bind_utilities.h

/*
 * Copyright 2022 Adobe. All rights reserved.
 * This file is licensed to you under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License. You may obtain a copy
 * of the License at http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software distributed under
 * the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR REPRESENTATIONS
 * OF ANY KIND, either express or implied. See the License for the specific language
 * governing permissions and limitations under the License.
 */
#pragma once
 
#include <lagrange/AttributeTypes.h>
#include <lagrange/NormalWeightingType.h>
#include <lagrange/cast_attribute.h>
#include <lagrange/combine_meshes.h>
#include <lagrange/compute_area.h>
#include <lagrange/compute_centroid.h>
#include <lagrange/compute_components.h>
#include <lagrange/compute_dihedral_angles.h>
#include <lagrange/compute_dijkstra_distance.h>
#include <lagrange/compute_edge_lengths.h>
#include <lagrange/compute_facet_circumcenter.h>
#include <lagrange/compute_facet_normal.h>
#include <lagrange/compute_greedy_coloring.h>
#include <lagrange/compute_mesh_covariance.h>
#include <lagrange/compute_normal.h>
#include <lagrange/compute_pointcloud_pca.h>
#include <lagrange/compute_seam_edges.h>
#include <lagrange/compute_tangent_bitangent.h>
#include <lagrange/compute_uv_charts.h>
#include <lagrange/compute_uv_distortion.h>
#include <lagrange/compute_uv_orientation.h>
#include <lagrange/compute_uv_tile_list.h>
#include <lagrange/compute_vertex_normal.h>
#include <lagrange/compute_vertex_valence.h>
#include <lagrange/disconnect_uv_charts.h>
#include <lagrange/extract_submesh.h>
#include <lagrange/filter_attributes.h>
#include <lagrange/get_unique_attribute_name.h>
#include <lagrange/internal/constants.h>
#include <lagrange/isoline.h>
#include <lagrange/map_attribute.h>
#include <lagrange/mesh_bbox.h>
#include <lagrange/normalize_meshes.h>
#include <lagrange/orient_outward.h>
#include <lagrange/orientation.h>
#include <lagrange/permute_facets.h>
#include <lagrange/permute_vertices.h>
#include <lagrange/python/binding.h>
#include <lagrange/python/tensor_utils.h>
#include <lagrange/python/utils/StackVector.h>
#include <lagrange/python/utils/StubType.h>
#include <lagrange/remap_vertices.h>
#include <lagrange/reorder_mesh.h>
#include <lagrange/select_facets_by_normal_similarity.h>
#include <lagrange/select_facets_in_frustum.h>
#include <lagrange/separate_by_components.h>
#include <lagrange/separate_by_facet_groups.h>
#include <lagrange/split_facets_by_material.h>
#include <lagrange/thicken_and_close_mesh.h>
#include <lagrange/topology.h>
#include <lagrange/transform_mesh.h>
#include <lagrange/triangulate_polygonal_facets.h>
#include <lagrange/unflip_uv_charts.h>
#include <lagrange/unify_index_buffer.h>
#include <lagrange/utils/fmt/format.h>
#include <lagrange/utils/invalid.h>
#include <lagrange/uv_mesh.h>
#include <lagrange/weld_indexed_attribute.h>
 
#include <optional>
#include <string_view>
#include <vector>
 
namespace lagrange::python {
 
LA_STUB_HINT(IterableUsageHint, "collections.abc.Iterable[AttributeUsage]");
LA_STUB_HINT(IterableElementHint, "collections.abc.Iterable[AttributeElement]");
 
template <typename Scalar, typename Index>
void bind_utilities(nanobind::module_& m)
{
    namespace nb = nanobind;
    using namespace nb::literals;
    using MeshType = SurfaceMesh<Scalar, Index>;
 
    nb::enum_<NormalWeightingType>(m, "NormalWeightingType", "Normal weighting type.")
        .value("Uniform", NormalWeightingType::Uniform, "Uniform weighting")
        .value(
            "CornerTriangleArea",
            NormalWeightingType::CornerTriangleArea,
            "Weight by corner triangle area")
        .value("Angle", NormalWeightingType::Angle, "Weight by corner angle");
 
    nb::class_<VertexNormalOptions>(
        m,
        "VertexNormalOptions",
        "Options for computing vertex normals")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &VertexNormalOptions::output_attribute_name,
            "Output attribute name. Default is `@vertex_normal`.")
        .def_rw(
            "weight_type",
            &VertexNormalOptions::weight_type,
            "Weighting type for normal computation. Default is Angle.")
        .def_rw(
            "weighted_corner_normal_attribute_name",
            &VertexNormalOptions::weighted_corner_normal_attribute_name,
            R"(Precomputed weighted corner normals attribute name (default: @weighted_corner_normal).
 
If attribute exists, the precomputed weighted corner normal will be used.)")
        .def_rw(
            "recompute_weighted_corner_normals",
            &VertexNormalOptions::recompute_weighted_corner_normals,
            "Whether to recompute weighted corner normals (default: false).")
        .def_rw(
            "keep_weighted_corner_normals",
            &VertexNormalOptions::keep_weighted_corner_normals,
            "Whether to keep the weighted corner normal attribute (default: false).")
        .def_rw(
            "distance_tolerance",
            &VertexNormalOptions::distance_tolerance,
            "Distance tolerance for degenerate edge check in polygon facets.");
 
    m.def(
        "compute_vertex_normal",
        &compute_vertex_normal<Scalar, Index>,
        "mesh"_a,
        "options"_a = VertexNormalOptions(),
        R"(Compute vertex normal.
 
:param mesh: Input mesh.
:param options: Options for computing vertex normals.
 
:returns: Vertex normal attribute id.)");
 
    m.def(
        "compute_vertex_normal",
        [](MeshType& mesh,
           std::optional<std::string_view> output_attribute_name,
           std::optional<NormalWeightingType> weight_type,
           std::optional<std::string_view> weighted_corner_normal_attribute_name,
           std::optional<bool> recompute_weighted_corner_normals,
           std::optional<bool> keep_weighted_corner_normals,
           std::optional<float> distance_tolerance) {
            VertexNormalOptions options;
            if (output_attribute_name) options.output_attribute_name = *output_attribute_name;
            if (weight_type) options.weight_type = *weight_type;
            if (weighted_corner_normal_attribute_name)
                options.weighted_corner_normal_attribute_name =
                    *weighted_corner_normal_attribute_name;
            if (recompute_weighted_corner_normals)
                options.recompute_weighted_corner_normals = *recompute_weighted_corner_normals;
            if (keep_weighted_corner_normals)
                options.keep_weighted_corner_normals = *keep_weighted_corner_normals;
            if (distance_tolerance) options.distance_tolerance = *distance_tolerance;
 
            return compute_vertex_normal<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        "weight_type"_a = nb::none(),
        "weighted_corner_normal_attribute_name"_a = nb::none(),
        "recompute_weighted_corner_normals"_a = nb::none(),
        "keep_weighted_corner_normals"_a = nb::none(),
        "distance_tolerance"_a = nb::none(),
        R"(Compute vertex normal (Pythonic API).
 
:param mesh: Input mesh.
:param output_attribute_name: Output attribute name.
:param weight_type: Weighting type for normal computation.
:param weighted_corner_normal_attribute_name: Precomputed weighted corner normals attribute name.
:param recompute_weighted_corner_normals: Whether to recompute weighted corner normals.
:param keep_weighted_corner_normals: Whether to keep the weighted corner normal attribute.
:param distance_tolerance: Distance tolerance for degenerate edge check.
                           (Only used to bypass degenerate edge in polygon facets.)
 
:returns: Vertex normal attribute id.)");
 
    nb::class_<FacetNormalOptions>(m, "FacetNormalOptions", "Facet normal computation options.")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &FacetNormalOptions::output_attribute_name,
            "Output attribute name. Default: `@facet_normal`");
 
    m.def(
        "compute_facet_normal",
        &compute_facet_normal<Scalar, Index>,
        "mesh"_a,
        "options"_a = FacetNormalOptions(),
        R"(Compute facet normal.
 
:param mesh: Input mesh.
:param options: Options for computing facet normals.
 
:returns: Facet normal attribute id.)");
 
    m.def(
        "compute_facet_normal",
        [](MeshType& mesh, std::optional<std::string_view> output_attribute_name) {
            FacetNormalOptions options;
            if (output_attribute_name) options.output_attribute_name = *output_attribute_name;
            return compute_facet_normal<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute facet normal (Pythonic API).
 
:param mesh: Input mesh.
:param output_attribute_name: Output attribute name.
 
:returns: Facet normal attribute id.)");
 
    nb::class_<NormalOptions>(m, "NormalOptions", "Normal computation options.")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &NormalOptions::output_attribute_name,
            "Output attribute name. Default: `@normal`")
        .def_rw(
            "weight_type",
            &NormalOptions::weight_type,
            "Weighting type for normal computation. Default is Angle.")
        .def_rw(
            "facet_normal_attribute_name",
            &NormalOptions::facet_normal_attribute_name,
            "Facet normal attribute name to use. Default is `@facet_normal`.")
        .def_rw(
            "recompute_facet_normals",
            &NormalOptions::recompute_facet_normals,
            "Whether to recompute facet normals. Default is false.")
        .def_rw(
            "keep_facet_normals",
            &NormalOptions::keep_facet_normals,
            "Whether to keep the computed facet normal attribute. Default is false.")
        .def_rw(
            "distance_tolerance",
            &NormalOptions::distance_tolerance,
            "Distance tolerance for degenerate edge check. (Only used to bypass degenerate edge in "
            "polygon facets.)");
 
    m.def(
        "compute_normal",
        [](MeshType& mesh,
           Scalar feature_angle_threshold,
           nb::object cone_vertices,
           std::optional<NormalOptions> normal_options) {
            NormalOptions options;
            if (normal_options.has_value()) {
                options = std::move(normal_options.value());
            }
 
            if (cone_vertices.is_none()) {
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, {}, options);
            } else if (nb::isinstance<nb::list>(cone_vertices)) {
                auto cone_vertices_list = nb::cast<std::vector<Index>>(cone_vertices);
                span<const Index> data{cone_vertices_list.data(), cone_vertices_list.size()};
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, data, options);
            } else if (nb::isinstance<Tensor<Index>>(cone_vertices)) {
                auto cone_vertices_tensor = nb::cast<Tensor<Index>>(cone_vertices);
                auto [data, shape, stride] = tensor_to_span(cone_vertices_tensor);
                la_runtime_assert(is_dense(shape, stride));
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, data, options);
            } else {
                throw std::runtime_error("Invalid cone_vertices type");
            }
        },
        "mesh"_a,
        "feature_angle_threshold"_a = lagrange::internal::pi / 4,
        "cone_vertices"_a = nb::none(),
        "options"_a = nb::none(),
        R"(Compute indexed normal attribute.
 
Edge with dihedral angles larger than `feature_angle_threshold` are considered as sharp edges.
Vertices listed in `cone_vertices` are considered as cone vertices, which is always sharp.
 
