Smooth.cpp

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#include <polyfem/mesh/remesh/PhysicsRemesher.hpp>
#include <polyfem/mesh/remesh/L2Projection.hpp>
#include <polyfem/utils/Logger.hpp>
#include <polyfem/assembler/MassMatrixAssembler.hpp>
 
#include <wmtk/ExecutionScheduler.hpp>
#include <wmtk/utils/TriQualityUtils.hpp>
#include <wmtk/utils/TetraQualityUtils.hpp>
#include <wmtk/utils/TupleUtils.hpp>
#include <wmtk/utils/AMIPS.h>
#include <wmtk/utils/AMIPS2D.h>
 
namespace polyfem::mesh
{
    template <class WMTKMesh>
    double get_quality(const WildRemesher<WMTKMesh> &m, const typename WMTKMesh::Tuple &t)
    {
        // Global ids of the vertices of the triangle
        auto vids = m.element_vids(t);
 
        // Temporary variable to store the stacked coordinates of the triangle
        constexpr int NDOF = WildRemesher<WMTKMesh>::DIM * WildRemesher<WMTKMesh>::VERTICES_PER_ELEMENT;
        std::array<double, NDOF> T;
        for (auto i = 0; i < WildRemesher<WMTKMesh>::VERTICES_PER_ELEMENT; i++)
            for (auto j = 0; j < WildRemesher<WMTKMesh>::DIM; j++)
                T[i * WildRemesher<WMTKMesh>::DIM + j] =
                    m.vertex_attrs[vids[i]].rest_position[j];
 
        // Energy evaluation
        double energy;
        if constexpr (std::is_same_v<wmtk::TriMesh, WMTKMesh>)
            energy = wmtk::AMIPS2D_energy(T);
        else
            energy = wmtk::AMIPS_energy(T);
 
        // Filter for numerical issues
        if (!std::isfinite(energy))
            return std::numeric_limits<double>::max();
 
        return energy;
    }
 
    template <class WMTKMesh>
    void project_local_quantities(
        WildRemesher<WMTKMesh> &m,
        LocalMesh<WildRemesher<WMTKMesh>> &old_local_mesh,
        LocalMesh<WildRemesher<WMTKMesh>> &new_local_mesh)
    {
        POLYFEM_REMESHER_SCOPED_TIMER("Project local quantities");
 
        const std::vector<basis::ElementBases> from_bases =
            old_local_mesh.build_bases(m.state.formulation());
        const std::vector<basis::ElementBases> to_bases =
            new_local_mesh.build_bases(m.state.formulation());
 
        const Eigen::MatrixXd &from_projection_quantities = old_local_mesh.projection_quantities();
        const Eigen::MatrixXd &to_projection_quantities = new_local_mesh.projection_quantities();
 
        // solve M x = A y for x where M is the mass matrix and A is the cross mass matrix.
        Eigen::SparseMatrix<double> M, A;
        {
            assembler::MassMatrixAssembler assembler;
            assembler::NoDensity no_density; // Density of one (i.e., no scaling of mass matrix)
            assembler::AssemblyValsCache cache;
 
            assembler.assemble(
                m.is_volume(), m.dim(), new_local_mesh.num_vertices(),
                no_density, to_bases, to_bases, cache, M);
            assert(M.rows() == new_local_mesh.num_vertices() * m.dim());
 
            assembler.assemble_cross(
                m.is_volume(), m.dim(),
                old_local_mesh.num_vertices(), from_bases, from_bases,
                new_local_mesh.num_vertices(), to_bases, to_bases,
                cache, A);
            assert(A.rows() == new_local_mesh.num_vertices() * m.dim());
            assert(A.cols() == old_local_mesh.num_vertices() * m.dim());
        }
 
        // --------------------------------------------------------------------
 
        // NOTE: This assumes the boundary is fixed.
        ipc::CollisionMesh collision_mesh;
        // ipc::CollisionMesh collision_mesh = ipc::CollisionMesh::build_from_full_mesh(
        //  local_mesh.rest_positions(), local_mesh.boundary_edges(), local_mesh.boundary_faces());
        // // Ignore all collisions between fixed elements.
        // std::vector<bool> is_vertex_fixed(local_mesh.num_vertices(), false);
        // for (const int vi : local_mesh.fixed_vertices())
        //  is_vertex_fixed[vi] = true;
        // collision_mesh.can_collide = [is_vertex_fixed, &collision_mesh](size_t vi, size_t vj) {
        //  return !is_vertex_fixed[collision_mesh.to_full_vertex_id(vi)]
        //         || !is_vertex_fixed[collision_mesh.to_full_vertex_id(vj)];
        // };
 
