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#ifndef GEOGRAM_MESH_MESH_SURFACE_INTERSECTION
#define GEOGRAM_MESH_MESH_SURFACE_INTERSECTION

#include <geogram/basic/common.h>
#include <geogram/mesh/mesh.h>
#include <geogram/mesh/mesh_io.h>
#include <geogram/numerics/exact_geometry.h>
#include <geogram/basic/process.h>
#include <geogram/basic/attributes.h>
#include <geogram/basic/debug_stream.h>
#include <functional>

/**
 * \file geogram/mesh/mesh_surface_intersection.h
 * \brief Functions for computing intersections between surfacic meshes and
 *        for boolean operations.
 */

namespace GEO {

    struct IsectInfo;

    /********************************************************************/

    /**
     * \brief Computes surface intersections
     * \details New vertices are stored with exact coordinates
     */
    class GEOGRAM_API MeshSurfaceIntersection {
    public:

    typedef exact::vec3h ExactPoint;

    MeshSurfaceIntersection(Mesh& M);
    ~MeshSurfaceIntersection();

    /**
     * \details A facet attribute of type index_t named "operand_bit" can
     *  indicate for each facet to which operand of a n-ary boolean
     *  operation it corresponds to (the same facet might belong to
     *  several operands). It is taken into account by the two variants of
     *  mesh_classify_intersections()
     */
    void intersect();

    /**
     * \brief Removes all the facets that are on the outer boundary
     * \pre set_radial_sort(true) was set before calling intersect()
     */
    void remove_external_shell();

    /**
     * \brief Removes all the facets that are not on the outer boundary
     * \pre set_radial_sort(true) was set before calling intersect()
     */
    void remove_internal_shells();


    void remove_fins();

    /**
     * \brief Classifies the facets and keep only
     *   the ones on the boundary of a combination of regions defined
     *   by a boolean expression.
     * \details A facet attribute of type index_t named "operand_bit"
     *  indicates for each facet to which operand of a n-ary boolean
     *  operation it corresponds to (the same facet might belong to
     *  several operands).
     * \pre set_radial_sort(true) was set before calling intersect()
     * \param[in] expr the boolean function in ASCII.
     *  One can use the following elements, and parentheses:
     *  - Variables: A..Z or x0..x31, correspond to the bits of the
     *    "operand_bit" attribute
     *  - the special variable '*' corresponds to the union of everything
     *  - and:        '&' or '*'
     *  - or:         '|' or '+'
     *  - xor:        '^'
     *  - difference: '-'
     *  - not:        '!' or '~'
     *  Special values for expr:
     *  - "union" (union of everything), synonym of '*'
     *  - "intersection" (intersection of everything).
     */
    void classify(const std::string& expr);


    /**
     * \brief Classifies a connected component
     * \param[in] component a connected component
     * \param[in] v a vertex of the connected component
     * \return the inclusion bits of the connected component relative
     *  to the operands
     */
    index_t classify_component(index_t component, index_t v);

    /**
     * \brief Classifies a vertex of the computed intersection
     * \param[in] component a component
     * \param[in] v a vertex of the component
     * \return the operand inclusion bits, or NO_INDEX if classification
     *  was not successful.
     * \details Uses raytracing along a random direction. The classification
     *  can be not successful if degenerate ray-triangle intersections are
     *  encountered. Then one needs to try again
     *  using tentatively_classify_component_vertex() (multiple times if
     *  required).
     */
    index_t tentatively_classify_component_vertex_fast(
        index_t component, index_t v
    );

    /**
     * \brief Classifies a vertex of the computed intersection
     * \param[in] component a component
     * \param[in] v a vertex of the component
     * \return the operand inclusion bits, or NO_INDEX if classification
     *  was not successful.
     * \details Uses raytracing along a random direction. The classification
     *  can be not successful if degenerate ray-triangle intersections are
     *  encountered. Then one needs to try again.
     */
    index_t tentatively_classify_component_vertex(
        index_t component, index_t v
    );


    /**
     * \brief Merge coplanar facets and retriangulate them using a
     *  Constrained Delaunay triangulation
     * \param[in] angle_tolerance angle tolerance for detecting coplanar
     *  facets and colinear edges (in degrees)
     */
    void simplify_coplanar_facets(double angle_tolerance = 0.0);

    /**
     * \brief Display information while computing the intersection.
     *  Default is unset.
     */
    void set_verbose(bool x) {
        verbose_ = x;
	if(!verbose_ && fine_verbose_) {
	    fine_verbose_ = false;
	}
    }

    /**
     * \brief Display detailed information while computing the intersection.
     *  Default is unset.
     */
    void set_fine_verbose(bool x) {
        fine_verbose_ = x;
	if(fine_verbose_ && !verbose_) {
	    verbose_ = true;
	}
    }

    /**
     * \brief Sets the threshold from which triangle is considered
     *  to be a monster.
     * \details Monster triangles are saved to a file for the zoo.
     * \param[in] nb if a triangle has more than \p nb intersections
     *  in it, then it is considered to be a monster.
     */
    void set_monster_threshold(index_t nb) {
        monster_threshold_ = nb;
    }

