CMesh2D.cpp

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#include <polyfem/mesh/mesh2D/CMesh2D.hpp>
#include <polyfem/mesh/mesh2D/Navigation.hpp>
 
#include <polyfem/mesh/MeshUtils.hpp>
#include <polyfem/mesh/mesh2D/Refinement.hpp>
#include <polyfem/io/MshReader.hpp>
#include <polyfem/utils/StringUtils.hpp>
#include <polyfem/utils/Logger.hpp>
 
#include <geogram/basic/file_system.h>
#include <geogram/mesh/mesh_io.h>
#include <geogram/mesh/mesh_geometry.h>
#include <geogram/mesh/mesh_repair.h>
 
#include <cassert>
#include <array>
#include <unordered_map>
#include <type_traits>
 
namespace polyfem
{
    using namespace io;
    using namespace utils;
 
    namespace mesh
    {
        void CMesh2D::remove_elements(const std::vector<bool> &keep)
        {
            assert(keep.size() == n_faces());
 
            std::unordered_map<std::pair<int, int>, int, utils::HashPair> old_edge_ids;
            std::unordered_map<std::pair<int, int>, EdgeNodes, utils::HashPair> old_edge_nodes;
            for (int e = 0; e < n_edges(); ++e)
            {
                const std::pair<int, int> key = std::minmax(edge_vertex(e, 0), edge_vertex(e, 1));
                if (has_boundary_ids())
                    old_edge_ids[key] = boundary_ids_[e];
                if (e < edge_nodes_.size())
                    old_edge_nodes[key] = edge_nodes_[e];
            }
 
            auto filter_nodes = [&keep](auto &nodes) {
                if (nodes.size() != keep.size())
                    return;
                std::decay_t<decltype(nodes)> filtered;
                for (int i = 0; i < keep.size(); ++i)
                    if (keep[i])
                        filtered.push_back(nodes[i]);
                nodes = std::move(filtered);
            };
            filter_nodes(face_nodes_);
            filter_nodes(cell_nodes_);
            filter_element_data(keep);
 
            GEO::vector<GEO::index_t> to_delete(mesh_.facets.nb(), 0);
            for (int f = 0; f < keep.size(); ++f)
                to_delete[f] = keep[f] ? 0 : 1;
            mesh_.facets.delete_elements(to_delete);
 
            c2e_.reset();
            boundary_vertices_.reset();
            boundary_edges_.reset();
            Navigation::prepare_mesh(mesh_);
            c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
            boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
            boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
 
            if (!old_edge_ids.empty())
            {
                boundary_ids_.resize(n_edges());
                for (int e = 0; e < n_edges(); ++e)
                {
                    const std::pair<int, int> key = std::minmax(edge_vertex(e, 0), edge_vertex(e, 1));
                    const auto it = old_edge_ids.find(key);
                    boundary_ids_[e] = it == old_edge_ids.end() ? get_default_boundary_id(e) : it->second;
                }
            }
            else
                boundary_ids_.clear();
 
            edge_nodes_.clear();
            if (!old_edge_nodes.empty())
            {
                edge_nodes_.resize(n_edges());
                for (int e = 0; e < n_edges(); ++e)
                {
                    const std::pair<int, int> key = std::minmax(edge_vertex(e, 0), edge_vertex(e, 1));
                    const auto it = old_edge_nodes.find(key);
                    if (it != old_edge_nodes.end())
                        edge_nodes_[e] = it->second;
                }
            }
 
            in_ordered_edges_.resize(n_edges(), 2);
            for (int e = 0; e < n_edges(); ++e)
                in_ordered_edges_.row(e) << edge_vertex(e, 0), edge_vertex(e, 1);
            compute_elements_tag();
        }
 
        void CMesh2D::refine(const int n_refinement, const double t)
        {
            // return;
            if (n_refinement <= 0)
            {
                return;
            }
 
            orders_.resize(0, 0);
 
            bool all_simplicial = true;
            for (int e = 0; e < n_elements(); ++e)
            {
                all_simplicial &= is_simplex(e);
            }
 
            for (int i = 0; i < n_refinement; ++i)
            {
                GEO::Mesh mesh;
                mesh.copy(mesh_);
 
                c2e_.reset();
                boundary_vertices_.reset();
                boundary_edges_.reset();
 
                mesh_.clear(false, false);
 
