationCriterion
            = !mSettings.averageResidualForcesCriterionThreshold.has_value()
              && pMesh->totalResidualForcesNorm / pMesh->totalExternalForcesNorm
                     < mSettings.totalExternalForcesNormPercentageTermination;
        const bool fullfillsAverageResidualForcesNormTerminationCriterion
            = mSettings.averageResidualForcesCriterionThreshold.has_value()
              && (pMesh->totalResidualForcesNorm / pMesh->VN()) / pMesh->totalExternalForcesNorm
                     < mSettings.averageResidualForcesCriterionThreshold.value();
        if ((fullfillsAverageResidualForcesNormTerminationCriterion
             || fullfillsResidualForcesNormTerminationCriterion)
            && numOfDampings > 0
            && (pJob->nodalForcedDisplacements.empty()
                || mCurrentSimulationStep > mSettings.gradualForcedDisplacementSteps)) {
            if (mSettings.beVerbose /*&& !mSettings.isDebugMode*/) {
                std::cout << "Simulation converged." << std::endl;
                printCurrentState();
                if (fullfillsResidualForcesNormTerminationCriterion) {
                    std::cout << "Converged using residual forces norm threshold criterion"
                              << std::endl;
                } else if (fullfillsAverageResidualForcesNormTerminationCriterion) {
                    std::cout << "Converged using average residual forces norm threshold criterion"
                              << std::endl;
                }
            }
            break;
        }
        // Residual forces norm convergence
        if ((pMesh->previousTotalKineticEnergy > pMesh->currentTotalKineticEnergy
             //          && mCurrentSimulationStep > movingAverageSampleSize
             )
            /* || (pMesh->totalResidualForcesNorm / mSettings.totalResidualForcesNormThreshold <= 1
              && mCurrentSimulationStep > 1)*/
            /*||
mesh->previousTotalPotentialEnergykN >
mesh->currentTotalPotentialEnergykN*/
            /*|| mesh->currentTotalPotentialEnergykN < minPotentialEnergy*/) {
            //        if (pMesh->totalResidualForcesNorm < totalResidualForcesNormThreshold) {
            const bool fullfillsKineticEnergyTerminationCriterion
                = mSettings.totalTranslationalKineticEnergyThreshold.has_value()
                  && pMesh->currentTotalTranslationalKineticEnergy
                         < mSettings.totalTranslationalKineticEnergyThreshold.value()
                  && mCurrentSimulationStep > 20 && numOfDampings > 0;
            //            const bool fullfillsMovingAverageNormTerminationCriterion
            //                = pMesh->residualForcesMovingAverage
            //                  < mSettings.residualForcesMovingAverageNormThreshold;
            /*pMesh->residualForcesMovingAverage < totalResidualForcesNormThreshold*/
            //            const bool fullfillsMovingAverageDerivativeNormTerminationCriterion
            //                = pMesh->residualForcesMovingAverageDerivativeNorm < 1e-4;
            const bool shouldTerminate = fullfillsKineticEnergyTerminationCriterion
                //                                                       || fullfillsMovingAverageNormTerminationCriterion
                //                || fullfillsMovingAverageDerivativeNormTerminationCriterion
                ;
            if (shouldTerminate) {
                if (mSettings.beVerbose /*&& !mSettings.isDebugMode*/) {
                    std::cout << "Simulation converged." << std::endl;
                    printCurrentState();
                    if (fullfillsKineticEnergyTerminationCriterion) {
                        std::cout << "The kinetic energy of the system was "
                                     " used as a convergence criterion"
                                  << std::endl;
                    }
                }
                //                if (mSettings.desiredGradualExternalLoadsSteps == externalLoadStep) {
                break;
                //                } else {
                //                    externalLoadStep++;
                //                    std::unordered_map<VertexIndex, Vector6d> nodalExternalForces
                //                        = pJob->nodalExternalForces;
                //                    double totalExternalForcesNorm = 0;
                //                    for (auto &nodalForce : nodalExternalForces) {
                //                        const double percentageOfExternalLoads
                //                            = double(externalLoadStep) / mSettings.desiredGradualExternalLoadsSteps;
                //                        nodalForce.second = nodalForce.second * percentageOfExternalLoads;
                //                        totalExternalForcesNorm += nodalForce.second.norm();
                //                    }
                //                    updateNodalExternalForces(nodalExternalForces, constrainedVertices);

