IdealWeightInverseMeanRatio.cpp

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

    Copyright 2004 Sandia Corporation and Argonne National
    Laboratory.  Under the terms of Contract DE-AC04-94AL85000
    with Sandia Corporation, the U.S. Government 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    [email protected], [email protected], [email protected],
    [email protected], [email protected], [email protected]

  ***************************************************************** */
/*!
  \file   IdealWeightInverseMeanRatio.cpp
  \brief

  \author Michael Brewer
  \author Todd Munson
  \author Thomas Leurent

  \date   2002-06-9
*/
#include "IdealWeightInverseMeanRatio.hpp"
#include "MeanRatioFunctions.hpp"
#include "MsqTimer.hpp"
#include "MsqDebug.hpp"
#include "MsqError.hpp"
#include "PatchData.hpp"

#include <vector>
using std::vector;
#include <cmath>

namespace MBMesquite
{

IdealWeightInverseMeanRatio::IdealWeightInverseMeanRatio( MsqError& err, double pow_dbl )
    : AveragingQM( QualityMetric::LINEAR )
{
    set_metric_power( pow_dbl, err );MSQ_ERRRTN( err );
}

IdealWeightInverseMeanRatio::IdealWeightInverseMeanRatio() : AveragingQM( QualityMetric::LINEAR )
{
    MsqError err;
    set_metric_power( 1.0, err );
    assert( !err );
}

std::string IdealWeightInverseMeanRatio::get_name() const
{
    return "Inverse Mean Ratio";
}

int IdealWeightInverseMeanRatio::get_negate_flag() const
{
    return b2Con.value() < 0 ? -1 : 1;
}

//! Sets the power value in the metric computation.
void IdealWeightInverseMeanRatio::set_metric_power( double pow_dbl, MsqError& err )
{
    if( fabs( pow_dbl ) <= MSQ_MIN )
    {
        MSQ_SETERR( err )( MsqError::INVALID_ARG );
        return;
    }
    a2Con = pow( .5, pow_dbl );
    b2Con = pow_dbl;
    c2Con = -pow_dbl;
    a3Con = pow( 1.0 / 3.0, pow_dbl );
    b3Con = pow_dbl;
    c3Con = -2.0 * pow_dbl / 3.0;
}

bool IdealWeightInverseMeanRatio::evaluate( PatchData& pd, size_t handle, double& m, MsqError& err )
{
    const MsqMeshEntity* e = &pd.element_by_index( handle );
    EntityTopology topo    = e->get_element_type();

    const MsqVertex* vertices = pd.get_vertex_array( err );
    MSQ_ERRZERO( err );
    const size_t* v_i = e->get_vertex_index_array();

    Vector3D n;  // Surface normal for 2D objects

    // Prism and Hex element descriptions
    static const int locs_pri[6][4] = { { 0, 1, 2, 3 }, { 1, 2, 0, 4 }, { 2, 0, 1, 5 },
                                        { 3, 5, 4, 0 }, { 4, 3, 5, 1 }, { 5, 4, 3, 2 } };
    static const int locs_hex[8][4] = { { 0, 1, 3, 4 }, { 1, 2, 0, 5 }, { 2, 3, 1, 6 }, { 3, 0, 2, 7 },
                                        { 4, 7, 5, 0 }, { 5, 4, 6, 1 }, { 6, 5, 7, 2 }, { 7, 6, 4, 3 } };

    const Vector3D d_con( 1.0, 1.0, 1.0 );

    int i;

    m                 = 0.0;
    bool metric_valid = false;
    switch( topo )
    {
        case TRIANGLE:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n            = n / n.length();  // Need unit normal
            mCoords[0]   = vertices[v_i[0]];
            mCoords[1]   = vertices[v_i[1]];
            mCoords[2]   = vertices[v_i[2]];
            metric_valid = m_fcn_2e( m, mCoords, n, a2Con, b2Con, c2Con );
            if( !metric_valid ) return false;
            break;

