TargetCalculator.cpp

Go to the documentation of this file.

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

    Copyright 2009 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

    (2009) kraftche@cae.wisc.edu

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

/** \file TargetCalculator.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "TargetCalculator.hpp"
#include "MsqError.hpp"
#include "PatchData.hpp"
#include "ReferenceMesh.hpp"
#include "MappingFunction.hpp"
#include <cassert>

namespace MBMesquite
{

double TargetCalculator::size( const MsqMatrix< 3, 3 >& W )
{
    return MBMesquite::cbrt( fabs( det( W ) ) );
}

double TargetCalculator::size( const MsqMatrix< 3, 2 >& W )
{
    return sqrt( length( W.column( 0 ) * W.column( 1 ) ) );
}

double TargetCalculator::size( const MsqMatrix< 2, 2 >& W )
{
    return sqrt( fabs( det( W ) ) );
}

MsqMatrix< 3, 3 > TargetCalculator::skew( const MsqMatrix< 3, 3 >& W )
{
    MsqVector< 3 > a1    = W.column( 0 ) * ( 1.0 / length( W.column( 0 ) ) );
    MsqVector< 3 > a2    = W.column( 1 ) * ( 1.0 / length( W.column( 1 ) ) );
    MsqVector< 3 > a3    = W.column( 2 ) * ( 1.0 / length( W.column( 2 ) ) );
    MsqVector< 3 > a1xa2 = a1 * a2;

    double lenx  = length( a1xa2 );
    double alpha = fabs( a1xa2 % a3 );
    double coeff = MBMesquite::cbrt( 1 / alpha );
    double dot   = a1xa2 % ( a1 * a3 );

    MsqMatrix< 3, 3 > q;
    q( 0, 0 ) = coeff;
    q( 0, 1 ) = coeff * ( a1 % a2 );
    q( 0, 2 ) = coeff * ( a1 % a3 );
    q( 1, 0 ) = 0.0;
    q( 1, 1 ) = coeff * lenx;
    q( 1, 2 ) = coeff * dot / lenx;
    q( 2, 0 ) = 0.0;
    q( 2, 1 ) = 0.0;
    q( 2, 2 ) = coeff * alpha / lenx;
    return q;
}

MsqMatrix< 2, 2 > TargetCalculator::skew( const MsqMatrix< 3, 2 >& W )
{
    MsqVector< 3 > alpha = W.column( 0 ) * W.column( 1 );
    double a1_sqr        = W.column( 0 ) % W.column( 0 );
    double a2_sqr        = W.column( 1 ) % W.column( 1 );
    double dot           = W.column( 0 ) % W.column( 1 );
    double a1a2          = sqrt( a1_sqr * a2_sqr );
    double coeff         = sqrt( a1a2 / length( alpha ) );

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = coeff;
    result( 0, 1 ) = coeff * dot / a1a2;
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = 1 / coeff;
    return result;
}

MsqMatrix< 2, 2 > TargetCalculator::skew( const MsqMatrix< 2, 2 >& W )
{
    double alpha  = fabs( det( W ) );
    double a1_sqr = W.column( 0 ) % W.column( 0 );
    double a2_sqr = W.column( 1 ) % W.column( 1 );
    double dot    = W.column( 0 ) % W.column( 1 );
    double a1a2   = sqrt( a1_sqr * a2_sqr );
    double coeff  = sqrt( a1a2 / alpha );

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = coeff;
    result( 0, 1 ) = coeff * dot / a1a2;
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = 1 / coeff;
    return result;
}

MsqMatrix< 3, 3 > TargetCalculator::aspect( const MsqMatrix< 3, 3 >& W )
{
    double a1    = length( W.column( 0 ) );
    double a2    = length( W.column( 1 ) );
    double a3    = length( W.column( 2 ) );
    double coeff = 1.0 / MBMesquite::cbrt( a1 * a2 * a3 );