                //                    if (!nodalExternalForces.empty()) {
                //                        mSettings.totalResidualForcesNormThreshold = 1e-2 * totalExternalForcesNorm;
                //                    }
                //                    if (mSettings.beVerbose) {
                //                        std::cout << "totalResidualForcesNormThreshold:"
                //                                  << mSettings.totalResidualForcesNormThreshold << std::endl;
                //                    }
                //                }
                //        }
            }

            if (mSettings.useKineticDamping) {
                applyKineticDamping(pJob);
                Dt *= mSettings.xi;
                if (mSettings.shouldCreatePlots) {
                    history.redMarks.push_back(mCurrentSimulationStep);
                }
            }
            //            if (mSettings.isDebugMode) {
            //                std::cout << Dt << std::endl;
            //            }
            //          std::cout << "Number of dampings:" << numOfDampings << endl;
            //          draw();
        }
    }
    auto endTime = std::chrono::high_resolution_clock::now();

    SimulationResults results = computeResults(pJob);
    results.executionTime = std::chrono::duration_cast<std::chrono::seconds>(endTime - beginTime)
                                .count();

    if (!mSettings.debugModeStep.has_value() && mSettings.shouldCreatePlots) {
        SimulationResultsReporter reporter;
        reporter.reportResults({results}, "Results", pJob->pMesh->getLabel());
    }

#ifdef POLYSCOPE_DEFINED
    if (mSettings.shouldDraw || mSettings.debugModeStep.has_value()) {
        polyscope::removeCurveNetwork(meshPolyscopeLabel);
        polyscope::removeCurveNetwork("Initial_" + meshPolyscopeLabel);
    }
#endif
    return results;
}
SimulationResults DRMSimulationModel::executeSimulation(const std::shared_ptr<SimulationJob> &pJob,
                                                        const Settings &settings,
                                                        const SimulationResults &solutionGuess)
{
    reset(pJob, settings);
    assert(pJob->pMesh != nullptr);

    if (!solutionGuess.displacements.empty()) {
        assert(!mSettings.linearGuessForceScaleFactor.has_value());
        applySolutionGuess(solutionGuess, pJob);
        shouldTemporarilyDampForces = true;
    }

    if (mSettings.linearGuessForceScaleFactor.has_value()) {
        const double forceScaleFactor = mSettings.linearGuessForceScaleFactor.value();
        for (auto &externalForce : pJob->nodalExternalForces) {
            externalForce.second = externalForce.second * forceScaleFactor;
        }
        LinearSimulationModel linearSimulationModel;
        SimulationResults simulationResults_fullPatternLinearModel = linearSimulationModel
                                                                         .executeSimulation(pJob);
        //        simulationResults_fullPatternLinearModel.save(fullResultsFolderPath);
        for (auto &externalForce : pJob->nodalExternalForces) {
            externalForce.second = externalForce.second / forceScaleFactor;
        }

        applySolutionGuess(simulationResults_fullPatternLinearModel, pJob);
        shouldTemporarilyDampForces = true;
    }

    SimulationResults results = executeSimulation(pJob); //calling the virtual function
    return results;
}

//#ifdef USE_ENSMALLEN

//void DRMSimulationModel::setJob(const std::shared_ptr<SimulationJob> &pJob)
//{
//    reset(pJob);

//    updateNodalExternalForces(pJob->nodalExternalForces, constrainedVertices);
//    //    arma::mat externalForces(pMesh->VN() * NumDoF);
//    //    for (int vi = 0; vi < pMesh->VN(); vi++) {
//    //        const Vector6d &nodeExternalForce = pMesh.vert[vi].node.externalForce;
//    //        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
//    //            externalForces(vi * NumDoF + dofi) = nodeExternalForce[dofi];
//    //        }
//    //    }
//}

