LaplacianSmoother.cpp

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/** @example LaplacianSmoother.cpp \n
 * \brief Perform Laplacian relaxation on a mesh and its dual \n
 * To run: mpiexec -np  LaplacianSmoother [filename]\n
 *
 * Briefly, Laplacian relaxation is a technique to smooth out a mesh.  The centroid of each cell is
 * computed from its vertex positions, then vertices are placed at the average of their connected
 * cells' centroids.
 *
 * In the parallel algorithm, an extra ghost layer of cells is exchanged.  This allows us to compute
 * the centroids for boundary cells on each processor where they appear; this eliminates the need
 * for one round of data exchange (for those centroids) between processors.  New vertex positions
 * must be sent from owning processors to processors sharing those vertices.  Convergence is
 * measured as the maximum distance moved by any vertex.
 *
 * In this implementation, a fixed number of iterations is performed.  The final mesh is output to
 * 'laplacianfinal.h5m' in the current directory (H5M format must be used since the file is written
 * in parallel).
 *
 * Usage: mpiexec -n 2 valgrind ./LaplacianSmoother -f input/surfrandomtris-64part.h5m -r 2 -p 2 -n
 * 25
 */

#include 
#include 
#include "moab/Core.hpp"
#ifdef MOAB_HAVE_MPI
#include "moab/ParallelComm.hpp"
#include "MBParallelConventions.h"
#endif
#include "moab/Skinner.hpp"
#include "moab/CN.hpp"
#include "moab/ProgOptions.hpp"
#include "moab/CartVect.hpp"
#include "moab/NestedRefine.hpp"
#include "moab/VerdictWrapper.hpp"
#include "matrix.h"

using namespace moab;
using namespace std;

#define WRITE_DEBUG_FILES

#ifdef MESH_DIR
string test_file_name = string( MESH_DIR ) + string( "/surfrandomtris-4part.h5m" );
#else
string test_file_name = string( "input/surfrandomtris-4part.h5m" );
#endif

#define RC MB_CHK_ERR( rval )
#define dbgprint( MSG )                                       \
    do                                                        \
    {                                                         \
        if( !global_rank ) std::cerr << ( MSG ) << std::endl; \
    } while( false )

ErrorCode perform_laplacian_smoothing( Core* mb,
                                       Range& cells,
                                       Range& verts,
                                       int dim,
                                       Tag fixed,
                                       bool use_hc    = false,
                                       bool use_acc   = false,
                                       int acc_method = 1,
                                       int num_its    = 10,
                                       double rel_eps = 1e-5,
                                       double alpha   = 0.0,
                                       double beta    = 0.5,
                                       int report_its = 1 );

ErrorCode hcFilter( Core* mb,
                    moab::ParallelComm* pcomm,
                    moab::Range& verts,
                    int dim,
                    Tag fixed,
                    std::vector< double >& verts_o,
                    std::vector< double >& verts_n,
                    double alpha,
                    double beta );

ErrorCode laplacianFilter( Core* mb,
                           moab::ParallelComm* pcomm,
                           moab::Range& verts,
                           int dim,
                           Tag fixed,
                           std::vector< double >& verts_o,
                           std::vector< double >& verts_n,
                           bool use_updated = true );

int main( int argc, char** argv )
{
    int num_its    = 10;
    int num_ref    = 0;
    int num_dim    = 2;
    int report_its = 1;
    int num_degree = 2;
    bool use_hc    = false;
    bool use_acc   = false;
    int acc_method = 1;
    double alpha = 0.5, beta = 0.0;
    double rel_eps        = 1e-5;
    const int nghostrings = 1;
    ProgOptions opts;
    ErrorCode rval;
    std::stringstream sstr;
    int global_rank;

    MPI_Init( &argc, &argv );
    MPI_Comm_rank( MPI_COMM_WORLD, &global_rank );

    // Decipher program options from user
    opts.addOpt< int >( std::string( "niter,n" ),
                        std::string( "Number of Laplacian smoothing iterations (default=10)" ), &num_its );
    opts.addOpt< double >( std::string( "eps,e" ),
                           std::string( "Tolerance for the Laplacian smoothing error (default=1e-5)" ), &rel_eps );
    opts.addOpt< double >( std::string( "alpha" ),
                           std::string( "Tolerance for the Laplacian smoothing error (default=0.0)" ), &alpha );
    opts.addOpt< double >( std::string( "beta" ),
                           std::string( "Tolerance for the Laplacian smoothing error (default=0.5)" ), &beta );
    opts.addOpt< int >( std::string( "dim,d" ), std::string( "Topological dimension of the mesh (default=2)" ),
                        &num_dim );
    opts.addOpt< std::string >( std::string( "file,f" ),
                                std::string( "Input mesh file to smoothen (default=surfrandomtris-4part.h5m)" ),
                                &test_file_name );
    opts.addOpt< int >(
        std::string( "nrefine,r" ),
        std::string( "Number of uniform refinements to perform and apply smoothing cycles (default=1)" ), &num_ref );
    opts.addOpt< int >( std::string( "ndegree,p" ), std::string( "Degree of uniform refinement (default=2)" ),
                        &num_degree );
    opts.addOpt< void >( std::string( "humphrey,c" ),
                         std::string( "Use Humphrey’s Classes algorithm to reduce shrinkage of "
                                      "Laplacian smoother (default=false)" ),
                         &use_hc );
    opts.addOpt< void >( std::string( "aitken,d" ),
                         std::string( "Use Aitken \\delta^2 acceleration to improve convergence of "
                                      "Lapalace smoothing algorithm (default=false)" ),
                         &use_acc );
    opts.addOpt< int >( std::string( "acc,a" ),
                        std::string( "Type of vector Aitken process to use for acceleration (default=1)" ),
                        &acc_method );

    opts.parseCommandLine( argc, argv );