    MsqMatrix< 3, 3 > result( coeff );
    result( 0, 0 ) *= a1;
    result( 1, 1 ) *= a2;
    result( 2, 2 ) *= a3;
    return result;
}

MsqMatrix< 2, 2 > TargetCalculator::aspect( const MsqMatrix< 3, 2 >& W )
{
    double a1_sqr   = W.column( 0 ) % W.column( 0 );
    double a2_sqr   = W.column( 1 ) % W.column( 1 );
    double sqrt_rho = sqrt( sqrt( a1_sqr / a2_sqr ) );

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = sqrt_rho;
    result( 0, 1 ) = 0.0;
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = 1 / sqrt_rho;
    return result;
}

MsqMatrix< 2, 2 > TargetCalculator::aspect( const MsqMatrix< 2, 2 >& W )
{
    double a1_sqr   = W.column( 0 ) % W.column( 0 );
    double a2_sqr   = W.column( 1 ) % W.column( 1 );
    double sqrt_rho = sqrt( sqrt( a1_sqr / a2_sqr ) );

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = sqrt_rho;
    result( 0, 1 ) = 0.0;
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = 1 / sqrt_rho;
    return result;
}

MsqMatrix< 3, 3 > TargetCalculator::shape( const MsqMatrix< 3, 3 >& W )
{
    MsqVector< 3 > a1    = W.column( 0 );
    MsqVector< 3 > a2    = W.column( 1 );
    MsqVector< 3 > a3    = W.column( 2 );
    MsqVector< 3 > a1xa2 = a1 * a2;

    double len1  = length( a1 );
    double lenx  = length( a1xa2 );
    double alpha = fabs( a1xa2 % a3 );
    double coeff = MBMesquite::cbrt( 1 / alpha );
    double inv1  = 1.0 / len1;
    double invx  = 1.0 / lenx;

    MsqMatrix< 3, 3 > q;
    q( 0, 0 ) = coeff * len1;
    q( 0, 1 ) = coeff * inv1 * ( a1 % a2 );
    q( 0, 2 ) = coeff * inv1 * ( a1 % a3 );
    q( 1, 0 ) = 0.0;
    q( 1, 1 ) = coeff * inv1 * lenx;
    q( 1, 2 ) = coeff * invx * inv1 * ( a1xa2 % ( a1 * a3 ) );
    q( 2, 0 ) = 0.0;
    q( 2, 1 ) = 0.0;
    q( 2, 2 ) = coeff * alpha * invx;
    return q;
}

MsqMatrix< 2, 2 > TargetCalculator::shape( const MsqMatrix< 3, 2 >& W )
{
    double len1       = length( W.column( 0 ) );
    double inv1       = 1.0 / len1;
    double root_alpha = sqrt( length( W.column( 0 ) * W.column( 1 ) ) );
    double coeff      = 1.0 / root_alpha;

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = coeff * len1;
    result( 0, 1 ) = coeff * inv1 * ( W.column( 0 ) % W.column( 1 ) );
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = root_alpha * inv1;
    return result;
}

MsqMatrix< 2, 2 > TargetCalculator::shape( const MsqMatrix< 2, 2 >& W )
{
    double len1       = length( W.column( 0 ) );
    double inv1       = 1.0 / len1;
    double root_alpha = sqrt( fabs( det( W ) ) );
    double coeff      = 1.0 / root_alpha;

