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/** \author Jia Pan */

#ifndef HPP_FCL_GJK_H
#define HPP_FCL_GJK_H

#include <vector>

#include <hpp/fcl/shape/geometric_shapes.h>
#include <hpp/fcl/math/transform.h>

namespace hpp
{
namespace fcl
{

namespace details
{

/// @brief the support function for shape
/// \param hint use to initialize the search when shape is a ConvexBase object.
Vec3f getSupport(const ShapeBase* shape, const Vec3f& dir, bool dirIsNormalized, int& hint); 

/// @brief Minkowski difference class of two shapes
///
/// @note The Minkowski difference is expressed in the frame of the first shape.
struct HPP_FCL_DLLAPI MinkowskiDiff
{
  /// @brief points to two shapes
  const ShapeBase* shapes[2];

  struct ShapeData {
    std::vector<int8_t> visited;
  };

  /// @brief Store temporary data for the computation of the support point for
  /// each shape.
  ShapeData data[2];

  /// @brief rotation from shape1 to shape0
  /// such that @f$ p_in_0 = oR1 * p_in_1 + ot1 @f$.
  Matrix3f oR1;

  /// @brief translation from shape1 to shape0
  /// such that @f$ p_in_0 = oR1 * p_in_1 + ot1 @f$.
  Vec3f ot1;

  /// @brief The radius of the sphere swepted volume.
  /// The 2 values correspond to the inflation of shape 0 and shape 1.
  Eigen::Array<FCL_REAL, 1, 2> inflation;

  /// @brief Number of points in a Convex object from which using a logarithmic
  /// support function is faster than a linear one.
  /// It defaults to 32.
  /// \note It must set before the call to \ref set.
  int linear_log_convex_threshold;

  typedef void (*GetSupportFunction) (const MinkowskiDiff& minkowskiDiff,
      const Vec3f& dir, bool dirIsNormalized, Vec3f& support0, Vec3f& support1,
      support_func_guess_t& hint, ShapeData data[2]);
  GetSupportFunction getSupportFunc;

  MinkowskiDiff() : linear_log_convex_threshold (32), getSupportFunc (NULL) {}

  /// Set the two shapes,
  /// assuming the relative transformation between them is identity.
  void set (const ShapeBase* shape0, const ShapeBase* shape1);

  /// Set the two shapes, with a relative transformation.
  void set (const ShapeBase* shape0, const ShapeBase* shape1,
      const Transform3f& tf0, const Transform3f& tf1);

  /// @brief support function for shape0
  inline Vec3f support0(const Vec3f& d, bool dIsNormalized, int& hint) const
  {
    return getSupport(shapes[0], d, dIsNormalized, hint);
  }

  /// @brief support function for shape1
  inline Vec3f support1(const Vec3f& d, bool dIsNormalized, int& hint) const
  {
    return oR1 * getSupport(shapes[1], oR1.transpose() * d, dIsNormalized, hint) + ot1;
  }

  /// @brief support function for the pair of shapes
  inline void support(const Vec3f& d, bool dIsNormalized, Vec3f& supp0, Vec3f& supp1, support_func_guess_t& hint) const
  {
    assert(getSupportFunc != NULL);
    getSupportFunc(*this, d, dIsNormalized, supp0, supp1, hint, const_cast<ShapeData*>(data));
  }
};

/// @brief class for GJK algorithm
///
/// @note The computations are performed in the frame of the first shape.
struct HPP_FCL_DLLAPI GJK
{
  struct HPP_FCL_DLLAPI SimplexV
  {
    /// @brief support vector for shape 0 and 1.
    Vec3f w0, w1; 
    /// @brief support vector (i.e., the furthest point on the shape along the support direction)
    Vec3f w;
  };

  typedef unsigned char vertex_id_t;

  struct HPP_FCL_DLLAPI Simplex
  {
    /// @brief simplex vertex
    SimplexV* vertex[4];
    /// @brief size of simplex (number of vertices)
    vertex_id_t rank;

    Simplex() {}
  };

  enum Status {Valid, Inside, Failed};

