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// $Id: quadrature_conical.h 3874 2010-07-02 21:57:26Z roystgnr $

// The libMesh Finite Element Library.
// Copyright (C) 2002-2008 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
  
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
  
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
  
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA


#ifndef __quadrature_conical_h__
#define __quadrature_conical_h__

// Local includes
#include "quadrature.h"

namespace libMesh
{

/**
 * This class implements the so-called conical product quadrature
 * rules for Tri and Tet elements. These rules are generally
 * non-optimal in the number of evaluation points, but have the nice
 * property of having all positive weights and being well-defined to
 * any order for which their underlying 1D Gauss and Jacobi quadrature
 * rules are available.
 *
 * The construction of these rules is given by e.g.
 *
 * Stroud, A.H. "Approximate Calculation of
 * Multiple Integrals.", 1972
 */
class QConical : public QBase
{
 public:

  /**
   * Constructor.  Declares the order of the quadrature rule.
   */
  QConical (const unsigned int _dim,
	    const Order _order=INVALID_ORDER);

  /**
   * Destructor.
   */
  ~QConical();

  /**
   * @returns the QuadratureType for this class
   */
  QuadratureType type() const { return QCONICAL; }

 private:

  void init_1D (const ElemType,
		unsigned int =0)
  {
    // See about making this non-pure virtual in the base class
    libmesh_error();
  }

  /**
   * The conical product rules are defined in 2D only for Tris.
   */
  void init_2D (const ElemType _type=INVALID_ELEM,
		unsigned int p_level=0);
  /**
   * The conical product rules are defined in 3D only for Tets.
   */
  void init_3D (const ElemType _type=INVALID_ELEM,
		unsigned int p_level=0);

  /**
   * Implementation of conical product rule for a Tri in 2D of
   * order = _order+2*p.
   */
  void conical_product_tri(unsigned int p);

  /**
   * Implementation of conical product rule for a Tet in 3D of
   * order = _order+2*p.
   */
  void conical_product_tet(unsigned int p);

  /**
   * Implementation of conical product rule for a Pyramid in 3D of
   * order = _order+2*p.
   */
  void conical_product_pyramid(unsigned int p);
};


} // namespace libMesh

#endif // #ifndef __quadrature_conical_h__