    /**
     * \brief In dry run mode, the computed local triangulations
     *  are not inserted in the global mesh. This is for benchmarking.
     *  Default is off.
     */
    void set_dry_run(bool x) {
        dry_run_ = x;
    }

    /**
     * \brief If set, compute constrained Delaunay triangulation
     *  in the intersected triangles. If there are intersections
     *  in coplanar facets, it guarantees uniqueness of their
     *  triangulation. Default is set.
     */
    void set_delaunay(bool x) {
        delaunay_ = x;
    }

    /**
     * \brief detect and compute intersections between facets that share
     *  a facet or an edge. Set to false if input is a set of conformal
     *  meshes. Default is set.
     */
    void set_detect_intersecting_neighbors(bool x) {
        detect_intersecting_neighbors_ = x;
    }

    /**
     * \brief Specifies whether surfaces should be duplicated and
     *  radial edges sorted in order to create the volumetric
     *  partition yielded by the intersection
     * \param[in] x true if radial edges should be sorted. Default is
     *  set
     */
    void set_radial_sort(bool x) {
        use_radial_sort_ = x;
    }

    /**
     * \brief Specifies whether coordinates should be normalized during
     *  computation. If set, original coordinates are restored at the
     *  end of intersect().
     * \param[in] x true if coordinates should be normalized. Default is
     *  set.
     */
    void set_normalize(bool x) {
        normalize_ = x;
    }


    /**
     * \brief Optionally save the skeleton (that is, the collection of
     *  non-manifold edges) to a given mesh. This option is not compatible
     *  with dry_run (throws an assertion fail if set).
     * \param[in] skeleton a pointer to the mesh that will receive the
     *  skeleton.
     * \param[in] trim_fins if set, do not keep bundles that have
     *  less than three halfedges.
     */
    void set_build_skeleton(Mesh* skeleton, bool trim_fins=false) {
        skeleton_ = skeleton;
        skeleton_trim_fins_ = trim_fins;
    }

    /**
     * \brief Specifies that attributes should be interpolated
     * \param[in] x true if attributes should be interpolated,
     *  false otherwise. Default is false.
     */
    void set_interpolate_attributes(bool x) {
        interpolate_attributes_ = x;
    }

    protected:
    /**
     * \brief substep of intersect(), prepares the mesh
     * \details Tesselates the facets if they are not triangulated,
     *  creates the operand bit for boolean op classification, removes
     *  the exactly degenerate triangles, colocate the points,
     *  optionally scales the coordinates and sets symbolic perturbation
     *  mode to lexicographic.
     */
    void intersect_prologue();

    /**
     * \brief substep of intersect(), finds all the intersection points
     *   and segments.
     * \param[out] intersections the vector of IsectInfo. Each IsectInfo
     *   is either an intersection vertex or a pair of intersection
     *   vertices. Intersection vertices are represented in symbolic
     *   form, as a couple of triangle indices plus a couple of triangle
     *   subregion id (TriangleRegion).
     * \details First uses a MeshFacetsAABB to detect candidate pairs
     *   of intersecting triangles, then calls triangles_intersection()
     *   in parallel. Finally, mesh facets are shuffled randomly, to
     *   ensure balanced multithreading for the subsequent steps.
     */
    void intersect_get_intersections(vector<IsectInfo>& intersections);

    /**
     * \brief substep of intersect(), inserts the intersection points
     *   and segments into the triangles.
     * \param[in,out] intersections the vector of IsectInfo. Each IsectInfo
     *   is either an intersection vertex or a pair of intersection
     *   vertices. Intersection vertices are represented in symbolic
     *   form, as a couple of triangle indices plus a couple of triangle
     *   subregion id (TriangleRegion).
     * \details Uses MeshInTriangle, a class derived from CDTBase2d,
     *   that computes a constrained Delaunay triangulation with
     *   intersection points represented with exact coordinates.
     *   Operates in parallel. Each thread computes constrained
     *   Delaunay triangulations independently, and commits them in the
     *   resulting mesh (with a lock to protect concurrent accesses).
     *   The initial mesh is copied (and kept in the mesh_copy_ member),
     *   so that concurrent read access do not need a lock.
     */
    void intersect_remesh_intersections(vector<IsectInfo>& intersections);

    /**
     * \brief subset of intersect(), cleans the resulting mesh and
     *   undoes optional geometric normalization.
     * \param[in] intersections the vector of IsectInfo. Each IsectInfo
     *   is either an intersection vertex or a pair of intersection
     *   vertices. Intersection vertices are represented in symbolic
     *   form, as a couple of triangle indices plus a couple of triangle
     *   subregion id (TriangleRegion).
     * \details find the intersection that landed exactly onto an
     *   existing mesh vertex and merges them. Removes the initial
     *   triangles that had intersections (they are replaced with new
     *   triangles). Merges duplicated triangles that come from
     *   coplanar regions. Undoes geometric normalizations. Restores
     *   initial symbolic perturbation mode.
     */
    void intersect_epilogue(const vector<IsectInfo>& intersections);