    MsqMatrix< 2, 2 > result;
    result( 0, 0 ) = coeff * len1;
    result( 0, 1 ) = coeff * inv1 * ( W.column( 0 ) % W.column( 1 ) );
    result( 1, 0 ) = 0.0;
    result( 1, 1 ) = root_alpha * inv1;
    return result;
}

bool TargetCalculator::factor_3D( const MsqMatrix< 3, 3 >& A,
                                  double& Lambda,
                                  MsqMatrix< 3, 3 >& V,
                                  MsqMatrix< 3, 3 >& Q,
                                  MsqMatrix< 3, 3 >& Delta,
                                  MsqError& /*err*/ )
{
    MsqVector< 3 > a1xa2 = A.column( 0 ) * A.column( 1 );
    double alpha         = a1xa2 % A.column( 2 );
    Lambda               = MBMesquite::cbrt( fabs( alpha ) );
    if( Lambda < DBL_EPSILON ) return false;

    double la1_sqr = A.column( 0 ) % A.column( 0 );
    double la1     = sqrt( la1_sqr );
    double la2     = length( A.column( 1 ) );
    double la3     = length( A.column( 2 ) );
    double lx      = length( a1xa2 );
    double a1dota2 = A.column( 0 ) % A.column( 1 );

    double inv_la1 = 1.0 / la1;
    double inv_lx  = 1.0 / lx;
    V.set_column( 0, A.column( 0 ) * inv_la1 );
    V.set_column( 1, ( la1_sqr * A.column( 1 ) - a1dota2 * A.column( 0 ) ) * inv_la1 * inv_lx );
    V.set_column( 2, ( alpha / ( fabs( alpha ) * lx ) ) * a1xa2 );

    double inv_la2      = 1.0 / la2;
    double inv_la3      = 1.0 / la3;
    double len_prod_rt3 = MBMesquite::cbrt( la1 * la2 * la3 );
    Q( 0, 0 )           = 1.0;
    Q( 1, 0 ) = Q( 2, 0 ) = 0.0;
    Q( 0, 1 )             = a1dota2 * inv_la1 * inv_la2;
    Q( 1, 1 )             = lx * inv_la1 * inv_la2;
    Q( 2, 1 )             = 0.0;
    Q( 0, 2 )             = ( A.column( 0 ) % A.column( 2 ) ) * inv_la1 * inv_la3;
    Q( 1, 2 )             = ( a1xa2 % ( A.column( 0 ) * A.column( 2 ) ) ) * inv_lx * inv_la1 * inv_la3;
    Q( 2, 2 )             = fabs( alpha ) * inv_lx * inv_la3;
    Q *= len_prod_rt3 / Lambda;

    double inv_prod_rt3 = 1.0 / len_prod_rt3;
    ;
    Delta( 0, 0 ) = la1 * inv_prod_rt3;
    Delta( 0, 1 ) = 0.0;
    Delta( 0, 2 ) = 0.0;
    Delta( 1, 0 ) = 0.0;
    Delta( 1, 1 ) = la2 * inv_prod_rt3;
    Delta( 1, 2 ) = 0.0;
    Delta( 2, 0 ) = 0.0;
    Delta( 2, 1 ) = 0.0;
    Delta( 2, 2 ) = la3 * inv_prod_rt3;

    return true;
}

bool TargetCalculator::factor_surface( const MsqMatrix< 3, 2 >& A,
                                       double& Lambda,
                                       MsqMatrix< 3, 2 >& V,
                                       MsqMatrix< 2, 2 >& Q,
                                       MsqMatrix< 2, 2 >& Delta,
                                       MsqError& /*err*/ )
{
    MsqVector< 3 > cross = A.column( 0 ) * A.column( 1 );
    double alpha         = length( cross );
    Lambda               = sqrt( alpha );
    if( Lambda < DBL_EPSILON ) return false;

    double la1_sqr = A.column( 0 ) % A.column( 0 );
    double la1     = sqrt( la1_sqr );
    double la2     = length( A.column( 1 ) );
    double inv_la1 = 1.0 / la1;
    double dot     = A.column( 0 ) % A.column( 1 );

