CollisionProxy.cpp

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#include "CollisionProxy.hpp"
 
#include <polyfem/mesh/collision_proxy/UpsampleMesh.hpp>
#include <polyfem/mesh/MeshUtils.hpp>
#include <polyfem/mesh/GeometryReader.hpp>
#include <polyfem/utils/Logger.hpp>
#include <polyfem/utils/MatrixUtils.hpp>
 
#include <SimpleBVH/BVH.hpp>
#include <igl/edges.h>
#include <igl/barycentric_coordinates.h>
#include <h5pp/h5pp.h>
// #include <fcpw/fcpw.h>
 
namespace polyfem::mesh
{
    namespace
    {
        template <typename T>
        using RowMajorMatrixX = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
 
        Eigen::MatrixXd uv_to_uvw(const Eigen::MatrixXd &uv, const int local_fid)
        {
            assert(uv.cols() == 2);
 
            Eigen::MatrixXd uvw = Eigen::MatrixXd::Zero(uv.rows(), 3);
            // u * A + v * B + w * C + (1 - u - v - w) * D
            switch (local_fid)
            {
            case 0:
                uvw.col(0) = uv.col(1);
                uvw.col(1) = uv.col(0);
                break;
            case 1:
                uvw.col(0) = uv.col(0);
                uvw.col(2) = uv.col(1);
                break;
            case 2:
                uvw.leftCols(2) = uv;
                uvw.col(2) = 1 - uv.col(0).array() - uv.col(1).array();
                break;
            case 3:
                uvw.col(1) = uv.col(1);
                uvw.col(2) = uv.col(0);
                break;
            default:
                log_and_throw_error("build_collision_proxy(): unknown local_fid={}", local_fid);
            }
            return uvw;
        }
 
        Eigen::MatrixXd extract_face_vertices(
            const basis::ElementBases &element, const int local_fid)
        {
            Eigen::MatrixXd UV(3, 2);
            // u * A + b * B + (1-u-v) * C
            UV.row(0) << 1, 0;
            UV.row(1) << 0, 1;
            UV.row(2) << 0, 0;
            const Eigen::MatrixXd UVW = uv_to_uvw(UV, local_fid);
 
            Eigen::MatrixXd V;
            element.eval_geom_mapping(UVW, V);
 
            return V;
        }
    } // namespace
 
    void build_collision_proxy(
        const std::vector<basis::ElementBases> &bases,
        const std::vector<basis::ElementBases> &geom_bases,
        const std::vector<LocalBoundary> &total_local_boundary,
        const int n_bases,
        const int dim,
        const double max_edge_length,
        Eigen::MatrixXd &proxy_vertices,
        Eigen::MatrixXi &proxy_faces,
        std::vector<Eigen::Triplet<double>> &displacement_map_entries,
        const CollisionProxyTessellation tessellation)
    {
        // for each boundary element (f):
        //     tessilate f with triangles of max edge length (fₜ)
        //     for each node (x) of fₜ with global index (i):
        //         for each basis (ϕⱼ) in f's parent element:
        //             set Vᵢ = x where Vᵢ is the i-th proxy vertex
        //             set W(i, j) = ϕⱼ(g⁻¹(x)) where g is the geometry mapping of f
        // caveats:
        // • if x is provided in parametric coordinates, we can skip evaluating g⁻¹
        //   - Vᵢ = g(x) instead
        // • the tessellations of all faces need to be stitched together
        //   - this means duplicate weights should be removed
 
        std::vector<double> proxy_vertices_list;
        std::vector<int> proxy_faces_list;
        std::vector<Eigen::Triplet<double>> displacement_map_entries_tmp;
 
