#ifndef FILE_SURFACE
#define FILE_SURFACE

/**************************************************************************/
/* File:   surface.hh                                                     */
/* Author: Joachim Schoeberl                                              */
/* Date:   1. Dez. 95                                                     */
/**************************************************************************/


namespace netgen 
{

  class TriangleApproximation;


  /**
     Basis class for implicit surface geometry.
     This class is used for generation of surface meshes
     in NETGEN 
  */
  class Surface
  {
  protected:
    /// invert normal vector
    bool inverse;
    /// maximal h in surface
    double maxh;
    /// name of surface
    char * name;
    /// boundary condition nr
    int bcprop;
    /// boundary condition label
    string bcname;
  
  public:
    Surface ();
    /** @name Tangential plane.
	The tangential plane is used for surface mesh generation.
    */
  
    virtual ~Surface();

  protected:
    /** @name Points in the surface defining tangential plane.
	Tangential plane is taken in p1, the local x-axis
	is directed to p2.
    */
    //@{
    ///
    Point<3> p1;
    ///
    Point<3> p2;
    //@}
    /** @name Base-vectos for local coordinate system. */
    //@{
    /// in plane, directed p1->p2
    Vec<3> ex;
    /// in plane
    Vec<3> ey;
    /// outer normal direction
    Vec<3> ez;
    //@}
  public:

    void SetName (const char * aname);
    const char * Name () const { return name; }

    //@{
    /**
       Defines tangential plane in ap1.
       The local x-coordinate axis points to the direction of ap2 */
    virtual void DefineTangentialPlane (const Point<3> & ap1, 
					const Point<3> & ap2);

    /// Transforms 3d point p3d to local coordinates pplane
    virtual void ToPlane (const Point<3> & p3d, Point<2> & pplane, 
			  double h, int & zone) const;
  
    /// Transforms point pplane in local coordinates to 3d point
    virtual void FromPlane (const Point<2> & pplane, 
			    Point<3> & p3d, double h) const;
    //@}


    /// Project point p onto surface (closest point)
    virtual void Project (Point<3> & p) const;

    /// Project along direction
    virtual void SkewProject(Point<3> & p, const Vec<3> & direction) const;

    /// Is current surface identic to surface 2 ?
    virtual int IsIdentic (const Surface & /* s2 */, int & /* inv */, 
			   double /* eps */) const
    { return 0; }
  
    ///
    virtual int PointOnSurface (const Point<3> & p,
				double eps = 1e-6) const;
  

    /** @name Implicit function.
	Calculate function value and derivatives.
    */
    //@{
    /// Calculate implicit function value in point point
    virtual double CalcFunctionValue (const Point<3> & point) const = 0;

    /**
       Calc gradient of implicit function.
       gradient should be O(1) at surface
    */
    virtual void CalcGradient (const Point<3> & point, Vec<3> & grad) const = 0;

    /**
       Calculate second derivatives of implicit function.
    */
    virtual void CalcHesse (const Point<3> & point, Mat<3> & hesse) const;

    /**
       Returns outer normal vector.
    */
    // virtual void GetNormalVector (const Point<3> & p, Vec<3> & n) const;
    virtual Vec<3> GetNormalVector (const Point<3> & p) const;

    /**
       Upper bound for spectral norm of Hesse-matrix
    */
    virtual double HesseNorm () const = 0;

    /**
       Upper bound for spectral norm of Hesse-matrix in the
       rad - environment of point c.
    */
    virtual double HesseNormLoc (const Point<3> & /* c */, 
				 double /* rad */) const
    { return HesseNorm (); }
    //@}


    ///
    virtual double MaxCurvature () const;
    ///
    virtual double MaxCurvatureLoc (const Point<3> & /* c */ , 
				    double /* rad */) const;

    /** Returns any point in the surface.
	Needed to start surface mesh generation e.g. on sphere */
    virtual Point<3> GetSurfacePoint () const = 0;

    ///
    bool Inverse () const { return inverse; }
    ///
    void SetInverse (bool ainverse) { inverse = ainverse; }
    /// 
    virtual void Print (ostream & str) const = 0;
  
    ///
    virtual void Reduce (const BoxSphere<3> & /* box */) { };
    ///
    virtual void UnReduce () { };

    /// set max h in surface
    void SetMaxH (double amaxh) { maxh = amaxh; }
    ///
    double GetMaxH () const { return maxh; }
    ///
    int GetBCProperty () const { return bcprop; }
    ///
    void SetBCProperty (int abc) { bcprop = abc; }

    /** Determine local mesh-size.
	Find 
	\[ h \leq hmax, \]
	such that
	\[ h  \times \kappa (x) \leq c \qquad \mbox{in} B(x, h), \]
	where kappa(x) is the curvature in x. */
    virtual double LocH (const Point<3> & p, double x, 
			 double c, double hmax) const;