    V.set_column( 0, A.column( 0 ) * inv_la1 );
    V.set_column( 1, ( la1_sqr * A.column( 1 ) - dot * A.column( 0 ) ) / ( la1 * alpha ) );

    double prod_rt2 = sqrt( la1 * la2 );
    Q( 0, 0 )       = prod_rt2 / Lambda;
    Q( 0, 1 )       = dot / ( prod_rt2 * Lambda );
    Q( 1, 0 )       = 0.0;
    Q( 1, 1 )       = 1.0 / Q( 0, 0 );

    double inv_prod_rt2 = 1.0 / prod_rt2;
    Delta( 0, 0 )       = la1 * inv_prod_rt2;
    Delta( 0, 1 )       = 0.0;
    Delta( 1, 0 )       = 0.0;
    Delta( 1, 1 )       = la2 * inv_prod_rt2;

    return true;
}

bool TargetCalculator::factor_2D( const MsqMatrix< 2, 2 >& A,
                                  double& Lambda,
                                  MsqMatrix< 2, 2 >& V,
                                  MsqMatrix< 2, 2 >& Q,
                                  MsqMatrix< 2, 2 >& Delta,
                                  MsqError& /*err*/ )
{
    double alpha = det( A );
    Lambda       = sqrt( fabs( alpha ) );
    if( Lambda < DBL_EPSILON ) return false;

    double la1_sqr = A.column( 0 ) % A.column( 0 );
    double la1     = sqrt( la1_sqr );
    double la2     = length( A.column( 1 ) );
    double inv_la1 = 1.0 / la1;
    double dot     = A.column( 0 ) % A.column( 1 );

    V.set_column( 0, A.column( 0 ) * inv_la1 );
    V.set_column( 1, ( la1_sqr * A.column( 1 ) - dot * A.column( 0 ) ) / ( la1 * alpha ) );

    double prod_rt2 = sqrt( la1 * la2 );
    Q( 0, 0 )       = prod_rt2 / Lambda;
    Q( 0, 1 )       = dot / ( prod_rt2 * Lambda );
    Q( 1, 0 )       = 0.0;
    Q( 1, 1 )       = 1.0 / Q( 0, 0 );

    double inv_prod_rt2 = 1.0 / prod_rt2;
    Delta( 0, 0 )       = la1 * inv_prod_rt2;
    Delta( 0, 1 )       = 0.0;
    Delta( 1, 0 )       = 0.0;
    Delta( 1, 1 )       = la2 * inv_prod_rt2;

    return true;
}

MsqMatrix< 3, 3 > TargetCalculator::new_orientation_3D( const MsqVector< 3 >& b1, const MsqVector< 3 >& b2 )
{
    double lb1_sqr       = b1 % b1;
    MsqVector< 3 > cross = b1 * b2;
    double lb1           = sqrt( lb1_sqr );
    double inv_lb1       = 1.0 / lb1;
    double inv_lx        = 1.0 / length( cross );
    MsqMatrix< 3, 3 > V;
    V.set_column( 0, inv_lb1 * b1 );
    V.set_column( 1, ( lb1_sqr * b2 - ( b1 % b2 ) * lb1 ) * inv_lb1 * inv_lx );
    V.set_column( 2, cross * inv_lx );
    return V;
}

MsqMatrix< 3, 2 > TargetCalculator::new_orientation_2D( const MsqVector< 3 >& b1, const MsqVector< 3 >& b2 )
{
    double lb1_sqr = b1 % b1;
    double inv_lb1 = 1.0 / sqrt( lb1_sqr );
    MsqMatrix< 3, 2 > V;
    V.set_column( 0, b1 * inv_lb1 );
    V.set_column( 1, ( lb1_sqr * b2 - ( b1 % b2 ) * b1 ) * ( inv_lb1 / length( b1 * b2 ) ) );
    return V;
}