//SimulationMesh *DRMSimulationModel::getDeformedMesh(const arma::mat &x)
//{
//    for (int vi = 0; vi < pMesh->VN(); vi++) {
//        Node &node = pMesh->nodes[vi];
//        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
//            node.displacements[dofi] = x(vi * DoF::NumDoF + dofi);
//        }
//    }

//    applyDisplacements(constrainedVertices);
//    if (!pJob->nodalForcedDisplacements.empty()) {
//        applyForcedDisplacements(pJob->nodalForcedDisplacements);
//    }

//    return pMesh.get();
//}

//double DRMSimulationModel::EvaluateWithGradient(const arma::mat &x, arma::mat &g)
//{
//    for (int vi = 0; vi < pMesh->VN(); vi++) {
//        Node &node = pMesh->nodes[vi];
//        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
//            node.displacements[dofi] = x(vi * DoF::NumDoF + dofi);
//        }
//    }

//    applyDisplacements(constrainedVertices);
//    if (!pJob->nodalForcedDisplacements.empty()) {
//        applyForcedDisplacements(pJob->nodalForcedDisplacements);
//    }
//    updateElementalLengths();
//    updateNormalDerivatives();
//    updateT1Derivatives();
//    updateRDerivatives();
//    updateT2Derivatives();
//    updateT3Derivatives();
//    updateResidualForcesOnTheFly(constrainedVertices);
//    for (int vi = 0; vi < pMesh->VN(); vi++) {
//        Node &node = pMesh->nodes[vi];
//        for (DoFType dofi = DoF::Ux; dofi < DoF::NumDoF; dofi++) {
//            g(vi * NumDoF + dofi) = node.force.residual[dofi];
//        }
//    }
//    mCurrentSimulationStep++;
//    const double PE = computeTotalPotentialEnergy();
//    std::cout << "PE:" << PE << std::endl;
//    return PE;
//}

//#endif

void DRMSimulationModel::Settings::save(const std::filesystem::path &jsonFilePath) const
{
    nlohmann::json json;
    json[GET_VARIABLE_NAME(shouldDraw)] = shouldDraw;
    json[GET_VARIABLE_NAME(beVerbose)] = beVerbose;
    json[GET_VARIABLE_NAME(shouldCreatePlots)] = shouldCreatePlots;
    json[GET_VARIABLE_NAME(Dtini)] = Dtini;
    json[GET_VARIABLE_NAME(xi)] = xi;
    json[GET_VARIABLE_NAME(gamma)] = gamma;
    json[GET_VARIABLE_NAME(useKineticDamping)] = totalResidualForcesNormThreshold;
    if (maxDRMIterations.has_value()) {
        json[GET_VARIABLE_NAME(jsonLabels.maxDRMIterations)] = maxDRMIterations.value();
    }
    if (debugModeStep.has_value()) {
        json[GET_VARIABLE_NAME(debugModeStep)] = debugModeStep.value();
    }
    if (totalTranslationalKineticEnergyThreshold.has_value()) {
        json[GET_VARIABLE_NAME(totalTranslationalKineticEnergyThreshold)]
            = totalTranslationalKineticEnergyThreshold.value();
    }
    if (averageResidualForcesCriterionThreshold.has_value()) {
        json[GET_VARIABLE_NAME(averageResidualForcesCriterionThreshold)]
            = averageResidualForcesCriterionThreshold.value();
    }
    if (linearGuessForceScaleFactor.has_value()) {
        json[GET_VARIABLE_NAME(linearGuessForceScaleFactor)] = linearGuessForceScaleFactor.value();
    }
    if (viscousDampingFactor.has_value()) {
        json[GET_VARIABLE_NAME(viscousDampingFactor)] = viscousDampingFactor.value();
    }
    json[GET_VARIABLE_NAME(useKineticDamping)] = useKineticDamping;
    //    if (intermediateResultsSaveStep.has_value()) {
    //        json[GET_VARIABLE_NAME(intermediateResultsSaveStep)] = intermediateResultsSaveStep.value();
    //    }