:param mesh: input mesh
:param feature_angle_threshold: feature angle threshold
:param cone_vertices: cone vertices
:param options: normal options
 
:returns: the id of the indexed normal attribute.
)");
 
    m.def(
        "compute_normal",
        [](MeshType& mesh,
           Scalar feature_angle_threshold,
           nb::object cone_vertices,
           std::optional<std::string_view> output_attribute_name,
           std::optional<NormalWeightingType> weight_type,
           std::optional<std::string_view> facet_normal_attribute_name,
           std::optional<bool> recompute_facet_normals,
           std::optional<bool> keep_facet_normals,
           std::optional<float> distance_tolerance) {
            NormalOptions options;
            if (output_attribute_name) options.output_attribute_name = *output_attribute_name;
            if (weight_type) options.weight_type = *weight_type;
            if (facet_normal_attribute_name)
                options.facet_normal_attribute_name = *facet_normal_attribute_name;
            if (recompute_facet_normals) options.recompute_facet_normals = *recompute_facet_normals;
            if (keep_facet_normals) options.keep_facet_normals = *keep_facet_normals;
            if (distance_tolerance) options.distance_tolerance = *distance_tolerance;
 
            if (cone_vertices.is_none()) {
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, {}, options);
            } else if (nb::isinstance<nb::list>(cone_vertices)) {
                auto cone_vertices_list = nb::cast<std::vector<Index>>(cone_vertices);
                span<const Index> data{cone_vertices_list.data(), cone_vertices_list.size()};
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, data, options);
            } else if (nb::isinstance<Tensor<Index>>(cone_vertices)) {
                auto cone_vertices_tensor = nb::cast<Tensor<Index>>(cone_vertices);
                auto [data, shape, stride] = tensor_to_span(cone_vertices_tensor);
                la_runtime_assert(is_dense(shape, stride));
                return compute_normal<Scalar, Index>(mesh, feature_angle_threshold, data, options);
            } else {
                throw std::runtime_error("Invalid cone_vertices type");
            }
        },
        "mesh"_a,
        "feature_angle_threshold"_a = lagrange::internal::pi / 4,
        "cone_vertices"_a = nb::none(),
        "output_attribute_name"_a = nb::none(),
        "weight_type"_a = nb::none(),
        "facet_normal_attribute_name"_a = nb::none(),
        "recompute_facet_normals"_a = nb::none(),
        "keep_facet_normals"_a = nb::none(),
        "distance_tolerance"_a = nb::none(),
        R"(Compute indexed normal attribute (Pythonic API).
 
:param mesh: input mesh
:param feature_angle_threshold: feature angle threshold
:param cone_vertices: cone vertices
:param output_attribute_name: output normal attribute name
:param weight_type: normal weighting type
:param facet_normal_attribute_name: facet normal attribute name
:param recompute_facet_normals: whether to recompute facet normals
:param keep_facet_normals: whether to keep the computed facet normal attribute
:param distance_tolerance: distance tolerance for degenerate edge check
                           (only used to bypass degenerate edges in polygon facets)
 
:returns: the id of the indexed normal attribute.)");
 
    using ConstArray3d = nb::ndarray<const double, nb::shape<-1, 3>, nb::c_contig, nb::device::cpu>;
    m.def(
        "compute_pointcloud_pca",
        [](ConstArray3d points, bool shift_centroid, bool normalize) {
            ComputePointcloudPCAOptions options;
            options.shift_centroid = shift_centroid;
            options.normalize = normalize;
            PointcloudPCAOutput<Scalar> output =
                compute_pointcloud_pca<Scalar>({points.data(), points.size()}, options);
            return std::make_tuple(output.center, output.eigenvectors, output.eigenvalues);
        },
        "points"_a,
        "shift_centroid"_a = ComputePointcloudPCAOptions().shift_centroid,
        "normalize"_a = ComputePointcloudPCAOptions().normalize,
        R"(Compute principal components of a point cloud.
 
:param points: Input points.
:param shift_centroid: When true: covariance = (P-centroid)^T (P-centroid), when false: covariance = (P)^T (P).
:param normalize: Should we divide the result by number of points?
 
:returns: tuple of (center, eigenvectors, eigenvalues).)");
 
    m.def(
        "compute_greedy_coloring",
        [](MeshType& mesh,
           AttributeElement element_type,
           size_t num_color_used,
           std::optional<std::string_view> output_attribute_name) {
            GreedyColoringOptions options;
            options.element_type = element_type;
            options.num_color_used = num_color_used;
            if (output_attribute_name) options.output_attribute_name = *output_attribute_name;
            return compute_greedy_coloring<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "element_type"_a = AttributeElement::Facet,
        "num_color_used"_a = 8,
        "output_attribute_name"_a = nb::none(),
        R"(Compute greedy coloring of mesh elements.
 
:param mesh: Input mesh.
:param element_type: Element type to be colored. Can be either Vertex or Facet.
:param num_color_used: Initial color palette size. The algorithm allocates more colors when neighbors exhaust the palette, and may use fewer.
:param output_attribute_name: Output attribute name.
 
:returns: Color attribute id.)");
 
    m.def(
        "normalize_mesh_with_transform",
        [](MeshType& mesh,
           bool normalize_normals,
           bool normalize_tangents_bitangents) -> Eigen::Matrix<Scalar, 4, 4> {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            return normalize_mesh_with_transform(mesh, options).matrix();
        },
        "mesh"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a mesh to fit into a unit box centered at the origin.
 
:param mesh: Input mesh.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.
 
:return Inverse transform, can be used to undo the normalization process.)");
 
 
    m.def(
        "normalize_mesh_with_transform_2d",
        [](MeshType& mesh,
           bool normalize_normals,
           bool normalize_tangents_bitangents) -> Eigen::Matrix<Scalar, 3, 3> {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            return normalize_mesh_with_transform<2>(mesh, options).matrix();
        },
        "mesh"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a mesh to fit into a unit box centered at the origin.
 
:param mesh: Input mesh.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.
 
:return Inverse transform, can be used to undo the normalization process.)");
 
    m.def(
        "normalize_mesh",
        [](MeshType& mesh, bool normalize_normals, bool normalize_tangents_bitangents) -> void {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            normalize_mesh(mesh, options);
        },
        "mesh"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a mesh to fit into a unit box centered at the origin.
 
:param mesh: Input mesh.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.)");
 
    m.def(
        "normalize_meshes_with_transform",
        [](std::vector<MeshType*> meshes,
           bool normalize_normals,
           bool normalize_tangents_bitangents) -> Eigen::Matrix<Scalar, 4, 4> {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            span<MeshType*> meshes_span(meshes.data(), meshes.size());
            return normalize_meshes_with_transform(meshes_span, options).matrix();
        },
        "meshes"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a mesh to fit into a unit box centered at the origin.
 
:param meshes: Input meshes.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.
 
:return Inverse transform, can be used to undo the normalization process.)");
 
    m.def(
        "normalize_meshes_with_transform_2d",
        [](std::vector<MeshType*> meshes,
           bool normalize_normals,
           bool normalize_tangents_bitangents) -> Eigen::Matrix<Scalar, 3, 3> {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            span<MeshType*> meshes_span(meshes.data(), meshes.size());
            return normalize_meshes_with_transform<2>(meshes_span, options).matrix();
        },
        "meshes"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a mesh to fit into a unit box centered at the origin.
 
:param meshes: Input meshes.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.
 
:return Inverse transform, can be used to undo the normalization process.)");
 
 
    m.def(
        "normalize_meshes",
        [](std::vector<MeshType*> meshes,
           bool normalize_normals,
           bool normalize_tangents_bitangents) {
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            span<MeshType*> meshes_span(meshes.data(), meshes.size());
            normalize_meshes(meshes_span, options);
        },
        "meshes"_a,
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        R"(Normalize a list of meshes to fit into a unit box centered at the origin.
 
:param meshes: Input meshes.
:param normalize_normals:             Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.)");
 
    m.def(
        "combine_meshes",
        [](std::vector<MeshType*> meshes, bool preserve_vertices) {
            return combine_meshes<Scalar, Index>(
                meshes.size(),
                [&](size_t i) -> const MeshType& { return *meshes[i]; },
                preserve_vertices);
        },
        "meshes"_a,
        "preserve_attributes"_a = true,
        R"(Combine a list of meshes into a single mesh.
 
:param meshes: Input meshes.
:param preserve_attributes: Whether to preserve attributes.
 
:returns: The combined mesh.)");
 
    m.def(
        "compute_seam_edges",
        [](MeshType& mesh,
           AttributeId indexed_attribute_id,
           std::optional<std::string_view> output_attribute_name,
           bool include_boundary_edges) {
            SeamEdgesOptions options;
            if (output_attribute_name) options.output_attribute_name = *output_attribute_name;
            options.include_boundary_edges = include_boundary_edges;
            return compute_seam_edges<Scalar, Index>(mesh, indexed_attribute_id, options);
        },
        "mesh"_a,
        "indexed_attribute_id"_a,
        "output_attribute_name"_a = nb::none(),
        "include_boundary_edges"_a = SeamEdgesOptions().include_boundary_edges,
        R"(Compute seam edges for a given indexed attribute.
 
:param mesh: Input mesh.
:param indexed_attribute_id: Input indexed attribute id.
:param output_attribute_name: Output attribute name.
:param include_boundary_edges: If true, boundary edges are also marked as seam edges.
 
:returns: Attribute id for the output per-edge seam attribute (1 is a seam, 0 is not).)");
 
    m.def(
        "orient_outward",
        [](MeshType& mesh, bool positive) {
            OrientOptions options;
            options.positive = positive;
            orient_outward<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "positive"_a = OrientOptions().positive,
        R"(Orient mesh facets to ensure positive or negative signed volume.
 
:param mesh: Input mesh.
:param positive: Whether to orient volumes positively or negatively.)");
 
    m.def(
        "unify_index_buffer",
        [](MeshType& mesh) { return unify_index_buffer(mesh); },
        "mesh"_a,
        R"(Unify the index buffer for all indexed attributes.
 
:param mesh: Input mesh.
 
:returns: Unified mesh.)");
 
    m.def(
        "unify_index_buffer",
        &lagrange::unify_index_buffer<Scalar, Index>,
        "mesh"_a,
        "attribute_ids"_a,
        R"(Unify the index buffer for selected attributes.
 
:param mesh: Input mesh.
:param attribute_ids: Attribute IDs to unify.
 
:returns: Unified mesh.)");
 
    m.def(
        "unify_index_buffer",
        &lagrange::unify_named_index_buffer<Scalar, Index>,
        "mesh"_a,
        "attribute_names"_a,
        R"(Unify the index buffer for selected attributes.
 
:param mesh: Input mesh.
:param attribute_names: Attribute names to unify.
 
:returns: Unified mesh.)");
 
    m.def(
        "triangulate_polygonal_facets",
        [](MeshType& mesh,
           std::string_view scheme,
           std::optional<std::variant<Tensor<Index>, Tensor<bool>, nb::list>> selected_facets) {
            lagrange::TriangulationOptions opt;
            if (scheme == "earcut") {
                opt.scheme = lagrange::TriangulationOptions::Scheme::Earcut;
            } else if (scheme == "centroid_fan") {
                opt.scheme = lagrange::TriangulationOptions::Scheme::CentroidFan;
            } else {
                throw Error(lagrange::format("Unsupported triangulation scheme {}", scheme));
            }
 
            if (!selected_facets.has_value()) {
                // By default, triangulate every polygonal facet.
                lagrange::triangulate_polygonal_facets(mesh, opt);
                return;
            }
 
            // Build a per-facet mask from either a list/tensor of facet ids or a boolean mask (a
            // length-num_facets tensor whose `True` entries mark facets to triangulate).
            const Index num_facets = mesh.get_num_facets();
            std::vector<uint8_t> should_triangulate(static_cast<size_t>(num_facets), 0);
            auto mark_ids = [&](span<const Index> ids) {
                for (Index f : ids) {
                    if (f >= num_facets) {
                        throw Error(
                            lagrange::format(
                                "Facet index {} is out of range (mesh has {} facets)",
                                f,
                                num_facets));
                    }
                    should_triangulate[f] = 1;
                }
            };
            auto& selected = selected_facets.value();
            if (const auto* list_ptr = std::get_if<nb::list>(&selected)) {
                auto ids = nb::cast<std::vector<Index>>(*list_ptr);
                mark_ids({ids.data(), ids.size()});
            } else if (auto* mask_ptr = std::get_if<Tensor<bool>>(&selected)) {
                // Boolean per-facet mask: entry `f` is true iff facet `f` should be triangulated.
                if (mask_ptr->ndim() != 1 ||
                    mask_ptr->shape(0) != static_cast<size_t>(num_facets)) {
                    throw Error(
                        lagrange::format(
                            "Facet mask must be a 1D array of length {} (the number of facets)",
                            num_facets));
                }
                // Access the 1D buffer through a typed view (same pattern as
                // `bind_surface_mesh.h`); Tensor<> enforces C-contiguity.
                auto mask_view = mask_ptr->template view<bool, nb::ndim<1>>();
                for (Index f = 0; f < num_facets; ++f) {
                    should_triangulate[f] = mask_view(f) ? 1 : 0;
                }
            } else {
                auto [data, shape, stride] = tensor_to_span(std::get<Tensor<Index>>(selected));
                la_runtime_assert(is_dense(shape, stride));
                mark_ids(data);
            }
 
            lagrange::triangulate_polygonal_facets(
                mesh,
                lagrange::function_ref<bool(Index)>(
                    [&](Index f) { return should_triangulate[f] != 0; }),
                opt);
        },
        "mesh"_a,
        "scheme"_a = "earcut",
        "selected_facets"_a = nb::none(),
        R"(Triangulate polygonal facets of the mesh.
 