    /**
     * \brief Acquires a lock on this mesh
     * \details A single thread can have the lock. When multiple threads
     *  want the lock, the ones that do not have it keep waiting until
     *  the one that owns the lock calls unlock(). All threads that modify
     *  the target mesh should call this function
     * \see unlock()
     */
    void lock() {
        Process::acquire_spinlock(lock_);
    }

    /**
     * \brief Releases the lock associated with this mesh
     */
    void unlock() {
        Process::release_spinlock(lock_);
    }

    /**
     * \brief Gets the exact point associated with a vertex
     * \details If the vertex has explicit exact coordinates associated
     *  with it, they are returned, else an exact ExactPoint is constructed
     *  from the double-precision coordinates stored in the mesh
     * \param[in] v a vertex of the mesh
     * \return the exact coordinates of this vertex, as a vector in
     *  homogeneous coordinates stored as expansions
     */
    ExactPoint exact_vertex(index_t v) const;

    /**
     * \brief Finds or creates a vertex in the mesh, by exact coordinates
     * \details If there is already a vertex with coordinates \p p, then
     *  the existing vertex is returned, else a new vertex is constructed.
     *  Note that only the vertices created by find_or_create_vertex() can
     *  be returned as existing vertices. Mesh vertices stored as double-
     *  precision coordinates are not retreived by this function.
     * \param[in] p the exact coordinates of a point
     * \return the index of a mesh vertex with \p p as coordinates
     */
    index_t find_or_create_exact_vertex(const ExactPoint& p);

    /**
     * \brief Gets the target mesh
     * \return a modifiable reference to the mesh that was passed to
     *  the constructor
     */
    Mesh& target_mesh() {
        return mesh_;
    }

    /**
     * \brief Gets the target mesh
     * \return a const reference to the mesh that was passed to
     *  the constructor
     */
    const Mesh& target_mesh() const {
        return mesh_;
    }

    /**
     * \brief Gets a copy of the initial mesh passed to the constructor
     * \details It is used by the multithreaded mesh intersection algorithm.
     *   Each thread needs to both access the initial geometry and create
     *   new vertices and triangles in the target mesh. Creating new mesh
     *   elements can reallocate the internal vectors of the mesh, and
     *   change the address of the elements. This should not occur while
     *   another thread is reading the mesh. Copying the initial geometry
     *   in another mesh prevents this type of problems.
     * \return a const reference to the mesh that was copied from the one
     *   passed to the constructor
     */
    const Mesh& readonly_mesh() const {
        return mesh_copy_;
    }

    class RadialSort;

    /**
     * \brief Builds the Weiler model
     * \details The Weiler model is a volumetric representation, where each
     *  facet is on the boundary of a closed region. Facets are duplicated,
     *  so that when two regions touch each other, each region has its own
     *  facet on the boundary. Two facets that touch in this way are
     *  connected by alpha3 links. Facets on the boundary of the same
     *  region are connected by alpha2 links.
     */
    void build_Weiler_model();

    /**
     * \brief Marks all the facets that are on the external shell
     */
    void mark_external_shell(vector<index_t>& on_external_shell);

    protected:

    /**
     * A class for sorting triangles around their common radial edge.
     */
    class GEOGRAM_API RadialSort {
    public:
        /**
         * \brief RadialSort constructor
         * \param[in] mesh the MeshSurfaceIntersection
         */
        RadialSort(
            const MeshSurfaceIntersection& mesh
        ) : mesh_(mesh),
            h_ref_(NO_INDEX),
            degenerate_(false)
        {
        }

        /**
         * \brief Initializes radial sorting around a given halfedge
         * \param[in] h_ref the reference halfedge
         */
        void init(index_t h_ref);

        /**
         * \brief Compares two halfedges
         * \param[in] h1 , h2 the two halfedges
         * \retval true if \p h1 should be before \p h2 in radial order
         * \retval false otherwise
         */
        bool operator()(index_t h1, index_t h2) const;

        /**
         * \brief Tests if a degeneracy was encountered
         * \retval true if there were two coplanar triangles on the same
         *  side relative to h_ref
         * \retval false otherwise
         */
        bool degenerate() const {
            return degenerate_;
        }

        /**
         * \brief Computes a vector of arbitrary length with its
         *  direction given by two points
         * \param[in] p1 , p2 the two points in homogeneous coordinates
         * \return a vector in cartesian coordinates with the same
         *  direction and orientation as \p p2 - \p p1
         */
        static exact::vec3 exact_direction(
            const ExactPoint& p1, const ExactPoint& p2
        );

        /**
         * \brief Computes an interval vector of arbitrary length with its
         *  direction given by two points
         * \param[in] p1 , p2 the two points in homogeneous coordinates
         * \return an interval vector in cartesian coordinates
         *  with the same direction and orientation as \p p2 - \p p1
         */
        static vec3I exact_direction_I(
            const ExactPoint& p1, const ExactPoint& p2
        );

    protected:

        /**
         * \brief Computes the relative orientations of two halfedges
         * \param[in] h1 , h2 the two halfedges
         * \retval POSITIVE if going from \p h1's triangle to
         *  \p h2's triangle is a left turn (with h_ref facing to you)
         * \retval ZERO if \p h1 and \p h2 have co-linear normals
         * \retval NEGATIVE otherwise
         */
        Sign h_orient(index_t h1, index_t h2) const;

        /**
         * \brief Computes the normal orientation of a halfedge
         *  relative to h_ref
         * \return the sign of the dot product between h_ref's triangle
         *  normal and \p h2's triangle normal.
         */
        Sign h_refNorient(index_t h2) const;

    public:
        void test(index_t h1, index_t h2) {
            (*this)(h1,h2);
            Sign o_ref1 = h_orient(h_ref_, h1);
            Sign o_ref2 = h_orient(h_ref_, h2);
            Sign oN_ref1 = h_refNorient(h1);
            Sign oN_ref2 = h_refNorient(h2);
            Sign o_12 = h_orient(h1,h2);
            std::cerr
                << " o_ref1=" << int(o_ref1) << " o_ref2=" << int(o_ref2)
                << " oN_ref1=" << int(oN_ref1) << " oN_ref2=" << int(oN_ref2)
                << " o_12=" << int(o_12)
                << std::endl;
        }


    private:
        const MeshSurfaceIntersection& mesh_;
        index_t h_ref_; // ---reference halfedge
        exact::vec3 U_ref_;   // -.
        exact::vec3 V_ref_;   //  +-reference basis
        exact::vec3 N_ref_;   // -'
        vec3I U_ref_I_; // -.
        vec3I V_ref_I_; //  +-reference basis (interval arithmetics)
        vec3I N_ref_I_; // _'
        mutable vector< std::pair<index_t, Sign> > refNorient_cache_;
        mutable bool degenerate_;
    };


    protected:
    Process::spinlock lock_;
    Mesh& mesh_;
    Mesh mesh_copy_;
    Attribute<const ExactPoint*> vertex_to_exact_point_;

#ifdef GEOGRAM_USE_EXACT_NT
    // Exact points are canonicalized
    // (by Numeric::optimize_number_representation(vec3HEx)) so
    // we can use this comparator that makes the global vertex map
    // much much faster.
    typedef vec3HExLexicoCompareCanonical ExactPointCompare;
#else
    // Generic comparator for global vertex map.
    typedef vec3HgLexicoCompare<exact::scalar> ExactPointCompare;
#endif
    std::map<ExactPoint,index_t,ExactPointCompare> exact_point_to_vertex_;

    bool verbose_;
    bool fine_verbose_;
    bool delaunay_;
    bool detect_intersecting_neighbors_;
    bool use_radial_sort_;

    PCK::SOSMode SOS_bkp_;
    bool rescale_;
    bool normalize_;
    vec3 normalize_center_;
    double normalize_radius_;

    index_t monster_threshold_;
    bool dry_run_;
    friend class MeshInTriangle;
    friend class CoplanarFacets;

    Mesh* skeleton_;
    bool skeleton_trim_fins_;
    bool interpolate_attributes_;

    /***************************************************/

    /**
     * \brief Halfedfge-like API wrappers on top of a triangulated mesh
     * \details These are volumetric halfedges, also called
     *  combinatorial 3-map, with both volumetric links (alpha3)
     *  and surfacic link (alpha2).
     *  One may refer to this webpage for the definition of a 3-map:
     *   https://doc.cgal.org/latest/Combinatorial_map/
     */
    class Halfedges {
    public:

        /**
         * \brief Halfedges constructor
         * \param[in] I a reference to the MeshSurfaceIntersection
         */
        Halfedges(MeshSurfaceIntersection& I) : mesh_(I.mesh_) {
        }

        /**
         * \brief Halfedges destructor
         */
        ~Halfedges() {
            // TODO: destroy alpha3 attribute (kept now for debugging
        }

        /**
         * \brief Initializes the structure
         * \details Needs to be called before any other function
         */
        void initialize() {
            facet_corner_alpha3_.bind(
                mesh_.facet_corners.attributes(), "alpha3"
            );
        }

        /**
         * \brief Gets the number of halfedegs in the map
         * \return the number of halfedges, that is, three times
         *  the number of triangles (halfedges are not stored explicitly).
         */
        index_t nb() const {
            return mesh_.facet_corners.nb();
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator corresponding to the first index.
         */
        index_as_iterator begin() const {
            return index_as_iterator(0);
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator to one position past the last index.
         */
        index_as_iterator end() const {
            return index_as_iterator(nb());
        }

        /**
         * \brief Gets the facet associated to a halfedge
         * \param[in] h a halfedge index
         * \return the facet index, that is, h/3
         */
        index_t facet(index_t h) const {
            return h/3;
        }

        /**
         * \brief gets the surfacic neighbor of a halfedge
         * \details see definition of a combinatorial 3-map
         *   here: https://doc.cgal.org/latest/Combinatorial_map/
         * \param[in] h a halfedge index
         * \return another halfedge in the same surface, connecting the same
         *  vertices as \p h, but in opposite order
         * \see sew2()
         */
        index_t alpha2(index_t h) const {
            index_t t1 = facet(h);
            index_t t2 = mesh_.facet_corners.adjacent_facet(h);
            if(t2 == NO_INDEX) {
                return NO_INDEX;
            }
            for(index_t h2: mesh_.facets.corners(t2)) {
                if(mesh_.facet_corners.adjacent_facet(h2) == t1) {
                    return h2;
                }
            }
            geo_assert_not_reached;
        }