                // TODO add tags to the refinement
                if (all_simplicial)
                {
                    refine_triangle_mesh(mesh, mesh_);
                }
                else if (t <= 0)
                {
                    refine_polygonal_mesh(mesh, mesh_, Polygons::catmul_clark_split_func());
                }
                else
                {
                    refine_polygonal_mesh(mesh, mesh_, Polygons::polar_split_func(t));
                }
 
                Navigation::prepare_mesh(mesh_);
                c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
                boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
                boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
            }
 
            compute_elements_tag();
            generate_edges(mesh_);
 
            in_ordered_vertices_ = Eigen::VectorXi::LinSpaced(mesh_.vertices.nb(), 0, mesh_.vertices.nb() - 1);
            assert(in_ordered_vertices_[0] == 0);
            assert(in_ordered_vertices_[1] == 1);
            assert(in_ordered_vertices_[2] == 2);
            assert(in_ordered_vertices_[in_ordered_vertices_.size() - 1] == mesh_.vertices.nb() - 1);
 
            in_ordered_edges_.resize(mesh_.edges.nb(), 2);
 
            for (int e = 0; e < (int)mesh_.edges.nb(); ++e)
            {
                for (int lv = 0; lv < 2; ++lv)
                {
                    in_ordered_edges_(e, lv) = mesh_.edges.vertex(e, lv);
                }
                assert(in_ordered_edges_(e, 0) != in_ordered_edges_(e, 1));
            }
            assert(in_ordered_edges_.size() > 0);
 
            in_ordered_faces_.resize(0, 0);
        }
 
        bool CMesh2D::load(const std::string &path)
        {
            // This method should be used for special loading, like hybrid in 3d
 
            // edge_nodes_.clear();
            // face_nodes_.clear();
            // cell_nodes_.clear();
            // order_ = 1;
 
            // c2e_.reset();
            // boundary_vertices_.reset();
            // boundary_edges_.reset();
 
            // mesh_.clear(false,false);
 
            // if (!StringUtils::endswith(path, "msh"))
            // {
            //  Eigen::MatrixXd vertices;
            //  Eigen::MatrixXi cells;
            //  std::vector<std::vector<int>> elements;
            //  std::vector<std::vector<double>> weights;
 
            //  if(!MshReader::load(path, vertices, cells, elements, weights))
            //      return false;
 
            //  build_from_matrices(vertices, cells);
            //  attach_higher_order_nodes(vertices, elements);
            //  cell_weights_ = weights;
            // }
            // else
            // {
            //  if(!mesh_load(path, mesh_))
            //      return false;
            // }
 
            // orient_normals_2d(mesh_);
            // Navigation::prepare_mesh(mesh_);
            // c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
            // boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
            // boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
 
            // compute_elements_tag();
            assert(false);
            return false;
        }
 
        bool CMesh2D::load(const GEO::Mesh &mesh)
        {
            edge_nodes_.clear();
            face_nodes_.clear();
            cell_nodes_.clear();
 
            c2e_.reset();
            boundary_vertices_.reset();
            boundary_edges_.reset();
 
            mesh_.clear(false, false);
            mesh_.copy(mesh);
 
            orient_normals_2d(mesh_);
            Navigation::prepare_mesh(mesh_);
            c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
            boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
            boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
 
            compute_elements_tag();
            return true;
        }
 
        bool CMesh2D::save(const std::string &path) const
        {
            if (!mesh_save(mesh_, path))
                return false;
 
            return true;
        }
 
        bool CMesh2D::build_from_matrices(const Eigen::MatrixXd &V, const Eigen::MatrixXi &F)
        {
            edge_nodes_.clear();
            face_nodes_.clear();
            cell_nodes_.clear();
 
            c2e_.reset();
            boundary_vertices_.reset();
            boundary_edges_.reset();
 
            mesh_.clear(false, false);
            to_geogram_mesh(V, F, mesh_);
 
            orient_normals_2d(mesh_);
            Navigation::prepare_mesh(mesh_);
 
            c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
            boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
            boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
 
            compute_elements_tag();
            return true;
        }
 
        void CMesh2D::attach_higher_order_nodes(const Eigen::MatrixXd &V, const std::vector<std::vector<int>> &nodes)
        {
            edge_nodes_.clear();
            face_nodes_.clear();
            cell_nodes_.clear();
 
            edge_nodes_.resize(n_edges());
            face_nodes_.resize(n_faces());
 
            orders_.resize(n_faces(), 1);
 
            assert(nodes.size() == n_faces());
 
            for (int f = 0; f < n_faces(); ++f)
            {
                auto index = get_index_from_face(f);
 
                const auto &nodes_ids = nodes[f];
 
                if (nodes_ids.size() == 3)
                {
                    orders_(f) = 1;
                    continue;
                }
                // P2
                else if (nodes_ids.size() == 6)
                {
                    orders_(f) = 2;
 
                    for (int le = 0; le < 3; ++le)
                    {
                        auto &n = edge_nodes_[index.edge];
 