:param mesh: The input mesh to be triangulated in place.
:param scheme: The triangulation scheme (options are 'earcut' and 'centroid_fan').
:param selected_facets: Optional subset of facets to triangulate. Either a list/array of facet ids,
    or a boolean per-facet mask (a length ``num_facets`` array whose ``True`` entries mark facets to
    triangulate). Honored by both schemes; facets not selected are left untouched. If omitted, all
    polygonal facets are triangulated.)");
 
    nb::enum_<ComponentOptions::ConnectivityType>(m, "ConnectivityType", "Mesh connectivity type")
        .value(
            "Vertex",
            ComponentOptions::ConnectivityType::Vertex,
            "Two facets are connected if they share a vertex")
        .value(
            "Edge",
            ComponentOptions::ConnectivityType::Edge,
            "Two facets are connected if they share an edge");
 
    m.def(
        "compute_components",
        [](MeshType& mesh,
           std::optional<std::string_view> output_attribute_name,
           std::optional<lagrange::ConnectivityType> connectivity_type,
           std::optional<nb::list>& blocker_elements) {
            lagrange::ComponentOptions opt;
            if (output_attribute_name.has_value()) {
                opt.output_attribute_name = output_attribute_name.value();
            }
            if (connectivity_type.has_value()) {
                opt.connectivity_type = connectivity_type.value();
            }
            std::vector<Index> blocker_elements_vec;
            if (blocker_elements.has_value()) {
                for (auto val : blocker_elements.value()) {
                    blocker_elements_vec.push_back(nb::cast<Index>(val));
                }
            }
            return lagrange::compute_components<Scalar, Index>(mesh, blocker_elements_vec, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        "connectivity_type"_a = nb::none(),
        "blocker_elements"_a = nb::none(),
        R"(Compute connected components.
 
This method will create a per-facet component id attribute named by the `output_attribute_name`
argument. Each component id is in [0, num_components-1] range.
 
:param mesh: The input mesh.
:param output_attribute_name: The name of the output attribute.
:param connectivity_type: The connectivity type.  Either "Vertex" or "Edge".
:param blocker_elements: The list of blocker element indices. If `connectivity_type` is `Edge`, facets adjacent to a blocker edge are not considered as connected through this edge. If `connectivity_type` is `Vertex`, facets sharing a blocker vertex are not considered as connected through this vertex.
 
:returns: The total number of components.)");
 
    nb::class_<VertexValenceOptions>(m, "VertexValenceOptions", "Vertex valence options")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &VertexValenceOptions::output_attribute_name,
            "The name of the output attribute")
        .def_rw(
            "induced_by_attribute",
            &VertexValenceOptions::induced_by_attribute,
            "Optional per-edge attribute used as indicator function to restrict the graph used for "
            "vertex valence computation");
 
    m.def(
        "compute_vertex_valence",
        &lagrange::compute_vertex_valence<Scalar, Index>,
        "mesh"_a,
        "options"_a = VertexValenceOptions(),
        R"(Compute vertex valence
 
:param mesh: The input mesh.
:param options: The vertex valence options.
 
:returns: The vertex valence attribute id.)");
 
    m.def(
        "compute_vertex_valence",
        [](MeshType& mesh,
           std::optional<std::string_view> output_attribute_name,
           std::optional<std::string_view> induced_by_attribute) {
            VertexValenceOptions opt;
            if (output_attribute_name.has_value()) {
                opt.output_attribute_name = output_attribute_name.value();
            }
            if (induced_by_attribute.has_value()) {
                opt.induced_by_attribute = induced_by_attribute.value();
            }
            return lagrange::compute_vertex_valence<Scalar, Index>(mesh, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        "induced_by_attribute"_a = nb::none(),
        R"(Compute vertex valence.
 
:param mesh: The input mesh.
:param output_attribute_name: The name of the output attribute.
:param induced_by_attribute: Optional per-edge attribute used as indicator function to restrict the graph used for vertex valence computation.
 
:returns: The vertex valence attribute id)");
 
    nb::class_<TangentBitangentOptions>(m, "TangentBitangentOptions", "Tangent bitangent options")
        .def(nb::init<>())
        .def_rw(
            "tangent_attribute_name",
            &TangentBitangentOptions::tangent_attribute_name,
            "The name of the output tangent attribute, default is `@tangent`")
        .def_rw(
            "bitangent_attribute_name",
            &TangentBitangentOptions::bitangent_attribute_name,
            "The name of the output bitangent attribute, default is `@bitangent`")
        .def_rw(
            "uv_attribute_name",
            &TangentBitangentOptions::uv_attribute_name,
            "The name of the uv attribute")
        .def_rw(
            "normal_attribute_name",
            &TangentBitangentOptions::normal_attribute_name,
            "The name of the normal attribute")
        .def_rw(
            "output_element_type",
            &TangentBitangentOptions::output_element_type,
            "The output element type")
        .def_rw(
            "pad_with_sign",
            &TangentBitangentOptions::pad_with_sign,
            "Whether to pad the output tangent/bitangent with sign")
        .def_rw(
            "orthogonalize_bitangent",
            &TangentBitangentOptions::orthogonalize_bitangent,
            "Whether to compute the bitangent as cross(normal, tangent). If false, the bitangent "
            "is computed as the derivative of v-coordinate")
        .def_rw(
            "keep_existing_tangent",
            &TangentBitangentOptions::keep_existing_tangent,
            "Whether to recompute tangent if the tangent attribute (specified by "
            "tangent_attribute_name) already exists. If true, bitangent is computed by normalizing "
            "cross(normal, tangent) and param orthogonalize_bitangent must be true.");
    nb::class_<TangentBitangentResult>(m, "TangentBitangentResult", "Tangent bitangent result")
        .def(nb::init<>())
        .def_rw(
            "tangent_id",
            &TangentBitangentResult::tangent_id,
            "The output tangent attribute id")
        .def_rw(
            "bitangent_id",
            &TangentBitangentResult::bitangent_id,
            "The output bitangent attribute id");
 
    m.def(
        "compute_tangent_bitangent",
        &lagrange::compute_tangent_bitangent<Scalar, Index>,
        "mesh"_a,
        "options"_a = TangentBitangentOptions(),
        R"(Compute tangent and bitangent vector attributes.
 
:param mesh: The input mesh.
:param options: The tangent bitangent options.
 
:returns: The tangent and bitangent attribute ids)");
 
    m.def(
        "compute_tangent_bitangent",
        [](MeshType& mesh,
           std::optional<std::string_view>(tangent_attribute_name),
           std::optional<std::string_view>(bitangent_attribute_name),
           std::optional<std::string_view>(uv_attribute_name),
           std::optional<std::string_view>(normal_attribute_name),
           std::optional<AttributeElement>(output_attribute_type),
           std::optional<bool>(pad_with_sign),
           std::optional<bool>(orthogonalize_bitangent),
           std::optional<bool>(keep_existing_tangent)) {
            TangentBitangentOptions opt;
            if (tangent_attribute_name.has_value()) {
                opt.tangent_attribute_name = tangent_attribute_name.value();
            }
            if (bitangent_attribute_name.has_value()) {
                opt.bitangent_attribute_name = bitangent_attribute_name.value();
            }
            if (uv_attribute_name.has_value()) {
                opt.uv_attribute_name = uv_attribute_name.value();
            }
            if (normal_attribute_name.has_value()) {
                opt.normal_attribute_name = normal_attribute_name.value();
            }
            if (output_attribute_type.has_value()) {
                opt.output_element_type = output_attribute_type.value();
            }
            if (pad_with_sign.has_value()) {
                opt.pad_with_sign = pad_with_sign.value();
            }
            if (orthogonalize_bitangent.has_value()) {
                opt.orthogonalize_bitangent = orthogonalize_bitangent.value();
            }
            if (keep_existing_tangent.has_value()) {
                opt.keep_existing_tangent = keep_existing_tangent.value();
            }
 
            auto r = compute_tangent_bitangent<Scalar, Index>(mesh, opt);
            return std::make_tuple(r.tangent_id, r.bitangent_id);
        },
        "mesh"_a,
        "tangent_attribute_name"_a = nb::none(),
        "bitangent_attribute_name"_a = nb::none(),
        "uv_attribute_name"_a = nb::none(),
        "normal_attribute_name"_a = nb::none(),
        "output_attribute_type"_a = nb::none(),
        "pad_with_sign"_a = nb::none(),
        "orthogonalize_bitangent"_a = nb::none(),
        "keep_existing_tangent"_a = nb::none(),
        R"(Compute tangent and bitangent vector attributes (Pythonic API).
 
:param mesh: The input mesh.
:param tangent_attribute_name: The name of the output tangent attribute.
:param bitangent_attribute_name: The name of the output bitangent attribute.
:param uv_attribute_name: The name of the uv attribute.
:param normal_attribute_name: The name of the normal attribute.
:param output_attribute_type: The output element type.
:param pad_with_sign: Whether to pad the output tangent/bitangent with sign.
:param orthogonalize_bitangent: Whether to compute the bitangent as sign * cross(normal, tangent).
:param keep_existing_tangent: Whether to recompute tangent if the tangent attribute (specified by tangent_attribute_name) already exists. If true, bitangent is computed by normalizing cross(normal, tangent) and param orthogonalize_bitangent must be true.
 
:returns: The tangent and bitangent attribute ids)");
 
    m.def(
        "map_attribute",
        static_cast<AttributeId (*)(MeshType&, AttributeId, std::string_view, AttributeElement)>(
            &lagrange::map_attribute<Scalar, Index>),
        "mesh"_a,
        "old_attribute_id"_a,
        "new_attribute_name"_a,
        "new_element"_a,
        R"(Map an attribute to a new element type.
 
:param mesh: The input mesh.
:param old_attribute_id: The id of the input attribute.
:param new_attribute_name: The name of the new attribute.
:param new_element: The new element type.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "map_attribute",
        static_cast<
            AttributeId (*)(MeshType&, std::string_view, std::string_view, AttributeElement)>(
            &lagrange::map_attribute<Scalar, Index>),
        "mesh"_a,
        "old_attribute_name"_a,
        "new_attribute_name"_a,
        "new_element"_a,
        R"(Map an attribute to a new element type.
 
