QualityAssessor.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   QualityAssessor.cpp
  \brief  Member function of the MBMesquite::QualityAssessor class

  \author Thomas Leurent
  \date   2002-05-23
*/

#include "QualityAssessor.hpp"
#include "QualityMetric.hpp"
#include "TMPQualityMetric.hpp"
#include "ElementMaxQM.hpp"
#include "ElementAvgQM.hpp"
#include "PatchData.hpp"
#include "MsqMeshEntity.hpp"
#include "MsqVertex.hpp"
#include "MsqDebug.hpp"
#include "MeshInterface.hpp"
#include "VertexPatches.hpp"
#include "ElementPatches.hpp"
#include "ParallelMeshInterface.hpp"
#include "ParallelHelperInterface.hpp"

#include <list>
#include <vector>
#include <iostream>
#include <fstream>
#include <iomanip>
#include <set>
#include <cmath>

#ifdef HAVE_SYS_IOCTL_H
#include <sys/ioctl.h>
#endif
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif
#ifdef HAVE_TERMIOS_H
#include <termios.h>
#endif

namespace MBMesquite
{

const char* default_name( bool free_only )
{
    static const char all_name[]  = "QualityAssessor";
    static const char free_name[] = "QualityAssessor(free only)";
    return free_only ? free_name : all_name;
}

QualityAssessor::QualityAssessor( bool p_print_summary,
                                  bool free_only,
                                  const char* inverted_tag_name,
                                  std::string p_name )
    : myData( new Data ), qualityAssessorName( p_name ), outputStream( std::cout ), printSummary( p_print_summary ),
      skipFixedSamples( free_only )
{
    if( inverted_tag_name ) tag_inverted_elements( inverted_tag_name );

    if( qualityAssessorName.empty() ) qualityAssessorName = default_name( free_only );

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = 0;
}

QualityAssessor::QualityAssessor( std::ostream& stream,
                                  bool free_only,
                                  const char* inverted_tag_name,
                                  std::string name )
    : myData( new Data ), qualityAssessorName( name ), outputStream( stream ), printSummary( true ),
      skipFixedSamples( free_only )
{
    if( inverted_tag_name ) tag_inverted_elements( inverted_tag_name );

    if( qualityAssessorName.empty() ) qualityAssessorName = default_name( free_only );

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = 0;
}

QualityAssessor::QualityAssessor( std::ostream& output_stream,
                                  QualityMetric* metric,
                                  int histogram_intervals,
                                  double power_mean,
                                  bool free_only,
                                  const char* metric_value_tag_name,
                                  const char* inverted_tag_name,
                                  std::string name )
    : myData( new Data ), qualityAssessorName( name ), outputStream( output_stream ), printSummary( true ),
      skipFixedSamples( free_only )
{
    if( inverted_tag_name ) tag_inverted_elements( inverted_tag_name );

    if( qualityAssessorName.empty() ) qualityAssessorName = default_name( free_only );

    set_stopping_assessment( metric, histogram_intervals, power_mean, metric_value_tag_name );

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = 0;
}

QualityAssessor::QualityAssessor( QualityMetric* metric,
                                  int histogram_intervals,
                                  double power_mean,
                                  bool free_only,
                                  const char* metric_value_tag_name,
                                  bool p_print_summary,
                                  const char* inverted_tag_name,
                                  std::string name )
    : myData( new Data ), qualityAssessorName( name ), outputStream( std::cout ), printSummary( p_print_summary ),
      skipFixedSamples( free_only )
{
    if( inverted_tag_name ) tag_inverted_elements( inverted_tag_name );

    if( qualityAssessorName.empty() ) qualityAssessorName = default_name( free_only );

    set_stopping_assessment( metric, histogram_intervals, power_mean, metric_value_tag_name );

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = 0;
}

QualityAssessor::QualityAssessor( const QualityAssessor& copy )
    : myData( copy.myData ), qualityAssessorName( copy.qualityAssessorName ), assessList( copy.assessList ),
      outputStream( copy.outputStream ), printSummary( copy.printSummary ), invertedTagName( copy.invertedTagName ),
      fixedTagName( copy.fixedTagName ), skipFixedSamples( copy.skipFixedSamples )

{
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        ( *iter )->referenceCount++;
    myData->referenceCount++;

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = copy.elementTypeCount[i - POLYGON];
}

QualityAssessor& QualityAssessor::operator=( const QualityAssessor& copy )
{
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        Assessor* assessor = *iter;
        if( 0 == --assessor->referenceCount ) delete assessor;
    }

    myData              = copy.myData;
    qualityAssessorName = copy.qualityAssessorName;
    assessList          = copy.assessList;
    printSummary        = copy.printSummary;
    invertedTagName     = copy.invertedTagName;
    fixedTagName        = copy.fixedTagName;
    skipFixedSamples    = copy.skipFixedSamples;

    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        ( *iter )->referenceCount++;
    myData->referenceCount++;

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = copy.elementTypeCount[i - POLYGON];

    return *this;
}

QualityAssessor::~QualityAssessor()
{
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        Assessor* assessor = *iter;
        if( 0 == --assessor->referenceCount ) delete assessor;
    }
    if( 0 == --myData->referenceCount ) delete myData;
}

double QualityAssessor::Assessor::get_average() const
{
    return count ? sum / count : 0;
}

double QualityAssessor::Assessor::get_rms() const
{
    return count ? sqrt( sqrSum / count ) : 0;
}

double QualityAssessor::Assessor::get_stddev() const
{
    double sqr = count ? sqrSum / count - sum * sum / ( (double)count * count ) : 0;
    return sqr < 0 ? 0 : sqrt( sqr );
}

double QualityAssessor::Assessor::get_power_mean() const
{
    return ( count && pMean ) ? pow( pSum / count, 1 / pMean ) : 0;
}

bool QualityAssessor::get_inverted_element_count( int& inverted_elems, int& inverted_samples, MsqError& err )
{
    if( myData->invertedElementCount == -1 )
    {
        MSQ_SETERR( err )
        ( "Number of inverted elements has not yet been calculated.", MsqError::INVALID_STATE );
        return false;
    }
    inverted_elems   = myData->invertedElementCount;
    inverted_samples = myData->invertedSampleCount;
    return true;
}

void QualityAssessor::add_quality_assessment( QualityMetric* metric,
                                              int histogram_intervals,
                                              double power_mean,
                                              const char* tag_name,
                                              const char* label )
{
    list_type::iterator i = find_or_add( metric, label );
    ( *i )->pMean         = power_mean;
    if( histogram_intervals > 0 )
        ( *i )->histogram.resize( histogram_intervals + 2 );
    else
        ( *i )->histogram.clear();
    ( *i )->haveHistRange = false;
    if( !tag_name )
        ( *i )->tagName.clear();
    else
        ( *i )->tagName = tag_name;
}

QualityAssessor::list_type::iterator QualityAssessor::find_or_add( QualityMetric* qm, const char* label )
{
    list_type::iterator iter;

    // If metric is already in list, find it
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        if( ( *iter )->qualMetric == qm ) break;

