MeshNodes.cpp

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#include <polyfem/mesh/MeshNodes.hpp>
#include <polyfem/mesh/mesh2D/CMesh2D.hpp>
#include <polyfem/mesh/mesh2D/NCMesh2D.hpp>
#include <polyfem/mesh/mesh3D/CMesh3D.hpp>
#include <polyfem/mesh/mesh3D/NCMesh3D.hpp>
 
namespace polyfem::mesh
{
    namespace
    {
 
        std::vector<bool> interface_edges(const Mesh2D &mesh)
        {
            std::vector<bool> is_interface(mesh.n_edges(), false);
            for (int f = 0; f < mesh.n_faces(); ++f)
            {
                if (mesh.is_cube(f))
                {
                    continue;
                } // Skip quads
 
                auto index = mesh.get_index_from_face(f, 0);
                for (int lv = 0; lv < mesh.n_face_vertices(f); ++lv)
                {
                    auto index2 = mesh.switch_face(index);
                    if (index2.face >= 0)
                    {
                        is_interface[index.edge] = true;
                    }
                    index = mesh.next_around_face(index);
                }
            }
            return is_interface;
        }
 
        std::vector<bool> interface_faces(const Mesh3D &mesh)
        {
            std::vector<bool> is_interface(mesh.n_faces(), false);
            for (int c = 0; c < mesh.n_cells(); ++c)
            {
                if (mesh.is_cube(c))
                {
                    continue;
                } // Skip hexes
 
                for (int lf = 0; lf < mesh.n_cell_faces(c); ++lf)
                {
                    auto index = mesh.get_index_from_element(c, lf, 0);
                    auto index2 = mesh.switch_element(index);
                    if (index2.element >= 0)
                    {
                        is_interface[index.face] = true;
                    }
                }
            }
            return is_interface;
        }
 
    } // anonymous namespace
 
    // -----------------------------------------------------------------------------
 
    MeshNodes::MeshNodes(const Mesh &mesh, const bool has_poly, const bool connect_nodes, const int max_nodes_per_edge, const int max_nodes_per_face, const int max_nodes_per_cell)
        : mesh_(mesh), connect_nodes_(connect_nodes), edge_offset_(mesh.n_vertices()), face_offset_(edge_offset_ + mesh.n_edges() * max_nodes_per_edge), cell_offset_(face_offset_ + mesh.n_faces() * max_nodes_per_face)
 
          ,
          max_nodes_per_edge_(max_nodes_per_edge), max_nodes_per_face_(max_nodes_per_face), max_nodes_per_cell_(max_nodes_per_cell)
    {
        // Initialization
        int n_nodes = cell_offset_ + mesh.n_cells() * max_nodes_per_cell;
        primitive_to_node_.assign(n_nodes, -1); // #v + #e + #f + #c
        nodes_.resize(n_nodes, mesh.dimension());
        is_boundary_.assign(n_nodes, false);
 
        if (has_poly)
            is_interface_.assign(n_nodes, false);
 
        // Vertex nodes
        for (int v = 0; v < mesh.n_vertices(); ++v)
        {
            // nodes_.row(v) = mesh.point(v);
            is_boundary_[v] = mesh.is_boundary_vertex(v);
        }
        // if (!vertices_only) {
        // Eigen::MatrixXd bary;
        // Edge nodes
        // mesh.edge_barycenters(bary);
 
        for (int e = 0; e < mesh.n_edges(); ++e)
        {
            // nodes_.row(edge_offset_ + e) = bary.row(e);
            const bool is_boundary = mesh.is_boundary_edge(e);
            for (int tmp = 0; tmp < max_nodes_per_edge; ++tmp)
                is_boundary_[edge_offset_ + max_nodes_per_edge * e + tmp] = is_boundary;
        }
        // Face nodes
        // mesh.face_barycenters(bary);
        for (int f = 0; f < mesh.n_faces(); ++f)
        {
            // nodes_.row(face_offset_ + f) = bary.row(f);
            for (int tmp = 0; tmp < max_nodes_per_face; ++tmp)
            {
                if (mesh.is_volume())
                {
                    is_boundary_[face_offset_ + max_nodes_per_face * f + tmp] = mesh.is_boundary_face(f);
                }
                else
                {
                    is_boundary_[face_offset_ + max_nodes_per_face * f + tmp] = false;
                }
            }
        }
        // Cell nodes
        // mesh.cell_barycenters(bary);
        for (int c = 0; c < mesh.n_cells(); ++c)
        {
            for (int tmp = 0; tmp < max_nodes_per_cell; ++tmp)
                is_boundary_[cell_offset_ + max_nodes_per_cell * c + tmp] = false;
        }
        // }
 