    //    if (saveIntermediateBestStates.has_value()) {
    //        json[GET_VARIABLE_NAME(saveIntermediateBestStates)] = saveIntermediateBestStates.value()
    //                                                                  ? "true"
    //                                                                  : "false";
    //    }

    std::filesystem::create_directories(jsonFilePath.parent_path());
    std::ofstream jsonFile(jsonFilePath);
    std::cout << "Saving DRM settings to:" << jsonFilePath << std::endl;
    jsonFile << json;
    jsonFile.close();
}

bool DRMSimulationModel::Settings::load(const std::filesystem::path &jsonFilePath)
{
    if (!std::filesystem::exists(std::filesystem::path(jsonFilePath))) {
        std::cerr << "The json file does not exist. Json file provided:" << jsonFilePath.string()
                  << std::endl;
        assert(false);
        return false;
    }

    if (std::filesystem::path(jsonFilePath).extension() != ".json") {
        std::cerr << "A json file is expected as input. The given file has the "
                     "following extension:"
                  << std::filesystem::path(jsonFilePath).extension() << std::endl;
        assert(false);
        return false;
    }

    nlohmann::json json;
    std::ifstream ifs(jsonFilePath.string());
    ifs >> json;

    if (json.contains(GET_VARIABLE_NAME(shouldDraw))) {
        shouldDraw = json.at(GET_VARIABLE_NAME(shouldDraw)) == "true" ? true : false;
    }
    if (json.contains(GET_VARIABLE_NAME(beVerbose))) {
        beVerbose = json.at(GET_VARIABLE_NAME(beVerbose)) == "true" ? true : false;
    }
    if (json.contains(GET_VARIABLE_NAME(shouldCreatePlots))) {
        shouldCreatePlots = json.at(GET_VARIABLE_NAME(shouldCreatePlots)) == "true" ? true : false;
    }
    if (json.contains(GET_VARIABLE_NAME(Dtini))) {
        Dtini = json.at(GET_VARIABLE_NAME(Dtini));
    }
    if (json.contains(GET_VARIABLE_NAME(xi))) {
        xi = json.at(GET_VARIABLE_NAME(xi));
    }
    if (json.contains(GET_VARIABLE_NAME(maxDRMIterations))) {
        maxDRMIterations = json.at(GET_VARIABLE_NAME(maxDRMIterations));
    }
    if (json.contains(GET_VARIABLE_NAME(debugModeStep))) {
        debugModeStep = json.at(GET_VARIABLE_NAME(debugModeStep));
    }
    if (json.contains(GET_VARIABLE_NAME(totalTranslationalKineticEnergyThreshold))) {
        totalTranslationalKineticEnergyThreshold = json.at(
            GET_VARIABLE_NAME(totalTranslationalKineticEnergyThreshold));
    }
    if (json.contains(GET_VARIABLE_NAME(gamma))) {
        gamma = json.at(GET_VARIABLE_NAME(gamma));
    }
    if (json.contains(GET_VARIABLE_NAME(averageResidualForcesCriterionThreshold))) {
        averageResidualForcesCriterionThreshold = json.at(
            GET_VARIABLE_NAME(averageResidualForcesCriterionThreshold));
    }
    if (json.contains(GET_VARIABLE_NAME(linearGuessForceScaleFactor))) {
        linearGuessForceScaleFactor = json.at(GET_VARIABLE_NAME(linearGuessForceScaleFactor));
    }

    //    if (json.contains(GET_VARIABLE_NAME(intermediateResultsSaveStep))) {
    //        intermediateResultsSaveStep = json.at(GET_VARIABLE_NAME(intermediateResultsSaveStep));
    //    }

    if (json.contains(GET_VARIABLE_NAME(saveIntermediateBestStates))) {
        saveIntermediateBestStates = json.at(GET_VARIABLE_NAME(saveIntermediateBestStates))
                                             == "true"
                                         ? true
                                         : false;
    }
    //    std::cout << json.dump() << std::endl;

    return true;
}