/** If, for the specified element type, the skew is constant for
 *  an ideal element and the aspect is identity everywhere within
 *  the element, pass back the constant skew/shape term and return
 *  true.  Otherwise return false.
 */
static inline bool ideal_constant_skew_I_3D( EntityTopology element_type, MsqMatrix< 3, 3 >& q )
{
    switch( element_type )
    {
        case HEXAHEDRON:
            q = MsqMatrix< 3, 3 >( 1.0 );  // Identity
            return false;
        case TETRAHEDRON:
            // [ x,   x/2, x/2 ] x^6 = 2
            // [ 0,   y,   y/3 ] y^2 = 3/4 x^2
            // [ 0,   0,   z   ] z^2 = 2/3 x^2
            q( 0, 0 ) = 1.122462048309373;
            q( 0, 1 ) = q( 0, 2 ) = 0.56123102415468651;
            q( 1, 0 ) = q( 2, 0 ) = q( 2, 1 ) = 0.0;
            q( 1, 1 )                         = 0.97208064861983279;
            q( 1, 2 )                         = 0.32402688287327758;
            q( 2, 2 )                         = 0.91648642466573493;
            return true;
        case PRISM:
            //            [ 1   0   0 ]
            //  a^(-1/3)  [ 0   1  1/2]
            //            [ 0   0   a ]
            //
            // a = sqrt(3)/2
            //
            q( 0, 0 ) = q( 1, 1 ) = 1.0491150634216482;
            q( 0, 1 ) = q( 0, 2 ) = q( 1, 0 ) = 0.0;
            q( 1, 2 )                         = 0.52455753171082409;
            q( 2, 0 ) = q( 2, 1 ) = 0.0;
            q( 2, 2 )             = 0.90856029641606972;
            return true;
        default:
            return false;
    }
}

/** If, for the specified element type, the skew is constant for
 *  an ideal element and the aspect is identity everywhere within
 *  the element, pass back the constant skew/shape term and return
 *  true.  Otherwise return false.
 */
static inline bool ideal_constant_skew_I_2D( EntityTopology element_type, MsqMatrix< 2, 2 >& q )
{
    switch( element_type )
    {
        case QUADRILATERAL:
            q = MsqMatrix< 2, 2 >( 1.0 );  // Identity
            return true;
        case TRIANGLE:
            // [ x, x/2 ]  x = pow(4/3, 0.25)
            // [ 0, y   ]  y = 1/x
            q( 0, 0 ) = 1.074569931823542;
            q( 0, 1 ) = 0.537284965911771;
            q( 1, 0 ) = 0.0;
            q( 1, 1 ) = 0.93060485910209956;
            return true;
        default:
            return false;
    }
}

void TargetCalculator::ideal_skew_3D( EntityTopology element_type,
                                      Sample s,
                                      const PatchData& pd,
                                      MsqMatrix< 3, 3 >& q,
                                      MsqError& err )
{
    if( !ideal_constant_skew_I_3D( element_type, q ) )
    {
        const MappingFunction3D* map = pd.get_mapping_function_3D( element_type );
        if( !map )
        {
            MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
            return;
        }
        map->ideal( s, q, err );MSQ_ERRRTN( err );
        q = TargetCalculator::skew( q );
    }
}

void TargetCalculator::ideal_skew_2D( EntityTopology element_type,
                                      Sample s,
                                      const PatchData& pd,
                                      MsqMatrix< 2, 2 >& q,
                                      MsqError& err )
{
    if( !ideal_constant_skew_I_2D( element_type, q ) )
    {
        const MappingFunction2D* map = pd.get_mapping_function_2D( element_type );
        if( !map )
        {
            MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
            return;
        }
        MsqMatrix< 3, 2 > J;
        map->ideal( s, J, err );MSQ_ERRRTN( err );
        q = TargetCalculator::skew( J );
    }
}

void TargetCalculator::ideal_shape_3D( EntityTopology element_type,
                                       Sample s,
                                       const PatchData& pd,
                                       MsqMatrix< 3, 3 >& q,
                                       MsqError& err )
{
    if( !ideal_constant_skew_I_3D( element_type, q ) )
    {
        const MappingFunction3D* map = pd.get_mapping_function_3D( element_type );
        if( !map )
        {
            MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
            return;
        }
        map->ideal( s, q, err );MSQ_ERRRTN( err );
        q = TargetCalculator::shape( q );
    }
}