        Eigen::MatrixXd UV;
        Eigen::MatrixXi F_local;
        if (tessellation == CollisionProxyTessellation::REGULAR)
        {
            // TODO: use max_edge_length to determine the tessellation
            regular_grid_triangle_barycentric_coordinates(/*n=*/10, UV, F_local);
        }
 
        for (const LocalBoundary &local_boundary : total_local_boundary)
        {
            if (local_boundary.type() != BoundaryType::TRI)
                log_and_throw_error("build_collision_proxy() is only implemented for tetrahedra!");
 
            const basis::ElementBases elm = bases[local_boundary.element_id()];
            const basis::ElementBases g = geom_bases[local_boundary.element_id()];
            for (int fi = 0; fi < local_boundary.size(); fi++)
            {
                const int local_fid = local_boundary.local_primitive_id(fi);
 
                if (tessellation == CollisionProxyTessellation::IRREGULAR)
                {
                    // Use the shape of f to determine the tessellation
                    const Eigen::MatrixXd node_positions = extract_face_vertices(g, local_fid);
                    irregular_triangle_barycentric_coordinates(
                        node_positions.row(0), node_positions.row(1), node_positions.row(2),
                        max_edge_length, UV, F_local);
                }
 
                // Convert UV to appropirate UVW based on the local face id
                Eigen::MatrixXd UVW = uv_to_uvw(UV, local_fid);
 
                Eigen::MatrixXd V_local;
                g.eval_geom_mapping(UVW, V_local);
                assert(V_local.rows() == UV.rows());
 
                const int offset = proxy_vertices_list.size() / dim;
                for (const double x : V_local.reshaped<Eigen::RowMajor>())
                    proxy_vertices_list.push_back(x);
                for (const int i : F_local.reshaped<Eigen::RowMajor>())
                    proxy_faces_list.push_back(i + offset);
 
                for (const basis::Basis &basis : elm.bases)
                {
                    assert(basis.global().size() == 1);
                    const int basis_id = basis.global()[0].index;
 
                    const Eigen::MatrixXd basis_values = basis(UVW);
 
                    for (int i = 0; i < basis_values.size(); i++)
                    {
                        displacement_map_entries_tmp.emplace_back(
                            offset + i, basis_id, basis_values(i));
                    }
                }
            }
        }
 
        // stitch collision proxy together
        stitch_mesh(
            Eigen::Map<RowMajorMatrixX<double>>(proxy_vertices_list.data(), proxy_vertices_list.size() / dim, dim),
            Eigen::Map<RowMajorMatrixX<int>>(proxy_faces_list.data(), proxy_faces_list.size() / dim, dim),
            displacement_map_entries_tmp,
            proxy_vertices, proxy_faces, displacement_map_entries);
    }
 
    // ========================================================================
 
    void build_collision_proxy_displacement_map(
        const std::vector<basis::ElementBases> &bases,
        const std::vector<basis::ElementBases> &geom_bases,
        const std::vector<mesh::LocalBoundary> &total_local_boundary,
        const int n_bases,
        const int dim,
        const Eigen::MatrixXd &proxy_vertices,
        std::vector<Eigen::Triplet<double>> &displacement_map_entries)
    {
        // for each vᵢ in proxy_vertices:
        //     find closest element (t)
        //     compute v̂ᵢ = g⁻¹(v) where g is the geometry mapping of t
        //     for each basis (ϕⱼ) in t:
        //         set W(i, j) = ϕⱼ(v̂ᵢ)
 
        // NOTE: this is only implemented for P1 geometry
        for (const basis::ElementBases &element_bases : geom_bases)
        {
            for (const basis::Basis &basis : element_bases.bases)
            {
                if (basis.order() != 1)
                    log_and_throw_error("build_collision_proxy_displacement_map() is only implemented for P1 geometry!");
            }
        }
 
        // --------------------------------------------------------------------
        // build a BVH to find which element each proxy vertex belongs to
        std::vector<std::array<Eigen::Vector3d, 2>> boxes(
            geom_bases.size(), {{Eigen::Vector3d::Zero(), Eigen::Vector3d::Zero()}});
        for (int i = 0; i < geom_bases.size(); i++)
        {
            const Eigen::MatrixXd nodes = geom_bases[i].nodes();
            boxes[i][0].head(dim) = nodes.colwise().minCoeff();
            boxes[i][1].head(dim) = nodes.colwise().maxCoeff();
        }
 
        SimpleBVH::BVH bvh;
        bvh.init(boxes);
 
        // --------------------------------------------------------------------
        // build wide BVH to find closest point on the surface
 