        case QUADRILATERAL:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n = n / n.length();  // Need unit normal
            for( i = 0; i < 4; ++i )
            {
                mCoords[0]   = vertices[v_i[locs_hex[i][0]]];
                mCoords[1]   = vertices[v_i[locs_hex[i][1]]];
                mCoords[2]   = vertices[v_i[locs_hex[i][2]]];
                metric_valid = m_fcn_2i( mMetrics[i], mCoords, n, a2Con, b2Con, c2Con, d_con );
                if( !metric_valid ) return false;
            }
            m = average_metrics( mMetrics, 4, err );
            break;

        case TETRAHEDRON:
            mCoords[0]   = vertices[v_i[0]];
            mCoords[1]   = vertices[v_i[1]];
            mCoords[2]   = vertices[v_i[2]];
            mCoords[3]   = vertices[v_i[3]];
            metric_valid = m_fcn_3e( m, mCoords, a3Con, b3Con, c3Con );
            if( !metric_valid ) return false;
            break;

        case PYRAMID:
            for( i = 0; i < 4; ++i )
            {
                mCoords[0]   = vertices[v_i[i]];
                mCoords[1]   = vertices[v_i[( i + 1 ) % 4]];
                mCoords[2]   = vertices[v_i[( i + 3 ) % 4]];
                mCoords[3]   = vertices[v_i[4]];
                metric_valid = m_fcn_3p( mMetrics[i], mCoords, a3Con, b3Con, c3Con );
                if( !metric_valid ) return false;
            }
            m = average_metrics( mMetrics, 4, err );
            MSQ_ERRZERO( err );
            break;

        case PRISM:
            for( i = 0; i < 6; ++i )
            {
                mCoords[0]   = vertices[v_i[locs_pri[i][0]]];
                mCoords[1]   = vertices[v_i[locs_pri[i][1]]];
                mCoords[2]   = vertices[v_i[locs_pri[i][2]]];
                mCoords[3]   = vertices[v_i[locs_pri[i][3]]];
                metric_valid = m_fcn_3w( mMetrics[i], mCoords, a3Con, b3Con, c3Con );
                if( !metric_valid ) return false;
            }
            m = average_metrics( mMetrics, 6, err );
            MSQ_ERRZERO( err );
            break;

        case HEXAHEDRON:
            for( i = 0; i < 8; ++i )
            {
                mCoords[0]   = vertices[v_i[locs_hex[i][0]]];
                mCoords[1]   = vertices[v_i[locs_hex[i][1]]];
                mCoords[2]   = vertices[v_i[locs_hex[i][2]]];
                mCoords[3]   = vertices[v_i[locs_hex[i][3]]];
                metric_valid = m_fcn_3i( mMetrics[i], mCoords, a3Con, b3Con, c3Con, d_con );
                if( !metric_valid ) return false;
            }
            m = average_metrics( mMetrics, 8, err );
            MSQ_ERRZERO( err );
            break;

        default:
            MSQ_SETERR( err )
            ( MsqError::UNSUPPORTED_ELEMENT, "Element type (%d) not supported in IdealWeightInverseMeanRatio",
              (int)topo );
            return false;
    }  // end switch over element type
    return true;
}

bool IdealWeightInverseMeanRatio::evaluate_with_gradient( PatchData& pd,
                                                          size_t handle,
                                                          double& m,
                                                          std::vector< size_t >& indices,
                                                          std::vector< Vector3D >& g,
                                                          MsqError& err )
{
    const MsqMeshEntity* e = &pd.element_by_index( handle );
    EntityTopology topo    = e->get_element_type();

    if( !analytical_average_gradient() && topo != TRIANGLE && topo != TETRAHEDRON )
    {
        static bool print = true;
        if( print )
        {
            MSQ_DBGOUT( 1 ) << "Analyical gradient not available for selected averaging scheme. "
                            << "Using (possibly much slower) numerical approximation of gradient"
                            << " of quality metric. " << std::endl;
            print = false;
        }
        return QualityMetric::evaluate_with_gradient( pd, handle, m, indices, g, err );
    }

    const MsqVertex* vertices = pd.get_vertex_array( err );
    MSQ_ERRZERO( err );
    const size_t* v_i = e->get_vertex_index_array();