        // --------------------------------------------------------------------
 
        std::vector<int> boundary_nodes;
        for (int d = 0; d < m.dim(); ++d)
        {
            // Internal vertices that are on the boundary of the local mesh
            for (const int fv : new_local_mesh.fixed_vertices())
                boundary_nodes.push_back(fv * m.dim() + d);
            // Boundary vertices that are on the boundary of the local mesh
            for (const int fv : new_local_mesh.boundary_facets().reshaped())
                boundary_nodes.push_back(fv * m.dim() + d);
        }
        std::sort(boundary_nodes.begin(), boundary_nodes.end());
        auto new_end = std::unique(boundary_nodes.begin(), boundary_nodes.end());
        boundary_nodes.erase(new_end, boundary_nodes.end());
 
        // --------------------------------------------------------------------
 
        Eigen::MatrixXd projected_quantities = to_projection_quantities;
        const int n_constrained_quantaties = projected_quantities.cols() / 3;
        const int n_unconstrained_quantaties = projected_quantities.cols() - n_constrained_quantaties;
 
        auto nl_solver = m.state.make_nl_solver(/*for_al=*/false);
        for (int i = 0; i < n_constrained_quantaties; ++i)
        {
            const auto level_before = logger().level();
            logger().set_level(spdlog::level::warn);
            projected_quantities.col(i) = constrained_L2_projection(
                nl_solver,
                // L2 projection form
                M, A, /*y=*/from_projection_quantities.col(i),
                // Inversion-free form
                new_local_mesh.rest_positions(), new_local_mesh.elements(), m.dim(),
                // Contact form
                collision_mesh, m.state.args["contact"]["dhat"],
                m.state.solve_data.contact_form
                    ? m.state.solve_data.contact_form->barrier_stiffness()
                    : 1.0,
                m.state.args["contact"]["use_convergent_formulation"],
                m.state.args["solver"]["contact"]["CCD"]["broad_phase"],
                m.state.args["solver"]["contact"]["CCD"]["tolerance"],
                m.state.args["solver"]["contact"]["CCD"]["max_iterations"],
                // Augmented lagrangian form
                boundary_nodes, /*obstacle_ndof=*/0, to_projection_quantities.col(i),
                // Initial guess
                to_projection_quantities.col(i));
            logger().set_level(level_before);
        }
 
        // Minimize the L2 norm with the boundary fixed.
        reduced_L2_projection(
            M, A, from_projection_quantities.rightCols(n_unconstrained_quantaties),
            boundary_nodes, projected_quantities.rightCols(n_unconstrained_quantaties));
 
        // --------------------------------------------------------------------
 
        assert(projected_quantities.rows() == m.dim() * new_local_mesh.num_vertices());
        for (int i = 0; i < new_local_mesh.num_vertices(); i++)
        {
            m.vertex_attrs[new_local_mesh.local_to_global()[i]].projection_quantities =
                projected_quantities.middleRows(m.dim() * i, m.dim());
        }
    }
 
    // =========================================================================
 
    template <class WMTKMesh>
    bool WildRemesher<WMTKMesh>::smooth_before(const Tuple &v)
    {
        if (!WMTKMesh::smooth_before(v))
            return false;
        return !vertex_attrs[v.vid(*this)].fixed;
    }
 
    template <class WMTKMesh>
    bool PhysicsRemesher<WMTKMesh>::smooth_before(const Tuple &v)
    {
        if (!Super::smooth_before(v))
            return false;
 
        if (this->op_cache == nullptr)
        {
            if constexpr (std::is_same_v<WMTKMesh, wmtk::TriMesh>)
                this->op_cache = std::make_shared<TriOperationCache>();
            else
                this->op_cache = std::make_shared<TetOperationCache>();
        }
 
        this->op_cache->local_energy = local_mesh_energy(
            vertex_attrs[v.vid(*this)].rest_position);
 
        return true;
    }
 
    // -------------------------------------------------------------------------
 
    template <class WMTKMesh>
    bool WildRemesher<WMTKMesh>::smooth_after(const Tuple &v)
    {
        if (!WMTKMesh::smooth_before(v))
            return false;
 
        const size_t vid = v.vid(*this);
 
        const std::vector<Tuple> one_ring = this->get_one_ring_elements_for_vertex(v);
        assert(one_ring.size() > 0);
 
        // ---------------------------------------------------------------------
        // 1. update rest position of new vertex
 
        // Computes the maximal error around the one ring
        // that is needed to ensure the operation will decrease the error measure
        double max_quality = 0;
        for (const Tuple &t : get_one_ring_elements_for_vertex(v))
            max_quality = std::max(max_quality, get_quality(*this, t));
        assert(max_quality > 0); // If max quality is zero it is likely that the triangles are flipped
 