        // Vertices only, no need to compute interface marker
        // if (vertices_only) { return; }
 
        // Compute edges/faces that are at interface with a polytope
        if (has_poly)
        {
            if (mesh.is_volume())
            {
                const Mesh3D *mesh3d = dynamic_cast<const Mesh3D *>(&mesh);
                assert(mesh3d);
                auto is_interface_face = interface_faces(*mesh3d);
                for (int f = 0; f < mesh.n_faces(); ++f)
                {
                    for (int tmp = 0; tmp < max_nodes_per_face; ++tmp)
                        is_interface_[face_offset_ + max_nodes_per_face * f + tmp] = is_interface_face[f];
                }
            }
            else
            {
                const Mesh2D *mesh2d = dynamic_cast<const Mesh2D *>(&mesh);
                assert(mesh2d);
                auto is_interface_edge = interface_edges(*mesh2d);
                for (int e = 0; e < mesh.n_edges(); ++e)
                {
                    for (int tmp = 0; tmp < max_nodes_per_edge; ++tmp)
                        is_interface_[edge_offset_ + max_nodes_per_edge * e + tmp] = is_interface_edge[e];
                }
            }
        }
    }
 
 
    int MeshNodes::node_id_from_primitive(int primitive_id)
    {
        if (primitive_to_node_[primitive_id] < 0 || !connect_nodes_)
        {
            primitive_to_node_[primitive_id] = n_nodes();
 
            in_ordered_vertices_.push_back(primitive_id);
            node_to_primitive_.push_back(primitive_id);
            node_to_primitive_gid_.push_back(primitive_id);
            assert(in_ordered_vertices_.size() == n_nodes());
 
            if (primitive_id < edge_offset_)
                nodes_.row(primitive_id) = mesh_.point(primitive_id);
            else if (primitive_id < face_offset_)
                nodes_.row(primitive_id) = mesh_.edge_barycenter(primitive_id - edge_offset_);
            else if (primitive_id < cell_offset_)
                nodes_.row(primitive_id) = mesh_.face_barycenter(primitive_id - face_offset_);
            else
                nodes_.row(primitive_id) = mesh_.cell_barycenter(primitive_id - cell_offset_);
        }
        return primitive_to_node_[primitive_id];
    }
 
    std::vector<int> MeshNodes::node_ids_from_edge(const Navigation::Index &index, const int n_new_nodes)
    {
        std::vector<int> res;
        if (n_new_nodes <= 0)
            return res;
 
        const Mesh2D *mesh2d = dynamic_cast<const Mesh2D *>(&mesh_);
        int start;
 
        if (connect_nodes_)
            start = edge_offset_ + index.edge * max_nodes_per_edge_;
        else
        {
            if (mesh2d->is_boundary_edge(index.edge) || mesh2d->switch_face(index).face > index.face)
                start = edge_offset_ + index.edge * max_nodes_per_edge_;
            else
                start = edge_offset_ + index.edge * max_nodes_per_edge_ + max_nodes_per_edge_ / 2;
        }
 
        // const auto v1 = mesh2d->point(index.vertex);
        // const auto v2 = mesh2d->point(mesh2d->switch_vertex(index).vertex);
        assert(start < primitive_to_node_.size());
        const int start_node_id = primitive_to_node_[start];
#ifndef NDEBUG
        if (!connect_nodes_)
        {
            assert(start_node_id < 0);
        }
#endif
        if (start_node_id < 0 || !connect_nodes_)
        {
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                // const double t = i/(n_new_nodes + 1.0);
 
                const int primitive_id = start + i - 1;
                assert(primitive_id < primitive_to_node_.size());
 
                const auto [node, node_id] = mesh2d->edge_node(index, n_new_nodes, i);
 
                primitive_to_node_[primitive_id] = n_nodes();
 