    // If metric not found in list, add it
    if( iter == assessList.end() )
    {
        Assessor* new_assessor       = new Assessor( qm, label );
        new_assessor->referenceCount = 1;
        if( qm->get_metric_type() == QualityMetric::VERTEX_BASED )
        {
            assessList.push_back( new_assessor );
            iter = --assessList.end();
        }
        else
        {
            assessList.push_front( new_assessor );
            iter = assessList.begin();
        }
    }

    return iter;
}

QualityAssessor::list_type::iterator QualityAssessor::find_stopping_assessment()
{
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        if( ( *iter )->stopping_function() ) break;
    return iter;
}

/*!Sets which QualityMetric and QAFunction
combination is used to determine the value return from assess_mesh_quality().
It first ensures that the inputed QAFunction was not HISTOGRAM.  It then
calls add_quality_assessment with the given QualityMetric and QAFunction,
to ensure that this combination will be computed.  Finally, it sets
the stoppingMetric pointer and the stoppingFunction data members.
\param qm Pointer to QualityMetric.
\param func (QAFUNCTION) Wrapper function for qm (e.g. MINIMUM, MAXIMUM,...).
    */
void QualityAssessor::set_stopping_assessment( QualityMetric* metric,
                                               int histogram_intervals,
                                               double power_mean,
                                               const char* tag_name,
                                               const char* label )
{
    list_type::iterator i = find_stopping_assessment();
    if( i != assessList.end() ) ( *i )->set_stopping_function( false );

    i             = find_or_add( metric, label );
    ( *i )->pMean = power_mean;
    if( histogram_intervals > 0 )
        ( *i )->histogram.resize( histogram_intervals + 2 );
    else
        ( *i )->histogram.clear();
    ( *i )->haveHistRange = false;
    if( !tag_name )
        ( *i )->tagName.clear();
    else
        ( *i )->tagName = tag_name;
    ( *i )->set_stopping_function( true );
}

/*!
Checks first to see if the QualityMetric, qm, has been added to this
QualityAssessor, and if it has not, adds it.  It then adds HISTOGRAM as a
QAFunciton for that metric.  It then sets the minimum and maximum values
for the histogram.
\param qm Pointer to the QualityMetric to be used in histogram.
\param min_val (double) Minimum range of histogram.
\param max_val (double) Maximum range of histogram.
\param intervals Number of histogram intervals
    */
void QualityAssessor::add_histogram_assessment( QualityMetric* metric,
                                                double min_val,
                                                double max_val,
                                                int intervals,
                                                double power_mean,
                                                const char* tag_name,
                                                const char* label )
{
    if( intervals < 1 ) intervals = 1;
    list_type::iterator i = find_or_add( metric, label );
    ( *i )->pMean         = power_mean;
    ( *i )->histMin       = min_val;
    ( *i )->histMax       = max_val;
    ( *i )->haveHistRange = min_val < max_val;
    ( *i )->histogram.resize( intervals + 2 );
    if( !tag_name )
        ( *i )->tagName.clear();
    else
        ( *i )->tagName = tag_name;
}

TagHandle QualityAssessor::get_tag( Mesh* mesh, std::string name, Mesh::TagType type, unsigned size, MsqError& err )
{
    TagHandle tag = mesh->tag_get( name, err );
    if( !err )
    {
        Mesh::TagType exist_type;
        std::string junk;
        unsigned exist_size;
        mesh->tag_properties( tag, junk, exist_type, exist_size, err );
        MSQ_ERRZERO( err );
        if( type != exist_type || size != exist_size )
        {
            MSQ_SETERR( err )
            ( MsqError::TAG_ALREADY_EXISTS, "Tag \"%s\" exists with incorrect type or length.", name.c_str() );
        }
    }
    else if( err.error_code() == MsqError::TAG_NOT_FOUND )
    {
        err.clear();
        tag = mesh->tag_create( name, type, size, 0, err );
        MSQ_ERRZERO( err );
    }
    else
    {
        MSQ_ERRZERO( err );
    }

    return tag;
}

void QualityAssessor::initialize_queue( MeshDomainAssoc* mesh_and_domain, const Settings* settings, MsqError& err )
{
    for( list_type::iterator i = assessList.begin(); i != assessList.end(); ++i )
    {
        ( *i )->get_metric()->initialize_queue( mesh_and_domain, settings, err );MSQ_ERRRTN( err );
    }
}

/*!
  Computes the quality data for a given
  MeshSet, ms. What quality information is calculated, depends
  on what has been requested through the use of the QualityAssessor
  constructor, add_quality_assessment(), and set_stopping_assessment().
  The resulting data is printed in a table unless disable_printing_results()
  has been called.  The double returned depends on the QualityMetric
  and QAFunction "return" combination, which can be set using
  set_stopping_assessemnt().
  \param ms (const MeshSet &) MeshSet used for quality assessment.
 */
double QualityAssessor::loop_over_mesh( MeshDomainAssoc* mesh_and_domain, const Settings* settings, MsqError& err )
{
    return loop_over_mesh_internal( mesh_and_domain, settings, NULL, err );
}

/*!
  Computes the quality data for a given
  MeshSet, ms. What quality information is calculated, depends
  on what has been requested through the use of the QualityAssessor
  constructor, add_quality_assessment(), and set_stopping_assessment().
  The resulting data is printed in a table unless disable_printing_results()
  has been called.  The double returned depends on the QualityMetric
  and QAFunction "return" combination, which can be set using
  set_stopping_assessemnt().
  \param ms (const MeshSet &) MeshSet used for quality assessment.
 */
double QualityAssessor::loop_over_mesh( ParallelMesh* mesh,
                                        MeshDomain* domain,
                                        const Settings* settings,
                                        MsqError& err )
{
    MeshDomainAssoc mesh_and_domain = MeshDomainAssoc( (Mesh*)mesh, domain, false, true );
    return loop_over_mesh_internal( &mesh_and_domain, settings, mesh->get_parallel_helper(), err );
}

double QualityAssessor::loop_over_mesh_internal( MeshDomainAssoc* mesh_and_domain,
                                                 const Settings* settings,
                                                 ParallelHelper* helper,
                                                 MsqError& err )
{
    // Clear out any previous data
    reset_data();

    // Clear culling flag, set hard fixed flag, etc on all vertices
    initialize_vertex_byte( mesh_and_domain, settings, err );
    MSQ_ERRZERO( err );

    Mesh* mesh         = mesh_and_domain->get_mesh();
    MeshDomain* domain = mesh_and_domain->get_domain();
    invalid_values     = false;

    PatchData patch;
    patch.set_mesh( mesh );
    patch.set_domain( domain );
    if( settings ) patch.attach_settings( settings );

    ElementPatches elem_patches;
    elem_patches.set_mesh( mesh );
    VertexPatches vert_patches( 1, false );
    vert_patches.set_mesh( mesh );

    std::vector< PatchSet::PatchHandle > patches;
    std::vector< PatchSet::PatchHandle >::iterator p;
    std::vector< Mesh::VertexHandle > patch_verts;
    std::vector< Mesh::ElementHandle > patch_elems;
    std::vector< size_t > metric_handles;

    // Check if we really need the helper
    if( helper && helper->get_nprocs() == 1 ) helper = 0;