        /**
         * \brief gets the volumetric neighbor of a halfedge
         * \details see definition of a combinatorial 3-map
         *   here: https://doc.cgal.org/latest/Combinatorial_map/
         * \param[in] h a halfedge index
         * \return another halfedge in a different volume, connecting
         *  the same vertices as \p h, but in opposite order
         * \see sew3()
         */
        index_t alpha3(index_t h) const {
            return facet_corner_alpha3_[h];
        }

        /**
         * \brief gets the volumetric neighbor of a facet
         * \param[in] f a facet
         * \return a facet with the same vertices as \p f but in
         *  opposite index
         */
        index_t facet_alpha3(index_t f) const {
            return alpha3(3*f)/3;
        }

        /**
         * \brief gets a vertex of an halfedge
         * \param[in] h the halfedge
         * \param[in] dlv the local index of the vertex, in {0,1,2}
         * \return
         *  - if \p dlv = 0 returns the origin vertex of \p h
         *  - if \p dlv = 1 returns the destination vertex of \p h
         *  - if \p dlv = 2 returns the vertex of the facet adjacent to \p h
         *    that is neither the origin nor the destination of \p h
         */
        index_t vertex(index_t h, index_t dlv) const {
            index_t f  = h/3;
            index_t lv = (h+dlv)%3;
            return mesh_.facets.vertex(f,lv);
        }


        /**
         * \brief Creates a surfacic link between two halfedges
         * \param[in] h1 , h2 the two halfedges to be connected
         * \pre \p h1 and \p h2 should have the same origins and
         *  destinations but in reverse order (\p h1 's origin should
         *  be \p h2 's destination and vice-versa).
         * \see alpha2()
         */
        void sew2(index_t h1, index_t h2) {
            geo_debug_assert(vertex(h1,0) == vertex(h2,1));
            geo_debug_assert(vertex(h2,0) == vertex(h1,1));
            index_t t1 = h1/3;
            index_t t2 = h2/3;
            mesh_.facet_corners.set_adjacent_facet(h1,t2);
            mesh_.facet_corners.set_adjacent_facet(h2,t1);
        }

        /**
         * \brief Creates a volumetric link between two halfedges
         * \param[in] h1 , h2 the two halfedges to be connected
         * \pre \p h1 and \p h2 should have the same origins and
         *  destinations but in reverse order (\p h1 's origin should
         *  be \p h2 's destination and vice-versa).
         * \see alpha3()
         */
        void sew3(index_t h1, index_t h2) {
            geo_debug_assert(vertex(h1,0) == vertex(h2,1));
            geo_debug_assert(vertex(h2,0) == vertex(h1,1));
            facet_corner_alpha3_[h1] = h2;
            facet_corner_alpha3_[h2] = h1;
        }

    private:
        Mesh& mesh_;
        Attribute<index_t> facet_corner_alpha3_;
    } halfedges_;

    /***************************************************/

    /**
     * \brief Represents the set of radial halfedge bundles
     * \details A Radial bundle corresponds to the set of halfedges
     *   connecting the same pair of vertices (and in the same order).
     */
    class RadialBundles {
    public:

        /**
         * \brief RadialBundles constructor
         * \param[in] I a reference to the MeshSurfaceIntersectionx
         */
        RadialBundles(MeshSurfaceIntersection& I) : I_(I), mesh_(I.mesh_) {
        }

        /**
         * \brief Initializes the structure
         * \details Needs to be called before any other function
         */
        void initialize();

        /**
         * \brief Gets the number of bundles
         */
        index_t nb() const {
            return bndl_start_.size() - 1;
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator corresponding to the first bundle
         */
        index_as_iterator begin() const {
            return index_as_iterator(0);
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator to one position past the last bundle
         */
        index_as_iterator end() const {
            return index_as_iterator(nb());
        }

        /**
         * \brief Gets the number of halfedges in a bundle
         * \param[in] bndl the bundle
         * \return the number of halfedges in \p bndl
         */
        index_t nb_halfedges(index_t bndl) const {
            geo_debug_assert(bndl < nb());
            return bndl_start_[bndl+1] - bndl_start_[bndl];
        }

        /**
         * \brief Gets a halfedge in a bundle from local index
         * \param[in] bndl the bundle
         * \param[in] li the local index of the halfedge in the bundle,
         *    in [0 .. nb_halfedges(bndl)-1]
         * \return the halfedge
         */
        index_t halfedge(index_t bndl, index_t li) const {
            geo_debug_assert(bndl < nb());
            geo_debug_assert(li < nb_halfedges(bndl));
            return H_[bndl_start_[bndl] + li];
        }