:param mesh: The input mesh.
:param old_attribute_name: The name of the input attribute.
:param new_attribute_name: The name of the new attribute.
:param new_element: The new element type.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "map_attribute_in_place",
        static_cast<AttributeId (*)(MeshType&, AttributeId, AttributeElement)>(
            &map_attribute_in_place<Scalar, Index>),
        "mesh"_a,
        "id"_a,
        "new_element"_a,
        R"(Map an attribute to a new element type in place.
 
:param mesh: The input mesh.
:param id: The id of the input attribute.
:param new_element: The new element type.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "map_attribute_in_place",
        static_cast<AttributeId (*)(MeshType&, std::string_view, AttributeElement)>(
            &map_attribute_in_place<Scalar, Index>),
        "mesh"_a,
        "name"_a,
        "new_element"_a,
        R"(Map an attribute to a new element type in place.
 
:param mesh: The input mesh.
:param name: The name of the input attribute.
:param new_element: The new element type.
 
:returns: The id of the new attribute.)");
 
    nb::class_<FacetAreaOptions>(m, "FacetAreaOptions", "Options for computing facet area.")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &FacetAreaOptions::output_attribute_name,
            "The name of the output attribute.");
 
    m.def(
        "compute_facet_area",
        &lagrange::compute_facet_area<Scalar, Index>,
        "mesh"_a,
        "options"_a = FacetAreaOptions(),
        R"(Compute facet area.
 
:param mesh: The input mesh.
:param options: The options for computing facet area.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "compute_facet_area",
        [](MeshType& mesh, std::optional<std::string_view> name) {
            FacetAreaOptions opt;
            if (name.has_value()) {
                opt.output_attribute_name = name.value();
            }
            return lagrange::compute_facet_area<Scalar, Index>(mesh, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute facet area (Pythonic API).
 
:param mesh: The input mesh.
:param output_attribute_name: The name of the output attribute.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "compute_facet_vector_area",
        [](MeshType& mesh, std::optional<std::string_view> name) {
            FacetVectorAreaOptions opt;
            if (name.has_value()) {
                opt.output_attribute_name = name.value();
            }
            return lagrange::compute_facet_vector_area<Scalar, Index>(mesh, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute facet vector area (Pythonic API).
 
Vector area is defined as the area multiplied by the facet normal.
For triangular facets, it is equivalent to half of the cross product of two edges.
For non-planar polygonal facets, the vector area offers a robust way to compute the area and normal.
The magnitude of the vector area is the largest area of any orthogonal projection of the facet.
The direction of the vector area is the normal direction that maximizes the projected area [1, 2].
 
[1] Sullivan, John M. "Curvatures of smooth and discrete surfaces." Discrete differential geometry.
Basel: Birkhäuser Basel, 2008. 175-188.
 
[2] Alexa, Marc, and Max Wardetzky. "Discrete Laplacians on general polygonal meshes." ACM SIGGRAPH
2011 papers. 2011. 1-10.
 
:param mesh: The input mesh.
:param output_attribute_name: The name of the output attribute.
 
:returns: The id of the new attribute.)");
 
    nb::class_<MeshAreaOptions>(m, "MeshAreaOptions", "Options for computing mesh area.")
        .def(nb::init<>())
        .def_rw(
            "input_attribute_name",
            &MeshAreaOptions::input_attribute_name,
            "The name of the pre-computed facet area attribute, default is `@facet_area`.")
        .def_rw(
            "use_signed_area",
            &MeshAreaOptions::use_signed_area,
            "Whether to use signed area.");
 
    m.def(
        "compute_mesh_area",
        &lagrange::compute_mesh_area<Scalar, Index>,
        "mesh"_a,
        "options"_a = MeshAreaOptions(),
        R"(Compute mesh area.
 
:param mesh: The input mesh.
:param options: The options for computing mesh area.
 
:returns: The mesh area.)");
 
    m.def(
        "compute_uv_area",
        &lagrange::compute_uv_area<Scalar, Index>,
        "mesh"_a,
        "options"_a = MeshAreaOptions(),
        R"(Compute UV mesh area.
 
:param mesh: The input mesh.
:param options: The options for computing mesh area.
 
:returns: The UV mesh area.)");
 
    m.def(
        "compute_mesh_area",
        [](MeshType& mesh,
           std::optional<std::string_view> input_attribute_name,
           std::optional<bool> use_signed_area) {
            MeshAreaOptions opt;
            if (input_attribute_name.has_value()) {
                opt.input_attribute_name = input_attribute_name.value();
            }
            if (use_signed_area.has_value()) {
                opt.use_signed_area = use_signed_area.value();
            }
            return compute_mesh_area(mesh, opt);
        },
        "mesh"_a,
        "input_attribute_name"_a = nb::none(),
        "use_signed_area"_a = nb::none(),
        R"(Compute mesh area (Pythonic API).
 
:param mesh: The input mesh.
:param input_attribute_name: The name of the pre-computed facet area attribute.
:param use_signed_area: Whether to use signed area.
 
:returns: The mesh area.)");
 
    nb::class_<FacetCentroidOptions>(m, "FacetCentroidOptions", "Facet centroid options.")
        .def(nb::init<>())
        .def_rw(
            "output_attribute_name",
            &FacetCentroidOptions::output_attribute_name,
            "The name of the output attribute.");
    m.def(
        "compute_facet_centroid",
        &lagrange::compute_facet_centroid<Scalar, Index>,
        "mesh"_a,
        "options"_a = FacetCentroidOptions(),
        R"(Compute facet centroid.
 
:param mesh: The input mesh.
:param options: The options for computing facet centroid.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "compute_facet_centroid",
        [](MeshType& mesh, std::optional<std::string_view> output_attribute_name) {
            FacetCentroidOptions opt;
            if (output_attribute_name.has_value()) {
                opt.output_attribute_name = output_attribute_name.value();
            }
            return lagrange::compute_facet_centroid<Scalar, Index>(mesh, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute facet centroid (Pythonic API).
 
:param mesh: Input mesh.
:param output_attribute_name: Output attribute name.
 
:returns: Attribute ID.)");
 
    m.def(
        "compute_facet_circumcenter",
        [](MeshType& mesh, std::optional<std::string_view> output_attribute_name) {
            FacetCircumcenterOptions opt;
            if (output_attribute_name.has_value()) {
                opt.output_attribute_name = output_attribute_name.value();
            }
            return lagrange::compute_facet_circumcenter<Scalar, Index>(mesh, opt);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute facet circumcenter (Pythonic API).
 
:param mesh: The input mesh.
:param output_attribute_name: The name of the output attribute.
 
:returns: The id of the new attribute.)");
 
    nb::enum_<MeshCentroidOptions::WeightingType>(
        m,
        "CentroidWeightingType",
        "Centroid weighting type.")
        .value("Uniform", MeshCentroidOptions::Uniform, "Uniform weighting.")
        .value("Area", MeshCentroidOptions::Area, "Area weighting.");
 
    nb::class_<MeshCentroidOptions>(m, "MeshCentroidOptions", "Mesh centroid options.")
        .def(nb::init<>())
        .def_rw("weighting_type", &MeshCentroidOptions::weighting_type, "The weighting type.")
        .def_rw(
            "facet_centroid_attribute_name",
            &MeshCentroidOptions::facet_centroid_attribute_name,
            "The name of the pre-computed facet centroid attribute if available.")
        .def_rw(
            "facet_area_attribute_name",
            &MeshCentroidOptions::facet_area_attribute_name,
            "The name of the pre-computed facet area attribute if available.");
 
    m.def(
        "compute_mesh_centroid",
        [](const MeshType& mesh, MeshCentroidOptions opt) {
            const Index dim = mesh.get_dimension();
            std::vector<Scalar> centroid(dim, invalid<Scalar>());
            compute_mesh_centroid<Scalar, Index>(mesh, centroid, opt);
            return centroid;
        },
        "mesh"_a,
        "options"_a = MeshCentroidOptions(),
        R"(Compute mesh centroid.
 
:param mesh: Input mesh.
:param options: Centroid computation options.
 
:returns: Mesh centroid coordinates.)");
 
    m.def(
        "compute_mesh_centroid",
        [](MeshType& mesh,
           std::optional<MeshCentroidOptions::WeightingType> weighting_type,
           std::optional<std::string_view> facet_centroid_attribute_name,
           std::optional<std::string_view> facet_area_attribute_name) {
            MeshCentroidOptions opt;
            if (weighting_type.has_value()) {
                opt.weighting_type = weighting_type.value();
            }
            if (facet_centroid_attribute_name.has_value()) {
                opt.facet_centroid_attribute_name = facet_centroid_attribute_name.value();
            }
            if (facet_area_attribute_name.has_value()) {
                opt.facet_area_attribute_name = facet_area_attribute_name.value();
            }
            const Index dim = mesh.get_dimension();
            std::vector<Scalar> centroid(dim, invalid<Scalar>());
            compute_mesh_centroid<Scalar, Index>(mesh, centroid, opt);
            return centroid;
        },
        "mesh"_a,
        "weighting_type"_a = nb::none(),
        "facet_centroid_attribute_name"_a = nb::none(),
        "facet_area_attribute_name"_a = nb::none(),
        R"(Compute mesh centroid (Pythonic API).
 
:param mesh: Input mesh.
:param weighting_type: Weighting type (default: Area).
:param facet_centroid_attribute_name: Pre-computed facet centroid attribute name.
:param facet_area_attribute_name: Pre-computed facet area attribute name.
 
:returns: Mesh centroid coordinates.)");
 
    m.def(
        "permute_vertices",
        [](MeshType& mesh, Tensor<Index> new_to_old) {
            auto [data, shape, stride] = tensor_to_span(new_to_old);
            la_runtime_assert(is_dense(shape, stride));
            permute_vertices<Scalar, Index>(mesh, data);
        },
        "mesh"_a,
        "new_to_old"_a,
        R"(Reorder vertices of a mesh in place based on a permutation.
 
:param mesh: input mesh
:param new_to_old: permutation vector for vertices)");
 
    m.def(
        "permute_facets",
        [](MeshType& mesh, Tensor<Index> new_to_old) {
            auto [data, shape, stride] = tensor_to_span(new_to_old);
            la_runtime_assert(is_dense(shape, stride));
            permute_facets<Scalar, Index>(mesh, data);
        },
        "mesh"_a,
        "new_to_old"_a,
        R"(Reorder facets of a mesh in place based on a permutation.
 
:param mesh: input mesh
:param new_to_old: permutation vector for facets)");
 
    nb::enum_<MappingPolicy>(m, "MappingPolicy", "Mapping policy for handling collisions.")
        .value("Average", MappingPolicy::Average, "Compute the average of the collided values.")
        .value("KeepFirst", MappingPolicy::KeepFirst, "Keep the first collided value.")
        .value("Error", MappingPolicy::Error, "Throw an error when collision happens.");
 
    nb::class_<RemapVerticesOptions>(m, "RemapVerticesOptions", "Options for remapping vertices.")
        .def(nb::init<>())
        .def_rw(
            "collision_policy_float",
            &RemapVerticesOptions::collision_policy_float,
            "The collision policy for float attributes.")
        .def_rw(
            "collision_policy_integral",
            &RemapVerticesOptions::collision_policy_integral,
            "The collision policy for integral attributes.");
 
    m.def(
        "remap_vertices",
        [](MeshType& mesh, Tensor<Index> old_to_new, RemapVerticesOptions opt) {
            auto [data, shape, stride] = tensor_to_span(old_to_new);
            la_runtime_assert(is_dense(shape, stride));
            remap_vertices<Scalar, Index>(mesh, data, opt);
        },
        "mesh"_a,
        "old_to_new"_a,
        "options"_a = RemapVerticesOptions(),
        R"(Remap vertices of a mesh in place based on a permutation.
 