    // Get any necessary tag handles.
    TagHandle invertedTag = 0;
    if( tagging_inverted_elements() )
    {
        invertedTag = get_tag( mesh, invertedTagName, Mesh::INT, 1, err );
        MSQ_ERRZERO( err );
    }
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        if( ( *iter )->write_to_tag() )
        {
            ( *iter )->tagHandle = get_tag( mesh, ( *iter )->tagName, Mesh::DOUBLE, 1, err );
            MSQ_ERRZERO( err );
        }
    }

    TagHandle fixedTag = 0;
    if( tagging_fixed_elements() )
    {
        fixedTag = get_tag( mesh, fixedTagName, Mesh::INT, 1, err );
        MSQ_ERRZERO( err );
    }

    // Record the type of metric for each assessment so that it can be
    // included in the QualitySummary report.
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        ElementAvgQM* avg_ptr    = dynamic_cast< ElementAvgQM* >( ( *iter )->get_metric() );
        ElementMaxQM* max_ptr    = dynamic_cast< ElementMaxQM* >( ( *iter )->get_metric() );
        TMPQualityMetric* tq_ptr = dynamic_cast< TMPQualityMetric* >( ( *iter )->get_metric() );
        if( avg_ptr )
            ( *iter )->assessScheme = ELEMENT_AVG_QM;
        else if( max_ptr )
            ( *iter )->assessScheme = ELEMENT_MAX_QM;
        else if( tq_ptr )
            ( *iter )->assessScheme = TMP_QUALITY_METRIC;
        else
            ( *iter )->assessScheme = QUALITY_METRIC;
    }

    // Check for any metrics for which a histogram is to be
    // calculated and for which the user has not specified
    // minimum and maximum values.
    // Element-based metrics are first in list, followed
    // by vertex-based metrics.  Find first vertex-based
    // metric also such that element metrics go from
    // assessList.begin() to elem_end and vertex metrics
    // go from elem_end to assessList.end()
    list_type::iterator elem_end       = assessList.end();
    bool need_second_pass_for_elements = false;
    bool need_second_pass_for_vertices = false;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        if( ( *iter )->get_metric()->get_metric_type() == QualityMetric::VERTEX_BASED ) break;

        if( ( *iter )->have_histogram() && !( *iter )->haveHistRange ) need_second_pass_for_elements = true;
    }
    elem_end = iter;
    for( ; iter != assessList.end(); ++iter )
    {
        if( ( *iter )->have_histogram() && !( *iter )->haveHistRange ) need_second_pass_for_vertices = true;
    }

    // Do element-based metrics
    elem_patches.get_patch_handles( patches, err );
    MSQ_ERRZERO( err );

    myData->invertedElementCount = myData->invertedSampleCount = myData->sampleCount = 0;
    myData->elementCount                                                             = patches.size();
    myData->freeElementCount                                                         = 0;

    int inverted, samples;
    bool first_pass = false;
    do
    {  // might need to loop twice to calculate histograms
        first_pass = !first_pass;

        // until there are no more patches
        // there is another get_next_patch at
        // the end of this loop
        for( p = patches.begin(); p != patches.end(); ++p )
        {
            elem_patches.get_patch( *p, patch_elems, patch_verts, err );
            MSQ_ERRZERO( err );

            if( helper )
            {
                bool ours = helper->is_our_element( patch_elems[0], err );
                MSQ_ERRZERO( err );
                if( !ours )
                {
                    --myData->elementCount;
                    continue;
                }
            }
            patch.set_mesh_entities( patch_elems, patch_verts, err );
            MSQ_ERRZERO( err );

            if( first_pass )
            {
                // record element type for use in print_summary
                for( size_t i = 0; i < patch.num_elements(); i++ )
                {
                    const MsqMeshEntity* elem = &patch.element_by_index( i );
                    EntityTopology topo       = elem->get_element_type();
                    elementTypeCount[topo - POLYGON]++;
                }
            }

            if( 0 == patch.num_free_vertices() )
            {
                if( tagging_fixed_elements() )
                {
                    Mesh::ElementHandle h = patch.get_element_handles_array()[0];
                    int val               = 1;
                    mesh->tag_set_element_data( fixedTag, 1, &h, &val, err );
                    MSQ_ERRZERO( err );
                }
                if( skipFixedSamples ) continue;
            }

            // first check for inverted elements
            if( first_pass )
            {
                ++myData->freeElementCount;
                inverted = samples = 0;
                patch.element_by_index( 0 ).check_element_orientation( patch, inverted, samples, err );
                MSQ_ERRZERO( err );
                myData->invertedElementCount += ( inverted != 0 );
                myData->invertedSampleCount += inverted;
                myData->sampleCount += samples;

                if( tagging_inverted_elements() )
                {
                    Mesh::ElementHandle h = patch.get_element_handles_array()[0];
                    int val               = ( inverted != 0 );
                    mesh->tag_set_element_data( invertedTag, 1, &h, &val, err );
                    MSQ_ERRZERO( err );
                }
            }

            // now process all element-based metrics
            for( iter = assessList.begin(); iter != elem_end; ++iter )
            {
                // If first pass, get values for all metrics
                if( first_pass )
                {
                    double value = 0.0;
                    metric_handles.clear();
                    QualityMetric* qm = ( *iter )->get_metric();
                    qm->get_single_pass( patch, metric_handles, skipFixedSamples, err );
                    MSQ_ERRZERO( err );
                    for( std::vector< size_t >::iterator j = metric_handles.begin(); j != metric_handles.end(); ++j )
                    {
                        bool valid = ( *iter )->get_metric()->evaluate( patch, *j, value, err );  // MSQ_ERRZERO(err);
                        if( err.error_code() == err.BARRIER_VIOLATED )
                        {
                            err.clear();
                            invalid_values = true;
                        }
                        ( *iter )->add_value( value );
                        if( !valid ) ( *iter )->add_invalid_value();
                    }
                    // we don't do tag stuff unless metric is truely element-based
                    // (only one value per element)
                    if( ( *iter )->write_to_tag() && metric_handles.size() == 1 )
                    {
                        Mesh::ElementHandle h = patch.get_element_handles_array()[0];
                        mesh->tag_set_element_data( ( *iter )->tagHandle, 1, &h, &value, err );
                        MSQ_ERRZERO( err );
                    }
                }
                // If second pass, only do metrics for which the
                // histogram hasn't been calculated yet.
                else if( ( *iter )->have_histogram() && !( *iter )->haveHistRange )
                {
                    metric_handles.clear();
                    QualityMetric* qm = ( *iter )->get_metric();
                    qm->get_evaluations( patch, metric_handles, skipFixedSamples, err );
                    MSQ_ERRZERO( err );
                    for( std::vector< size_t >::iterator j = metric_handles.begin(); j != metric_handles.end(); ++j )
                    {
                        double value;
                        ( *iter )->get_metric()->evaluate( patch, *j, value, err );
                        MSQ_ERRZERO( err );
                        ( *iter )->add_hist_value( value );
                    }
                }
            }
        }
        if( MSQ_CHKERR( err ) ) return 0.0;

        // Fix up any histogram ranges which were calculated
        for( iter = assessList.begin(); iter != elem_end; ++iter )
            if( ( *iter )->have_histogram() && !( *iter )->haveHistRange )
                if( first_pass )
                {
                    if( helper )
                    {
                        helper->communicate_min_max_to_all( &( ( *iter )->minimum ), &( ( *iter )->maximum ), err );
                        MSQ_ERRZERO( err );
                    }