void TargetCalculator::ideal_shape_2D( EntityTopology element_type,
                                       Sample s,
                                       const PatchData& pd,
                                       MsqMatrix< 2, 2 >& q,
                                       MsqError& err )
{
    if( !ideal_constant_skew_I_2D( element_type, q ) )
    {
        const MappingFunction2D* map = pd.get_mapping_function_2D( element_type );
        if( !map )
        {
            MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
            return;
        }
        MsqMatrix< 3, 2 > J;
        map->ideal( s, J, err );MSQ_ERRRTN( err );
        q = TargetCalculator::shape( J );
    }
}

MsqMatrix< 3, 3 > TargetCalculator::new_aspect_3D( const MsqVector< 3 >& r )
{
    MsqMatrix< 3, 3 > W( 0.0 );
    W( 0, 0 ) = MBMesquite::cbrt( r[0] * r[0] / ( r[1] * r[2] ) );
    W( 1, 1 ) = MBMesquite::cbrt( r[1] * r[1] / ( r[0] * r[2] ) );
    W( 2, 2 ) = MBMesquite::cbrt( r[2] * r[2] / ( r[1] * r[0] ) );
    return W;
}

MsqMatrix< 2, 2 > TargetCalculator::new_aspect_2D( const MsqVector< 2 >& r )
{
    return new_aspect_2D( r[0] / r[1] );
}

MsqMatrix< 2, 2 > TargetCalculator::new_aspect_2D( double rho )
{
    MsqMatrix< 2, 2 > W( sqrt( rho ) );
    W( 1, 1 ) = 1.0 / W( 0, 0 );
    return W;
}

static NodeSet get_nodeset( EntityTopology type, int num_nodes, MsqError& err )
{
    bool midedge, midface, midvol;
    TopologyInfo::higher_order( type, num_nodes, midedge, midface, midvol, err );
    if( MSQ_CHKERR( err ) ) return NodeSet();

    NodeSet bits;
    bits.set_all_corner_nodes( type );
    if( midedge ) bits.set_all_mid_edge_nodes( type );
    if( midface ) bits.set_all_mid_face_nodes( type );
    if( TopologyInfo::dimension( type ) == 3 && midvol ) bits.set_mid_region_node();

    return bits;
}

void TargetCalculator::jacobian_3D( PatchData& pd,
                                    EntityTopology type,
                                    int num_nodes,
                                    Sample location,
                                    const Vector3D* coords,
                                    MsqMatrix< 3, 3 >& J,
                                    MsqError& err )
{
    // Get element properties
    NodeSet bits = get_nodeset( type, num_nodes, err );MSQ_ERRRTN( err );
    const MappingFunction3D* mf = pd.get_mapping_function_3D( type );
    if( !mf )
    {
        MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
        return;
    }

    // Get mapping function derivatives
    const int MAX_NODES = 27;
    assert( num_nodes <= MAX_NODES );
    size_t indices[MAX_NODES], n;
    MsqVector< 3 > derivs[MAX_NODES];
    mf->derivatives( location, bits, indices, derivs, n, err );MSQ_ERRRTN( err );

    // calculate Jacobian
    assert( sizeof( Vector3D ) == sizeof( MsqVector< 3 > ) );
    const MsqVector< 3 >* verts = reinterpret_cast< const MsqVector< 3 >* >( coords );
    assert( n > 0 );
    J = outer( verts[indices[0]], derivs[0] );
    for( size_t i = 1; i < n; ++i )
        J += outer( verts[indices[i]], derivs[i] );
}

void TargetCalculator::jacobian_2D( PatchData& pd,
                                    EntityTopology type,
                                    int num_nodes,
                                    Sample location,
                                    const Vector3D* coords,
                                    MsqMatrix< 3, 2 >& J,
                                    MsqError& err )
{
    // Get element properties
    NodeSet bits = get_nodeset( type, num_nodes, err );MSQ_ERRRTN( err );
    const MappingFunction2D* mf = pd.get_mapping_function_2D( type );
    if( !mf )
    {
        MSQ_SETERR( err )( MsqError::UNSUPPORTED_ELEMENT );
        return;
    }