        // assert(dim == 3);
        // fcpw::Scene<3> scene;
        // {
        //  std::vector<Eigen::Vector3d> vertices;
        //  vertices.reserve(geom_bases.size() * 4);
        //  std::vector<std::array<int, 3>> faces;
        //  faces.reserve(geom_bases.size() * 4);
        //  for (const basis::ElementBases &elm : geom_bases)
        //  {
        //      const int offset = vertices.size();
        //      for (int i = 0; i < 4; i++)
        //          vertices.push_back(elm.bases[i].global()[0].node);
        //      faces.push_back({{offset + 0, offset + 1, offset + 2}});
        //      faces.push_back({{offset + 0, offset + 1, offset + 3}});
        //      faces.push_back({{offset + 0, offset + 2, offset + 3}});
        //      faces.push_back({{offset + 1, offset + 2, offset + 3}});
        //  }
 
        //  scene.setObjectTypes({{fcpw::PrimitiveType::Triangle}});
        //  scene.setObjectVertexCount(vertices.size(), /*object_id=*/0);
        //  scene.setObjectTriangleCount(faces.size(), /*object_id=*/0);
 
        //  for (int i = 0; i < vertices.size(); i++)
        //  {
        //      scene.setObjectVertex(vertices[i].cast<float>(), i, /*object_id=*/0);
        //  }
 
        //  // specify the triangle indices
        //  for (int i = 0; i < faces.size(); i++)
        //  {
        //      scene.setObjectTriangle(faces[i].data(), i, 0);
        //  }
 
        //  scene.build(fcpw::AggregateType::Bvh_SurfaceArea, true); // the second boolean argument enables vectorization
        // }
 
        // --------------------------------------------------------------------
 
        for (int i = 0; i < proxy_vertices.rows(); i++)
        {
            Eigen::Vector3d v = Eigen::Vector3d::Zero();
            v.head(dim) = proxy_vertices.row(i);
 
            std::vector<unsigned int> candidates;
            bvh.intersect_box(v, v, candidates);
 
            // find which element the proxy vertex belongs to
            int closest_element_id = -1;
            VectorNd vhat;
            for (const unsigned int element_id : candidates)
            {
                const Eigen::MatrixXd nodes = geom_bases[element_id].nodes();
                if (dim == 2)
                {
                    assert(nodes.rows() == 3);
                    Eigen::RowVector3d bc;
                    igl::barycentric_coordinates(
                        proxy_vertices.row(i), nodes.row(0), nodes.row(1), nodes.row(2), bc);
                    vhat = bc.head<2>();
                }
                else
                {
                    assert(dim == 3 && nodes.rows() == 4);
                    Eigen::RowVector4d bc;
                    igl::barycentric_coordinates(
                        proxy_vertices.row(i), nodes.row(0), nodes.row(1), nodes.row(2), nodes.row(3), bc);
                    vhat = bc.head<3>();
                }
                if (vhat.minCoeff() >= 0 && vhat.maxCoeff() <= 1 && vhat.sum() <= 1)
                {
                    closest_element_id = element_id;
                    break;
                }
            }
 
            if (closest_element_id < 0)
            {
                // perform a closest point query
                log_and_throw_error("build_collision_proxy_displacement_map(): closest point query not implemented!");
                // fcpw::Interaction<3> cpq_interaction;
                // scene.findClosestPoint(v.cast<float>(), cpq_interaction);
 
                // closest_element_id = cpq_interaction.primitiveIndex / 4;
 
                // const Eigen::MatrixXd nodes = geom_bases[closest_element_id].nodes();
 
                // assert(dim == 3 && nodes.rows() == 4);
                // Eigen::RowVector4d bc;
                // igl::barycentric_coordinates(
                //  proxy_vertices.row(i), nodes.row(0), nodes.row(1), nodes.row(2), nodes.row(3), bc);
                // vhat = bc.head<3>();
            }
 
            // compute the displacement map entries
            for (const basis::Basis &basis : bases[closest_element_id].bases)
            {
                assert(basis.global().size() == 1);
                const int j = basis.global()[0].index;
                displacement_map_entries.emplace_back(i, j, basis(vhat.transpose())(0));
            }
        }
    }
 