                    ( *iter )->calculate_histogram_range();
                    // Uncomment the following to have the QA keep the first
                    // calculated histogram range for all subsequent iterations.
                    //          else
                    //            (*iter)->haveHistRange = true;
                }
    } while( first_pass && need_second_pass_for_elements && !invalid_values );

    // Do vertex-based metrics
    if( assessList.end() != elem_end )
    {
        vert_patches.get_patch_handles( patches, err );
        MSQ_ERRZERO( err );

        first_pass = false;
        do
        {  // might need to loop twice to calculate histograms
            first_pass = !first_pass;

            // until there are no more patches
            // there is another get_next_patch at
            // the end of this loop
            for( p = patches.begin(); p != patches.end(); ++p )
            {
                vert_patches.get_patch( *p, patch_elems, patch_verts, err );
                MSQ_ERRZERO( err );
                patch.set_mesh_entities( patch_elems, patch_verts, err );
                MSQ_ERRZERO( err );
                if( skipFixedSamples && 0 == patch.num_free_vertices() ) continue;

                Mesh::VertexHandle vert_handle = reinterpret_cast< Mesh::VertexHandle >( *p );

                for( iter = elem_end; iter != assessList.end(); ++iter )
                {
                    // If first pass, get values for all metrics
                    if( first_pass )
                    {
                        double value = 0.0;
                        metric_handles.clear();
                        QualityMetric* qm = ( *iter )->get_metric();
                        qm->get_single_pass( patch, metric_handles, skipFixedSamples, err );
                        MSQ_ERRZERO( err );
                        for( std::vector< size_t >::iterator j = metric_handles.begin(); j != metric_handles.end();
                             ++j )
                        {
                            bool valid = ( *iter )->get_metric()->evaluate( patch, *j, value, err );
                            MSQ_ERRZERO( err );
                            ( *iter )->add_value( value );
                            if( !valid ) ( *iter )->add_invalid_value();
                        }
                        // we don't do tag stuff unless metric is truely vertex-based
                        // (only one value per vertex)
                        if( ( *iter )->write_to_tag() && metric_handles.size() == 1 )
                        {
                            mesh->tag_set_vertex_data( ( *iter )->tagHandle, 1, &vert_handle, &value, err );
                            MSQ_ERRZERO( err );
                        }
                    }
                    // If second pass, only do metrics for which the
                    // histogram hasn't been calculated yet.
                    else if( ( *iter )->have_histogram() && !( *iter )->haveHistRange )
                    {
                        metric_handles.clear();
                        QualityMetric* qm = ( *iter )->get_metric();
                        qm->get_evaluations( patch, metric_handles, skipFixedSamples, err );
                        MSQ_ERRZERO( err );
                        for( std::vector< size_t >::iterator j = metric_handles.begin(); j != metric_handles.end();
                             ++j )
                        {
                            double value;
                            ( *iter )->get_metric()->evaluate( patch, *j, value, err );
                            MSQ_ERRZERO( err );
                            ( *iter )->add_hist_value( value );
                        }
                    }
                }
            }
            if( MSQ_CHKERR( err ) ) return 0.0;

            // Fix up any histogram ranges which were calculated
            for( iter = elem_end; iter != assessList.end(); ++iter )
                if( ( *iter )->have_histogram() && !( *iter )->haveHistRange )
                    if( first_pass )
                    {
                        if( helper )
                        {
                            helper->communicate_min_max_to_all( &( ( *iter )->minimum ), &( ( *iter )->maximum ), err );
                            MSQ_ERRZERO( err );
                        }
                        ( *iter )->calculate_histogram_range();
                        // Uncomment the following to have the QA keep the first
                        // calculated histogram range for all subsequent iterations.
                        //          else
                        //            (*iter)->haveHistRange = true;
                    }
        } while( first_pass && need_second_pass_for_vertices && !invalid_values );
    }

    if( helper )
    {
        for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        {

            helper->communicate_min_max_to_zero( &( ( *iter )->minimum ), &( ( *iter )->maximum ), err );
            MSQ_ERRZERO( err );

            helper->communicate_sums_to_zero( &myData->freeElementCount, &myData->invertedElementCount,
                                              &myData->elementCount, &myData->invertedSampleCount, &myData->sampleCount,
                                              &( ( *iter )->count ), &( ( *iter )->numInvalid ), &( ( *iter )->sum ),
                                              &( ( *iter )->sqrSum ), err );
            MSQ_ERRZERO( err );

            if( ( *iter )->have_power_mean() )
            {
                helper->communicate_power_sum_to_zero( &( ( *iter )->pMean ), err );
                MSQ_ERRZERO( err );
            }

            if( ( *iter )->have_histogram() )
            {
                helper->communicate_histogram_to_zero( ( *iter )->histogram, err );
                MSQ_ERRZERO( err );
            }
        }
    }

    // Print results, if requested
    if( printSummary && ( !helper || helper->get_rank() == 0 ) ) print_summary( this->outputStream );

    list_type::iterator i = find_stopping_assessment();
    return i == assessList.end() ? 0 : ( *i )->stopping_function_value();
}

bool QualityAssessor::invalid_elements() const
{
    bool result = false;
    list_type::const_iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        if( ( *iter )->get_invalid_element_count() ) result = true;
    return result;
}

void QualityAssessor::reset_data()
{
    list_type::iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        ( *iter )->reset_data();
    myData->invertedElementCount = -1;
    myData->invertedSampleCount  = -1;

    for( int i = POLYGON; i <= MIXED; i++ )
        elementTypeCount[i - POLYGON] = 0;
}

void QualityAssessor::scale_histograms( QualityAssessor* optimized )
{
    // find the histograms to scale
    list_type::iterator iter;
    list_type::iterator initial;
    list_type::iterator optimal;
    bool initial_found = false, optimal_found = false;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        if( ( *iter )->histogram.size() > 0 )
        {
            if( initial_found == false )
            {
                initial       = iter;
                initial_found = true;
                break;
            }
        }
    }
    for( iter = optimized->assessList.begin(); iter != optimized->assessList.end(); ++iter )
    {
        if( ( *iter )->histogram.size() > 0 )
        {
            optimal       = iter;
            optimal_found = true;
            break;
        }
    }
    if( !initial_found || !optimal_found )
    {
        // issue warning: orig histograms not found
        if( !initial_found )
            outputStream << "WARNING: 'before' histogram not found" << std::endl;
        else
            outputStream << "WARNING: 'after' histogram not found" << std::endl;
        return;
    }

    // check number of intervals (bins) for each histogram
    int num_intervals = ( *initial )->histogram.size() - 2;
    if( num_intervals != int( ( *optimal )->histogram.size() - 2 ) )
    {
        // issue warning: number of intervals not the same
        outputStream << "WARNING: histogram intervals are not the same" << std::endl;
        return;
    }

    // calculate new max and min values
    double combined_min, combined_max;
    if( ( *initial )->histMin < ( *optimal )->histMin )
        combined_min = ( *initial )->histMin;
    else
        combined_min = ( *optimal )->histMin;

    if( ( *initial )->histMax > ( *optimal )->histMax )
        combined_max = ( *initial )->histMax;
    else
        combined_max = ( *optimal )->histMax;

