SmoothingForms.cpp

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#include <polyfem/optimization/forms/SmoothingForms.hpp>
 
#include <polyfem/varforms/diff/DifferentiableVarForm.hpp>
#include <polyfem/utils/MatrixUtils.hpp>
#include <polyfem/utils/Types.hpp>
 
#include <Eigen/Core>
 
#include <cassert>
#include <memory>
#include <numeric>
#include <set>
#include <utility>
#include <vector>
 
namespace polyfem::solver
{
    BoundarySmoothingForm::BoundarySmoothingForm(
        const VariableToSimulationGroup &variable_to_simulations,
        std::shared_ptr<const varform::DifferentiableVarForm> varform,
        const bool scale_invariant,
        const int power,
        const std::vector<int> &surface_selections,
        const std::vector<int> &active_dims) : AdjointForm(variable_to_simulations), varform_(std::move(varform)), scale_invariant_(scale_invariant), power_(power), active_dims_(active_dims)
    {
        const auto &mesh = varform_->get_mesh();
        const int dim = mesh.dimension();
        const int n_verts = mesh.n_vertices();
        assert(mesh.is_simplicial());
        // empty implies all active.
        if (active_dims_.empty())
        {
            active_dims_.resize(dim);
            std::iota(active_dims_.begin(), active_dims_.end(), 0);
        }
 
        surface_ids_ = std::set(surface_selections.begin(), surface_selections.end());
 
        // collect active nodes
        std::vector<bool> active_mask;
        active_mask.assign(n_verts, false);
        std::vector<Eigen::Triplet<bool>> T_adj;
 
        for (int b = 0; b < mesh.n_boundary_elements(); b++)
        {
            const int boundary_id = mesh.get_boundary_id(b);
            if (!surface_ids_.empty() && surface_ids_.find(boundary_id) == surface_ids_.end())
                continue;
 
            for (int lv = 0; lv < dim; lv++)
            {
                active_mask[mesh.boundary_element_vertex(b, lv)] = true;
            }
 
            for (int lv1 = 0; lv1 < dim; lv1++)
                for (int lv2 = 0; lv2 < lv1; lv2++)
                {
                    const int v1 = mesh.boundary_element_vertex(b, lv1);
                    const int v2 = mesh.boundary_element_vertex(b, lv2);
                    T_adj.emplace_back(v2, v1, true);
                    T_adj.emplace_back(v1, v2, true);
                }
        }
 
        adj.setZero();
        adj.resize(n_verts, n_verts);
        adj.setFromTriplets(T_adj.begin(), T_adj.end());
 
        std::vector<int> degrees(n_verts, 0);
        for (int k = 0; k < adj.outerSize(); ++k)
            for (Eigen::SparseMatrix<bool, Eigen::RowMajor>::InnerIterator it(adj, k); it; ++it)
                degrees[k]++;
 
        L.setZero();
        L.resize(n_verts, n_verts);
        if (!scale_invariant_)
        {
            std::vector<Eigen::Triplet<double>> T_L;
            for (int k = 0; k < adj.outerSize(); ++k)
            {
                if (!active_mask[k])
                    continue;
                T_L.emplace_back(k, k, 1);
                for (Eigen::SparseMatrix<bool, Eigen::RowMajor>::InnerIterator it(adj, k); it; ++it)
                {
                    assert(it.row() == k);
                    T_L.emplace_back(it.row(), it.col(), -1. / degrees[k]);
                }
            }
            L.setFromTriplets(T_L.begin(), T_L.end());
            L.prune([](int i, int j, double val) { return abs(val) > 1e-12; });
        }
    }
 
    double BoundarySmoothingForm::value_unweighted(const Eigen::VectorXd &x) const
    {
        const auto &mesh = varform_->get_mesh();
        const int dim = mesh.dimension();
        const int n_verts = mesh.n_vertices();
 
        double val = 0;
        if (scale_invariant_)
        {
            for (int b = 0; b < adj.rows(); b++)
            {
                polyfem::RowVectorNd s;
                s.setZero(dim);
                double sum_norm = 0;
                int valence = 0;
                for (Eigen::SparseMatrix<bool, Eigen::RowMajor>::InnerIterator it(adj, b); it; ++it)
                {
                    assert(it.col() != b);
                    polyfem::RowVectorNd x = mesh.point(b) - mesh.point(it.col());
                    s += x;
                    sum_norm += x.norm();
                    valence += 1;
                }
                if (valence)
                {
                    s = s / sum_norm;
                    val += pow(s.norm(), power_);
                }
            }
        }
        else
        {
            Eigen::MatrixXd V;
            varform_->get_vertices(V);
 
            val = (L * V(Eigen::all, active_dims_)).squaredNorm();
        }
 
        return val;
    }
 
    void BoundarySmoothingForm::compute_partial_gradient(const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const
    {
        const auto &mesh = varform_->get_mesh();
        const int dim = mesh.dimension();
        const int n_verts = mesh.n_vertices();
 
        Eigen::VectorXd grad;
        if (scale_invariant_)
        {
            grad.setZero(n_verts * dim);
            for (int b = 0; b < adj.rows(); b++)
            {
                polyfem::RowVectorNd s;
                s.setZero(dim);
                double sum_norm = 0;
                polyfem::RowVectorNd sum_normalized = s;
                int valence = 0;
                for (Eigen::SparseMatrix<bool, Eigen::RowMajor>::InnerIterator it(adj, b); it; ++it)
                {
                    assert(it.col() != b);
                    polyfem::RowVectorNd x = mesh.point(b) - mesh.point(it.col());
                    s += x;
                    sum_norm += x.norm();
                    sum_normalized += x.normalized();
                    valence += 1;
                }
                if (valence)
                {
                    s = s / sum_norm;
                    const double coeff = power_ * pow(s.norm(), power_ - 2.) / sum_norm;
 
                    grad.segment(b * dim, dim) += (s * valence - s.squaredNorm() * sum_normalized) * coeff;
                    for (Eigen::SparseMatrix<bool, Eigen::RowMajor>::InnerIterator it(adj, b); it; ++it)
                        grad.segment(it.col() * dim, dim) -= (s + s.squaredNorm() * (mesh.point(it.col()) - mesh.point(b)).normalized()) * coeff;
                }
            }
        }
        else
        {
            Eigen::MatrixXd V;
            varform_->get_vertices(V);
 
            Eigen::MatrixXd grad_mat = 2 * (L.transpose() * (L * V));
            for (int d = 0; d < dim; d++)
                if (std::find(active_dims_.begin(), active_dims_.end(), d) == active_dims_.end())
                    grad_mat.col(d).setZero();
            grad = utils::flatten(grad_mat);
        }
 
        gradv = weight() * variable_to_simulations_.apply_parametrization_jacobian(ParameterType::Shape, *varform_, x, [&grad]() {
            return grad;
        });
    }
} // namespace polyfem::solver