    Vector3D n;  // Surface normal for 2D objects

    // Prism and Hex element descriptions
    static const int locs_pri[6][4] = { { 0, 1, 2, 3 }, { 1, 2, 0, 4 }, { 2, 0, 1, 5 },
                                        { 3, 5, 4, 0 }, { 4, 3, 5, 1 }, { 5, 4, 3, 2 } };
    static const int locs_hex[8][4] = { { 0, 1, 3, 4 }, { 1, 2, 0, 5 }, { 2, 3, 1, 6 }, { 3, 0, 2, 7 },
                                        { 4, 7, 5, 0 }, { 5, 4, 6, 1 }, { 6, 5, 7, 2 }, { 7, 6, 4, 3 } };

    const Vector3D d_con( 1.0, 1.0, 1.0 );

    int i;

    bool metric_valid = false;
    const uint32_t fm = fixed_vertex_bitmap( pd, e, indices );

    m = 0.0;

    switch( topo )
    {
        case TRIANGLE:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            g.resize( 3 );
            if( !g_fcn_2e( m, arrptr( g ), mCoords, n, a2Con, b2Con, c2Con ) ) return false;
            break;

        case QUADRILATERAL:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            for( i = 0; i < 4; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                if( !g_fcn_2i( mMetrics[i], mGradients + 3 * i, mCoords, n, a2Con, b2Con, c2Con, d_con ) ) return false;
            }

            g.resize( 4 );
            m = average_corner_gradients( QUADRILATERAL, fm, 4, mMetrics, mGradients, arrptr( g ), err );
            MSQ_ERRZERO( err );
            break;

        case TETRAHEDRON:
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            mCoords[3] = vertices[v_i[3]];
            g.resize( 4 );
            metric_valid = g_fcn_3e( m, arrptr( g ), mCoords, a3Con, b3Con, c3Con );
            if( !metric_valid ) return false;
            break;

        case PYRAMID:
            for( i = 0; i < 4; ++i )
            {
                mCoords[0]   = vertices[v_i[i]];
                mCoords[1]   = vertices[v_i[( i + 1 ) % 4]];
                mCoords[2]   = vertices[v_i[( i + 3 ) % 4]];
                mCoords[3]   = vertices[v_i[4]];
                metric_valid = g_fcn_3p( mMetrics[i], mGradients + 4 * i, mCoords, a3Con, b3Con, c3Con );
                if( !metric_valid ) return false;
            }

            g.resize( 5 );
            m = average_corner_gradients( PYRAMID, fm, 4, mMetrics, mGradients, arrptr( g ), err );
            MSQ_ERRZERO( err );
            break;

        case PRISM:
            for( i = 0; i < 6; ++i )
            {
                mCoords[0] = vertices[v_i[locs_pri[i][0]]];
                mCoords[1] = vertices[v_i[locs_pri[i][1]]];
                mCoords[2] = vertices[v_i[locs_pri[i][2]]];
                mCoords[3] = vertices[v_i[locs_pri[i][3]]];
                if( !g_fcn_3w( mMetrics[i], mGradients + 4 * i, mCoords, a3Con, b3Con, c3Con ) ) return false;
            }

            g.resize( 6 );
            m = average_corner_gradients( PRISM, fm, 6, mMetrics, mGradients, arrptr( g ), err );
            MSQ_ERRZERO( err );
            break;

        case HEXAHEDRON:
            for( i = 0; i < 8; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                mCoords[3] = vertices[v_i[locs_hex[i][3]]];
                if( !g_fcn_3i( mMetrics[i], mGradients + 4 * i, mCoords, a3Con, b3Con, c3Con, d_con ) ) return false;
            }

            g.resize( 8 );
            m = average_corner_gradients( HEXAHEDRON, fm, 8, mMetrics, mGradients, arrptr( g ), err );
            MSQ_ERRZERO( err );
            break;