    // put the before quality values into the correct new bins

    // First and last values in array are counts of valuesnum_intervals+1
    // outside the user-specified range of the histogram
    // (below and above, respectively.)
    std::vector< int > new_initial_histogram;
    new_initial_histogram.resize( ( *initial )->histogram.size(), 0 );
    new_initial_histogram[0] = ( *initial )->histogram[0];
    new_initial_histogram[new_initial_histogram.size() - 1] =
        ( *initial )->histogram[( *initial )->histogram.size() - 1];

    // Re-calculate which interval the value is in.  Add one
    // because first entry is for values below user-specifed
    // minimum value for histogram.
    double combined_range = combined_max - combined_min;
    double initial_min    = ( *initial )->histMin;
    double optimal_min    = ( *optimal )->histMin;
    double initial_range  = ( *initial )->histMax - ( *initial )->histMin;
    double optimal_range  = ( *optimal )->histMax - ( *optimal )->histMin;
    double combined_step  = combined_range / num_intervals;
    double initial_step   = initial_range / num_intervals;
    double optimal_step   = optimal_range / num_intervals;
    // round steps to 3 significant digits
    if( combined_step >= 0.001 ) combined_step = round_to_3_significant_digits( combined_step );
    if( initial_step >= 0.001 ) initial_step = round_to_3_significant_digits( initial_step );
    if( optimal_step >= 0.001 ) optimal_step = round_to_3_significant_digits( optimal_step );

    // populate initial histogram
    if( initial_range == combined_range )
    {
        // just copy histogram
        new_initial_histogram = ( *initial )->histogram;
    }
    else
    {
        for( size_t i = 1; i < new_initial_histogram.size() - 1; i++ )
        {
            double combined_bin_value = combined_min + ( combined_step * ( i - 1 ) );
            for( size_t j = 1; j < new_initial_histogram.size() - 1; j++ )
            {
                double initial_bin_value = initial_min + ( initial_step * ( j - 1 ) );
                if( initial_bin_value >= combined_bin_value && initial_bin_value < combined_bin_value + combined_step )
                {
                    new_initial_histogram[i] += ( *initial )->histogram[j];
                }
            }
        }
    }

    // put the optimal quality values into the correct new bins
    std::vector< int > new_optimal_histogram;
    new_optimal_histogram.resize( ( *optimal )->histogram.size(), 0 );
    new_optimal_histogram[0] = ( *optimal )->histogram[0];
    new_optimal_histogram[new_optimal_histogram.size() - 1] =
        ( *optimal )->histogram[( *optimal )->histogram.size() - 1];

    // populate optimal histogram
    if( optimal_range == combined_range )
    {
        // just copy histogram
        new_optimal_histogram = ( *optimal )->histogram;
    }
    else
    {
        for( size_t i = 1; i < new_optimal_histogram.size() - 1; i++ )
        {
            double combined_bin_value = combined_min + ( combined_step * ( i - 1 ) );
            for( size_t j = 1; j < new_optimal_histogram.size() - 1; j++ )
            {
                double optimal_bin_value = optimal_min + ( optimal_step * ( j - 1 ) );
                if( optimal_bin_value >= combined_bin_value && optimal_bin_value < combined_bin_value + combined_step )
                {
                    new_optimal_histogram[i] += ( *optimal )->histogram[j];
                }
            }
        }
    }

    // determine largest number of values in a 'bin' for both histograms
    unsigned i;
    int max_interval_num = 1;
    for( i = 0; i < new_initial_histogram.size(); ++i )
    {
        if( new_initial_histogram[i] > max_interval_num ) max_interval_num = new_initial_histogram[i];
    }
    for( i = 0; i < new_optimal_histogram.size(); ++i )
    {
        if( new_optimal_histogram[i] > max_interval_num ) max_interval_num = new_optimal_histogram[i];
    }

    // calculate how many bar graph characters will represent the
    // largest 'bin' value.
    // create the 'before' histogram
    int termwidth         = get_terminal_width();
    const char indent[]   = "   ";
    const char GRAPH_CHAR = '=';                              // Character used to create bar graphs
    const int TOTAL_WIDTH = termwidth > 30 ? termwidth : 70;  // Width of histogram
    int GRAPHW            = TOTAL_WIDTH - sizeof( indent );

    if( 0 == max_interval_num ) return;  // no data

    // Calculate width of field containing counts for
    // histogram intervals (log10(max_interval)).
    int num_width = 1;
    for( int temp = max_interval_num; temp > 0; temp /= 10 )
        ++num_width;
    GRAPHW -= num_width;

    // Create an array of bar graph characters for use in output
    std::vector< char > graph_chars( GRAPHW + 1, GRAPH_CHAR );

    // Check if bar-graph should be linear or log10 plot
    // Do log plot if standard deviation is less that 1.5
    // histogram intervals.

    bool log_plot = false;
    double stddev = ( *initial )->get_stddev();
    if( stddev > 0 && stddev < 2.0 * combined_step )
    {
        int new_interval = (int)( log10( (double)( 1 + max_interval_num ) ) );
        if( new_interval > 0 )
        {
            log_plot         = true;
            max_interval_num = new_interval;
        }
    }
    // output the 'before' histogram

    // Write title
    outputStream << std::endl << "************** Common-scale Histograms **************" << std::endl << std::endl;
    outputStream << indent << ( *initial )->get_label() << " histogram (initial mesh):";
    if( log_plot ) outputStream << " (log10 plot)";
    outputStream << std::endl;

    // Calculate width of a single quality interval value
    double interval_value  = 0.0;
    int max_interval_width = 0;
    std::stringstream str_stream;
    std::string interval_string;
    for( i = 0; i < new_initial_histogram.size(); ++i )
    {
        interval_value = combined_min + (i)*combined_step;
        if( combined_step >= .001 ) interval_value = round_to_3_significant_digits( interval_value );
        str_stream.clear();
        str_stream.str( "" );
        interval_string = "";
        str_stream << interval_value;
        interval_string = str_stream.str();
        if( interval_string.length() > (size_t)max_interval_width ) max_interval_width = interval_string.length();
    }

    // adjust graph width for actual size of interval values
    GRAPHW = GRAPHW - ( max_interval_width * 2 ) - 5;

    // For each interval of histogram
    for( i = 0; i < new_initial_histogram.size(); ++i )
    {
        // First value is the count of the number of values that
        // were below the minimum value of the histogram.
        if( 0 == i )
        {
            if( 0 == new_initial_histogram[i] ) continue;
            outputStream << indent << std::setw( max_interval_width ) << "under min";
        }
        // Last value is the count of the number of values that
        // were above the maximum value of the histogram.
        else if( i + 1 == new_initial_histogram.size() )
        {
            if( 0 == new_initial_histogram[i] ) continue;
            outputStream << indent << std::setw( max_interval_width ) << "over max";
        }
        // Anything else is a valid interval of the histogram.
        // Print the range for each interval.
        else
        {
            double start_value = combined_min + ( i - 1 ) * combined_step;
            double end_value   = combined_min + (i)*combined_step;

            if( combined_step >= 0.001 )
            {
                start_value = round_to_3_significant_digits( start_value );
                end_value   = round_to_3_significant_digits( end_value );
            }

            outputStream << indent << "(" << std::setw( max_interval_width ) << std::right << start_value << "-"
                         << std::setw( max_interval_width ) << std::left << end_value << ") |";
        }