                in_ordered_vertices_.push_back(node_id);
                node_to_primitive_.push_back(primitive_id);
                node_to_primitive_gid_.push_back(index.edge);
 
                nodes_.row(primitive_id) = node;
 
                res.push_back(primitive_to_node_[primitive_id]);
                assert(in_ordered_vertices_.size() == n_nodes());
            }
        }
        else
        {
            const auto [v, _] = mesh2d->edge_node(index, n_new_nodes, 1);
 
            if ((node_position(start_node_id) - v).norm() < 1e-10)
            {
                for (int i = 0; i < n_new_nodes; ++i)
                {
                    const int primitive_id = start + i;
                    res.push_back(primitive_to_node_[primitive_id]);
                }
            }
            else
            {
                for (int i = n_new_nodes - 1; i >= 0; --i)
                {
                    const int primitive_id = start + i;
                    res.push_back(primitive_to_node_[primitive_id]);
                }
            }
        }
 
        assert(res.size() == size_t(n_new_nodes));
        return res;
    }
 
    std::vector<int> MeshNodes::node_ids_from_edge(const Navigation3D::Index &index, const int n_new_nodes)
    {
        std::vector<int> res;
        if (n_new_nodes <= 0)
            return res;
 
        const int start = edge_offset_ + index.edge * max_nodes_per_edge_;
 
        const Mesh3D *mesh3d = dynamic_cast<const Mesh3D *>(&mesh_);
 
        const int start_node_id = primitive_to_node_[start];
        if (start_node_id < 0)
        {
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                const auto [node, node_id] = mesh3d->edge_node(index, n_new_nodes, i);
 
                const int primitive_id = start + i - 1;
                primitive_to_node_[primitive_id] = n_nodes();
 
                in_ordered_vertices_.push_back(node_id);
                node_to_primitive_.push_back(primitive_id);
                node_to_primitive_gid_.push_back(index.edge);
 
                nodes_.row(primitive_id) = node;
 
                res.push_back(primitive_to_node_[primitive_id]);
                assert(in_ordered_vertices_.size() == n_nodes());
            }
        }
        else
        {
            const auto [v, _] = mesh3d->edge_node(index, n_new_nodes, 1);
            if ((node_position(start_node_id) - v).norm() < 1e-10)
            {
                for (int i = 0; i < n_new_nodes; ++i)
                {
                    const int primitive_id = start + i;
                    res.push_back(primitive_to_node_[primitive_id]);
                }
            }
            else
            {
                for (int i = n_new_nodes - 1; i >= 0; --i)
                {
                    const int primitive_id = start + i;
                    res.push_back(primitive_to_node_[primitive_id]);
                }
            }
        }
 
        assert(res.size() == size_t(n_new_nodes));
        return res;
    }
 
    std::vector<int> MeshNodes::node_ids_from_face(const Navigation::Index &index, const int n_new_nodes)
    {
        std::vector<int> res;
        if (n_new_nodes <= 0)
            return res;
 
        // assert(mesh_.is_simplex(index.face));
        const int start = face_offset_ + index.face * max_nodes_per_face_;
        const int start_node_id = primitive_to_node_[start];
 
        const Mesh2D *mesh2d = dynamic_cast<const Mesh2D *>(&mesh_);
 
        if (start_node_id < 0 || !connect_nodes_)
        {
            int loc_index = 0;
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                const int end = mesh2d->is_simplex(index.face) ? (n_new_nodes - i + 1) : n_new_nodes;
                for (int j = 1; j <= end; ++j)
                {
                    const auto [node, node_id] = mesh2d->face_node(index, n_new_nodes, i, j);
 
                    const int primitive_id = start + loc_index;
                    primitive_to_node_[primitive_id] = n_nodes();
 
                    in_ordered_vertices_.push_back(node_id);
                    node_to_primitive_.push_back(primitive_id);
                    node_to_primitive_gid_.push_back(index.face);
 
                    nodes_.row(primitive_id) = node;
 
                    res.push_back(primitive_to_node_[primitive_id]);
 
                    assert(in_ordered_vertices_.size() == n_nodes());
 
                    ++loc_index;
                }
            }
        }
        else
        {
            assert(false);
        }
 
