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       1                 :            : /* *****************************************************************
       2                 :            :     MESQUITE -- The Mesh Quality Improvement Toolkit
       3                 :            : 
       4                 :            :     Copyright 2006 Sandia National Laboratories.  Developed at the
       5                 :            :     University of Wisconsin--Madison under SNL contract number
       6                 :            :     624796.  The U.S. Government and the University of Wisconsin
       7                 :            :     retain certain rights to this software.
       8                 :            : 
       9                 :            :     This library is free software; you can redistribute it and/or
      10                 :            :     modify it under the terms of the GNU Lesser General Public
      11                 :            :     License as published by the Free Software Foundation; either
      12                 :            :     version 2.1 of the License, or (at your option) any later version.
      13                 :            : 
      14                 :            :     This library is distributed in the hope that it will be useful,
      15                 :            :     but WITHOUT ANY WARRANTY; without even the implied warranty of
      16                 :            :     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      17                 :            :     Lesser General Public License for more details.
      18                 :            : 
      19                 :            :     You should have received a copy of the GNU Lesser General Public License
      20                 :            :     (lgpl.txt) along with this library; if not, write to the Free Software
      21                 :            :     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      22                 :            : 
      23                 :            :     (2006) [email protected]
      24                 :            : 
      25                 :            :   ***************************************************************** */
      26                 :            : 
      27                 :            : /** \file TriLagrangeShape.hpp
      28                 :            :  *  \brief
      29                 :            :  *  \author Jason Kraftcheck
      30                 :            :  */
      31                 :            : 
      32                 :            : #ifndef MSQ_TRI_LAGRANGE_SHAPE_HPP
      33                 :            : #define MSQ_TRI_LAGRANGE_SHAPE_HPP
      34                 :            : 
      35                 :            : #include "Mesquite.hpp"
      36                 :            : #include "MappingFunction.hpp"
      37                 :            : 
      38                 :            : namespace MBMesquite
      39                 :            : {
      40                 :            : 
      41                 :            : /**\brief Lagrange shape function for triangle elements
      42                 :            :  *
      43                 :            :  * This class implements the MappingFunction interface, providing
      44                 :            :  * a Lagrange shape function for 6-node triangle.
      45                 :            :  *
      46                 :            :  * \f$\vec{x}(r,s) = sum_{i=0}^{n-1} N_i(r,s) \vec{x_i}\f$
      47                 :            :  *
      48                 :            :  * \f$N_1 = t(2t - 1)\f$
      49                 :            :  *
      50                 :            :  * \f$N_2 = r(2r - 1)\f$
      51                 :            :  *
      52                 :            :  * \f$N_3 = s(2s - 1)\f$
      53                 :            :  *
      54                 :            :  * \f$N_4 = 4rt\f$
      55                 :            :  *
      56                 :            :  * \f$N_5 = 4rs\f$
      57                 :            :  *
      58                 :            :  * \f$N_6 = 4st\f$
      59                 :            :  *
      60                 :            :  * \f$t = 1 - r - s\f$
      61                 :            :  */
      62         [ -  + ]:        394 : class MESQUITE_EXPORT TriLagrangeShape : public MappingFunction2D
      63                 :            : {
      64                 :            :   public:
      65                 :            :     virtual EntityTopology element_topology() const;
      66                 :            : 
      67                 :            :     virtual int num_nodes() const;
      68                 :            : 
      69                 :            :     virtual NodeSet sample_points( NodeSet higher_order_nodes ) const;
      70                 :            : 
      71                 :            :     virtual void coefficients( Sample location, NodeSet nodeset, double* coeff_out, size_t* indices_out,
      72                 :            :                                size_t& num_coeff_out, MsqError& err ) const;
      73                 :            : 
      74                 :            :     virtual void derivatives( Sample location, NodeSet nodeset, size_t* vertex_indices_out,
      75                 :            :                               MsqVector< 2 >* d_coeff_d_xi_out, size_t& num_vtx, MsqError& err ) const;
      76                 :            : 
      77                 :            :     virtual void ideal( Sample location, MsqMatrix< 3, 2 >& jacobian_out, MsqError& err ) const;
      78                 :            : };
      79                 :            : 
      80                 :            : }  // namespace MBMesquite
      81                 :            : 
      82                 :            : #endif