:param mesh: input mesh
:param old_to_new: permutation vector for vertices
:param options: options for remapping vertices)");
 
    m.def(
        "remap_vertices",
        [](MeshType& mesh,
           Tensor<Index> old_to_new,
           std::optional<MappingPolicy> collision_policy_float,
           std::optional<MappingPolicy> collision_policy_integral) {
            RemapVerticesOptions opt;
            if (collision_policy_float.has_value()) {
                opt.collision_policy_float = collision_policy_float.value();
            }
            if (collision_policy_integral.has_value()) {
                opt.collision_policy_integral = collision_policy_integral.value();
            }
            auto [data, shape, stride] = tensor_to_span(old_to_new);
            la_runtime_assert(is_dense(shape, stride));
            remap_vertices<Scalar, Index>(mesh, data, opt);
        },
        "mesh"_a,
        "old_to_new"_a,
        "collision_policy_float"_a = nb::none(),
        "collision_policy_integral"_a = nb::none(),
        R"(Remap vertices of a mesh in place based on a permutation (Pythonic API).
 
:param mesh: input mesh
:param old_to_new: permutation vector for vertices
:param collision_policy_float: The collision policy for float attributes.
:param collision_policy_integral: The collision policy for integral attributes.)");
 
    m.def(
        "reorder_mesh",
        [](MeshType& mesh, std::string_view method) {
            lagrange::ReorderingMethod reorder_method;
            if (method == "Lexicographic" || method == "lexicographic") {
                reorder_method = ReorderingMethod::Lexicographic;
            } else if (method == "Morton" || method == "morton") {
                reorder_method = ReorderingMethod::Morton;
            } else if (method == "Hilbert" || method == "hilbert") {
                reorder_method = ReorderingMethod::Hilbert;
            } else if (method == "None" || method == "none") {
                reorder_method = ReorderingMethod::None;
            } else {
                throw std::runtime_error(lagrange::format("Invalid reordering method: {}", method));
            }
 
            lagrange::reorder_mesh(mesh, reorder_method);
        },
        "mesh"_a,
        "method"_a = "Morton",
        R"(Reorder a mesh in place.
 
:param mesh: input mesh
:param method: reordering method, options are 'Lexicographic', 'Morton', 'Hilbert', 'None' (default is 'Morton').)",
        nb::sig(
            "def reorder_mesh(mesh: SurfaceMesh, "
            "method: typing.Literal['Lexicographic', 'Morton', 'Hilbert', 'None']) -> None"));
 
    m.def(
        "separate_by_facet_groups",
        [](MeshType& mesh,
           Tensor<Index> facet_group_indices,
           std::string_view source_vertex_attr_name,
           std::string_view source_facet_attr_name,
           bool map_attributes) {
            SeparateByFacetGroupsOptions options;
            options.source_vertex_attr_name = source_vertex_attr_name;
            options.source_facet_attr_name = source_facet_attr_name;
            options.map_attributes = map_attributes;
            auto [data, shape, stride] = tensor_to_span(facet_group_indices);
            la_runtime_assert(is_dense(shape, stride));
            return separate_by_facet_groups<Scalar, Index>(mesh, data, options);
        },
        "mesh"_a,
        "facet_group_indices"_a,
        "source_vertex_attr_name"_a = "",
        "source_facet_attr_name"_a = "",
        "map_attributes"_a = false,
        R"(Extract a set of submeshes based on facet groups.
 
:param mesh:                    The source mesh.
:param facet_group_indices:     The group index for each facet. Each group index must be in the range of [0, max(facet_group_indices)]
:param source_vertex_attr_name: The optional attribute name to track source vertices.
:param source_facet_attr_name:  The optional attribute name to track source facets.
:param map_attributes:          Map attributes from the source to target meshes.
 
:returns: A list of meshes, one for each facet group.
)");
 
    m.def(
        "separate_by_components",
        [](MeshType& mesh,
           std::string_view source_vertex_attr_name,
           std::string_view source_facet_attr_name,
           bool map_attributes,
           ConnectivityType connectivity_type) {
            SeparateByComponentsOptions options;
            options.source_vertex_attr_name = source_vertex_attr_name;
            options.source_facet_attr_name = source_facet_attr_name;
            options.map_attributes = map_attributes;
            options.connectivity_type = connectivity_type;
            return separate_by_components(mesh, options);
        },
        "mesh"_a,
        "source_vertex_attr_name"_a = "",
        "source_facet_attr_name"_a = "",
        "map_attributes"_a = false,
        "connectivity_type"_a = ConnectivityType::Edge,
        R"(Extract a set of submeshes based on connected components.
 
:param mesh:                    The source mesh.
:param source_vertex_attr_name: The optional attribute name to track source vertices.
:param source_facet_attr_name:  The optional attribute name to track source facets.
:param map_attributes:          Map attributes from the source to target meshes.
:param connectivity_type:       The connectivity used for component computation.
 
:returns: A list of meshes, one for each connected component.
)");
 
    m.def(
        "extract_submesh",
        [](MeshType& mesh,
           std::variant<Tensor<Index>, nb::list> selected_facets,
           std::string_view source_vertex_attr_name,
           std::string_view source_facet_attr_name,
           bool map_attributes) {
            SubmeshOptions options;
            options.source_vertex_attr_name = source_vertex_attr_name;
            options.source_facet_attr_name = source_facet_attr_name;
            options.map_attributes = map_attributes;
            if (std::holds_alternative<nb::list>(selected_facets)) {
                auto selected_facets_list =
                    nb::cast<std::vector<Index>>(std::get<nb::list>(selected_facets));
                span<const Index> data{selected_facets_list.data(), selected_facets_list.size()};
                return extract_submesh<Scalar, Index>(mesh, data, options);
            } else {
                auto selected_facets_tensor = std::get<Tensor<Index>>(selected_facets);
                auto [data, shape, stride] = tensor_to_span(selected_facets_tensor);
                la_runtime_assert(is_dense(shape, stride));
                return extract_submesh<Scalar, Index>(mesh, data, options);
            }
        },
        "mesh"_a,
        "selected_facets"_a,
        "source_vertex_attr_name"_a = "",
        "source_facet_attr_name"_a = "",
        "map_attributes"_a = false,
        R"(Extract a submesh based on the selected facets.
 
:param mesh:                    The source mesh.
:param selected_facets:         A list or tensor of facet ids to extract.
:param source_vertex_attr_name: The optional attribute name to track source vertices.
:param source_facet_attr_name:  The optional attribute name to track source facets.
:param map_attributes:          Map attributes from the source to target meshes.
 
:returns: A mesh that contains only the selected facets.
)");
 
    m.def(
        "compute_dihedral_angles",
        [](MeshType& mesh,
           std::optional<std::string_view> output_attribute_name,
           std::optional<std::string_view> facet_normal_attribute_name,
           std::optional<bool> recompute_facet_normals,
           std::optional<bool> keep_facet_normals) {
            DihedralAngleOptions options;
            if (output_attribute_name.has_value()) {
                options.output_attribute_name = output_attribute_name.value();
            }
            if (facet_normal_attribute_name.has_value()) {
                options.facet_normal_attribute_name = facet_normal_attribute_name.value();
            }
            if (recompute_facet_normals.has_value()) {
                options.recompute_facet_normals = recompute_facet_normals.value();
            }
            if (keep_facet_normals.has_value()) {
                options.keep_facet_normals = keep_facet_normals.value();
            }
            return compute_dihedral_angles(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        "facet_normal_attribute_name"_a = nb::none(),
        "recompute_facet_normals"_a = nb::none(),
        "keep_facet_normals"_a = nb::none(),
        R"(Compute dihedral angles for each edge.
 
The dihedral angle of an edge is defined as the angle between the __normals__ of two facets adjacent
to the edge. The dihedral angle is always in the range [0, pi] for manifold edges. For boundary
edges, the dihedral angle defaults to 0.  For non-manifold edges, the dihedral angle is not
well-defined and will be set to the special value 2 * π.
 
:param mesh:                        The source mesh.
:param output_attribute_name:       The optional edge attribute name to store the dihedral angles.
:param facet_normal_attribute_name: The optional attribute name to store the facet normals.
:param recompute_facet_normals:     Whether to recompute facet normals.
:param keep_facet_normals:          Whether to keep newly computed facet normals. It has no effect on pre-existing facet normals.
 
:return: The edge attribute id of dihedral angles.)");
 
    m.def(
        "compute_edge_lengths",
        [](MeshType& mesh, std::optional<std::string_view> output_attribute_name) {
            EdgeLengthOptions options;
            if (output_attribute_name.has_value())
                options.output_attribute_name = output_attribute_name.value();
            return compute_edge_lengths(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Compute edge lengths.
 
:param mesh:                  The source mesh.
:param output_attribute_name: The optional edge attribute name to store the edge lengths.
 
:return: The edge attribute id of edge lengths.)");
 
    m.def(
        "compute_dijkstra_distance",
        [](MeshType& mesh,
           Index seed_facet,
           const nb::list& barycentric_coords,
           std::optional<Scalar> radius,
           std::string_view output_attribute_name,
           bool output_involved_vertices) {
            DijkstraDistanceOptions<Scalar, Index> options;
            options.seed_facet = seed_facet;
            for (auto val : barycentric_coords) {
                options.barycentric_coords.push_back(nb::cast<Scalar>(val));
            }
            if (radius.has_value()) {
                options.radius = radius.value();
            }
            options.output_attribute_name = output_attribute_name;
            options.output_involved_vertices = output_involved_vertices;
            return compute_dijkstra_distance(mesh, options);
        },
        "mesh"_a,
        "seed_facet"_a,
        "barycentric_coords"_a,
        "radius"_a = nb::none(),
        "output_attribute_name"_a = DijkstraDistanceOptions<Scalar, Index>{}.output_attribute_name,
        "output_involved_vertices"_a =
            DijkstraDistanceOptions<Scalar, Index>{}.output_involved_vertices,
        R"(Compute Dijkstra distance from a seed facet.
 
:param mesh:                  The source mesh.
:param seed_facet:            The seed facet index.
:param barycentric_coords:    The barycentric coordinates of the seed facet.
:param radius:                The maximum radius of the dijkstra distance.
:param output_attribute_name: The output attribute name to store the dijkstra distance.
:param output_involved_vertices: Whether to output the list of involved vertices.)");
 
    m.def(
        "weld_indexed_attribute",
        [](MeshType& mesh,
           AttributeId attribute_id,
           std::optional<double> epsilon_rel,
           std::optional<double> epsilon_abs,
           std::optional<double> angle_abs,
           std::optional<std::vector<size_t>> exclude_vertices) {
            WeldOptions options;
            options.epsilon_rel = epsilon_rel;
            options.epsilon_abs = epsilon_abs;
            options.angle_abs = angle_abs;
            if (exclude_vertices.has_value()) {
                const auto& exclude_vertices_vec = exclude_vertices.value();
                options.exclude_vertices = {
                    exclude_vertices_vec.data(),
                    exclude_vertices_vec.size()};
            }
            return weld_indexed_attribute(mesh, attribute_id, options);
        },
        "mesh"_a,
        "attribute_id"_a,
        "epsilon_rel"_a = nb::none(),
        "epsilon_abs"_a = nb::none(),
        "angle_abs"_a = nb::none(),
        "exclude_vertices"_a = nb::none(),
        R"(Weld indexed attribute.
 
:param mesh:         The source mesh to be updated in place.
:param attribute_id: The indexed attribute id to weld.
:param epsilon_rel:  The relative tolerance for welding.
:param epsilon_abs:  The absolute tolerance for welding.
:param angle_abs:    The absolute angle tolerance for welding.
:param exclude_vertices: Optional list of vertex indices to exclude from welding.)");
 
    m.def(
        "compute_euler",
        &compute_euler<Scalar, Index>,
        "mesh"_a,
        R"(Compute the Euler characteristic.
 