        default:
            MSQ_SETERR( err )
            ( MsqError::UNSUPPORTED_ELEMENT, "Element type (%d) not supported in IdealWeightInverseMeanRatio",
              (int)topo );
            return false;
    }  // end switch over element type

    remove_fixed_gradients( topo, fm, g );
    return true;
}

bool IdealWeightInverseMeanRatio::evaluate_with_Hessian_diagonal( PatchData& pd,
                                                                  size_t handle,
                                                                  double& m,
                                                                  std::vector< size_t >& indices,
                                                                  std::vector< Vector3D >& g,
                                                                  std::vector< SymMatrix3D >& h,
                                                                  MsqError& err )
{
    const MsqMeshEntity* e = &pd.element_by_index( handle );
    EntityTopology topo    = e->get_element_type();

    if( !analytical_average_hessian() && topo != TRIANGLE && topo != TETRAHEDRON )
    {
        static bool print = true;
        if( print )
        {
            MSQ_DBGOUT( 1 ) << "Analyical gradient not available for selected averaging scheme. "
                            << "Using (possibly much slower) numerical approximation of gradient"
                            << " of quality metric. " << std::endl;
            print = false;
        }
        return QualityMetric::evaluate_with_Hessian_diagonal( pd, handle, m, indices, g, h, err );
    }

    const MsqVertex* vertices = pd.get_vertex_array( err );
    MSQ_ERRZERO( err );
    const size_t* v_i = e->get_vertex_index_array();

    Vector3D n;  // Surface normal for 2D objects

    // Prism and Hex element descriptions
    static const int locs_pri[6][4] = { { 0, 1, 2, 3 }, { 1, 2, 0, 4 }, { 2, 0, 1, 5 },
                                        { 3, 5, 4, 0 }, { 4, 3, 5, 1 }, { 5, 4, 3, 2 } };
    static const int locs_hex[8][4] = { { 0, 1, 3, 4 }, { 1, 2, 0, 5 }, { 2, 3, 1, 6 }, { 3, 0, 2, 7 },
                                        { 4, 7, 5, 0 }, { 5, 4, 6, 1 }, { 6, 5, 7, 2 }, { 7, 6, 4, 3 } };

    const Vector3D d_con( 1.0, 1.0, 1.0 );

    int i;

    bool metric_valid = false;
    const uint32_t fm = fixed_vertex_bitmap( pd, e, indices );

    m = 0.0;

    switch( topo )
    {
        case TRIANGLE:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            g.resize( 3 );
            h.resize( 3 );
            if( !h_fcn_2e( m, arrptr( g ), mHessians, mCoords, n, a2Con, b2Con, c2Con ) ) return false;
            h[0] = mHessians[0].upper();
            h[1] = mHessians[3].upper();
            h[2] = mHessians[5].upper();
            break;

        case QUADRILATERAL:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            for( i = 0; i < 4; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                if( !h_fcn_2i( mMetrics[i], mGradients + 3 * i, mHessians + 6 * i, mCoords, n, a2Con, b2Con, c2Con,
                               d_con ) )
                    return false;
            }

            g.resize( 4 );
            h.resize( 4 );
            m = average_corner_hessian_diagonals( QUADRILATERAL, fm, 4, mMetrics, mGradients, mHessians, arrptr( g ),
                                                  arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        case TETRAHEDRON:
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            mCoords[3] = vertices[v_i[3]];
            g.resize( 4 );
            h.resize( 4 );
            metric_valid = h_fcn_3e( m, arrptr( g ), mHessians, mCoords, a3Con, b3Con, c3Con );
            if( !metric_valid ) return false;
            h[0] = mHessians[0].upper();
            h[1] = mHessians[4].upper();
            h[2] = mHessians[7].upper();
            h[3] = mHessians[9].upper();
            break;

