TargetMetricUtil.hpp

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

    Copyright 2007 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2007) kraftche@cae.wisc.edu

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

/** \file TargetMetricUtil.hpp
 *  \brief A collection of utility code used by QualtiyMetrics
 *         composed of TMP Target Metrics
 *  \author Jason Kraftcheck
 */

#ifndef MSQ_TARGET_METRIC_UTIL_HPP
#define MSQ_TARGET_METRIC_UTIL_HPP

#include "Mesquite.hpp"
#include "SymMatrix3D.hpp"
#include <vector>
#include <cassert>

namespace MBMesquite
{

template < unsigned R, unsigned C >
class MsqMatrix;
template < unsigned C >
class MsqVector;
class PatchData;
class MsqError;
class Vector3D;
class Matrix3D;

/**\brief Calculate R and Z such that \f$W\prime = Z^{-1} W\f$ and
 *        \f$A\prime = (RZ)^{-1} A\f$
 *
 * Calculate the matrices required to transform the active and target
 * matrices from the 3x2 surface domain to a 2x2 2D domain.
 *\param A    Input: Element Jacobian matrix.
 *\param W_32 Input: Target Jacobian matrix.
 *\param W_22 Output: 2D Target matrix.
 *\param RZ   Output: Product of R and Z needed to calculate the 2D
 *            element matrix.
 */
void surface_to_2d( const MsqMatrix< 3, 2 >& A,
                    const MsqMatrix< 3, 2 >& W_32,
                    MsqMatrix< 2, 2 >& W_22,
                    MsqMatrix< 3, 2 >& RZ );
/*
void surface_to_2d( const MsqMatrix<3,2>& A_in,
                    const MsqMatrix<3,2>& W_in,
                    MsqMatrix<2,2>& A_out,
                    MsqMatrix<2,2>& W_out );
*/
void get_sample_pt_evaluations( PatchData& pd, std::vector< size_t >& handles, bool free, MsqError& err );

void get_elem_sample_points( PatchData& pd, size_t elem, std::vector< size_t >& handles, MsqError& err );

/**\brief Calculate gradient from derivatives of mapping function terms
 *        and derivatives of target metric. */
template < int DIM >
inline void gradient( size_t num_free_verts,
                      const MsqVector< DIM >* dNdxi,
                      const MsqMatrix< 3, DIM >& dmdA,
                      std::vector< Vector3D >& grad )
{
    grad.clear();
    grad.resize( num_free_verts, Vector3D( 0, 0, 0 ) );
    for( size_t i = 0; i < num_free_verts; ++i )
        grad[i] = Vector3D( ( dmdA * dNdxi[i] ).data() );
}

/**\brief Calculate Hessian from derivatives of mapping function terms
 *        and derivatives of target metric. */
template < int DIM, typename MAT >
inline void hessian( size_t num_free_verts,
                     const MsqVector< DIM >* dNdxi,
                     const MsqMatrix< DIM, DIM >* d2mdA2,
                     MAT* hess )
{
    MsqMatrix< 1, DIM > tmp[DIM][DIM];
    size_t h = 0;  // index of current Hessian block

    for( size_t i = 0; i < num_free_verts; ++i )
    {

        // Populate TMP with vector-matrix procucts common
        // to terms of this Hessian row.
        const MsqMatrix< 1, DIM >& gi = transpose( dNdxi[i] );
        switch( DIM )
        {
            case 3:
                tmp[0][2] = gi * d2mdA2[2];
                tmp[1][2] = gi * d2mdA2[4];
                tmp[2][0] = gi * transpose( d2mdA2[2] );
                tmp[2][1] = gi * transpose( d2mdA2[4] );
                tmp[2][2] = gi * d2mdA2[5];
            case 2:
                tmp[0][1] = gi * d2mdA2[1];
                tmp[1][0] = gi * transpose( d2mdA2[1] );
                tmp[1][1] = gi * d2mdA2[DIM];
            case 1:
                tmp[0][0] = gi * d2mdA2[0];
            case 0:
                break;
            default:
                assert( false );
        }

        // Calculate Hessian diagonal block
        MAT& H = hess[h++];
        switch( DIM )
        {
            case 3:
                H( 0, 2 ) = H( 2, 0 ) = tmp[0][2] * transpose( gi );
                H( 1, 2 ) = H( 2, 1 ) = tmp[1][2] * transpose( gi );
                H( 2, 2 )             = tmp[2][2] * transpose( gi );
            case 2:
                H( 0, 1 ) = H( 1, 0 ) = tmp[0][1] * transpose( gi );
                H( 1, 1 )             = tmp[1][1] * transpose( gi );
            case 1:
                H( 0, 0 ) = tmp[0][0] * transpose( gi );
            case 0:
                break;
            default:
                assert( false );
        }

        // Calculate remainder of Hessian row
        for( size_t j = i + 1; j < num_free_verts; ++j )
        {
            MAT& HH                       = hess[h++];
            const MsqMatrix< DIM, 1 >& gj = dNdxi[j];
            switch( DIM )
            {
                case 3:
                    HH( 0, 2 ) = tmp[0][2] * gj;
                    HH( 1, 2 ) = tmp[1][2] * gj;
                    HH( 2, 0 ) = tmp[2][0] * gj;
                    HH( 2, 1 ) = tmp[2][1] * gj;
                    HH( 2, 2 ) = tmp[2][2] * gj;
                case 2:
                    HH( 0, 1 ) = tmp[0][1] * gj;
                    HH( 1, 0 ) = tmp[1][0] * gj;
                    HH( 1, 1 ) = tmp[1][1] * gj;
                case 1:
                    HH( 0, 0 ) = tmp[0][0] * gj;
                case 0:
                    break;
                default:
                    assert( false );
            }
        }
    }
}

/**\brief Calculate Hessian from derivatives of mapping function terms
 *        and derivatives of target metric. */
template < int DIM >
inline void hessian_diagonal( size_t num_free_verts,
                              const MsqVector< DIM >* dNdxi,
                              const MsqMatrix< DIM, DIM >* d2mdA2,
                              SymMatrix3D* diagonal )
{
    for( size_t i = 0; i < num_free_verts; ++i )
    {
        SymMatrix3D& H = diagonal[i];
        for( unsigned j = 0; j < ( ( DIM ) * ( DIM + 1 ) / 2 ); ++j )
            H[j] = transpose( dNdxi[i] ) * d2mdA2[j] * dNdxi[i];
    }
}

#ifdef PRINT_INFO
template < int R, int C >
inline void write_vect( char n, const MsqMatrix< R, C >& M )
{
    std::cout << "  " << n << ':';
    for( int c = 0; c < C; ++c )
    {
        std::cout << '[';
        for( int r = 0; r < R; ++r )
            std::cout << M( r, c ) << ' ';
        std::cout << ']';
    }
    std::cout << std::endl;
}

template < int D >
inline void print_info( size_t elem,
                        Sample sample,
                        const MsqMatrix< 3, D >& A,
                        const MsqMatrix< 3, D >& W,
                        const MsqMatrix< D, D >& T )
{
    std::cout << "Elem " << elem << " Dim " << sample.dimension << " Num " << sample.number << " :" << std::endl;
    write_vect< 3, D >( 'A', A );
    write_vect< 3, D >( 'W', W );
    write_vect< D, D >( 'T', T );
}
#endif

}  // namespace MBMesquite

#endif