    // ========================================================================
 
    void load_collision_proxy(
        const std::string &mesh_filename,
        const std::string &weights_filename,
        const Eigen::VectorXi &in_node_to_node,
        const json &transformation,
        Eigen::MatrixXd &vertices,
        Eigen::VectorXi &codim_vertices,
        Eigen::MatrixXi &edges,
        Eigen::MatrixXi &faces,
        std::vector<Eigen::Triplet<double>> &displacement_map_entries)
    {
        load_collision_proxy_mesh(mesh_filename, transformation, vertices, codim_vertices, edges, faces);
        load_collision_proxy_displacement_map(weights_filename, in_node_to_node, vertices.rows(), displacement_map_entries);
    }
 
    void load_collision_proxy_mesh(
        const std::string &mesh_filename,
        const json &transformation,
        Eigen::MatrixXd &vertices,
        Eigen::VectorXi &codim_vertices,
        Eigen::MatrixXi &edges,
        Eigen::MatrixXi &faces)
    {
        Eigen::MatrixXi codim_edges;
        read_surface_mesh(mesh_filename, vertices, codim_vertices, codim_edges, faces);
 
        if (faces.size())
            igl::edges(faces, edges);
 
        utils::append_rows(edges, codim_edges);
 
        // Transform the collision proxy
        std::array<RowVectorNd, 2> bbox;
        bbox[0] = vertices.colwise().minCoeff();
        bbox[1] = vertices.colwise().maxCoeff();
 
        MatrixNd A;
        VectorNd b;
        // TODO: pass correct unit scale
        construct_affine_transformation(
            /*unit_scale=*/1, transformation,
            (bbox[1] - bbox[0]).cwiseAbs().transpose(),
            A, b);
        vertices = (vertices * A.transpose()).rowwise() + b.transpose();
    }
 
    void load_collision_proxy_displacement_map(
        const std::string &weights_filename,
        const Eigen::VectorXi &in_node_to_node,
        const size_t num_proxy_vertices,
        std::vector<Eigen::Triplet<double>> &displacement_map_entries)
    {
#ifndef NDEBUG
        const size_t num_fe_nodes = in_node_to_node.size();
#endif
        h5pp::File file(weights_filename, h5pp::FileAccess::READONLY);
        const std::array<long, 2> shape = file.readAttribute<std::array<long, 2>>("weight_triplets", "shape");
        assert(shape[0] == num_proxy_vertices && shape[1] == num_fe_nodes);
        Eigen::VectorXd values = file.readDataset<Eigen::VectorXd>("weight_triplets/values");
        Eigen::VectorXi rows = file.readDataset<Eigen::VectorXi>("weight_triplets/rows");
        Eigen::VectorXi cols = file.readDataset<Eigen::VectorXi>("weight_triplets/cols");
        assert(rows.maxCoeff() < num_proxy_vertices);
        assert(cols.maxCoeff() < num_fe_nodes);
 
        // TODO: use these to build the in_node_to_node map
        // const Eigen::VectorXi in_ordered_vertices = file.exist("ordered_vertices") ? H5Easy::load<Eigen::VectorXi>(file, "ordered_vertices") : mesh->in_ordered_vertices();
        // const Eigen::MatrixXi in_ordered_edges = file.exist("ordered_edges") ? H5Easy::load<Eigen::MatrixXi>(file, "ordered_edges") : mesh->in_ordered_edges();
        // const Eigen::MatrixXi in_ordered_faces = file.exist("ordered_faces") ? H5Easy::load<Eigen::MatrixXi>(file, "ordered_faces") : mesh->in_ordered_faces();
 
        displacement_map_entries.clear();
        displacement_map_entries.reserve(values.size());
 
        assert(in_node_to_node.size() == num_fe_nodes);
        for (int i = 0; i < values.size(); i++)
        {
            // Rearrange the columns based on the FEM mesh node order
            displacement_map_entries.emplace_back(rows[i], in_node_to_node[cols[i]], values[i]);
        }
    }
} // namespace polyfem::mesh