    /**
       Gets Approximation by triangles,
       where qual is about the number of triangles per radius
    */
    virtual void GetTriangleApproximation (TriangleApproximation & /* tas */, 
					   const Box<3> & /* boundingbox */, 
					   double /* facets */ ) const { };


    string GetBCName() const { return bcname; }

    void SetBCName( string abc ) { bcname = abc; }
  };


  inline ostream & operator<< (ostream & ost, const Surface & surf)
  {
    surf.Print(ost);
    return ost;
  }



  typedef enum { IS_OUTSIDE = 0, IS_INSIDE = 1, DOES_INTERSECT = 2}
    INSOLID_TYPE;




  class DummySurface : public Surface
  {
    virtual double CalcFunctionValue (const Point<3> & /* point */) const
    { return 0; }

    virtual void CalcGradient (const Point<3> & /* point */, Vec<3> & grad) const
    { grad = Vec<3> (0,0,0); }
  
    virtual Point<3> GetSurfacePoint () const
    { return Point<3> (0,0,0); }

    virtual double HesseNorm () const
    { return 0; }

    virtual void Project (Point<3> & /* p */) const
    { ; }

    virtual void Print (ostream & ost) const
    { ost << "dummy surface"; }
  };



  class Primitive
  {

  public:

    Primitive ();

    virtual ~Primitive();

  
    /*
      Check, whether box intersects solid defined by surface.

      return values:
      0 .. box outside solid \\
      1 .. box in solid \\
      2 .. can't decide (allowed, iff box is close to solid)
    */
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const = 0;
    virtual INSOLID_TYPE PointInSolid (const Point<3> & p,
				       double eps) const = 0;

    virtual void GetTangentialSurfaceIndices (const Point<3> & p, 
					      Array<int> & surfind, double eps) const;

    virtual INSOLID_TYPE VecInSolid (const Point<3> & p,
				     const Vec<3> & v,
				     double eps) const = 0;

    // checks if lim s->0 lim t->0  p + t(v1 + s v2) in solid
    virtual INSOLID_TYPE VecInSolid2 (const Point<3> & p,
				      const Vec<3> & v1,
				      const Vec<3> & v2,
				      double eps) const;

    // checks if  p + s v1 + s*s/2 v2 is inside
    virtual INSOLID_TYPE VecInSolid3 (const Point<3> & p,
				      const Vec<3> & v1,
				      const Vec<3> & v2,
				      double eps) const;

    // like VecInSolid2, but second order approximation
    virtual INSOLID_TYPE VecInSolid4 (const Point<3> & p,
				      const Vec<3> & v,
				      const Vec<3> & v2,
				      const Vec<3> & m,
				      double eps) const;

    virtual void GetTangentialVecSurfaceIndices (const Point<3> & p, const Vec<3> & v,
						 Array<int> & surfind, double eps) const;

    virtual void GetTangentialVecSurfaceIndices2 (const Point<3> & p, const Vec<3> & v1, const Vec<3> & v2,
						  Array<int> & surfind, double eps) const;


    virtual void CalcSpecialPoints (Array<Point<3> > & /* pts */) const { ; }
    virtual void AnalyzeSpecialPoint (const Point<3> & /* pt */, 
				      Array<Point<3> > & /* specpts */) const { ; }
    virtual Vec<3> SpecialPointTangentialVector (const Point<3> & /* p */, 
						 int /* s1 */, int /* s2 */) const 
    { return Vec<3> (0,0,0); }

  
    virtual int GetNSurfaces() const = 0;
    virtual Surface & GetSurface (int i = 0) = 0;
    virtual const Surface & GetSurface (int i = 0) const = 0;

    Array<int> surfaceids;
    Array<int> surfaceactive;

    int GetSurfaceId (int i = 0) const;
    void SetSurfaceId (int i, int id);
    int SurfaceActive (int i) const { return surfaceactive[i]; }
    virtual int SurfaceInverted (int /* i */ = 0) const { return 0; }

    virtual void GetPrimitiveData (const char *& classname, 
				   Array<double> & coeffs) const;
    virtual void SetPrimitiveData (Array<double> & coeffs);
    static Primitive * CreatePrimitive (const char * classname);


    virtual void Reduce (const BoxSphere<3> & /* box */) { };
    virtual void UnReduce () { };

    virtual Primitive * Copy () const;
    virtual void Transform (Transformation<3> & trans);
  };




  class OneSurfacePrimitive : public Surface, public Primitive
  {
  public:
    OneSurfacePrimitive();
    ~OneSurfacePrimitive();

    virtual INSOLID_TYPE PointInSolid (const Point<3> & p,
				       double eps) const;
    virtual INSOLID_TYPE VecInSolid (const Point<3> & p,
				     const Vec<3> & v,
				     double eps) const;
    virtual INSOLID_TYPE VecInSolid2 (const Point<3> & p,
				      const Vec<3> & v1,
				      const Vec<3> & v2,
				      double eps) const;

    virtual INSOLID_TYPE VecInSolid3 (const Point<3> & p,
				      const Vec<3> & v1,
				      const Vec<3> & v2,
				      double eps) const;

    virtual INSOLID_TYPE VecInSolid4 (const Point<3> & p,
				      const Vec<3> & v,
				      const Vec<3> & v2,
				      const Vec<3> & m,
				      double eps) const;

    virtual int GetNSurfaces() const;
    virtual Surface & GetSurface (int i = 0);
    virtual const Surface & GetSurface (int i = 0) const;
  };






  /**
     Projects point to edge.
     The point hp is projected to the edge descibed by f1 and f2.
     It is assumed that the edge is non-degenerated, and the
     (generalized) Newton method converges.
  */
  extern void ProjectToEdge (const Surface * f1, 
			     const Surface * f2,
			     Point<3> & hp);


}

#endif
