/* ***************************************************************** 
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2006 Lawrence Livermore National Laboratory.  Under 
    the terms of Contract B545069 with the University of Wisconsin -- 
    Madison, Lawrence Livermore National Laboratory retains certain
    rights in this software.

    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 
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA

    (2006) kraftche@cae.wisc.edu    

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

/** \file LinearPrism.hpp
 *  \brief mapping function for linear prism
 *  \author Jason Kraftcheck 
 */

#ifndef MSQ_LINEAR_PRISM_HPP
#define MSQ_LINEAR_PRISM_HPP

#include "Mesquite.hpp"
#include "Mesquite_MappingFunction.hpp"

namespace MESQUITE_NS {

/**\brief Linear mapping function for a prism element
 *
 * \f$ \vec{x}(\vec{\xi})=\sum_{i=1}^6 N_i(\vec{\xi})\vec{x_i} \f$
 * - \f$ N_1(\vec{\xi})=(1-\xi)(1-\eta-\zeta) \f$
 * - \f$ N_2(\vec{\xi})=(1-\xi)(\eta)         \f$
 * - \f$ N_3(\vec{\xi})=(1-\xi)(\zeta)        \f$
 * - \f$ N_4(\vec{\xi})=(  \xi)(1-\eta-\zeta) \f$
 * - \f$ N_5(\vec{\xi})=(  \xi)(\eta)         \f$
 * - \f$ N_6(\vec{\xi})=(  \xi)(\zeta)        \f$
 * \f$ \xi,\eta,\zeta \in [0,1] \f$
 * \f$ \eta + \zeta \leq 1 \f$
 *
 * The logical center of the element is at: 
 * \f$ (\xi,\eta,\zeta) = (0,\frac{1}{3},\frac{1}{3}) \f$
 */ 
class MESQUITE_EXPORT LinearPrism : public MappingFunction3D
{
public:

  virtual
  EntityTopology element_topology() const;
  
  virtual
  int num_nodes() const;
  
  virtual 
  void coefficients( Sample location,
                     NodeSet nodeset,
                     double* coeff_out,
                     size_t* indices_out,
                     size_t& num_coeff_out,
                     MsqError& err ) const;
  
  virtual 
  void derivatives( Sample location,
                    NodeSet nodeset,
                    size_t* vertex_indices_out,
                    MsqVector<3>* d_coeff_d_xi_out,
                    size_t& num_vtx,
                    MsqError& err ) const;

  virtual
  void ideal( Sample location, 
              MsqMatrix<3,3>& jacobian_out,
              MsqError& err ) const;
};



} // namespace Mesquite

#endif