        // Print bar graph

        // First calculate the number of characters to output
        int num_graph;
        if( log_plot )
            num_graph = GRAPHW * (int)log10( (double)( 1 + new_initial_histogram[i] ) ) / max_interval_num;
        else
            num_graph = GRAPHW * new_initial_histogram[i] / max_interval_num;

        // print num_graph characters using array of fill characters.
        graph_chars[num_graph] = '\0';
        outputStream << arrptr( graph_chars );
        graph_chars[num_graph] = GRAPH_CHAR;

        // Print interval count.
        outputStream << new_initial_histogram[i] << std::endl;
    }

    outputStream << "  metric was evaluated " << ( *initial )->count << " times." << std::endl << std::endl;

    // output the 'after' histogram
    outputStream << std::endl << indent << ( *optimal )->get_label() << " histogram (optimal mesh):";
    if( log_plot ) outputStream << " (log10 plot)";
    outputStream << std::endl;

    // For each interval of histogram
    for( i = 0; i < new_optimal_histogram.size(); ++i )
    {
        // First value is the count of the number of values that
        // were below the minimum value of the histogram.
        if( 0 == i )
        {
            if( 0 == new_optimal_histogram[i] ) continue;
            outputStream << indent << std::setw( max_interval_width ) << "under min";
        }
        // Last value is the count of the number of values that
        // were above the maximum value of the histogram.
        else if( i + 1 == new_optimal_histogram.size() )
        {
            if( 0 == new_optimal_histogram[i] ) continue;
            outputStream << indent << std::setw( max_interval_width ) << "over max";
        }
        // Anything else is a valid interval of the histogram.
        // Print the range for each interval.
        else
        {
            double start_value = combined_min + ( i - 1 ) * combined_step;
            double end_value   = combined_min + (i)*combined_step;

            if( combined_step >= 0.001 )
            {
                start_value = round_to_3_significant_digits( start_value );
                end_value   = round_to_3_significant_digits( end_value );
            }

            outputStream << indent << "(" << std::setw( max_interval_width ) << std::right << start_value << "-"
                         << std::setw( max_interval_width ) << std::left << end_value << ") |";
        }

        // Print bar graph

        // First calculate the number of characters to output
        int num_graph;
        if( log_plot )
            num_graph = GRAPHW * (int)log10( (double)( 1 + new_optimal_histogram[i] ) ) / max_interval_num;
        else
            num_graph = GRAPHW * new_optimal_histogram[i] / max_interval_num;

        // print num_graph characters using array of fill characters.
        graph_chars[num_graph] = '\0';
        outputStream << arrptr( graph_chars );
        graph_chars[num_graph] = GRAPH_CHAR;

        // Print interval count.
        outputStream << new_optimal_histogram[i] << std::endl;
    }

    outputStream << "  metric was evaluated " << ( *optimal )->count << " times." << std::endl << std::endl;

    return;
}

QualityAssessor::Assessor::Assessor( QualityMetric* metric, const char* label )
    : qualMetric( metric ), mLabel( label ? std::string( label ) : metric->get_name() ), pMean( 0.0 ),
      haveHistRange( false ), histMin( 1.0 ), histMax( 0.0 ), tagHandle( 0 ), stoppingFunction( false ),
      referenceCount( 0 ), assessScheme( NO_SCHEME )
{
    reset_data();
}

const QualityAssessor::Assessor* QualityAssessor::get_results( QualityMetric* metric ) const
{
    list_type::const_iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        if( ( *iter )->get_metric() == metric ) return *iter;
    return 0;
}

const QualityAssessor::Assessor* QualityAssessor::get_results( const char* name ) const
{
    list_type::const_iterator iter;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        if( ( *iter )->get_label() == name ) return *iter;
    return 0;
}

void QualityAssessor::Assessor::get_histogram( double& lower_bound_out,
                                               double& upper_bound_out,
                                               std::vector< int >& counts_out,
                                               MsqError& err ) const
{
    if( !have_histogram() )
    {
        MSQ_SETERR( err )( "No histogram calculated.", MsqError::INVALID_STATE );
        return;
    }

    lower_bound_out = histMin;
    upper_bound_out = histMax;
    counts_out      = histogram;
}

void QualityAssessor::Assessor::reset_data()
{
    count        = 0;
    sum          = 0;
    maximum      = -HUGE_VAL;
    minimum      = HUGE_VAL;
    sqrSum       = 0;
    pSum         = 0;
    numInvalid   = 0;
    assessScheme = NO_SCHEME;
    // zero histogram data
    size_t hist_size = histogram.size();
    histogram.clear();
    histogram.resize( hist_size, 0 );
}

void QualityAssessor::Assessor::add_value( double metric_value )
{
    sum += metric_value;
    sqrSum += metric_value * metric_value;
    if( metric_value > maximum ) maximum = metric_value;
    if( metric_value < minimum ) minimum = metric_value;
    // Only add value to histogram data from this function if
    // the user has specified the range.  If user has not
    // specified the range, QualityAssessor will call add_hist_value()
    // directly once the range has been calculated.
    if( have_histogram() && haveHistRange ) add_hist_value( metric_value );

    if( have_power_mean() ) pSum += pow( metric_value, pMean );

    ++count;
}

void QualityAssessor::Assessor::add_invalid_value()
{
    ++numInvalid;
}

void QualityAssessor::Assessor::add_hist_value( double metric_value )
{
    // First and last values in array are counts of values
    // outside the user-specified range of the histogram
    // (below and above, respectively.)
    if( metric_value < histMin )
        ++histogram[0];
    else if( metric_value > histMax )
        ++histogram[histogram.size() - 1];
    else
    {
        // Calculate which interval the value is in.  Add one
        // because first entry is for values below user-specifed
        // minimum value for histogram.
        double range = histMax - histMin;
        double fract;
        if( range > DBL_EPSILON )
            fract = ( metric_value - histMin ) / range;
        else
            fract = 0.0;
        unsigned cell;
        if( fabs( fract - 1.0 ) < histMax * DBL_EPSILON )
            cell = histogram.size() - 1;
        else
            cell = 1 + (int)( ( fract * ( histogram.size() - 2 ) ) );

        // Add value to interval.
        ++histogram[cell];
    }
}

void QualityAssessor::Assessor::calculate_histogram_range()
{
    double lower_bound = minimum;
    int num_intervals  = histogram.size();
    double step        = ( maximum - lower_bound ) / num_intervals;
    if( step == 0 ) step = 1.0;
    double size = pow( 10.0, floor( log10( step / ( num_intervals - 1 ) ) ) );
    if( size < 1e-6 ) size = 1.0;
    histMin = lower_bound;
    histMax = lower_bound + num_intervals * size * ceil( step / size );
}

void QualityAssessor::print_summary( std::ostream& stream ) const
{
    const int NAMEW = 19;  // Width of name column in table output
    const int NUMW  = 12;  // Width of value columns in table output

    // Print title
    stream << std::endl
           << "************** " << qualityAssessorName << " Summary **************" << std::endl
           << std::endl;

    if( myData->freeElementCount != myData->elementCount )
        stream << "  Evaluating quality for " << myData->freeElementCount << " free elements of "
               << myData->elementCount << " total elements." << std::endl;
    else
        stream << "  Evaluating quality for " << myData->elementCount << " elements." << std::endl;