:param mesh: The source mesh.
 
:return: The Euler characteristic.)");
 
    m.def(
        "is_closed",
        &is_closed<Scalar, Index>,
        "mesh"_a,
        R"(Check if the mesh is closed.
 
A mesh is considered closed if it has no boundary edges.
 
:param mesh: The source mesh.
 
:return: Whether the mesh is closed.)");
 
    m.def(
        "is_vertex_manifold",
        &is_vertex_manifold<Scalar, Index>,
        "mesh"_a,
        R"(Check if the mesh is vertex manifold.
 
:param mesh: The source mesh.
 
:return: Whether the mesh is vertex manifold.)");
 
    m.def(
        "is_edge_manifold",
        &is_edge_manifold<Scalar, Index>,
        "mesh"_a,
        R"(Check if the mesh is edge manifold.
 
:param mesh: The source mesh.
 
:return: Whether the mesh is edge manifold.)");
 
    m.def("is_manifold", &is_manifold<Scalar, Index>, "mesh"_a, R"(Check if the mesh is manifold.
 
A mesh considered as manifold if it is both vertex and edge manifold.
 
:param mesh: The source mesh.
 
:return: Whether the mesh is manifold.)");
 
    m.def(
        "compute_vertex_is_manifold",
        [](MeshType& mesh, std::string_view output_attribute_name) {
            VertexManifoldOptions options;
            options.output_attribute_name = output_attribute_name;
            return compute_vertex_is_manifold(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = VertexManifoldOptions().output_attribute_name,
        R"(Compute whether each vertex is manifold.
 
A vertex is considered manifold if its one-ring neighborhood is homeomorphic to a disk.
 
:param mesh: The source mesh.
:param output_attribute_name: The output vertex attribute name.
 
:return: The attribute id of a vertex attribute indicating whether a vertex is manifold.)");
 
    m.def(
        "compute_edge_is_manifold",
        [](MeshType& mesh, std::string_view output_attribute_name) {
            EdgeManifoldOptions options;
            options.output_attribute_name = output_attribute_name;
            return compute_edge_is_manifold(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = EdgeManifoldOptions().output_attribute_name,
        R"(Compute whether each edge is manifold.
 
An edge is considered manifold if it is adjacent to one or two facets.
 
:param mesh: The source mesh.
:param output_attribute_name: The output edge attribute name.
 
:return: The attribute id of an edge attribute indicating whether an edge is manifold.)");
 
    m.def(
        "is_oriented",
        &is_oriented<Scalar, Index>,
        "mesh"_a,
        R"(Check if the mesh is oriented.
 
A mesh is oriented if all interior edges are oriented. An interior edge is considered as
oriented if it has the same number of half-edges for each edge direction. I.e. the number of
facets that use the edge in one direction equals the number of facets that use the edge in the
opposite direction. Boundary edges are always considered as oriented.
 
:param mesh: The source mesh.
 
:return: Whether the mesh is oriented.)");
 
    m.def(
        "compute_edge_is_oriented",
        [](MeshType& mesh, std::string_view output_attribute_name) {
            OrientationOptions options;
            options.output_attribute_name = output_attribute_name;
            return compute_edge_is_oriented(mesh, options);
        },
        "mesh"_a,
        "output_attribute_name"_a = OrientationOptions().output_attribute_name,
        R"(Compute whether each edge is oriented.
 
An interior edge is considered as oriented if it has the same number of half-edges for each edge
direction. I.e. the number of facets that use the edge in one direction equals to the number of
facets that use the edge in the opposite direction. Boundary edges are always considered as
oriented.
 
:param mesh: The source mesh.
:param output_attribute_name: The output edge attribute name.
 
:return: The attribute id of an edge attribute indicating whether an edge is oriented.)");
 
    m.def(
        "transform_mesh",
        [](MeshType& mesh,
           StubType<Eigen::Matrix<Scalar, 4, 4>, ArrayLikeHint> affine_transform,
           bool normalize_normals,
           bool normalize_tangents_bitangents,
           bool reorient,
           bool in_place) -> std::optional<MeshType> {
            Eigen::Transform<Scalar, 3, Eigen::Affine> M(affine_transform.value);
            TransformOptions options;
            options.normalize_normals = normalize_normals;
            options.normalize_tangents_bitangents = normalize_tangents_bitangents;
            options.reorient = reorient;
 
            std::optional<MeshType> result;
            if (in_place) {
                transform_mesh(mesh, M, options);
            } else {
                result = transformed_mesh(mesh, M, options);
            }
            return result;
        },
        "mesh"_a,
        "affine_transform"_a,
        nb::kw_only(),
        "normalize_normals"_a = TransformOptions().normalize_normals,
        "normalize_tangents_bitangents"_a = TransformOptions().normalize_tangents_bitangents,
        "reorient"_a = TransformOptions().reorient,
        "in_place"_a = true,
        R"(Apply affine transformation to a mesh.
 
:param mesh: Input mesh.
:param affine_transform: Affine transformation matrix.
:param normalize_normals: Whether to normalize normals.
:param normalize_tangents_bitangents: Whether to normalize tangents and bitangents.
:param reorient: If the transform has a negative determinant, flip facets and reorient attributes (normals, tangents, bitangents).
:param in_place: Whether to apply transformation in place.
 
:returns: Transformed mesh if in_place is False.)");
 
    nb::enum_<DistortionMetric>(m, "DistortionMetric", "Distortion metric.")
        .value("Dirichlet", DistortionMetric::Dirichlet, "Dirichlet energy")
        .value("InverseDirichlet", DistortionMetric::InverseDirichlet, "Inverse Dirichlet energy")
        .value(
            "SymmetricDirichlet",
            DistortionMetric::SymmetricDirichlet,
            "Symmetric Dirichlet energy")
        .value("AreaRatio", DistortionMetric::AreaRatio, "Area ratio")
        .value("MIPS", DistortionMetric::MIPS, "Most isotropic parameterization energy");
 
    m.def(
        "compute_uv_distortion",
        [](MeshType& mesh,
           std::string_view uv_attribute_name,
           std::string_view output_attribute_name,
           DistortionMetric metric) {
            UVDistortionOptions opt;
            opt.uv_attribute_name = uv_attribute_name;
            opt.output_attribute_name = output_attribute_name;
            opt.metric = metric;
            return compute_uv_distortion(mesh, opt);
        },
        "mesh"_a,
        "uv_attribute_name"_a = "@uv",
        "output_attribute_name"_a = "@uv_measure",
        "metric"_a = lagrange::DistortionMetric::MIPS,
        R"(Compute UV distortion.
 
:param mesh: Input mesh.
:param uv_attribute_name: UV attribute name (default: "@uv").
:param output_attribute_name: Output attribute name (default: "@uv_measure").
:param metric: Distortion metric (default: MIPS).
 
:returns: Facet attribute ID for distortion.)");
 
    m.def(
        "trim_by_isoline",
        [](const MeshType& mesh,
           std::variant<AttributeId, std::string_view> attribute,
           double isovalue,
           bool keep_below,
           bool keep_attributes) {
            IsolineOptions opt;
            if (std::holds_alternative<AttributeId>(attribute)) {
                opt.attribute_id = std::get<AttributeId>(attribute);
            } else {
                opt.attribute_id = mesh.get_attribute_id(std::get<std::string_view>(attribute));
            }
            opt.isovalue = isovalue;
            opt.keep_below = keep_below;
            opt.keep_attributes = keep_attributes;
            return trim_by_isoline(mesh, opt);
        },
        "mesh"_a,
        "attribute"_a,
        "isovalue"_a = IsolineOptions().isovalue,
        "keep_below"_a = IsolineOptions().keep_below,
        "keep_attributes"_a = IsolineOptions().keep_attributes,
        R"(Trim a triangle mesh by an isoline.
 
:param mesh: Input triangle mesh.
:param attribute: Attribute ID or name of scalar field (vertex or indexed).
:param isovalue: Isovalue to trim with.
:param keep_below: Whether to keep the part below the isoline.
:param keep_attributes: Whether to propagate input mesh attributes to the output mesh.
 
:returns: Trimmed mesh.)");
 
    m.def(
        "extract_isoline",
        [](const MeshType& mesh,
           std::variant<AttributeId, std::string_view> attribute,
           double isovalue,
           bool keep_attributes) {
            IsolineOptions opt;
            if (std::holds_alternative<AttributeId>(attribute)) {
                opt.attribute_id = std::get<AttributeId>(attribute);
            } else {
                opt.attribute_id = mesh.get_attribute_id(std::get<std::string_view>(attribute));
            }
            opt.isovalue = isovalue;
            opt.keep_attributes = keep_attributes;
            return extract_isoline(mesh, opt);
        },
        "mesh"_a,
        "attribute"_a,
        "isovalue"_a = IsolineOptions().isovalue,
        "keep_attributes"_a = IsolineOptions().keep_attributes,
        R"(Extract the isoline of an implicit function defined on the mesh vertices/corners.
 
The input mesh must be a triangle mesh.
 
:param mesh:       Input triangle mesh to extract the isoline from.
:param attribute:  Attribute id or name of the scalar field to use. Can be a vertex or indexed attribute.
:param isovalue:   Isovalue to extract.
:param keep_attributes: Whether to propagate input mesh attributes to the output mesh.
 
:return: A mesh whose facets is a collection of size 2 elements representing the extracted isoline.)");
 
    m.def(
        "insert_isoline",
        [](const MeshType& mesh,
           std::variant<AttributeId, std::string_view> attribute,
           double isovalue,
           bool keep_attributes) {
            IsolineOptions opt;
            if (std::holds_alternative<AttributeId>(attribute)) {
                opt.attribute_id = std::get<AttributeId>(attribute);
            } else {
                opt.attribute_id = mesh.get_attribute_id(std::get<std::string_view>(attribute));
            }
            opt.isovalue = isovalue;
            opt.keep_attributes = keep_attributes;
            return insert_isoline(mesh, opt);
        },
        "mesh"_a,
        "attribute"_a,
        "isovalue"_a = IsolineOptions().isovalue,
        "keep_attributes"_a = IsolineOptions().keep_attributes,
        R"(Insert the isoline of an implicit function into a triangle mesh.
 
Unlike trimming, the whole mesh is retained; facets crossed by the isoline are split so that the
isoline appears as a chain of edges in the output. A triangle crossed in its interior is split into
a triangle and a quad, so the output is in general a mixed triangle/quad mesh. When the isoline
passes exactly through an existing vertex (or lies along an edge), the split degenerates: the
triangle may instead be split into two triangles, or left unchanged.
 
:param mesh:       Input triangle mesh to insert the isoline into.
:param attribute:  Attribute id or name of the scalar field to use. Can be a vertex or indexed attribute.
:param isovalue:   Isovalue to insert.
:param keep_attributes: Whether to propagate input mesh attributes to the output mesh.
 
:return: The input mesh with the isoline inserted as a chain of edges.)");
 
    using AttributeNameOrId = AttributeFilter::AttributeNameOrId;
    m.def(
        "filter_attributes",
        [](MeshType& mesh,
           std::optional<std::vector<AttributeNameOrId>> included_attributes,
           std::optional<std::vector<AttributeNameOrId>> excluded_attributes,
           StubType<std::optional<std::unordered_set<AttributeUsage>>, IterableUsageHint>
               included_usages,
           StubType<std::optional<std::unordered_set<AttributeElement>>, IterableElementHint>
               included_element_types) {
            AttributeFilter filter;
            if (included_attributes.has_value()) {
                filter.included_attributes = included_attributes.value();
            }
            if (excluded_attributes.has_value()) {
                filter.excluded_attributes = excluded_attributes.value();
            }
            if (included_usages.value.has_value()) {
                filter.included_usages.clear_all();
                for (auto usage : included_usages.value.value()) {
                    filter.included_usages.set(usage);
                }
            }
            if (included_element_types.value.has_value()) {
                filter.included_element_types.clear_all();
                for (auto element_type : included_element_types.value.value()) {
                    filter.included_element_types.set(element_type);
                }
            }
            return filter_attributes(mesh, filter);
        },
        "mesh"_a,
        "included_attributes"_a = nb::none(),
        "excluded_attributes"_a = nb::none(),
        "included_usages"_a = nb::none(),
        "included_element_types"_a = nb::none(),
        R"(Filters the attributes of mesh according to user specifications.
 