        /**
         * \brief Sets a halfedge in a bundle
         * \param[in] bndl the bundle
         * \param[in] li the local index of the halfedge in the bunble,
         *    in [0 .. nb_halfedges(bndl)-1]
         * \param[in] h the new halfedge
         */
        void set_halfedge(index_t bndl, index_t li, index_t h) {
            geo_debug_assert(bndl < nb());
            geo_debug_assert(li < nb_halfedges(bndl));
            H_[bndl_start_[bndl] + li] = h;
        }

        /**
         * \brief gets the halfedges in a bundle
         * \param[in] bndl bundle index
         * \return a modifiable sequence of halfedge indices
         */
        index_ptr_range halfedges(index_t bndl) {
            return index_ptr_range(
                H_, bndl_start_[bndl], bndl_start_[bndl+1]
            );
        }

        /**
         * \brief gets the halfedges in a bundle
         * \param[in] bndl bundle index
         * \return a non-modifiable sequence of halfedge indices
         */
        const_index_ptr_range halfedges(index_t bndl) const {
            return const_index_ptr_range(
                H_, bndl_start_[bndl], bndl_start_[bndl+1]
            );
        }

        /**
         * \brief gets one of the vertices at the two extremities of a bundle
         * \param[in] bndl bundle index
         * \param[in] lv local vertex index, in {0,1}
         * \return if \p lv = 0 the source vertex, if \p lv = 1 the
         *  destination vertex
         */
        index_t vertex(index_t bndl, index_t lv) const {
            geo_debug_assert(bndl_start_[bndl+1] - bndl_start_[bndl] > 0);
            index_t h = H_[bndl_start_[bndl]];
            return I_.halfedges_.vertex(h,lv);
        }

        /**
         * \brief gets the first bundle starting from a vertex
         * \param[in] v the vertex
         * \details bundles starting from the same vertex are chained
         * \return the index of the first bundle starting from \p v, or
         *   NO_INDEX if there is no such bundle
         */
        index_t vertex_first_bundle(index_t v) const {
            return v_first_bndl_[v];
        }

        /**
         * \brief gets the next bundle around a vertex
         * \param[in] bndl the bundle
         * \details bundles starting from the same vertex are chained
         * \return the index of the next bundle that has the same origin
         *  vertex as \p bndl, or NO_INDEX if there is no such bundle
         */
        index_t next_around_vertex(index_t bndl) const {
            return bndl_next_around_v_[bndl];
        }

        /**
         * \brief gets the bumber of bundles around a vertex
         * \param[in] v the vertex
         * \return the number of bundles starting from \p v
         */
        index_t nb_bundles_around_vertex(index_t v) const {
            index_t result = 0;
            for(
                index_t bndl = vertex_first_bundle(v);
                bndl != NO_INDEX;
                bndl = next_around_vertex(bndl)
            ) {
                ++result;
            }
            return result;
        }

        /**
         * \brief gets the opposite bundle
         * \param[in] bndl a bundle index
         * \return the bundle connecting the same vertices as a given
         *  bundle but in the reverse order
         */
        index_t opposite(index_t bndl) {
            geo_debug_assert(bndl < nb());
            return (bndl >= nb()/2) ? (bndl-nb()/2) : (bndl+nb()/2);
        }

        /**
         * \brief gets the predecessor of a bundle along its polyline
         * \return the bundle arriving at the source vertex if it exists and
         *  is unique, NO_INDEX otherwise
         */
        index_t prev_along_polyline(index_t bndl) {
            index_t v = vertex(bndl,0);
            if(nb_bundles_around_vertex(v) != 2) {
                return NO_INDEX;
            }
            for(
                index_t bndl2 = vertex_first_bundle(v);
                bndl2 != NO_INDEX; bndl2 = next_around_vertex(bndl2)
            ) {
                if(bndl2 != bndl) {
                    return opposite(bndl2);
                }
            }
            geo_assert_not_reached;
        }

        /**
         * \brief gets the successor of a bundle along its polyline
         * \return the bundle originated at the destination vertex
         *  if it exists and is unique, NO_INDEX otherwise
         */
        index_t next_along_polyline(index_t bndl) {
            index_t v = vertex(bndl,1);
            if(nb_bundles_around_vertex(v) != 2) {
                return NO_INDEX;
            }
            for(
                index_t bndl2 = vertex_first_bundle(v);
                bndl2 != NO_INDEX; bndl2 = next_around_vertex(bndl2)
            ) {
                if(opposite(bndl2) != bndl) {
                    return bndl2;
                }
            }
            geo_assert_not_reached;
        }

        /**
         * \brief Sorts the halfedges of the bundle in-place
         * \param[in] bndl the bundle
         * \param[in] RS a RadialSort structure (that caches
         *  some information)
         * \retval true if radial sort was successful
         * \retval false otherwise (may happen with expansion_nt)
         */
        bool radial_sort(index_t bndl, RadialSort& RS) {
            geo_debug_assert(bndl < nb());
            if(nb_halfedges(bndl) <= 2) {
                return true;
            }
            auto b = H_.begin() + std::ptrdiff_t(bndl_start_[bndl]);
            auto e = H_.begin() + std::ptrdiff_t(bndl_start_[bndl+1]);
            RS.init(*b);
            std::sort(
                b, e,
                [&](index_t h1, index_t h2)->bool {
                    return RS(h1,h2);
                }
            );
            bool OK = !RS.degenerate();
            bndl_is_sorted_[bndl] = OK;
            return OK;
        }