  MinkowskiDiff const* shape;
  Vec3f ray;
  support_func_guess_t support_hint;
  /// The distance computed by GJK. The possible values are
  /// - \f$ d = - R - 1 \f$ when a collision is detected and GJK
  ///   cannot compute penetration informations.
  /// - \f$ - R \le d \le 0 \f$ when a collision is detected and GJK can
  ///   compute penetration informations.
  /// - \f$ 0 < d \le d_{ub} \f$ when there is no collision and GJK can compute
  ///   the closest points.
  /// - \f$ d_{ub} < d \f$ when there is no collision and GJK cannot compute the
  ///   closest points.
  ///
  /// where \f$ d \f$ is the GJK::distance, \f$ R \f$ is the sum of the \c shape
  /// MinkowskiDiff::inflation and \f$ d_{ub} \f$ is the
  /// GJK::distance_upper_bound.
  FCL_REAL distance;
  Simplex simplices[2];


  /// \param max_iterations_ number of iteration before GJK returns failure.
  /// \param tolerance_ precision of the algorithm.
  ///
  /// The tolerance argument is useful for continuous shapes and for polyhedron
  /// with some vertices closer than this threshold.
  ///
  /// Suggested values are 100 iterations and a tolerance of 1e-6.
  GJK(unsigned int max_iterations_, FCL_REAL tolerance_)  : max_iterations(max_iterations_),
                                                            tolerance(tolerance_)
  {
    initialize(); 
  }
  
  void initialize();

  /// @brief GJK algorithm, given the initial value guess
  Status evaluate(const MinkowskiDiff& shape, const Vec3f& guess,
      const support_func_guess_t& supportHint = support_func_guess_t::Zero());

  /// @brief apply the support function along a direction, the result is return in sv
  inline void getSupport(const Vec3f& d, bool dIsNormalized, SimplexV& sv,
      support_func_guess_t& hint) const
  {
    shape->support(d, dIsNormalized, sv.w0, sv.w1, hint);
    sv.w.noalias() = sv.w0 - sv.w1;
  }

  /// @brief whether the simplex enclose the origin
  bool encloseOrigin();

  /// @brief get the underlying simplex using in GJK, can be used for cache in next iteration
  inline Simplex* getSimplex() const
  {
    return simplex;
  }

  /// Tells whether the closest points are available.
  bool hasClosestPoints ()
  {
    return distance < distance_upper_bound;
  }

  /// Tells whether the penetration information.
  ///
  /// In such case, most indepth points and penetration depth can be retrieved
  /// from GJK. Calling EPA has an undefined behaviour.
  bool hasPenetrationInformation (const MinkowskiDiff& shape)
  {
    return distance > - shape.inflation.sum();
  }

  /// Get the closest points on each object.
  /// @return true on success
  bool getClosestPoints (const MinkowskiDiff& shape, Vec3f& w0, Vec3f& w1);

  /// @brief get the guess from current simplex
  Vec3f getGuessFromSimplex() const;

  /// @brief Distance threshold for early break.
  /// GJK stops when it proved the distance is more than this threshold.
  /// @note The closest points will be erroneous in this case.
  ///       If you want the closest points, set this to infinity (the default).
  void setDistanceEarlyBreak (const FCL_REAL& dup)
  {
    distance_upper_bound = dup;
  }

private:
  SimplexV store_v[4];
  SimplexV* free_v[4];
  vertex_id_t nfree;
  vertex_id_t current;
  Simplex* simplex;
  Status status;

  unsigned int max_iterations;
  FCL_REAL tolerance;
  FCL_REAL distance_upper_bound;

  /// @brief discard one vertex from the simplex
  inline void removeVertex(Simplex& simplex);

  /// @brief append one vertex to the simplex
  inline void appendVertex(Simplex& simplex, const Vec3f& v, bool isNormalized,
      support_func_guess_t& hint);

  /// @brief Project origin (0) onto line a-b
  bool projectLineOrigin(const Simplex& current, Simplex& next);

  /// @brief Project origin (0) onto triangle a-b-c
  bool projectTriangleOrigin(const Simplex& current, Simplex& next);