                        // nodes not aleardy created
                        if (n.nodes.size() <= 0)
                        {
                            n.v1 = index.vertex;
                            n.v2 = switch_vertex(index).vertex;
 
                            int node_index = 0;
                            if ((n.v1 == nodes_ids[0] && n.v2 == nodes_ids[1]) || (n.v2 == nodes_ids[0] && n.v1 == nodes_ids[1]))
                                node_index = 3;
                            else if ((n.v1 == nodes_ids[1] && n.v2 == nodes_ids[2]) || (n.v2 == nodes_ids[1] && n.v1 == nodes_ids[2]))
                                node_index = 4;
                            else
                                node_index = 5;
 
                            n.nodes.resize(1, 2);
                            n.nodes << V(nodes_ids[node_index], 0), V(nodes_ids[node_index], 1);
                            n.nodes_ids.push_back(nodes_ids[node_index]);
                        }
                        index = next_around_face(index);
                    }
                }
                // P3
                else if (nodes_ids.size() == 10)
                {
                    orders_(f) = 3;
 
                    for (int le = 0; le < 3; ++le)
                    {
                        auto &n = edge_nodes_[index.edge];
 
                        // nodes not aleardy created
                        if (n.nodes.size() <= 0)
                        {
                            n.v1 = index.vertex;
                            n.v2 = switch_vertex(index).vertex;
 
                            int node_index1 = 0;
                            int node_index2 = 0;
                            if (n.v1 == nodes_ids[0] && n.v2 == nodes_ids[1])
                            {
                                node_index1 = 3;
                                node_index2 = 4;
                            }
                            else if (n.v2 == nodes_ids[0] && n.v1 == nodes_ids[1])
                            {
                                node_index1 = 4;
                                node_index2 = 3;
                            }
                            else if (n.v1 == nodes_ids[1] && n.v2 == nodes_ids[2])
                            {
                                node_index1 = 5;
                                node_index2 = 6;
                            }
                            else if (n.v2 == nodes_ids[1] && n.v1 == nodes_ids[2])
                            {
                                node_index1 = 6;
                                node_index2 = 5;
                            }
                            else if (n.v1 == nodes_ids[2] && n.v2 == nodes_ids[0])
                            {
                                node_index1 = 7;
                                node_index2 = 8;
                            }
                            else
                            {
                                assert(n.v2 == nodes_ids[2] && n.v1 == nodes_ids[0]);
                                node_index1 = 8;
                                node_index2 = 7;
                            }
 
                            n.nodes.resize(2, 2);
                            n.nodes.row(0) << V(nodes_ids[node_index1], 0), V(nodes_ids[node_index1], 1);
                            n.nodes.row(1) << V(nodes_ids[node_index2], 0), V(nodes_ids[node_index2], 1);
 
                            n.nodes_ids.push_back(nodes_ids[node_index1]);
                            n.nodes_ids.push_back(nodes_ids[node_index2]);
                        }
                        index = next_around_face(index);
                    }
 
                    {
                        auto &n = face_nodes_[f];
                        n.v1 = mesh_.facets.vertex(f, 0);
                        n.v2 = mesh_.facets.vertex(f, 1);
                        n.v3 = mesh_.facets.vertex(f, 2);
                        n.nodes.resize(1, 2);
                        n.nodes << V(nodes_ids[9], 0), V(nodes_ids[9], 1);
                        n.nodes_ids.push_back(nodes_ids[9]);
                    }
                }
                // P4
                else if (nodes_ids.size() == 15)
                {
                    orders_(f) = 4;
                    assert(false);
                    // unsupported P4 for geometry, need meshes for testing
                }
                // unsupported
                else
                {
                    assert(false);
                }
            }
 
            if (orders_.maxCoeff() == 1)
                orders_.resize(0, 0);
        }
 
        std::pair<RowVectorNd, int> CMesh2D::edge_node(const Navigation::Index &index, const int n_new_nodes, const int i) const
        {
            if (orders_.size() <= 0 || orders_(index.face) == 1 || edge_nodes_.empty() || edge_nodes_[index.edge].nodes.rows() != n_new_nodes)
            {
                const auto v1 = point(index.vertex);
                const auto v2 = point(switch_vertex(index).vertex);
 