        case PYRAMID:
            for( i = 0; i < 4; ++i )
            {
                mCoords[0] = vertices[v_i[i]];
                mCoords[1] = vertices[v_i[( i + 1 ) % 4]];
                mCoords[2] = vertices[v_i[( i + 3 ) % 4]];
                mCoords[3] = vertices[v_i[4]];
                metric_valid =
                    h_fcn_3p( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con );

                if( !metric_valid ) return false;
            }

            g.resize( 5 );
            h.resize( 5 );
            m = average_corner_hessian_diagonals( PYRAMID, fm, 4, mMetrics, mGradients, mHessians, arrptr( g ),
                                                  arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        case PRISM:
            for( i = 0; i < 6; ++i )
            {
                mCoords[0] = vertices[v_i[locs_pri[i][0]]];
                mCoords[1] = vertices[v_i[locs_pri[i][1]]];
                mCoords[2] = vertices[v_i[locs_pri[i][2]]];
                mCoords[3] = vertices[v_i[locs_pri[i][3]]];
                if( !h_fcn_3w( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con ) )
                    return false;
            }

            g.resize( 6 );
            h.resize( 6 );
            m = average_corner_hessian_diagonals( PRISM, fm, 6, mMetrics, mGradients, mHessians, arrptr( g ),
                                                  arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        case HEXAHEDRON:
            for( i = 0; i < 8; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                mCoords[3] = vertices[v_i[locs_hex[i][3]]];
                if( !h_fcn_3i( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con,
                               d_con ) )
                    return false;
            }

            g.resize( 8 );
            h.resize( 8 );
            m = average_corner_hessian_diagonals( HEXAHEDRON, fm, 8, mMetrics, mGradients, mHessians, arrptr( g ),
                                                  arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        default:
            MSQ_SETERR( err )
            ( MsqError::UNSUPPORTED_ELEMENT, "Element type (%d) not supported in IdealWeightInverseMeanRatio",
              (int)topo );
            return false;
    }  // end switch over element type

    remove_fixed_diagonals( topo, fm, g, h );
    return true;
}

bool IdealWeightInverseMeanRatio::evaluate_with_Hessian( PatchData& pd,
                                                         size_t handle,
                                                         double& m,
                                                         std::vector< size_t >& indices,
                                                         std::vector< Vector3D >& g,
                                                         std::vector< Matrix3D >& h,
                                                         MsqError& err )
{
    const MsqMeshEntity* e = &pd.element_by_index( handle );
    EntityTopology topo    = e->get_element_type();

    if( !analytical_average_hessian() && topo != TRIANGLE && topo != TETRAHEDRON )
    {
        static bool print = true;
        if( print )
        {
            MSQ_DBGOUT( 1 ) << "Analyical gradient not available for selected averaging scheme. "
                            << "Using (possibly much slower) numerical approximation of gradient"
                            << " of quality metric. " << std::endl;
            print = false;
        }
        return QualityMetric::evaluate_with_Hessian( pd, handle, m, indices, g, h, err );
    }

    const MsqVertex* vertices = pd.get_vertex_array( err );
    MSQ_ERRZERO( err );
    const size_t* v_i = e->get_vertex_index_array();

    Vector3D n;  // Surface normal for 2D objects

    // Prism and Hex element descriptions
    static const int locs_pri[6][4] = { { 0, 1, 2, 3 }, { 1, 2, 0, 4 }, { 2, 0, 1, 5 },
                                        { 3, 5, 4, 0 }, { 4, 3, 5, 1 }, { 5, 4, 3, 2 } };
    static const int locs_hex[8][4] = { { 0, 1, 3, 4 }, { 1, 2, 0, 5 }, { 2, 3, 1, 6 }, { 3, 0, 2, 7 },
                                        { 4, 7, 5, 0 }, { 5, 4, 6, 1 }, { 6, 5, 7, 2 }, { 7, 6, 4, 3 } };

    const Vector3D d_con( 1.0, 1.0, 1.0 );

    int i;

    bool metric_valid = false;
    const uint32_t fm = fixed_vertex_bitmap( pd, e, indices );

    m = 0.0;