  /// @brief Project origin (0) onto tetrahedran a-b-c-d
  bool projectTetrahedraOrigin(const Simplex& current, Simplex& next);
};


static const size_t EPA_MAX_FACES = 128;
static const size_t EPA_MAX_VERTICES = 64;
static const FCL_REAL EPA_EPS = 0.000001;
static const size_t EPA_MAX_ITERATIONS = 255;

/// @brief class for EPA algorithm
struct HPP_FCL_DLLAPI EPA
{
  typedef GJK::SimplexV SimplexV;
  struct HPP_FCL_DLLAPI SimplexF
  {
    Vec3f n;
    FCL_REAL d;
    SimplexV* vertex[3]; // a face has three vertices
    SimplexF* f[3]; // a face has three adjacent faces
    SimplexF* l[2]; // the pre and post faces in the list
    size_t e[3];
    size_t pass;

    SimplexF () : n(Vec3f::Zero()) {};
  };

  struct HPP_FCL_DLLAPI SimplexList
  {
    SimplexF* root;
    size_t count;
    SimplexList() : root(NULL), count(0) {}
    void append(SimplexF* face)
    {
      face->l[0] = NULL;
      face->l[1] = root;
      if(root) root->l[0] = face;
      root = face;
      ++count;
    }

    void remove(SimplexF* face)
    {
      if(face->l[1]) face->l[1]->l[0] = face->l[0];
      if(face->l[0]) face->l[0]->l[1] = face->l[1];
      if(face == root) root = face->l[1];
      --count;
    }
  };

  static inline void bind(SimplexF* fa, size_t ea, SimplexF* fb, size_t eb)
  {
    fa->e[ea] = eb; fa->f[ea] = fb;
    fb->e[eb] = ea; fb->f[eb] = fa;
  }

  struct HPP_FCL_DLLAPI SimplexHorizon
  {
    SimplexF* cf; // current face in the horizon
    SimplexF* ff; // first face in the horizon
    size_t nf; // number of faces in the horizon
    SimplexHorizon() : cf(NULL), ff(NULL), nf(0) {}
  };

private:
  unsigned int max_face_num;
  unsigned int max_vertex_num;
  unsigned int max_iterations;
  FCL_REAL tolerance;

public:

  enum Status {
    Failed              = 0,
    Valid               = 1,
    AccuracyReached     = 1 << 1 | Valid ,
    Degenerated         = 1 << 1 | Failed,
    NonConvex           = 2 << 1 | Failed,
    InvalidHull         = 3 << 1 | Failed,
    OutOfFaces          = 4 << 1 | Failed,
    OutOfVertices       = 5 << 1 | Failed,
    FallBack            = 6 << 1 | Failed
  };
  
  Status status;
  GJK::Simplex result;
  Vec3f normal;
  FCL_REAL depth;
  SimplexV* sv_store;
  SimplexF* fc_store;
  size_t nextsv;
  SimplexList hull, stock;

  EPA(unsigned int max_face_num_, unsigned int max_vertex_num_, unsigned int max_iterations_, FCL_REAL tolerance_) : max_face_num(max_face_num_),
                                                                                                                     max_vertex_num(max_vertex_num_),
                                                                                                                     max_iterations(max_iterations_),
                                                                                                                     tolerance(tolerance_)
  {
    initialize();
  }

  ~EPA()
  {
    delete [] sv_store;
    delete [] fc_store;
  }

  void initialize();

  /// \return a Status which can be demangled using (status & Valid) or
  ///         (status & Failed). The other values provide a more detailled
  ///         status
  Status evaluate(GJK& gjk, const Vec3f& guess);

  /// Get the closest points on each object.
  /// @return true on success
  bool getClosestPoints (const MinkowskiDiff& shape, Vec3f& w0, Vec3f& w1);

private:
  bool getEdgeDist(SimplexF* face, SimplexV* a, SimplexV* b, FCL_REAL& dist);

  SimplexF* newFace(SimplexV* a, SimplexV* b, SimplexV* vertex, bool forced);

  /// @brief Find the best polytope face to split
  SimplexF* findBest();

  /// @brief the goal is to add a face connecting vertex w and face edge f[e] 
  bool expand(size_t pass, SimplexV* w, SimplexF* f, size_t e, SimplexHorizon& horizon);  
};


} // details



}


} // namespace hpp

#endif