        // Collects the coordinate of all vertices in the 1-ring
        constexpr int NDOF = DIM * VERTICES_PER_ELEMENT;
        std::vector<std::array<double, NDOF>> assembles(one_ring.size());
 
        // For each triangle, make a reordered copy of the vertices so that
        // the vertex to optimize is always the first
        for (int i = 0; i < one_ring.size(); i++)
        {
            const Tuple &t = one_ring[i];
            auto t_id = t.fid(*this);
 
            assert(!is_inverted(t));
            const auto local_verts = orient_preserve_element_reorder(element_vids(t), vid);
 
            for (auto j = 0; j < VERTICES_PER_ELEMENT; j++)
                for (auto d = 0; d < DIM; d++)
                    assembles[i][j * DIM + d] = vertex_attrs[local_verts[j]].rest_position[d];
        }
 
        // Make a backup of the current configuration
        LocalMesh<This> old_local_mesh(*this, one_ring, false);
        const VectorNd old_rest_position = vertex_attrs[vid].rest_position;
 
        // Minimize distortion using newton's method
        const auto log_lvl = wmtk::logger().level();
        wmtk::logger().set_level(spdlog::level::warn);
        if constexpr (DIM == 2)
            vertex_attrs[vid].rest_position = wmtk::newton_method_from_stack_2d(
                assembles, wmtk::AMIPS2D_energy, wmtk::AMIPS2D_jacobian, wmtk::AMIPS2D_hessian);
        else
            vertex_attrs[vid].rest_position = wmtk::newton_method_from_stack(
                assembles, wmtk::AMIPS_energy, wmtk::AMIPS_jacobian, wmtk::AMIPS_hessian);
        wmtk::logger().set_level(log_lvl);
 
        // The AMIPS energy should have prevented inversions
        if (std::any_of(one_ring.begin(), one_ring.end(), [this](const Tuple &t) {
                return this->is_rest_inverted(t);
            }))
        {
            assert(false);
            return false;
        }
 
        // ---------------------------------------------------------------------
        // 2. project quantities so to minimize the L2 error
 
        // Adjust the previous displacements so they results in the same previous positions
        vertex_attrs[vid].projection_quantities.leftCols(n_quantities() / 3) +=
            old_rest_position - vertex_attrs[vid].rest_position;
 
        LocalMesh<This> new_local_mesh(*this, one_ring, false);
 
        project_local_quantities(*this, old_local_mesh, new_local_mesh);
 
        // The Constrained L2 Projection should have prevented inversions
        if (std::any_of(one_ring.begin(), one_ring.end(), [this](const Tuple &t) {
                return this->is_inverted(t);
            }))
        {
            assert(false);
            return false;
        }
 
        return true;
    }
 
    template <class WMTKMesh>
    bool PhysicsRemesher<WMTKMesh>::smooth_after(const Tuple &v)
    {
        utils::Timer timer(this->timings["Smooth vertex after"]);
        timer.start();
        if (!Super::smooth_after(v))
            return false;
        // local relaxation has its own timers
        timer.stop();
 
        // ---------------------------------------------------------------------
        // 3. perform a local relaxation of the n-ring to get an estimate of the
        //    energy decrease.
        const std::vector<Tuple> one_ring = this->get_one_ring_elements_for_vertex(v);
        return local_relaxation(one_ring, args["smooth"]["acceptance_tolerance"]);
    }
 
    template <class WMTKMesh>
    void WildRemesher<WMTKMesh>::smooth_vertices()
    {
        executor.priority = [](const WildRemesher<WMTKMesh> &m, std::string op, const Tuple &v) -> double {
            double max_quality = 0;
            for (const Tuple &t : m.get_one_ring_elements_for_vertex(v))
                max_quality = std::max(max_quality, get_quality(m, t));
            assert(max_quality > 0); // If max quality is zero it is likely that the triangles are flipped
            return max_quality;
        };
        executor.should_renew = [](auto) { return true; };
        executor.renew_neighbor_tuples = [](auto &, auto, auto &) -> Operations { return {}; };
 
        const int max_iters = args["smooth"]["max_iters"];
        for (int i = 0; i < max_iters; i++)
        {
            Operations smooths;
            for (auto &v : WMTKMesh::get_vertices())
                smooths.emplace_back("vertex_smooth", v);
            executor(*this, smooths);
            if (executor.cnt_success() == 0)
                break;
        }
    }
 
    // ------------------------------------------------------------------------
    // Template specializations
 
    template class WildRemesher<wmtk::TriMesh>;
    template class WildRemesher<wmtk::TetMesh>;
    template class PhysicsRemesher<wmtk::TriMesh>;
    template class PhysicsRemesher<wmtk::TetMesh>;
 
} // namespace polyfem::mesh