TriangleMesh.h

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// ----------------------------------------------------------------------------
// -                        Open3D: www.open3d.org                            -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2026 www.open3d.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
 
#pragma once
 
#include <Eigen/Core>
#include <memory>
#include <numeric>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>
 
#include "open3d/geometry/Image.h"
#include "open3d/geometry/MeshBase.h"
#include "open3d/utility/Helper.h"
 
namespace open3d {
namespace geometry {
 
class PointCloud;
class TetraMesh;
 
class TriangleMesh : public MeshBase {
public:
    TriangleMesh() : MeshBase(Geometry::GeometryType::TriangleMesh) {}
    TriangleMesh(const std::vector<Eigen::Vector3d> &vertices,
                 const std::vector<Eigen::Vector3i> &triangles)
        : MeshBase(Geometry::GeometryType::TriangleMesh, vertices),
          triangles_(triangles) {}
    ~TriangleMesh() override {}
 
public:
    virtual TriangleMesh &Clear() override;
    virtual TriangleMesh &Transform(
            const Eigen::Matrix4d &transformation) override;
    virtual TriangleMesh &Rotate(const Eigen::Matrix3d &R,
                                 const Eigen::Vector3d &center) override;
 
public:
    TriangleMesh &operator+=(const TriangleMesh &mesh);
    TriangleMesh operator+(const TriangleMesh &mesh) const;
 
    bool HasTriangles() const {
        return vertices_.size() > 0 && triangles_.size() > 0;
    }
 
    bool HasTriangleNormals() const {
        return HasTriangles() && triangles_.size() == triangle_normals_.size();
    }
 
    bool HasAdjacencyList() const {
        return vertices_.size() > 0 &&
               adjacency_list_.size() == vertices_.size();
    }
 
    bool HasTriangleUvs() const {
        return HasTriangles() && triangle_uvs_.size() == 3 * triangles_.size();
    }
 
    bool HasTextures() const {
        bool is_all_texture_valid = std::accumulate(
                textures_.begin(), textures_.end(), true,
                [](bool a, const Image &b) { return a && !b.IsEmpty(); });
        return !textures_.empty() && is_all_texture_valid;
    }
 
    bool HasMaterials() const { return !materials_.empty(); }
 
    bool HasTriangleMaterialIds() const {
        return HasTriangles() &&
               triangle_material_ids_.size() == triangles_.size();
    }
 
    TriangleMesh &NormalizeNormals() {
        MeshBase::NormalizeNormals();
        for (size_t i = 0; i < triangle_normals_.size(); i++) {
            triangle_normals_[i].normalize();
            if (std::isnan(triangle_normals_[i](0))) {
                triangle_normals_[i] = Eigen::Vector3d(0.0, 0.0, 1.0);
            }
        }
        return *this;
    }
 
    TriangleMesh &ComputeTriangleNormals(bool normalized = true);
 
    TriangleMesh &ComputeVertexNormals(bool normalized = true);
 
    TriangleMesh &ComputeAdjacencyList();
 
    TriangleMesh &RemoveDuplicatedVertices();
 
    TriangleMesh &RemoveDuplicatedTriangles();
 
    TriangleMesh &RemoveUnreferencedVertices();
 
    TriangleMesh &RemoveDegenerateTriangles();
 
    TriangleMesh &RemoveNonManifoldEdges();
 