        /**
         * \brief Sets the halfedges of a bundle
         * \details Used when radial sorting can be replaced with
         *  combinatorial propagation.
         * \param[in] bndl a bundle
         * \param[in] halfedges the sorted list of the halfedges
         *  in the bundle
         */
        void set_sorted_halfedges(
            index_t bndl, const vector<index_t>& halfedges
        ) {
            geo_debug_assert(halfedges.size() == nb_halfedges(bndl));
            for(index_t i=0; i<halfedges.size(); ++i) {
                set_halfedge(bndl, i, halfedges[i]);
            }
            bndl_is_sorted_[bndl] = true;
        }

        /**
         * \brief Indicates where to find a chart in a bundle
         * \details the first index is a chart index, and the second index
         *  indicates which halfedge in a bundle is incident to that chart.
         */
        typedef std::pair<index_t, index_t> ChartPos;

        /**
         * \brief Gets the sorted list of charts around bundle
         * \param[in] bndl a bundle
         * \param[out] chart_pos a list of (chart id, halfedge index)
         *  couples, sorted by chart id, and where the halfedge index
         *  is the original index in the bundle before sorting
         */
        void get_sorted_incident_charts(
            index_t bndl, vector<ChartPos>& chart_pos
        );

        bool is_sorted(index_t bndl) const {
            geo_assert(bndl < nb());
            return bndl_is_sorted_[bndl];
        }

        // private:
        MeshSurfaceIntersection& I_;
        Mesh& mesh_;
        Attribute<index_t> facet_chart_;
        vector<index_t> H_;
        vector<index_t> bndl_start_;
        vector<index_t> v_first_bndl_;
        vector<index_t> bndl_next_around_v_;
        vector<bool> bndl_is_sorted_;
    } radial_bundles_;

    /***************************************************/

    class RadialPolylines {
    public:
        /**
         * \brief RadialPolylines constructor
         * \param[in] I a reference to the MeshSurfaceIntersectionx
         */
        RadialPolylines(MeshSurfaceIntersection& I) : I_(I), mesh_(I.mesh_) {
        }

        /**
         * \brief Initializes the structure
         * \details Needs to be called before any other function
         */
        void initialize();

        /**
         * \brief Sorts all the bundles of all polylines
         * \details The "chart" facet attribute needs to be initialized with
         *  all surface connected components before calling this function.
         */
        void radial_sort();

        /**
         * \brief Gets the number of polylines
         */
        index_t nb() const {
            return polyline_start_.size() - 1;
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator corresponding to the first polyline
         */
        index_as_iterator begin() const {
            return index_as_iterator(0);
        }

        /**
         * \brief used by range-based for
         * \return a non-iterator to one position past the last polyline
         */
        index_as_iterator end() const {
            return index_as_iterator(nb());
        }

        /**
         * \brief gets the bundles in a polyline
         * \param[in] polyline index of the polyline
         * \return a non-modifiable sequence of bundle indices
         */
        const_index_ptr_range bundles(index_t polyline) const {
            geo_debug_assert(polyline < nb());
            return const_index_ptr_range(
                B_, polyline_start_[polyline], polyline_start_[polyline+1]
            );
        }

        index_t nb_bundles(index_t polyline) const {
            geo_debug_assert(polyline < nb());
            return polyline_start_[polyline+1] - polyline_start_[polyline];
        }

        index_t bundle(index_t polyline, index_t li) const {
            geo_debug_assert(polyline < nb());
            geo_debug_assert(li < nb_bundles(polyline));
            return B_[polyline_start_[polyline] + li];
        }

        /**
         * \brief Copies the set of polylines to a mesh
         * \details Used for visualization purposes
         * \param[out] to a mesh that will contain all the polygonal lines
         * \param[in] trim_fins if set, do not keep bundles that have
         *  less than three halfedges.
         */
        void get_skeleton(Mesh& to, bool trim_fins=false);

    private:
        MeshSurfaceIntersection& I_;
        Mesh& mesh_;
        vector<index_t> B_;
        vector<index_t> polyline_start_;
    } radial_polylines_;
    };

    /********************************************************************/

    enum MeshBooleanOperationFlags {
	MESH_BOOL_OPS_DEFAULT     = 0,
	MESH_BOOL_OPS_VERBOSE     = 1,
	MESH_BOOL_OPS_ATTRIBS     = 2,
	MESH_BOOL_OPS_NO_SIMPLIFY = 4
    };