                const double t = i / (n_new_nodes + 1.0);
 
                return std::make_pair((1 - t) * v1 + t * v2, -1);
            }
 
            const auto &n = edge_nodes_[index.edge];
            if (n.v1 == index.vertex)
                return std::make_pair(n.nodes.row(i - 1), n.nodes_ids[i - 1]);
            else
            {
                assert(n.v2 == index.vertex);
                return std::make_pair(n.nodes.row(n.nodes.rows() - i), n.nodes_ids[n.nodes_ids.size() - i]);
            }
        }
 
        std::pair<RowVectorNd, int> CMesh2D::face_node(const Navigation::Index &index, const int n_new_nodes, const int i, const int j) const
        {
            if (is_simplex(index.face))
            {
                if (orders_.size() <= 0 || orders_(index.face) == 1 || orders_(index.face) == 2 || face_nodes_.empty() || face_nodes_[index.face].nodes.rows() != n_new_nodes)
                {
                    const auto v1 = point(index.vertex);
                    const auto v2 = point(switch_vertex(index).vertex);
                    const auto v3 = point(switch_vertex(switch_edge(index)).vertex);
 
                    const double b2 = i / (n_new_nodes + 2.0);
                    const double b3 = j / (n_new_nodes + 2.0);
                    const double b1 = 1 - b3 - b2;
                    assert(b3 < 1);
                    assert(b3 > 0);
 
                    return std::make_pair(b1 * v1 + b2 * v2 + b3 * v3, -1);
                }
 
                assert(orders_(index.face) == 3);
                // unsupported P4 for geometry
                const auto &n = face_nodes_[index.face];
                return std::make_pair(n.nodes.row(0), n.nodes_ids[0]);
            }
            else if (is_cube(index.face))
            {
                // supports only blilinear quads
                assert(orders_.size() <= 0 || orders_(index.face) == 1);
 
                const auto v1 = point(index.vertex);
                const auto v2 = point(switch_vertex(index).vertex);
                const auto v3 = point(switch_vertex(switch_edge(switch_vertex(index))).vertex);
                const auto v4 = point(switch_vertex(switch_edge(index)).vertex);
 
                const double b1 = i / (n_new_nodes + 1.0);
                const double b2 = j / (n_new_nodes + 1.0);
 
                return std::make_pair(v1 * (1 - b1) * (1 - b2) + v2 * b1 * (1 - b2) + v3 * b1 * b2 + v4 * (1 - b1) * b2, -1);
            }
 
            assert(false);
            return std::make_pair(RowVectorNd(2, 1), -1);
        }
 
        void CMesh2D::bounding_box(RowVectorNd &min, RowVectorNd &max) const
        {
            GEO::vec3 min_corner, max_corner;
            GEO::get_bbox(mesh_, &min_corner[0], &max_corner[0]);
            min.resize(2);
            max.resize(2);
 
            min(0) = min_corner.x;
            min(1) = min_corner.y;
 
            max(0) = max_corner.x;
            max(1) = max_corner.y;
        }
 
        void CMesh2D::normalize()
        {
 
            GEO::vec3 min_corner, max_corner;
            GEO::get_bbox(mesh_, &min_corner[0], &max_corner[0]);
            GEO::vec3 extent = max_corner - min_corner;
            double scaling = std::max(extent[0], std::max(extent[1], extent[2]));
            // const GEO::vec3 origin = 0.5 * (min_corner + max_corner);
            const GEO::vec3 origin = min_corner;
            for (GEO::index_t v = 0; v < mesh_.vertices.nb(); ++v)
            {
                mesh_.vertices.point(v) = (mesh_.vertices.point(v) - origin) / scaling;
            }
            Eigen::RowVector2d shift;
            shift << origin[0], origin[1];
            for (auto &n : edge_nodes_)
            {
                if (n.nodes.size() > 0)
                    n.nodes = (n.nodes.rowwise() - shift) / scaling;
            }
            for (auto &n : face_nodes_)
            {
                if (n.nodes.size() > 0)
                    n.nodes = (n.nodes.rowwise() - shift) / scaling;
            }
 
            logger().debug("-- bbox before normalization:");
            logger().debug("   min   : {} {}", min_corner[0], min_corner[1]);
            logger().debug("   max   : {} {}", max_corner[0], max_corner[1]);
            logger().debug("   extent: {} {}", max_corner[0] - min_corner[0], max_corner[1] - min_corner[1]);
            GEO::get_bbox(mesh_, &min_corner[0], &max_corner[0]);
            logger().debug("-- bbox after normalization:");
            logger().debug("   min   : {} {}", min_corner[0], min_corner[1]);
            logger().debug("   max   : {} {}", max_corner[0], max_corner[1]);
            logger().debug("   extent: {} {}", max_corner[0] - min_corner[0], max_corner[1] - min_corner[1]);
 