    switch( topo )
    {
        case TRIANGLE:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            g.resize( 3 );
            h.resize( 6 );
            if( !h_fcn_2e( m, arrptr( g ), arrptr( h ), mCoords, n, a2Con, b2Con, c2Con ) ) return false;
            break;

        case QUADRILATERAL:
            pd.get_domain_normal_at_element( e, n, err );
            MSQ_ERRZERO( err );
            n /= n.length();  // Need unit normal
            for( i = 0; i < 4; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                if( !h_fcn_2i( mMetrics[i], mGradients + 3 * i, mHessians + 6 * i, mCoords, n, a2Con, b2Con, c2Con,
                               d_con ) )
                    return false;
            }

            g.resize( 4 );
            h.resize( 10 );
            m = average_corner_hessians( QUADRILATERAL, fm, 4, mMetrics, mGradients, mHessians, arrptr( g ),
                                         arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        case TETRAHEDRON:
            mCoords[0] = vertices[v_i[0]];
            mCoords[1] = vertices[v_i[1]];
            mCoords[2] = vertices[v_i[2]];
            mCoords[3] = vertices[v_i[3]];
            g.resize( 4 );
            h.resize( 10 );
            metric_valid = h_fcn_3e( m, arrptr( g ), arrptr( h ), mCoords, a3Con, b3Con, c3Con );
            if( !metric_valid ) return false;
            break;

        case PYRAMID:
            for( i = 0; i < 4; ++i )
            {
                mCoords[0] = vertices[v_i[i]];
                mCoords[1] = vertices[v_i[( i + 1 ) % 4]];
                mCoords[2] = vertices[v_i[( i + 3 ) % 4]];
                mCoords[3] = vertices[v_i[4]];
                metric_valid =
                    h_fcn_3p( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con );

                if( !metric_valid ) return false;
            }

            g.resize( 5 );
            h.resize( 15 );
            m = average_corner_hessians( PYRAMID, fm, 4, mMetrics, mGradients, mHessians, arrptr( g ), arrptr( h ),
                                         err );
            MSQ_ERRZERO( err );
            break;

        case PRISM:
            for( i = 0; i < 6; ++i )
            {
                mCoords[0] = vertices[v_i[locs_pri[i][0]]];
                mCoords[1] = vertices[v_i[locs_pri[i][1]]];
                mCoords[2] = vertices[v_i[locs_pri[i][2]]];
                mCoords[3] = vertices[v_i[locs_pri[i][3]]];
                if( !h_fcn_3w( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con ) )
                    return false;
            }

            g.resize( 6 );
            h.resize( 21 );
            m = average_corner_hessians( PRISM, fm, 6, mMetrics, mGradients, mHessians, arrptr( g ), arrptr( h ), err );
            MSQ_ERRZERO( err );
            break;

        case HEXAHEDRON:
            for( i = 0; i < 8; ++i )
            {
                mCoords[0] = vertices[v_i[locs_hex[i][0]]];
                mCoords[1] = vertices[v_i[locs_hex[i][1]]];
                mCoords[2] = vertices[v_i[locs_hex[i][2]]];
                mCoords[3] = vertices[v_i[locs_hex[i][3]]];
                if( !h_fcn_3i( mMetrics[i], mGradients + 4 * i, mHessians + 10 * i, mCoords, a3Con, b3Con, c3Con,
                               d_con ) )
                    return false;
            }

            g.resize( 8 );
            h.resize( 36 );
            m = average_corner_hessians( HEXAHEDRON, fm, 8, mMetrics, mGradients, mHessians, arrptr( g ), arrptr( h ),
                                         err );
            MSQ_ERRZERO( err );
            break;

        default:
            MSQ_SETERR( err )
            ( MsqError::UNSUPPORTED_ELEMENT, "Element type (%d) not supported in IdealWeightInverseMeanRatio",
              (int)topo );
            return false;
    }  // end switch over element type

    remove_fixed_gradients( topo, fm, g );
    remove_fixed_hessians( topo, fm, h );
    return true;
}

}  // namespace MBMesquite