#ifndef NDEBUG
        if (mesh2d->is_simplex(index.face))
            assert(res.size() == size_t(n_new_nodes * (n_new_nodes + 1) / 2));
        else
            assert(res.size() == size_t(n_new_nodes * n_new_nodes));
#endif
        return res;
    }
 
    std::vector<int> MeshNodes::node_ids_from_face(const Navigation3D::Index &index, const int n_new_nodes)
    {
        std::vector<int> res;
        if (n_new_nodes <= 0)
            return res;
 
        // assert(mesh_.is_simplex(index.element));
        const Mesh3D *mesh3d = dynamic_cast<const Mesh3D *>(&mesh_);
        int start;
 
        if (connect_nodes_)
            start = face_offset_ + index.face * max_nodes_per_face_;
        else
        {
            if (mesh3d->is_boundary_face(index.face) || mesh3d->switch_element(index).element > index.element)
                start = face_offset_ + index.face * max_nodes_per_face_;
            else
                start = face_offset_ + index.face * max_nodes_per_face_ + max_nodes_per_face_ / 2;
        }
 
        const int start_node_id = primitive_to_node_[start];
 
#ifndef NDEBUG
        if (!connect_nodes_)
        {
            assert(start_node_id < 0);
        }
#endif
 
        if (start_node_id < 0 || !connect_nodes_)
        {
            int loc_index = 0;
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                const int end = mesh3d->is_simplex(index.element) ? (n_new_nodes - i + 1) : n_new_nodes;
                for (int j = 1; j <= end; ++j)
                {
                    const int primitive_id = start + loc_index;
                    const auto [node, node_id] = mesh3d->face_node(index, n_new_nodes, i, j);
 
                    primitive_to_node_[primitive_id] = n_nodes();
 
                    in_ordered_vertices_.push_back(node_id);
                    node_to_primitive_.push_back(primitive_id);
                    node_to_primitive_gid_.push_back(index.face);
 
                    nodes_.row(primitive_id) = node;
 
                    res.push_back(primitive_to_node_[primitive_id]);
                    assert(in_ordered_vertices_.size() == n_nodes());
 
                    ++loc_index;
                }
            }
        }
        else
        {
            if (n_new_nodes == 1)
            {
                res.push_back(start_node_id);
            }
            else
            {
                const int total_nodes = mesh3d->is_simplex(index.element) ? (n_new_nodes * (n_new_nodes + 1) / 2) : (n_new_nodes * n_new_nodes);
                for (int i = 1; i <= n_new_nodes; ++i)
                {
                    const int end = mesh3d->is_simplex(index.element) ? (n_new_nodes - i + 1) : n_new_nodes;
                    for (int j = 1; j <= end; ++j)
                    {
                        const auto [p, _] = mesh3d->face_node(index, n_new_nodes, i, j);
 
                        bool found = false;
                        for (int k = start; k < start + total_nodes; ++k)
                        {
                            const double dist = (nodes_.row(k) - p).norm();
                            if (dist < 1e-10)
                            {
                                res.push_back(primitive_to_node_[k]);
                                found = true;
                                break;
                            }
                        }
 
                        assert(found);
                    }
                }
            }
        }
 
#ifndef NDEBUG
        if (mesh3d->is_simplex(index.element))
            assert(res.size() == size_t(n_new_nodes * (n_new_nodes + 1) / 2));
        else
            assert(res.size() == size_t(n_new_nodes * n_new_nodes));
#endif
        return res;
    }
 
    std::vector<int> MeshNodes::node_ids_from_cell(const Navigation3D::Index &index, const int n_new_nodes)
    {
        std::vector<int> res;
        const int start = cell_offset_ + index.element * max_nodes_per_cell_;
        const Mesh3D *mesh3d = dynamic_cast<const Mesh3D *>(&mesh_);
 
        if (mesh3d->is_simplex(index.element))
        {
            int loc_index = 0;
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                const int endj = (n_new_nodes - i + 1);
                for (int j = 1; j <= endj; ++j)
                {
                    const int endk = (n_new_nodes - i - j + 2);
                    for (int k = 1; k <= endk; ++k)
                    {
                        const int primitive_id = start + loc_index;
 
                        auto [node, node_id] = mesh3d->cell_node(index, n_new_nodes, i, j, k);
 