    TriangleMesh &MergeCloseVertices(double eps);
 
    std::shared_ptr<TriangleMesh> FilterSharpen(
            int number_of_iterations,
            double strength,
            FilterScope scope = FilterScope::All) const;
 
    std::shared_ptr<TriangleMesh> FilterSmoothSimple(
            int number_of_iterations,
            FilterScope scope = FilterScope::All) const;
 
    std::shared_ptr<TriangleMesh> FilterSmoothLaplacian(
            int number_of_iterations,
            double lambda_filter,
            FilterScope scope = FilterScope::All) const;
 
    std::shared_ptr<TriangleMesh> FilterSmoothTaubin(
            int number_of_iterations,
            double lambda_filter = 0.5,
            double mu = -0.53,
            FilterScope scope = FilterScope::All) const;
 
    int EulerPoincareCharacteristic() const;
 
    std::vector<Eigen::Vector2i> GetNonManifoldEdges(
            bool allow_boundary_edges = true) const;
 
    bool IsEdgeManifold(bool allow_boundary_edges = true) const;
 
    std::vector<int> GetNonManifoldVertices() const;
 
    bool IsVertexManifold() const;
 
    std::vector<Eigen::Vector2i> GetSelfIntersectingTriangles() const;
 
    bool IsSelfIntersecting() const;
 
    bool IsBoundingBoxIntersecting(const TriangleMesh &other) const;
 
    bool IsIntersecting(const TriangleMesh &other) const;
 
    bool IsOrientable() const;
 
    bool IsWatertight() const;
 
    bool OrientTriangles();
 
    std::unordered_map<Eigen::Vector2i,
                       std::vector<int>,
                       utility::hash_eigen<Eigen::Vector2i>>
    GetEdgeToTrianglesMap() const;
 
    std::unordered_map<Eigen::Vector2i,
                       std::vector<int>,
                       utility::hash_eigen<Eigen::Vector2i>>
    GetEdgeToVerticesMap() const;
 
    static double ComputeTriangleArea(const Eigen::Vector3d &p0,
                                      const Eigen::Vector3d &p1,
                                      const Eigen::Vector3d &p2);
 
    double GetTriangleArea(size_t triangle_idx) const;
 
    static inline Eigen::Vector3i GetOrderedTriangle(int vidx0,
                                                     int vidx1,
                                                     int vidx2) {
        if (vidx0 > vidx2) {
            std::swap(vidx0, vidx2);
        }
        if (vidx0 > vidx1) {
            std::swap(vidx0, vidx1);
        }
        if (vidx1 > vidx2) {
            std::swap(vidx1, vidx2);
        }
        return Eigen::Vector3i(vidx0, vidx1, vidx2);
    }
 
    double GetSurfaceArea() const;
 
    double GetSurfaceArea(std::vector<double> &triangle_areas) const;
 
    double GetVolume() const;
 
    static Eigen::Vector4d ComputeTrianglePlane(const Eigen::Vector3d &p0,
                                                const Eigen::Vector3d &p1,
                                                const Eigen::Vector3d &p2);
 
    Eigen::Vector4d GetTrianglePlane(size_t triangle_idx) const;
 
    static inline Eigen::Vector2i GetOrderedEdge(int vidx0, int vidx1) {
        return Eigen::Vector2i(std::min(vidx0, vidx1), std::max(vidx0, vidx1));
    }
 
    std::shared_ptr<PointCloud> SamplePointsUniformlyImpl(
            size_t number_of_points,
            const std::vector<double> &triangle_areas,
            bool use_triangle_normal);
 
    std::shared_ptr<PointCloud> SamplePointsUniformly(
            size_t number_of_points, bool use_triangle_normal = false);
 
    std::shared_ptr<PointCloud> SamplePointsPoissonDisk(
            size_t number_of_points,
            double init_factor = 5,
            const std::shared_ptr<PointCloud> pcl_init = nullptr,
            bool use_triangle_normal = false);
 
    std::shared_ptr<TriangleMesh> SubdivideMidpoint(
            int number_of_iterations) const;
 
    std::shared_ptr<TriangleMesh> SubdivideLoop(int number_of_iterations) const;
 
    std::shared_ptr<TriangleMesh> SimplifyVertexClustering(
            double voxel_size,
            SimplificationContraction contraction =
                    SimplificationContraction::Average) const;
 
    std::shared_ptr<TriangleMesh> SimplifyQuadricDecimation(
            int target_number_of_triangles,
            double maximum_error,
            double boundary_weight) const;
 