    // Print element type totals
    std::string str_value = "";
    for( int i = POLYGON; i <= MIXED; i++ )
    {
        if( elementTypeCount[i - POLYGON] )
        {
            str_value = element_name_as_string( i );
            if( str_value != "" )
                stream << "  This mesh had " << elementTypeCount[i - POLYGON] << " " << str_value << " elements."
                       << std::endl;
        }
    }

    if( myData->invertedElementCount )
    {
        stream << "  THERE ARE " << myData->invertedElementCount << " INVERTED ELEMENTS. " << std::endl
               << "  (Elements invalid at " << myData->invertedSampleCount << " of " << myData->sampleCount
               << " sample locations.)" << std::endl
               << std::endl;
    }
    else
    {
        stream << "  There were no inverted elements detected. " << std::endl;
    }

    // Check if there are invalid values for any metric
    list_type::const_iterator iter;
    bool some_invalid = false;
    for( iter = assessList.begin(); iter != assessList.end(); ++iter )
    {
        if( ( *iter )->get_invalid_element_count() )
        {
            some_invalid = true;
            stream << "  " << ( *iter )->get_invalid_element_count() << " OF " << ( *iter )->get_count()
                   << " ENTITIES EVALUATED TO AN UNDEFINED VALUE FOR " << ( *iter )->get_label() << std::endl
                   << std::endl;
        }
    }
    if( !some_invalid )
    {
        stream << "  No entities had undefined values for any computed metric." << std::endl << std::endl;
    }

    if( !invalid_values )
    {
        // Check if a user-define power-mean was calculated for any of the metrics
        std::set< double > pmeans;
        for( iter = assessList.begin(); iter != assessList.end(); ++iter )
            if( ( *iter )->have_power_mean() ) pmeans.insert( ( *iter )->get_power() );

        // If power-mean of 1 or 2 was requested, change titles rather
        // than printing redundant values
        std::string average_str( "average" ), rms_str( "rms" );
        if( pmeans.find( 1.0 ) != pmeans.end() )
        {
            pmeans.erase( pmeans.find( 1.0 ) );
            average_str = "1-mean";
        }
        if( pmeans.find( 2.0 ) != pmeans.end() )
        {
            pmeans.erase( pmeans.find( 2.0 ) );
            rms_str = "2-mean";
        }

        // Number of values in table
        unsigned num_values = pmeans.size() + 5;

        // Decide how wide of a table field should be used for the metric name
        unsigned twidth    = get_terminal_width();
        unsigned maxnwidth = NAMEW;
        if( twidth )
        {
            unsigned valwidth = NUMW * num_values;
            maxnwidth         = valwidth < twidth ? twidth - valwidth : 0;
        }
        unsigned namewidth = 0;
        for( iter = assessList.begin(); iter != assessList.end(); ++iter )
            if( ( *iter )->get_label().size() > namewidth ) namewidth = ( *iter )->get_label().size();
        if( namewidth > maxnwidth ) namewidth = maxnwidth;
        if( namewidth < 7 )  // at least enough width for the column header
            namewidth = 7;

        int number_of_assessments = 0;

        // print metric values
        for( iter = assessList.begin(); iter != assessList.end(); ++iter )
        {
            if( number_of_assessments > 0 ) stream << "    -------------------------------------------" << std::endl;

            // print assessment method used to calculate the statistics
            if( ( *iter )->assessScheme == TMP_QUALITY_METRIC )
                stream << "     Sample Point Quality Statistics" << std::endl << std::endl;
            else
                stream << "     Element Quality Statistics" << std::endl << std::endl;

            // print comlumn label line
            std::set< double >::const_iterator piter;
            stream << std::setw( NUMW ) << "minimum";
            for( piter = pmeans.begin(); piter != pmeans.end() && *piter < 1.0; ++piter )
                stream << std::setw( NUMW - 6 ) << *piter << "-mean ";
            stream << std::setw( NUMW ) << average_str;
            for( ; piter != pmeans.end() && *piter < 2.0; ++piter )
                stream << std::setw( NUMW - 6 ) << *piter << "-mean ";
            stream << std::setw( NUMW ) << rms_str;
            for( ; piter != pmeans.end(); ++piter )
                stream << std::setw( NUMW - 6 ) << *piter << "-mean ";
            stream << std::setw( NUMW ) << "maximum";
            stream << std::setw( NUMW ) << "std.dev.";
            stream << std::endl;

            stream << std::setw( NUMW ) << ( *iter )->get_minimum();
            // print power-means with P less than 1.0
            for( piter = pmeans.begin(); piter != pmeans.end() && *piter < 1.0; ++piter )
            {
                if( ( *iter )->have_power_mean() && ( *iter )->get_power() == *piter )
                    stream << std::setw( NUMW ) << ( *iter )->get_power_mean();
                else
                    stream << std::setw( NUMW ) << " ";
            }
            // print average
            stream << std::setw( NUMW ) << ( *iter )->get_average();
            // print power-means with P less than 2.0
            for( ; piter != pmeans.end() && *piter < 2.0; ++piter )
            {
                if( ( *iter )->have_power_mean() && ( *iter )->get_power() == *piter )
                    stream << std::setw( NUMW ) << ( *iter )->get_power_mean();
                else
                    stream << std::setw( NUMW ) << " ";
            }
            // print RMS
            stream << std::setw( NUMW ) << ( *iter )->get_rms();
            // print power-means with P greater than 2.0
            for( ; piter != pmeans.end(); ++piter )
            {
                if( ( *iter )->have_power_mean() && ( *iter )->get_power() == *piter )
                    stream << std::setw( NUMW ) << ( *iter )->get_power_mean();
                else
                    stream << std::setw( NUMW ) << " ";
            }
            // print maximum and standard deviation
            stream << std::setw( NUMW ) << ( *iter )->get_maximum();
            stream << std::setw( NUMW ) << ( *iter )->get_stddev();
            stream << std::endl << std::endl;

            stream << "     Number of statistics = " << ( *iter )->get_count() << std::endl;

            // print name
            stream << "     Metric = " << ( *iter )->get_label() << std::endl;

            // Output the method used to calcualte the quality values
            switch( ( *iter )->assessScheme )
            {
                case ELEMENT_AVG_QM:
                    stream << "     Element Quality = average over metric values at the elements' "
                              "sample points"
                           << std::endl
                           << std::endl;
                    break;
                case ELEMENT_MAX_QM:
                    stream << "     Element Quality = maximum over metric values at the elements' "
                              "sample points"
                           << std::endl
                           << std::endl;
                    break;
                case TMP_QUALITY_METRIC:
                    stream << std::endl << std::endl;
                    break;
                case QUALITY_METRIC:
                    stream << "     Element Quality not based on sample points." << std::endl << std::endl;
                    break;
                default:
                    stream << "     Scheme used for deriving qualitiy values unknown" << std::endl << std::endl;
            }
            if( ( *iter )->have_histogram() ) ( *iter )->print_histogram( stream, get_terminal_width() );
            number_of_assessments++;
        }
    }
    else
    {
        stream << "  Element Quality Statistics are Undefined for this Metric because" << std::endl
               << "  there are Inverted Elements" << std::endl
               << std::endl;
    }
}

void QualityAssessor::Assessor::print_histogram( std::ostream& stream, int termwidth ) const
{
    // Portability notes:
    //  Use log10 rather than log10f because the float variations require
    //  including platform-dependent headers on some platforms.
    //  Explicitly cast log10 argument to double because some platforms
    //  have overloaded float and double variations in C++ making an
    //  implicit cast from an integer ambiguous.