                        primitive_to_node_[primitive_id] = n_nodes();
 
                        in_ordered_vertices_.push_back(node_id);
                        node_to_primitive_.push_back(primitive_id);
                        node_to_primitive_gid_.push_back(index.element);
 
                        nodes_.row(primitive_id) = node;
                        res.push_back(primitive_to_node_[primitive_id]);
                        assert(in_ordered_vertices_.size() == n_nodes());
 
                        ++loc_index;
                    }
                }
            }
        }
        else
        {
            int loc_index = 0;
            for (int i = 1; i <= n_new_nodes; ++i)
            {
                for (int j = 1; j <= n_new_nodes; ++j)
                {
                    for (int k = 1; k <= n_new_nodes; ++k)
                    {
                        const int primitive_id = start + loc_index;
 
                        const auto [node, node_id] = mesh3d->cell_node(index, n_new_nodes, i, j, k);
                        primitive_to_node_[primitive_id] = n_nodes();
 
                        in_ordered_vertices_.push_back(node_id);
                        node_to_primitive_.push_back(primitive_id);
                        node_to_primitive_gid_.push_back(index.element);
 
                        nodes_.row(primitive_id) = node;
                        res.push_back(primitive_to_node_[primitive_id]);
                        assert(in_ordered_vertices_.size() == n_nodes());
 
                        ++loc_index;
                    }
                }
            }
        }
 
#ifndef NDEBUG
        if (res.size() == 1 && connect_nodes_)
        {
            const int idx = node_id_from_cell(index.element);
            assert(idx == res.front());
        }
#endif
 
#ifndef NDEBUG
        if (mesh3d->is_simplex(index.element))
        {
            int n_cell_nodes = 0;
            for (int pp = 0; pp <= n_new_nodes; ++pp)
                n_cell_nodes += (pp * (pp + 1) / 2);
            assert(res.size() == size_t(n_cell_nodes));
        }
        else
            assert(res.size() == size_t(n_new_nodes * n_new_nodes * n_new_nodes));
#endif
 
        return res;
    }
 
    int MeshNodes::node_id_from_vertex(int v)
    {
        return node_id_from_primitive(v);
    }
 
    int MeshNodes::node_id_from_edge(int e)
    {
        return node_id_from_primitive(edge_offset_ + e * max_nodes_per_edge_);
    }
 
    int MeshNodes::node_id_from_face(int f)
    {
        return node_id_from_primitive(face_offset_ + f * max_nodes_per_face_);
    }
 
    int MeshNodes::node_id_from_cell(int c)
    {
        return node_id_from_primitive(cell_offset_ + c * max_nodes_per_cell_);
    }
 
 
    int MeshNodes::vertex_from_node_id(int node_id) const
    {
        const int res = node_to_primitive_[node_id];
        assert(res >= 0 && res < edge_offset_);
        return res;
    }
 
    int MeshNodes::edge_from_node_id(int node_id) const
    {
        const int res = node_to_primitive_[node_id];
        assert(res >= edge_offset_ && res < face_offset_);
        return res - edge_offset_;
    }
 
    int MeshNodes::face_from_node_id(int node_id) const
    {
        const int res = node_to_primitive_[node_id];
        assert(res >= face_offset_ && res < cell_offset_);
        return res - face_offset_;
    }
 
    int MeshNodes::cell_from_node_id(int node_id) const
    {
        const int res = node_to_primitive_[node_id];
        assert(res >= cell_offset_ && res < n_nodes());
        return res - cell_offset_;
    }
 
 
    std::vector<int> MeshNodes::boundary_nodes() const
    {
        std::vector<int> res;
        res.reserve(n_nodes());
        for (size_t prim_id = 0; prim_id < primitive_to_node_.size(); ++prim_id)
        {
            int node_id = primitive_to_node_[prim_id];
            if (node_id >= 0 && is_boundary_[prim_id])
            {
                res.push_back(node_id);
            }
        }
        return res;
    }
 
    int MeshNodes::count_nonnegative_nodes(int start_i, int end_i) const
    {
        int count = 0;
        for (int i = start_i; i < end_i; i++)
            count += primitive_to_node_[i] >= 0;
        return count;
    }
 
} // namespace polyfem::mesh