            Eigen::MatrixXd p0, p1, p;
            get_edges(p0, p1);
            p = p0 - p1;
            logger().debug("-- edge length after normalization:");
            logger().debug("   min: {}", p.rowwise().norm().minCoeff());
            logger().debug("   max: {}", p.rowwise().norm().maxCoeff());
            logger().debug("   avg: {}", p.rowwise().norm().mean());
        }
 
        double CMesh2D::edge_length(const int gid) const
        {
            const int v0 = mesh_.edges.vertex(gid, 0);
            const int v1 = mesh_.edges.vertex(gid, 1);
 
            return (point(v0) - point(v1)).norm();
        }
 
        void CMesh2D::set_point(const int global_index, const RowVectorNd &p)
        {
            mesh_.vertices.point(global_index).x = p(0);
            mesh_.vertices.point(global_index).y = p(1);
        }
 
        RowVectorNd CMesh2D::point(const int global_index) const
        {
            const double *ptr = mesh_.vertices.point_ptr(global_index);
            RowVectorNd p(2);
            p(0) = ptr[0];
            p(1) = ptr[1];
            return p;
        }
 
        bool CMesh2D::is_boundary_element(const int element_global_id) const
        {
            auto index = get_index_from_face(element_global_id);
 
            for (int i = 0; i < n_face_vertices(element_global_id); ++i)
            {
                if (is_boundary_edge(index.edge))
                    return true;
 
                index = next_around_face(index);
            }
 
            return false;
        }
 
        // void CMesh2D::triangulate_faces(Eigen::MatrixXi &tris, Eigen::MatrixXd &pts, std::vector<int> &ranges) const
        // {
        //  ranges.clear();
 
        //  std::vector<Eigen::MatrixXi> local_tris(mesh_.facets.nb());
        //  std::vector<Eigen::MatrixXd> local_pts(mesh_.facets.nb());
 
        //  int total_tris = 0;
        //  int total_pts = 0;
 
        //  ranges.push_back(0);
 
        //  for (GEO::index_t f = 0; f < mesh_.facets.nb(); ++f)
        //  {
        //      const int n_vertices = mesh_.facets.nb_vertices(f);
 
        //      Eigen::MatrixXd face_pts(n_vertices, 2);
        //      // Eigen::MatrixXi edges(n_vertices,2);
        //      local_tris[f].resize(n_vertices - 2, 3);
 
        //      for (int i = 0; i < n_vertices; ++i)
        //      {
        //          const int vertex = mesh_.facets.vertex(f, i);
        //          const double *pt = mesh_.vertices.point_ptr(vertex);
        //          face_pts(i, 0) = pt[0];
        //          face_pts(i, 1) = pt[1];
 
        //          // edges(i, 0) = i;
        //          // edges(i, 1) = (i+1) % n_vertices;
        //      }
 
        //      for (int i = 1; i < n_vertices - 1; ++i)
        //      {
        //          local_tris[f].row(i - 1) << 0, i, i + 1;
        //      }
 
        //      local_pts[f] = face_pts;
 
        //      total_tris += local_tris[f].rows();
        //      total_pts += local_pts[f].rows();
 
        //      ranges.push_back(total_tris);
 
        //      assert(local_pts[f].rows() == face_pts.rows());
        //  }
 
        //  tris.resize(total_tris, 3);
        //  pts.resize(total_pts, 2);
 
        //  int tri_index = 0;
        //  int pts_index = 0;
        //  for (std::size_t i = 0; i < local_tris.size(); ++i)
        //  {
        //      tris.block(tri_index, 0, local_tris[i].rows(), local_tris[i].cols()) = local_tris[i].array() + pts_index;
        //      tri_index += local_tris[i].rows();
 
        //      pts.block(pts_index, 0, local_pts[i].rows(), local_pts[i].cols()) = local_pts[i];
        //      pts_index += local_pts[i].rows();
        //  }
        // }
 
        void CMesh2D::compute_elements_tag()
        {
            elements_tag_.clear();
            compute_element_tags(mesh_, elements_tag_);
        }
 
        void CMesh2D::update_elements_tag()
        {
            compute_element_tags(mesh_, elements_tag_);
        }
 