    /**
     * \brief Computes a boolean operation with two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] operation one of "A+B", "A*B", "A-B", "B-A"
     * \param[in] flags MESH_BOOL_OPS_DEFAULT or an '|'-combination of:
     *   - MESH_BOOL_OPS_VERBOSE: displays additional information
     *   - MESH_BOOL_OPS_ATTRIBS: interpolates attributes
     *      (implies MESH_BOOL_OPS_NO_SIMPLIFY)
     *   - MESH_BOOL_OPS_NO_SIMPLIFY: do not simplify coplanar facets
     */
    void GEOGRAM_API mesh_boolean_operation(
        Mesh& result, const Mesh& A, const Mesh& B, const std::string& operation,
        MeshBooleanOperationFlags flags = MESH_BOOL_OPS_DEFAULT
    );

    /**
     * \brief Computes a boolean operation with two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] operation one of "A+B", "A*B", "A-B", "B-A"
     * \param[in] verbose if set, display additional information
     *   during computation
     */
    inline void mesh_boolean_operation(
        Mesh& result, const Mesh& A, const Mesh& B, const std::string& operation,
        bool verbose
    ) {
	mesh_boolean_operation(
	    result, A, B, operation,
	    verbose ? MESH_BOOL_OPS_VERBOSE : MESH_BOOL_OPS_DEFAULT
	);
    }

    /**
     * \brief Computes the union of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] flags MESH_BOOL_OPS_DEFAULT or an '|'-combination of:
     *   - MESH_BOOL_OPS_VERBOSE: displays additional information
     *   - MESH_BOOL_OPS_ATTRIBS: interpolates attributes
     *      (implies MESH_BOOL_OPS_NO_SIMPLIFY)
     *   - MESH_BOOL_OPS_NO_SIMPLIFY: do not simplify coplanar facets
     */
    inline void mesh_union(
        Mesh& result, const Mesh& A, const Mesh& B,
	MeshBooleanOperationFlags flags=MESH_BOOL_OPS_DEFAULT
    ) {
        mesh_boolean_operation(result, A, B, "A+B", flags);
    }

    /**
     * \brief Computes the union of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] verbose if set, display additional
     *  information during computation
     */
    inline void mesh_union(
        Mesh& result, const Mesh& A, const Mesh& B, bool verbose
    ) {
        mesh_boolean_operation(result, A, B, "A+B", verbose);
    }


    /**
     * \brief Computes the intersection of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] flags MESH_BOOL_OPS_DEFAULT or an '|'-combination of:
     *   - MESH_BOOL_OPS_VERBOSE: displays additional information
     *   - MESH_BOOL_OPS_ATTRIBS: interpolates attributes
     *      (implies MESH_BOOL_OPS_NO_SIMPLIFY)
     *   - MESH_BOOL_OPS_NO_SIMPLIFY: do not simplify coplanar facets
     */
    inline void mesh_intersection(
        Mesh& result, const Mesh& A, const Mesh& B,
	MeshBooleanOperationFlags flags=MESH_BOOL_OPS_DEFAULT
    ) {
        mesh_boolean_operation(result, A, B, "A*B", flags);
    }

    /**
     * \brief Computes the intersection of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] verbose if set, display additional information
     *  during computation
     */
    inline void mesh_intersection(
        Mesh& result, const Mesh& A, const Mesh& B, bool verbose
    ) {
        mesh_boolean_operation(result, A, B, "A*B", verbose);
    }

    /**
     * \brief Computes the difference of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] flags MESH_BOOL_OPS_DEFAULT or an '|'-combination of:
     *   - MESH_BOOL_OPS_VERBOSE: displays additional information
     *   - MESH_BOOL_OPS_ATTRIBS: interpolates attributes
     *      (implies MESH_BOOL_OPS_NO_SIMPLIFY)
     *   - MESH_BOOL_OPS_NO_SIMPLIFY: do not simplify coplanar facets
     */
    inline void mesh_difference(
        Mesh& result, const Mesh& A, const Mesh& B,
	MeshBooleanOperationFlags flags=MESH_BOOL_OPS_DEFAULT
    ) {
        mesh_boolean_operation(result, A, B, "A-B", flags);
    }

    /**
     * \brief Computes the difference of two surface meshes.
     * \details A and B need to be two closed surface
     *  mesh without intersections.
     * \param[in] A , B the two operands.
     * \param[out] result the computed mesh.
     * \param[in] verbose if set, display additional information
     *  during computation
     */
    inline void mesh_difference(
        Mesh& result, const Mesh& A, const Mesh& B, bool verbose
    ) {
        mesh_boolean_operation(result, A, B, "A-B", verbose);
    }

    /**
     * \brief Attempts to make a surface mesh conformal by
     *  removing intersecting facets and re-triangulating the holes.
     * \param[in] verbose if set, display additional information
     *  during computation
     */
    void GEOGRAM_API mesh_remove_intersections(
        Mesh& M, index_t max_iter = 3, bool verbose=false
    );

    /**
     * \brief Tests whether two mesh facets have a non-degenerate intersection.
     * \details If the facets are polygonal, they are triangulated from the
     *  first vertex, and intersections between each pair of triangles is
     *  tested.
     * \retval true if the two facets have an intersection. If they share a
     *  vertex, it does not count as an intersection.
     * \retval false otherwise.
     */
    bool GEOGRAM_API mesh_facets_have_intersection(
        Mesh& M, index_t f1, index_t f2
    );

    /**************************************************************************/
}

#endif