:param mesh: Input mesh.
:param included_attributes: List of attribute names or ids to include. By default, all attributes are included.
:param excluded_attributes: List of attribute names or ids to exclude. By default, no attribute is excluded.
:param included_usages: List of attribute usages to include. By default, all usages are included.
:param included_element_types: List of attribute element types to include. By default, all element types are included.)");
 
    m.def(
        "cast_attribute",
        [](MeshType& mesh,
           std::variant<AttributeId, std::string_view> input_attribute,
           nb::type_object dtype,
           std::optional<std::string_view> output_attribute_name) {
            auto cast = [&](AttributeId attr_id) {
                auto np = nb::module_::import_("numpy");
                if (output_attribute_name.has_value()) {
                    auto name = output_attribute_name.value();
                    if (dtype.is(&PyFloat_Type)) {
                        // Native python float is a C double.
                        return cast_attribute<double>(mesh, attr_id, name);
                    } else if (dtype.is(&PyLong_Type)) {
                        // Native python int maps to int64.
                        return cast_attribute<int64_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("float32"))) {
                        return cast_attribute<float>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("float64"))) {
                        return cast_attribute<double>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("int8"))) {
                        return cast_attribute<int8_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("int16"))) {
                        return cast_attribute<int16_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("int32"))) {
                        return cast_attribute<int32_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("int64"))) {
                        return cast_attribute<int64_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("uint8"))) {
                        return cast_attribute<uint8_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("uint16"))) {
                        return cast_attribute<uint16_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("uint32"))) {
                        return cast_attribute<uint32_t>(mesh, attr_id, name);
                    } else if (dtype.is(np.attr("uint64"))) {
                        return cast_attribute<uint64_t>(mesh, attr_id, name);
                    } else {
                        throw nb::type_error("Unsupported `dtype`!");
                    }
                } else {
                    if (dtype.is(&PyFloat_Type)) {
                        // Native python float is a C double.
                        return cast_attribute_in_place<double>(mesh, attr_id);
                    } else if (dtype.is(&PyLong_Type)) {
                        // Native python int maps to int64.
                        return cast_attribute_in_place<int64_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("float32"))) {
                        return cast_attribute_in_place<float>(mesh, attr_id);
                    } else if (dtype.is(np.attr("float64"))) {
                        return cast_attribute_in_place<double>(mesh, attr_id);
                    } else if (dtype.is(np.attr("int8"))) {
                        return cast_attribute_in_place<int8_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("int16"))) {
                        return cast_attribute_in_place<int16_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("int32"))) {
                        return cast_attribute_in_place<int32_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("int64"))) {
                        return cast_attribute_in_place<int64_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("uint8"))) {
                        return cast_attribute_in_place<uint8_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("uint16"))) {
                        return cast_attribute_in_place<uint16_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("uint32"))) {
                        return cast_attribute_in_place<uint32_t>(mesh, attr_id);
                    } else if (dtype.is(np.attr("uint64"))) {
                        return cast_attribute_in_place<uint64_t>(mesh, attr_id);
                    } else {
                        throw nb::type_error("Unsupported `dtype`!");
                    }
                }
            };
 
            if (std::holds_alternative<AttributeId>(input_attribute)) {
                return cast(std::get<AttributeId>(input_attribute));
            } else {
                AttributeId id = mesh.get_attribute_id(std::get<std::string_view>(input_attribute));
                return cast(id);
            }
        },
        "mesh"_a,
        "input_attribute"_a,
        "dtype"_a,
        "output_attribute_name"_a = nb::none(),
        R"(Cast an attribute to a new dtype.
 
:param mesh:            The input mesh.
:param input_attribute: The input attribute id or name.
:param dtype:           The new dtype.
:param output_attribute_name: The output attribute name. If none, cast will replace the input attribute.
 
:returns: The id of the new attribute.)");
 
    m.def(
        "get_unique_attribute_name",
        [](const MeshType& mesh,
           std::string_view name,
           std::string separator,
           std::string postfix,
           int max_increment,
           bool emit_warning) {
            UniqueAttributeNameOptions options;
            options.separator = std::move(separator);
            options.postfix = std::move(postfix);
            options.max_increment = max_increment;
            options.emit_warning = emit_warning;
            return get_unique_attribute_name(mesh, name, options);
        },
        "mesh"_a,
        "name"_a,
        "separator"_a = UniqueAttributeNameOptions().separator,
        "postfix"_a = UniqueAttributeNameOptions().postfix,
        "max_increment"_a = UniqueAttributeNameOptions().max_increment,
        "emit_warning"_a = UniqueAttributeNameOptions().emit_warning,
        R"(Get a unique attribute name for a mesh.
 
If the desired name does not exist on the mesh it is returned as-is. If it
already exists, a suffix of the form ``{separator}{count}{postfix}`` is appended
until a unique name is found. An exception is raised if no unique name can be
found after ``max_increment`` attempts.
 
:param mesh: The input mesh.
:param name: The desired attribute name.
:param separator: Separator between the base name and counter (default: ".").
:param postfix: Postfix to append after the counter (default: "").
:param max_increment: Maximum number of attempts to find a unique name (default: 1000).
:param emit_warning: Whether to log a warning when a collision is detected (default: True).
 
:returns: A unique attribute name.)");
 
    m.def(
        "compute_mesh_covariance",
        [](MeshType& mesh,
           StubType<std::array<Scalar, 3>, ArrayLikeHint> center,
           std::optional<std::string_view> active_facets_attribute_name)
            -> std::array<std::array<Scalar, 3>, 3> {
            MeshCovarianceOptions options;
            options.center = center.value;
            options.active_facets_attribute_name = active_facets_attribute_name;
            return compute_mesh_covariance<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "center"_a,
        "active_facets_attribute_name"_a = nb::none(),
        R"(Compute the covariance matrix of a mesh w.r.t. a center (Pythonic API).
 
:param mesh: Input mesh.
:param center: The center of the covariance computation.
:param active_facets_attribute_name: (optional) Attribute name of whether a facet should be considered in the computation.
 
:returns: The 3 by 3 covariance matrix, which should be symmetric.)");
 
    m.def(
        "select_facets_by_normal_similarity",
        [](MeshType& mesh,
           Index seed_facet_id,
           std::optional<double> flood_error_limit,
           std::optional<double> flood_second_to_first_order_limit_ratio,
           std::optional<std::string_view> facet_normal_attribute_name,
           std::optional<std::string_view> is_facet_selectable_attribute_name,
           std::optional<std::string_view> output_attribute_name,
           std::optional<std::string_view> search_type,
           std::optional<int> num_smooth_iterations) {
            // Set options in the C++ struct
            SelectFacetsByNormalSimilarityOptions options;
            if (flood_error_limit.has_value())
                options.flood_error_limit = flood_error_limit.value();
            if (flood_second_to_first_order_limit_ratio.has_value())
                options.flood_second_to_first_order_limit_ratio =
                    flood_second_to_first_order_limit_ratio.value();
            if (facet_normal_attribute_name.has_value())
                options.facet_normal_attribute_name = facet_normal_attribute_name.value();
            if (is_facet_selectable_attribute_name.has_value()) {
                options.is_facet_selectable_attribute_name = is_facet_selectable_attribute_name;
            }
            if (output_attribute_name.has_value())
                options.output_attribute_name = output_attribute_name.value();
            if (search_type.has_value()) {
                if (search_type.value() == "BFS")
                    options.search_type = SelectFacetsByNormalSimilarityOptions::SearchType::BFS;
                else if (search_type.value() == "DFS")
                    options.search_type = SelectFacetsByNormalSimilarityOptions::SearchType::DFS;
                else
                    throw std::runtime_error(
                        lagrange::format("Invalid search type: {}", search_type.value()));
            }
            if (num_smooth_iterations.has_value())
                options.num_smooth_iterations = num_smooth_iterations.value();
 
            return select_facets_by_normal_similarity<Scalar, Index>(mesh, seed_facet_id, options);
        },
        "mesh"_a, /* `_a` is a literal for nanobind to create nb::args, a required argument */
        "seed_facet_id"_a,
        "flood_error_limit"_a = nb::none(),
        "flood_second_to_first_order_limit_ratio"_a = nb::none(),
        "facet_normal_attribute_name"_a = nb::none(),
        "is_facet_selectable_attribute_name"_a = nb::none(),
        "output_attribute_name"_a = nb::none(),
        "search_type"_a = nb::none(),
        "num_smooth_iterations"_a = nb::none(),
        R"(Select facets by normal similarity (Pythonic API).
 
:param mesh: Input mesh.
:param seed_facet_id: Index of the seed facet.
:param flood_error_limit: Tolerance for normals of the seed and the selected facets. Higher limit leads to larger selected region.
:param flood_second_to_first_order_limit_ratio: Ratio of the flood_error_limit and the tolerance for normals of neighboring selected facets. Higher ratio leads to more curvature in selected region.
:param facet_normal_attribute_name: Attribute name of the facets normal. If the mesh doesn't have this attribute, it will call compute_facet_normal to compute it.
:param is_facet_selectable_attribute_name: If provided, this function will look for this attribute to determine if a facet is selectable.
:param output_attribute_name: Attribute name of whether a facet is selected.
:param search_type: Use 'BFS' for breadth-first search or 'DFS' for depth-first search.
:param num_smooth_iterations: Number of iterations to smooth the boundary of the selected region.
 
:returns: Id of the attribute on whether a facet is selected.)",
        nb::sig(
            "def select_facets_by_normal_similarity(mesh: SurfaceMesh, "
            "seed_facet_id: int, "
            "flood_error_limit: typing.Optional[float] = None, "
            "flood_second_to_first_order_limit_ratio: typing.Optional[float] = None, "
            "facet_normal_attribute_name: typing.Optional[str] = None, "
            "is_facet_selectable_attribute_name: typing.Optional[str] = None, "
            "output_attribute_name: typing.Optional[str] = None, "
            "search_type: typing.Optional[typing.Literal['BFS', 'DFS']] = None,"
            "num_smooth_iterations: typing.Optional[int] = None) -> int"));
 
    m.def(
        "select_facets_in_frustum",
        [](MeshType& mesh,
           StubType<std::array<std::array<Scalar, 3>, 4>, ArrayLikeHint> frustum_plane_points,
           StubType<std::array<std::array<Scalar, 3>, 4>, ArrayLikeHint> frustum_plane_normals,
           std::optional<bool> greedy,
           std::optional<std::string_view> output_attribute_name) {
            // Set options in the C++ struct
            Frustum<Scalar> frustum;
            for (size_t i = 0; i < 4; ++i) {
                frustum.planes[i].point = frustum_plane_points.value[i];
                frustum.planes[i].normal = frustum_plane_normals.value[i];
            }
            FrustumSelectionOptions options;
            if (greedy.has_value()) options.greedy = greedy.value();
            if (output_attribute_name.has_value())
                options.output_attribute_name = output_attribute_name.value();
 
            return select_facets_in_frustum<Scalar, Index>(mesh, frustum, options);
        },
        "mesh"_a,
        "frustum_plane_points"_a,
        "frustum_plane_normals"_a,
        "greedy"_a = nb::none(),
        "output_attribute_name"_a = nb::none(),
        R"(Select facets in a frustum (Pythonic API).
 