    // Get mapping function derivatives
    const int MAX_NODES = 9;
    assert( num_nodes <= MAX_NODES );
    size_t indices[MAX_NODES], n;
    MsqVector< 2 > derivs[MAX_NODES];
    mf->derivatives( location, bits, indices, derivs, n, err );MSQ_ERRRTN( err );

    // calculate Jacobian
    assert( sizeof( Vector3D ) == sizeof( MsqVector< 3 > ) );
    const MsqVector< 3 >* verts = reinterpret_cast< const MsqVector< 3 >* >( coords );
    assert( n > 0 );
    J = outer( verts[indices[0]], derivs[0] );
    for( size_t i = 1; i < n; ++i )
        J += outer( verts[indices[i]], derivs[i] );
}

void TargetCalculator::get_refmesh_Jacobian_3D( ReferenceMeshInterface* ref_mesh,
                                                PatchData& pd,
                                                size_t element,
                                                Sample sample,
                                                MsqMatrix< 3, 3 >& W_out,
                                                MsqError& err )
{
    // get element
    MsqMeshEntity& elem       = pd.element_by_index( element );
    const EntityTopology type = elem.get_element_type();
    const unsigned n          = elem.node_count();

    const unsigned MAX_NODES = 27;
    assert( n <= MAX_NODES );

    // get vertices
    Mesh::VertexHandle elem_verts[MAX_NODES];
    const std::size_t* vtx_idx        = elem.get_vertex_index_array();
    const Mesh::VertexHandle* vtx_hdl = pd.get_vertex_handles_array();
    for( unsigned i = 0; i < n; ++i )
        elem_verts[i] = vtx_hdl[vtx_idx[i]];

    // get vertex coordinates
    Vector3D vert_coords[MAX_NODES];
    ref_mesh->get_reference_vertex_coordinates( elem_verts, n, vert_coords, err );MSQ_ERRRTN( err );

    // calculate Jacobian
    jacobian_3D( pd, type, n, sample, vert_coords, W_out, err );MSQ_ERRRTN( err );
}

void TargetCalculator::get_refmesh_Jacobian_2D( ReferenceMeshInterface* ref_mesh,
                                                PatchData& pd,
                                                size_t element,
                                                Sample sample,
                                                MsqMatrix< 3, 2 >& W_out,
                                                MsqError& err )
{
    // get element
    MsqMeshEntity& elem       = pd.element_by_index( element );
    const EntityTopology type = elem.get_element_type();
    const unsigned n          = elem.node_count();

    const unsigned MAX_NODES = 9;
    assert( n <= MAX_NODES );

    // get vertices
    Mesh::VertexHandle elem_verts[MAX_NODES];
    const std::size_t* vtx_idx        = elem.get_vertex_index_array();
    const Mesh::VertexHandle* vtx_hdl = pd.get_vertex_handles_array();
    for( unsigned i = 0; i < n; ++i )
        elem_verts[i] = vtx_hdl[vtx_idx[i]];

    // get vertex coordinates
    Vector3D vert_coords[MAX_NODES];
    ref_mesh->get_reference_vertex_coordinates( elem_verts, n, vert_coords, err );MSQ_ERRRTN( err );

    // calculate Jacobian
    jacobian_2D( pd, type, n, sample, vert_coords, W_out, err );MSQ_ERRRTN( err );
}

TargetCalculator::~TargetCalculator() {}

void TargetCalculator::initialize_queue( MeshDomainAssoc*, const Settings*, MsqError& ) {}

}  // namespace MBMesquite