        RowVectorNd CMesh2D::edge_barycenter(const int index) const
        {
            const int v0 = mesh_.edges.vertex(index, 0);
            const int v1 = mesh_.edges.vertex(index, 1);
 
            return 0.5 * (point(v0) + point(v1));
        }
 
        void CMesh2D::compute_body_ids(const std::function<int(const size_t, const std::vector<int> &, const RowVectorNd &)> &marker)
        {
            body_ids_.resize(n_elements());
            std::fill(body_ids_.begin(), body_ids_.end(), -1);
 
            for (int e = 0; e < n_elements(); ++e)
            {
                const auto bary = face_barycenter(e);
                body_ids_[e] = marker(e, element_vertices(e), bary);
            }
        }
 
        void CMesh2D::compute_boundary_ids(const std::function<int(const size_t, const std::vector<int> &, const RowVectorNd &, bool)> &marker)
        {
            boundary_ids_.resize(n_edges());
 
            for (int e = 0; e < n_edges(); ++e)
            {
                bool is_boundary = is_boundary_edge(e);
                const auto p = edge_barycenter(e);
                std::vector<int> vs = {edge_vertex(e, 0), edge_vertex(e, 1)};
                std::sort(vs.begin(), vs.end());
                boundary_ids_[e] = marker(e, vs, p, is_boundary);
            }
        }
 
        void CMesh2D::append(const Mesh &mesh)
        {
            assert(typeid(mesh) == typeid(CMesh2D));
            Mesh::append(mesh);
 
            const CMesh2D &mesh2d = dynamic_cast<const CMesh2D &>(mesh);
 
            const int n_v = n_vertices();
            const int n_f = n_faces();
 
            mesh_.vertices.create_vertices(mesh2d.n_vertices());
            for (int i = n_v; i < (int)mesh_.vertices.nb(); ++i)
            {
                GEO::vec3 &p = mesh_.vertices.point(i);
                set_point(i, mesh2d.point(i - n_v));
            }
 
            std::vector<GEO::index_t> indices;
            for (int i = 0; i < mesh2d.n_faces(); ++i)
            {
                indices.clear();
                for (int j = 0; j < mesh2d.mesh_.facets.nb_vertices(i); ++j)
                    indices.push_back(mesh2d.mesh_.facets.vertex(i, j) + n_v);
 
                mesh_.facets.create_polygon(indices.size(), &indices[0]);
            }
 
            assert(n_vertices() == n_v + mesh2d.n_vertices());
            assert(n_faces() == n_f + mesh2d.n_faces());
 
            c2e_.reset();
            boundary_vertices_.reset();
            boundary_edges_.reset();
            Navigation::prepare_mesh(mesh_);
            c2e_ = std::make_unique<GEO::Attribute<GEO::index_t>>(mesh_.facet_corners.attributes(), "edge_id");
            boundary_vertices_ = std::make_unique<GEO::Attribute<bool>>(mesh_.vertices.attributes(), "boundary_vertex");
            boundary_edges_ = std::make_unique<GEO::Attribute<bool>>(mesh_.edges.attributes(), "boundary_edge");
        }
 
        std::unique_ptr<Mesh> CMesh2D::copy() const
        {
            std::unique_ptr<CMesh2D> copy_mesh = std::make_unique<CMesh2D>();
            copy_mesh->load(this->mesh_);
 
            // Manually copy parent's data
            copy_mesh->elements_tag_ = this->elements_tag_;
            copy_mesh->node_ids_ = this->node_ids_;
            copy_mesh->boundary_ids_ = this->boundary_ids_;
            copy_mesh->body_ids_ = this->body_ids_;
            copy_mesh->geometry_ids_ = this->geometry_ids_;
            copy_mesh->orders_ = this->orders_;
            copy_mesh->is_rational_ = this->is_rational_;
            copy_mesh->edge_nodes_ = this->edge_nodes_;
            copy_mesh->face_nodes_ = this->face_nodes_;
            copy_mesh->cell_nodes_ = this->cell_nodes_;
            copy_mesh->cell_weights_ = this->cell_weights_;
            copy_mesh->in_ordered_vertices_ = this->in_ordered_vertices_;
            copy_mesh->in_ordered_edges_ = this->in_ordered_edges_;
            copy_mesh->in_ordered_faces_ = this->in_ordered_faces_;
 
            return copy_mesh;
        }
    } // namespace mesh
} // namespace polyfem