#ifndef FILE_ALGPRIM
#define FILE_ALGPRIM


/**************************************************************************/
/* File:   algprim.hpp                                                    */
/* Author: Joachim Schoeberl                                              */
/* Date:   1. Dez. 95                                                     */
/**************************************************************************/

namespace netgen
{

  /*

  Quadric Surfaces (Plane, Sphere, Cylinder)
  
  */


  /**
     A quadric surface.
     surface defined by
     cxx x^2 + cyy y^2 + czz z^2 + cxy x y + cxz x z + cyz y z +
     cx x + cy y + cz z + c1 = 0.
  **/
  class QuadraticSurface : public  OneSurfacePrimitive
  {
  protected:
    double cxx, cyy, czz, cxy, cxz, cyz, cx, cy, cz, c1;

  public:
    virtual double CalcFunctionValue (const Point<3> & point) const;
    virtual void CalcGradient (const Point<3> & point, Vec<3> & grad) const;
    virtual void CalcHesse (const Point<3> & point, Mat<3> & hesse) const;
    /*
      virtual int RootInBox (const Box<3> & box) 
      const { return 0; }
      virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) 
      const { return DOES_INTERSECT; }
    */
    virtual double HesseNorm () const { return cxx + cyy + czz; }

    virtual Point<3> GetSurfacePoint () const;


    virtual void Print (ostream & ist) const;
    virtual void Read (istream & ist);
    void PrintCoeff (ostream & ost) const;
  };


  /// A Plane (i.e., the plane and everything behind it).
  class Plane : public QuadraticSurface
  {
    /// a point in the plane
    Point<3> p;
    /// outward normal vector 
    Vec<3> n;

    double eps_base;

  public:
    ///
    Plane (const Point<3> & ap, Vec<3> an);

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

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


    virtual int IsIdentic (const Surface & s2, int & inv, double eps) const;

    ///
    virtual void DefineTangentialPlane (const Point<3> & ap1, 
					const Point<3> & ap2);
    ///
    virtual void ToPlane (const Point<3> & p3d, 
			  Point<2> & pplane, double h,
			  int & zone) const;
    ///
    virtual void FromPlane (const Point<2> & pplane, 
			    Point<3> & p3d, 
			    double h) const;
    ///
    virtual void Project (Point<3> & p) const;

    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;

    ///
    inline virtual double CalcFunctionValue (const Point<3> & p3d) const
    {return cx * p3d(0) + cy * p3d(1) + cz * p3d(2) + c1;}
    ///
    virtual void CalcGradient (const Point<3> & point, 
			       Vec<3> & grad) const;
    ///
    virtual void CalcHesse (const Point<3> & point, 
			    Mat<3> & hesse) const;
    ///
    virtual double HesseNorm () const;
    ///
    virtual Point<3> GetSurfacePoint () const;
    ///
    virtual void GetTriangleApproximation 
    (TriangleApproximation & tas, 
     const Box<3> & boundingbox, double facets) const;
  protected:
    void CalcData();
  };

  // typedef Plane Plane;


  ///
  class Sphere : public QuadraticSurface
  {
    ///
    Point<3> c;
    ///
    double r, invr;
  public:
    ///
    Sphere (const Point<3> & ac, double ar);

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

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

    virtual double CalcFunctionValue (const Point<3> & point) const;


    virtual int IsIdentic (const Surface & s2, int & inv, double eps) const;

    ///
    virtual void DefineTangentialPlane (const Point<3> & ap1, 
					const Point<3> & ap2);
    ///
    virtual void ToPlane (const Point<3> & p3d, 
			  Point<2> & pplane, double h,
			  int & zone) const;
    ///
    virtual void FromPlane (const Point<2> & pplane, 
			    Point<3> & p, double h) const;
    ///
    virtual void Project (Point<3> & p) const;

    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
    ///
    virtual double HesseNorm () const;
    ///
    virtual Point<3> GetSurfacePoint () const;
    ///
    const Point<3> & Center () const { return c; }
    ///
    double Radius () const { return r; }

    ///
    virtual void GetTriangleApproximation (TriangleApproximation & tas, 
					   const Box<3> & bbox, 
					   double facets) const;
  };


  ///
  class Cylinder : public QuadraticSurface
  {
    ///
    Point<3> a, b;
    ///
    double r;
    ///
    Vec<3> vab;

  public:
    Cylinder (const Point<3> & aa, const Point<3> & ab, double ar);
    Cylinder (Array<double> & coeffs);

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

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

    ///
    virtual int IsIdentic (const Surface & s2, int & inv, double eps) const;
    ///
    virtual void DefineTangentialPlane (const Point<3> & ap1, 
					const Point<3> & ap2);
    ///
    virtual void ToPlane (const Point<3> & p, 
			  Point<2> & pplane, 
			  double h,
			  int & zone) const;
    ///
    virtual void FromPlane (const Point<2> & pplane, 
			    Point<3> & p, 
			    double h) const;
    ///
    virtual void Project (Point<3> & p) const;

    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
    ///
    virtual double HesseNorm () const;
    ///
    virtual Point<3> GetSurfacePoint () const;
    ///
    virtual void GetTriangleApproximation (TriangleApproximation & tas, 
					   const Box<3> & bbox, 
					   double facets) const;
  };