    const char indent[]   = "   ";
    const char GRAPH_CHAR = '=';                              // Character used to create bar graphs
    const int TOTAL_WIDTH = termwidth > 30 ? termwidth : 70;  // Width of histogram
    int GRAPHW            = TOTAL_WIDTH - sizeof( indent );

    // range is either user-specified (histMin & histMax) or
    // calculated (minimum & maximum)
    double min, max;
    min = histMin;
    max = histMax;
    // Witdh of one interval of histogram
    double step = ( max - min ) / ( histogram.size() - 2 );
    // round step to 3 significant digits

    if( step >= 0.001 ) step = round_to_3_significant_digits( step );

    // Find maximum value for an interval bin of the histogram
    unsigned i;
    int max_bin_value = 1;
    for( i = 0; i < histogram.size(); ++i )
        if( histogram[i] > max_bin_value ) max_bin_value = histogram[i];

    if( 0 == max_bin_value ) return;  // no data

    // Calculate width of field containing counts for
    // histogram intervals (log10(max_bin_value)).
    int num_width = 1;
    for( int temp = max_bin_value; temp > 0; temp /= 10 )
        ++num_width;
    GRAPHW -= num_width;

    // Create an array of bar graph characters for use in output
    std::vector< char > graph_chars( GRAPHW + 1, GRAPH_CHAR );

    // Check if bar-graph should be linear or log10 plot
    // Do log plot if standard deviation is less that 1.5
    // histogram intervals.
    bool log_plot = false;
    double stddev = get_stddev();
    if( stddev > 0 && stddev < 2.0 * step )
    {
        int new_interval = (int)( log10( (double)( 1 + max_bin_value ) ) );
        if( new_interval > 0 )
        {
            log_plot      = true;
            max_bin_value = new_interval;
        }
    }

    // Write title
    stream << indent << get_label() << " histogram:";
    if( log_plot ) stream << " (log10 plot)";
    stream << std::endl;

    // Calculate width of a single quality interval value

    double interval_value  = 0.0;
    int max_interval_width = 0;
    std::stringstream str_stream;
    std::string interval_string;
    for( i = 0; i < histogram.size(); ++i )
    {
        interval_value = min + (i)*step;
        if( step >= 0.001 ) interval_value = round_to_3_significant_digits( interval_value );
        str_stream.clear();
        str_stream.str( "" );
        interval_string = "";
        str_stream << interval_value;
        interval_string = str_stream.str();
        if( interval_string.length() > (size_t)max_interval_width ) max_interval_width = interval_string.length();
    }

    // adjust graph width for actual size of interval values
    GRAPHW = GRAPHW - ( max_interval_width * 2 ) - 5;

    // For each interval of histogram
    for( i = 0; i < histogram.size(); ++i )
    {
        // First value is the count of the number of values that
        // were below the minimum value of the histogram.
        if( 0 == i )
        {
            if( 0 == histogram[i] ) continue;
            stream << indent << std::setw( max_interval_width ) << "under min";
        }
        // Last value is the count of the number of values that
        // were above the maximum value of the histogram.
        else if( i + 1 == histogram.size() )
        {
            if( 0 == histogram[i] ) continue;
            stream << indent << std::setw( max_interval_width ) << "over max";
        }
        // Anything else is a valid interval of the histogram.
        // Print the range for each interval.
        else
        {
            double start_value = min + ( i - 1 ) * step;
            double end_value   = min + (i)*step;
            if( step >= 0.001 )
            {
                start_value = round_to_3_significant_digits( start_value );
                end_value   = round_to_3_significant_digits( end_value );
            }

            stream << indent << "(" << std::setw( max_interval_width ) << std::right << start_value << "-"
                   << std::setw( max_interval_width ) << std::left << end_value << ") |";

            // reset stream alignment to right (the default)
            stream << std::right;
        }

        // Print bar graph

        // First calculate the number of characters to output
        int num_graph;
        if( log_plot )
            num_graph = GRAPHW * (int)log10( (double)( 1 + histogram[i] ) ) / max_bin_value;
        else
            num_graph = GRAPHW * histogram[i] / max_bin_value;

        // print num_graph characters using array of fill characters.
        graph_chars[num_graph] = '\0';
        stream << arrptr( graph_chars );
        graph_chars[num_graph] = GRAPH_CHAR;

        // Print interval count.
        stream << histogram[i] << std::endl;
    }
    stream << "  metric was evaluated " << count << " times." << std::endl << std::endl;
}

#ifdef _WIN32
#define fileno( A ) _fileno( ( A ) )
#endif
int QualityAssessor::get_terminal_width() const
{
#ifdef TIOCGWINSZ
    int fd = -1;
    if( &outputStream == &std::cout )
        fd = fileno( stdout );
    else if( &outputStream == &std::cerr )
        fd = fileno( stderr );
#ifdef FSTREAM_HAS_FD
    else if( std::ofstream* f = dynamic_cast< std::ofstream* >( &outputStream ) )
        fd = f->rdbuf()->fd();
#endif

    if( fd >= 0 )
    {
        struct winsize ws;
        if( ioctl( fd, TIOCGWINSZ, &ws ) >= 0 ) return ws.ws_col;
    }
#endif

    return 0;
}

std::string QualityAssessor::element_name_as_string( int enum_name )
{
    std::string str_value = "";

    switch( enum_name )
    {
        case POLYGON:
            str_value.assign( "polygon" );
            break;
        case TRIANGLE:
            str_value.assign( "triangle" );
            break;
        case QUADRILATERAL:
            str_value.assign( "quadrilateral" );
            break;
        case POLYHEDRON:
            str_value.assign( "polyhedron" );
            break;
        case TETRAHEDRON:
            str_value.assign( "tetrahedron" );
            break;
        case HEXAHEDRON:
            str_value.assign( "hexahedron" );
            break;
        case PRISM:
            str_value.assign( "prism" );
            break;
        case SEPTAHEDRON:
            str_value.assign( "septahedron" );
            break;
        case MIXED:
            str_value.assign( "mixed" );
            break;
        case PYRAMID:
            str_value.assign( "pyramid" );
            break;
    }

    return str_value;
}

double QualityAssessor::round_to_3_significant_digits( double number )
{
    double result = number;
    double p      = 1.0;

    if( number > 0 && number < 1000 )
    {
        if( number < 1000 )
        {
            while( number < 100 )
            {
                number *= 10;
                p *= 10;
            }
        }
        else
        {
            while( number >= 1000 )
            {
                number /= 10;
                p /= 10;
            }
        }
        int z  = int( number + 0.5 );
        result = z / p;
    }

    return result;
}

double QualityAssessor::Assessor::stopping_function_value() const
{
    return have_power_mean() ? get_power_mean() : get_average();
}

}  // namespace MBMesquite