    std::shared_ptr<TriangleMesh> SelectByIndex(
            const std::vector<size_t> &indices, bool cleanup = true) const;
 
    std::shared_ptr<TriangleMesh> Crop(
            const AxisAlignedBoundingBox &bbox) const;
 
    std::shared_ptr<TriangleMesh> Crop(const OrientedBoundingBox &bbox) const;
 
    std::tuple<std::vector<int>, std::vector<size_t>, std::vector<double>>
    ClusterConnectedTriangles() const;
 
    void RemoveTrianglesByIndex(const std::vector<size_t> &triangle_indices);
 
    void RemoveTrianglesByMask(const std::vector<bool> &triangle_mask);
 
    void RemoveVerticesByIndex(const std::vector<size_t> &vertex_indices);
 
    void RemoveVerticesByMask(const std::vector<bool> &vertex_mask);
 
    std::shared_ptr<TriangleMesh> DeformAsRigidAsPossible(
            const std::vector<int> &constraint_vertex_indices,
            const std::vector<Eigen::Vector3d> &constraint_vertex_positions,
            size_t max_iter,
            DeformAsRigidAsPossibleEnergy energy =
                    DeformAsRigidAsPossibleEnergy::Spokes,
            double smoothed_alpha = 0.01) const;
 
    static std::shared_ptr<TriangleMesh> CreateFromPointCloudAlphaShape(
            const PointCloud &pcd,
            double alpha,
            std::shared_ptr<TetraMesh> tetra_mesh = nullptr,
            std::vector<size_t> *pt_map = nullptr);
 
    static std::shared_ptr<TriangleMesh> CreateFromPointCloudBallPivoting(
            const PointCloud &pcd, const std::vector<double> &radii);
 
    static std::tuple<std::shared_ptr<TriangleMesh>, std::vector<double>>
    CreateFromPointCloudPoisson(const PointCloud &pcd,
                                size_t depth = 8,
                                float width = 0.0f,
                                float scale = 1.1f,
                                bool linear_fit = false,
                                int n_threads = -1,
                                int full_depth = 5,
                                float samples_per_node = 1.5f,
                                float point_weight = 2.0f);
 
    static std::shared_ptr<TriangleMesh> CreateTetrahedron(
            double radius = 1.0, bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateOctahedron(
            double radius = 1.0, bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateIcosahedron(
            double radius = 1.0, bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateFromOrientedBoundingBox(
            const OrientedBoundingBox &obox,
            const Eigen::Vector3d &scale = Eigen::Vector3d::Ones(),
            bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateFromOrientedBoundingEllipsoid(
            const OrientedBoundingEllipsoid &obel,
            const Eigen::Vector3d &scale = Eigen::Vector3d::Ones(),
            int resolution = 20,
            bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateBox(
            double width = 1.0,
            double height = 1.0,
            double depth = 1.0,
            bool create_uv_map = false,
            bool map_texture_to_each_face = false);
 
    static std::shared_ptr<TriangleMesh> CreateSphere(
            double radius = 1.0,
            int resolution = 20,
            bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateEllipsoid(
            double radius_x = 1.0,
            double radius_y = 1.0,
            double radius_z = 1.0,
            int resolution = 20,
            bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateCylinder(
            double radius = 1.0,
            double height = 2.0,
            int resolution = 20,
            int split = 4,
            bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateCone(double radius = 1.0,
                                                    double height = 2.0,
                                                    int resolution = 20,
                                                    int split = 1,
                                                    bool create_uv_map = false);
 
    static std::shared_ptr<TriangleMesh> CreateTorus(
            double torus_radius = 1.0,
            double tube_radius = 0.5,
            int radial_resolution = 30,
            int tubular_resolution = 20);
 