  ///
  class EllipticCylinder : public QuadraticSurface
  {
  private:
    ///
    Point<3> a;
    ///
    Vec<3> vl, vs;
    ///
    Vec<3> vab, t0vec, t1vec;
    ///
    double vabl, t0, t1;
  public:
    ///
    EllipticCylinder (const Point<3> & aa,
		      const Vec<3> & avl, const Vec<3> & avs);
    EllipticCylinder (Array<double> & coeffs);


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

    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
    ///
    virtual double HesseNorm () const;
    ///
    virtual Point<3> GetSurfacePoint () const;

    virtual void GetTriangleApproximation (TriangleApproximation & tas, 
					   const Box<3> & bbox, 
					   double facets) const;

  
    virtual double MaxCurvature () const;

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


  private:
    void CalcData();
  };






  ///
  class Ellipsoid : public QuadraticSurface
  {
  private:
    ///
    Point<3> a;
    ///
    Vec<3> v1, v2, v3;
    ///
    double rmin;
  public:
    ///
    Ellipsoid (const Point<3> & aa,
	       const Vec<3> & av1, 
	       const Vec<3> & av2,
	       const Vec<3> & av3);
    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
    ///
    virtual double HesseNorm () const;
    ///
    virtual double MaxCurvature () const;
    ///
    virtual Point<3> GetSurfacePoint () const;

    virtual void GetTriangleApproximation (TriangleApproximation & tas, 
					   const Box<3> & bbox, 
					   double facets) const;

  private:
    void CalcData();
  };








  ///
  class Cone : public QuadraticSurface
  {
    ///
    Point<3> a, b;
    ///
    double ra, rb, minr;
    ///
    Vec<3> vab, t0vec, t1vec;
    ///
    double vabl, t0, t1;
  public:
    ///
    Cone (const Point<3> & aa, const Point<3> & ab, double ara, double arb);
    ///
    static Primitive * CreateDefault ();
    virtual void GetPrimitiveData (const char *& classname, Array<double> & coeffs) const;
    virtual void SetPrimitiveData (Array<double> & coeffs);

    ///
    virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
    ///
    virtual double HesseNorm () const;

    virtual double LocH (const Point<3> & p, double x, 
			 double c, double hmax) const;

    ///
    virtual Point<3> GetSurfacePoint () const;

    virtual void GetTriangleApproximation (TriangleApproximation & tas, 
					   const Box<3> & bbox, 
					   double facets) const;

  private:
    void CalcData();
  };








  /// Torus 
	       /// Lorenzo Codecasa (codecasa@elet.polimi.it)
	       /// April 27th, 2005 
	       /// 
	       /// begin...
	       class Torus : public OneSurfacePrimitive
	       { 
		 /// center of the torus
		 Point<3> c;
		 /// vector normal to the symmetry plane of the torus
		 Vec<3> n;
		 /// Large radius of the torus
		 double R;
		 /// Small radius of the torus
		 double r;
  
	       public:
		 /// OK
		 Torus (const Point<3> & ac, const Vec<3> & an, double aR, double ar);
		 /// OK
		 const Point<3> & Center () const { return c; }
		 /// OK
		 const Vec<3> & NormalToPlane () const { return n; }
		 /// OK
		 double LargeRadius () const { return R; }
		 /// OK
		 double SmallRadius () const { return r; }
		 /// OK
		 virtual double CalcFunctionValue (const Point<3> & point) const;
		 /// OK
		 virtual void CalcGradient (const Point<3> & point, Vec<3> & grad) const;
		 /// OK
		 virtual void CalcHesse (const Point<3> & point, Mat<3> & hesse) const;
		 /// OK
		 virtual double HesseNorm () const;
		 /// OK
		 virtual Point<3> GetSurfacePoint () const;
		 /// OK
		 virtual void GetPrimitiveData (const char *& classname, 
						Array<double> & coeffs) const;
		 /// OK			 
		 virtual void SetPrimitiveData (Array<double> & coeffs);
		 /// OK
		 static Primitive * CreateDefault ();
		 /// OK
		 virtual Primitive * Copy () const;
		 /// OK
		 virtual void Transform (Transformation<3> & trans);
		 /// OK
		 virtual int IsIdentic (const Surface & s2, int & inv, double eps) const;
		 /// OK
		 /// virtual void DefineTangentialPlane (const Point<3> & ap1, 
		 //				      const Point<3> & ap2);
		 /// OK
		 /// virtual void ToPlane (const Point<3> & p3d, 
		 ///			Point<2> & pplane, 
		 ///			double h, int & zone) const;
		 /// OK
		 /// virtual void FromPlane (const Point<2> & pplane, 
		 //			  Point<3> & p, double h) const;
		 /// OK
		 /// virtual void Project (Point<3> & p) const;
		 /// OK
		 virtual INSOLID_TYPE BoxInSolid (const BoxSphere<3> & box) const;
		 /// OK
		 virtual void GetTriangleApproximation (TriangleApproximation & tas, 
							const Box<3> & bbox, 
							double facets) const;
		 /// OK		 
		 virtual void Print (ostream & ist) const;
		 /// OK
		 virtual void Read (istream & ist);
	       };

  /// ...end


}





#endif