:param mesh: Input mesh.
:param frustum_plane_points: Four points on each of the frustum planes.
:param frustum_plane_normals: Four normals of each of the frustum planes.
:param greedy: If true, the function returns as soon as the first facet is found.
:param output_attribute_name: Attribute name of whether a facet is selected.
 
:returns: Whether any facets got selected.)");
 
    m.def(
        "thicken_and_close_mesh",
        [](MeshType& mesh,
           std::optional<Scalar> offset_amount,
           std::variant<std::monostate, std::array<double, 3>, std::string_view> direction,
           std::optional<double> mirror_ratio,
           std::optional<size_t> num_segments,
           std::optional<std::vector<std::string>> indexed_attributes) {
            ThickenAndCloseOptions options;
 
            if (auto array_val = std::get_if<std::array<double, 3>>(&direction)) {
                options.direction = *array_val;
            } else if (auto string_val = std::get_if<std::string_view>(&direction)) {
                options.direction = *string_val;
            }
            options.offset_amount = offset_amount.value_or(options.offset_amount);
            options.mirror_ratio = std::move(mirror_ratio);
            options.num_segments = num_segments.value_or(options.num_segments);
            options.indexed_attributes = indexed_attributes.value_or(options.indexed_attributes);
 
            return thicken_and_close_mesh<Scalar, Index>(mesh, options);
        },
        "mesh"_a,
        "offset_amount"_a = nb::none(),
        "direction"_a = nb::none(),
        "mirror_ratio"_a = nb::none(),
        "num_segments"_a = nb::none(),
        "indexed_attributes"_a = nb::none(),
        R"(Thicken a mesh by offsetting it, and close the shape into a thick 3D solid.
 
:param mesh: Input mesh.
:param direction: Direction of the offset. Can be an attribute name or a fixed 3D vector.
:param offset_amount: Amount of offset.
:param mirror_ratio: Ratio of the offset amount to mirror the mesh.
:param num_segments: Number of segments to use for the thickening.
:param indexed_attributes: List of indexed attributes to copy to the new mesh.
 
:returns: The thickened and closed mesh.)");
 
    m.def(
        "extract_boundary_loops",
        &extract_boundary_loops<Scalar, Index>,
        "mesh"_a,
        R"(Extract boundary loops from a mesh.
 
:param mesh: Input mesh.
 
:returns: A list of boundary loops, each represented as a list of vertex indices.)");
 
    m.def(
        "extract_boundary_edges",
        [](MeshType& mesh) {
            mesh.initialize_edges();
            Index num_edges = mesh.get_num_edges();
            std::vector<Index> bd_edges;
            bd_edges.reserve(num_edges);
            for (Index ei = 0; ei < num_edges; ++ei) {
                if (mesh.is_boundary_edge(ei)) {
                    bd_edges.push_back(ei);
                }
            }
            return bd_edges;
        },
        "mesh"_a,
        R"(Extract boundary edges from a mesh.
 
:param mesh: Input mesh.
 
:returns: A list of boundary edge indices.)");
 
    m.def(
        "compute_uv_charts",
        [](MeshType& mesh,
           std::string_view uv_attribute_name,
           std::string_view output_attribute_name,
           std::string_view connectivity_type) {
            UVChartOptions options;
            options.uv_attribute_name = uv_attribute_name;
            options.output_attribute_name = output_attribute_name;
            if (connectivity_type == "Vertex") {
                options.connectivity_type = UVChartOptions::ConnectivityType::Vertex;
            } else if (connectivity_type == "Edge") {
                options.connectivity_type = UVChartOptions::ConnectivityType::Edge;
            } else {
                throw std::runtime_error(
                    lagrange::format("Invalid connectivity type: {}", connectivity_type));
            }
            return compute_uv_charts(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = UVChartOptions().uv_attribute_name,
        "output_attribute_name"_a = UVChartOptions().output_attribute_name,
        "connectivity_type"_a = "Edge",
        R"(Compute UV charts.
 
:param mesh: Input mesh.
:param uv_attribute_name: Name of the UV attribute.
:param output_attribute_name: Name of the output attribute to store the chart ids.
:param connectivity_type: Type of connectivity to use for chart computation. Can be "Vertex" or "Edge".
 
:returns: The number of charts.)");
 
    nb::class_<UVOrientationCount>(m, "UVOrientationCount", "Counts of per-facet UV orientations.")
        .def(nb::init<>())
        .def_rw(
            "positive",
            &UVOrientationCount::positive,
            "Number of CCW (positively oriented) facets.")
        .def_rw(
            "degenerate",
            &UVOrientationCount::degenerate,
            "Number of degenerate (zero-area) facets.")
        .def_rw(
            "negative",
            &UVOrientationCount::negative,
            "Number of CW (negatively oriented / flipped) facets.");
 
    m.def(
        "compute_uv_orientation",
        [](MeshType& mesh,
           std::string_view uv_attribute_name,
           std::string_view output_attribute_name) {
            UVOrientationOptions options;
            options.uv_attribute_name = uv_attribute_name;
            options.output_attribute_name = output_attribute_name;
            return compute_uv_orientation(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = UVOrientationOptions().uv_attribute_name,
        "output_attribute_name"_a = UVOrientationOptions().output_attribute_name,
        R"(Compute a per-facet orientation attribute using Shewchuk's exact ``orient2D`` predicate.
 
Each facet is assigned an ``int8`` value: ``+1`` for CCW (positively oriented), ``0`` for
degenerate, ``-1`` for CW (negatively oriented / flipped).
 
:param mesh: Input triangle mesh.
:param uv_attribute_name: Name of the UV attribute. If empty, uses the first UV attribute.
:param output_attribute_name: Name of the output per-facet attribute (int8).
 
:returns: A :class:`UVOrientationCount` with counts of positive, degenerate, and negative facets.)");
 
    m.def(
        "unflip_uv_charts",
        [](MeshType& mesh,
           std::string_view uv_attribute_name,
           std::string_view chart_id_attribute_name) {
            UnflipUVChartsOptions options;
            options.uv_attribute_name = uv_attribute_name;
            options.chart_id_attribute_name = chart_id_attribute_name;
            return unflip_uv_charts(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = UnflipUVChartsOptions().uv_attribute_name,
        "chart_id_attribute_name"_a = UnflipUVChartsOptions().chart_id_attribute_name,
        R"(Mirror the UV positions of every UV vertex in any chart that is "flipped" by negating
its U coordinate. A chart is considered flipped when either its total signed UV area is negative,
OR every triangle in the chart is individually flipped (per :func:`compute_uv_orientation`); the
latter rule catches charts whose floating-point area sum is non-negative due to nearly-degenerate
triangles. Assumes UV vertices are not shared across charts.
 
:param mesh: Input triangle mesh. The UV attribute must be indexed.
:param uv_attribute_name: Name of the UV attribute. If empty, uses the first indexed UV attribute.
:param chart_id_attribute_name: Optional per-facet chart id attribute name. If empty, charts are
                                computed automatically using edge connectivity on the UV mesh.
 
:returns: The number of charts that were unflipped.)");
 
    m.def(
        "disconnect_uv_charts",
        [](MeshType& mesh,
           std::string_view uv_attribute_name,
           std::string_view chart_id_attribute_name) {
            DisconnectUVChartsOptions options;
            options.uv_attribute_name = uv_attribute_name;
            options.chart_id_attribute_name = chart_id_attribute_name;
            return disconnect_uv_charts(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = DisconnectUVChartsOptions().uv_attribute_name,
        "chart_id_attribute_name"_a = DisconnectUVChartsOptions().chart_id_attribute_name,
        R"(Disconnect UV charts by duplicating UV vertices shared across different charts.
 
After this operation, no two facets belonging to different UV charts will share a UV vertex
index. Without any input chart id attribute, this eliminates non-manifold UV vertices (pinch
points) where charts touch at a single vertex.
 
:param mesh:                    Input mesh. The UV attribute must be indexed.
:param uv_attribute_name:       Name of the UV attribute. If empty, uses the first indexed UV attribute.
:param chart_id_attribute_name: Optional per-facet chart id attribute name. If empty, chart ids
                                are computed automatically using edge connectivity on the UV mesh.
 
:returns: The number of UV vertices that were duplicated.)");
 
    m.def(
        "uv_mesh_view",
        [](const MeshType& mesh, std::string_view uv_attribute_name) {
            UVMeshOptions options;
            options.uv_attribute_name = uv_attribute_name;
            return uv_mesh_view(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = UVMeshOptions().uv_attribute_name,
        R"(Extract a UV mesh view from a 3D mesh.
 
:param mesh: Input mesh.
:param uv_attribute_name: Name of the (indexed or vertex) UV attribute.
 
:return: A new mesh representing the UV mesh.)");
    m.def(
        "uv_mesh_ref",
        [](MeshType& mesh, std::string_view uv_attribute_name) {
            UVMeshOptions options;
            options.uv_attribute_name = uv_attribute_name;
            return uv_mesh_ref(mesh, options);
        },
        "mesh"_a,
        "uv_attribute_name"_a = UVMeshOptions().uv_attribute_name,
        R"(Extract a UV mesh reference from a 3D mesh.
 
:param mesh: Input mesh.
:param uv_attribute_name: Name of the (indexed or vertex) UV attribute.
 
:return: A new mesh representing the UV mesh.)");
 
    m.def(
        "split_facets_by_material",
        &split_facets_by_material<Scalar, Index>,
        "mesh"_a,
        "material_attribute_name"_a,
        R"(Split mesh facets based on a material attribute.
 
@param mesh: Input mesh on which material segmentation will be applied in place.
@param material_attribute_name: Name of the material attribute to use for inserting boundaries.
 
@note The material attribute should be n by k vertex attribute, where n is the number of vertices,
and k is the number of materials. The value at row i and column j indicates the probability of vertex
i belonging to material j. The function will insert boundaries between different materials based on
the material attribute.
)");
 
    m.def(
        "mesh_bbox",
        [](MeshType& mesh) -> std::tuple<Eigen::VectorX<Scalar>, Eigen::VectorX<Scalar>> {
            const Index dim = mesh.get_dimension();
            if (dim == 2) {
                auto box = mesh_bbox<2, Scalar, Index>(mesh);
                return {Eigen::VectorX<Scalar>(box.min()), Eigen::VectorX<Scalar>(box.max())};
            } else if (dim == 3) {
                auto box = mesh_bbox<3, Scalar, Index>(mesh);
                return {Eigen::VectorX<Scalar>(box.min()), Eigen::VectorX<Scalar>(box.max())};
            }
            throw nb::value_error("mesh_bbox only supports 2D or 3D meshes.");
        },
        "mesh"_a,
        R"(Compute the axis-aligned bounding box of a mesh.
 
:param mesh: Input mesh (must be 2D or 3D).
 
:returns: A tuple ``(min, max)`` of corner coordinates. For a mesh with no vertices, an empty box is returned, where ``min`` is component-wise greater than ``max``.)");
 
    m.def(
        "compute_uv_tile_list",
        &compute_uv_tile_list<Scalar, Index>,
        "mesh"_a,
        R"(Extract the list of all UV tiles that a mesh's parametrization spans.
 
UV tiles are understood to be a regular unit grid in UV space. Tiles are unioned across
every attribute marked with UV usage (both indexed and per-vertex), adding an entry for
each distinct integer ``(floor(u), floor(v))`` pair found.
 
:param mesh: Input mesh to be analyzed.
 
:returns: A list of integer ``(u, v)`` coordinate pairs, one per UV tile.)");
}
 
} // namespace lagrange::python