    //
    static std::shared_ptr<TriangleMesh> CreateArrow(
            double cylinder_radius = 1.0,
            double cone_radius = 1.5,
            double cylinder_height = 5.0,
            double cone_height = 4.0,
            int resolution = 20,
            int cylinder_split = 4,
            int cone_split = 1);
 
    static std::shared_ptr<TriangleMesh> CreateCoordinateFrame(
            double size = 1.0,
            const Eigen::Vector3d &origin = Eigen::Vector3d(0.0, 0.0, 0.0));
 
    static std::shared_ptr<TriangleMesh> CreateMobius(int length_split = 70,
                                                      int width_split = 15,
                                                      int twists = 1,
                                                      double radius = 1,
                                                      double flatness = 1,
                                                      double width = 1,
                                                      double scale = 1);
 
protected:
    // Forward child class type to avoid indirect nonvirtual base
    TriangleMesh(Geometry::GeometryType type) : MeshBase(type) {}
 
    std::unordered_map<Eigen::Vector2i,
                       double,
                       utility::hash_eigen<Eigen::Vector2i>>
    ComputeEdgeWeightsCot(
            const std::unordered_map<Eigen::Vector2i,
                                     std::vector<int>,
                                     utility::hash_eigen<Eigen::Vector2i>>
                    &edges_to_vertices,
            double min_weight = std::numeric_limits<double>::lowest()) const;
 
public:
    std::vector<Eigen::Vector3i> triangles_;
    std::vector<Eigen::Vector3d> triangle_normals_;
    std::vector<std::unordered_set<int>> adjacency_list_;
    std::vector<Eigen::Vector2d> triangle_uvs_;
 
    struct Material {
        struct MaterialParameter {
            float f4[4] = {0};
 
            MaterialParameter() {
                f4[0] = 0;
                f4[1] = 0;
                f4[2] = 0;
                f4[3] = 0;
            }
 
            MaterialParameter(const float v1,
                              const float v2,
                              const float v3,
                              const float v4) {
                f4[0] = v1;
                f4[1] = v2;
                f4[2] = v3;
                f4[3] = v4;
            }
 
            MaterialParameter(const float v1, const float v2, const float v3) {
                f4[0] = v1;
                f4[1] = v2;
                f4[2] = v3;
                f4[3] = 1;
            }
 
            MaterialParameter(const float v1, const float v2) {
                f4[0] = v1;
                f4[1] = v2;
                f4[2] = 0;
                f4[3] = 0;
            }
 
            explicit MaterialParameter(const float v1) {
                f4[0] = v1;
                f4[1] = 0;
                f4[2] = 0;
                f4[3] = 0;
            }
 
            static MaterialParameter CreateRGB(const float r,
                                               const float g,
                                               const float b) {
                return {r, g, b, 1.f};
            }
 
            float r() const { return f4[0]; }
            float g() const { return f4[1]; }
            float b() const { return f4[2]; }
            float a() const { return f4[3]; }
        };
 
        MaterialParameter baseColor;
        float baseMetallic = 0.f;
        float baseRoughness = 1.f;
        float baseReflectance = 0.5f;
        float baseClearCoat = 0.f;
        float baseClearCoatRoughness = 0.f;
        float baseAnisotropy = 0.f;
 
        std::shared_ptr<Image> albedo;
        std::shared_ptr<Image> normalMap;
        std::shared_ptr<Image> ambientOcclusion;
        std::shared_ptr<Image> metallic;
        std::shared_ptr<Image> roughness;
        std::shared_ptr<Image> reflectance;
        std::shared_ptr<Image> clearCoat;
        std::shared_ptr<Image> clearCoatRoughness;
        std::shared_ptr<Image> anisotropy;
 
        std::unordered_map<std::string, MaterialParameter> floatParameters;
        std::unordered_map<std::string, Image> additionalMaps;
    };
 
    std::vector<std::pair<std::string, Material>> materials_;
 
    std::vector<int> triangle_material_ids_;
    std::vector<Image> textures_;
};
 
}  // namespace geometry
}  // namespace open3d