    // get MOAB and ParallelComm instances
    Core* mb = new Core;
    if( NULL == mb ) return 1;
    int global_size = 1;

    // get the ParallelComm instance
    ParallelComm* pcomm = new ParallelComm( mb, MPI_COMM_WORLD );
    global_size         = pcomm->size();

    string roptions, woptions;
    if( global_size > 1 )
    {  // if reading in parallel, need to tell it how
        sstr.str( "" );
        sstr << "PARALLEL=READ_PART;PARTITION=PARALLEL_PARTITION;PARALLEL_RESOLVE_SHARED_ENTS;"
                "PARALLEL_GHOSTS="
             << num_dim << ".0." << nghostrings << ";DEBUG_IO=0;DEBUG_PIO=0";
        roptions = sstr.str();
        woptions = "PARALLEL=WRITE_PART";
    }

    // read the file
    moab::EntityHandle fileset, currset;
    rval = mb->create_meshset( MESHSET_SET, fileset );
    RC;
    currset = fileset;
    rval    = mb->load_file( test_file_name.c_str(), &fileset, roptions.c_str() );
    RC;

    std::vector< EntityHandle > hsets( num_ref + 1, fileset );
    if( num_ref )
    {
        // Perform uniform refinement of the smoothed mesh
#ifdef MOAB_HAVE_MPI
        NestedRefine* uref = new NestedRefine( mb, pcomm, currset );
#else
        NestedRefine* uref = new NestedRefine( mb, 0, currset );
#endif

        std::vector< int > num_degrees( num_ref, num_degree );
        rval = uref->generate_mesh_hierarchy( num_ref, &num_degrees[0], hsets );
        RC;

        // Now exchange 1 layer of ghost elements, using vertices as bridge
        // (we could have done this as part of reading process, using the PARALLEL_GHOSTS read
        // option)
        rval = uref->exchange_ghosts( hsets, nghostrings );
        RC;

        delete uref;
    }

    for( int iref = 0; iref <= num_ref; ++iref )
    {

        // specify which set we are currently working on
        currset = hsets[iref];

        // make tag to specify fixed vertices, since it's input to the algorithm; use a default
        // value of non-fixed so we only need to set the fixed tag for skin vertices
        Tag fixed;
        int def_val = 0;
        rval        = mb->tag_get_handle( "fixed", 1, MB_TYPE_INTEGER, fixed, MB_TAG_CREAT | MB_TAG_DENSE, &def_val );
        RC;

        // get all vertices and cells
        Range verts, cells, skin_verts;
        rval = mb->get_entities_by_type( currset, MBVERTEX, verts );
        RC;
        rval = mb->get_entities_by_dimension( currset, num_dim, cells );
        RC;
        dbgprint( "Found " << verts.size() << " vertices and " << cells.size() << " elements" );

        // get the skin vertices of those cells and mark them as fixed; we don't want to fix the
        // vertices on a part boundary, but since we exchanged a layer of ghost cells, those
        // vertices aren't on the skin locally ok to mark non-owned skin vertices too, I won't move
        // those anyway use MOAB's skinner class to find the skin
        Skinner skinner( mb );
        rval = skinner.find_skin( currset, cells, true, skin_verts );
        RC;  // 'true' param indicates we want vertices back, not cells

        std::vector< int > fix_tag( skin_verts.size(), 1 );  // initialized to 1 to indicate fixed
        rval = mb->tag_set_data( fixed, skin_verts, &fix_tag[0] );
        RC;
        // exchange tags on owned verts for fixed points
        if( global_size > 1 )
        {
#ifdef MOAB_HAVE_MPI
            rval = pcomm->exchange_tags( fixed, skin_verts );
            RC;
#endif
        }

        // now perform the Laplacian relaxation
        rval = perform_laplacian_smoothing( mb, cells, verts, num_dim, fixed, use_hc, use_acc, acc_method, num_its,
                                            rel_eps, alpha, beta, report_its );
        RC;

        // output file, using parallel write
        sstr.str( "" );
        sstr << "LaplacianSmoother_" << iref << ".h5m";
        rval = mb->write_file( sstr.str().c_str(), "H5M", woptions.c_str(), &currset, 1 );
        RC;

        // delete fixed tag, since we created it here
        rval = mb->tag_delete( fixed );
        RC;
    }

    delete pcomm;
    // delete MOAB instance
    delete mb;

    MPI_Finalize();
    return 0;
}

ErrorCode perform_laplacian_smoothing( Core* mb,
                                       Range& cells,
                                       Range& verts,
                                       int dim,
                                       Tag fixed,
                                       bool use_hc,
                                       bool use_acc,
                                       int acc_method,
                                       int num_its,
                                       double rel_eps,
                                       double alpha,
                                       double beta,
                                       int report_its )
{
    ErrorCode rval;
    int global_rank = 0, global_size = 1;
    int nacc = 2; /* nacc_method: 1 = Method 2 from [1], 2 = Method 3 from [1] */
    std::vector< double > verts_acc1, verts_acc2, verts_acc3;
    double rat_theta = rel_eps, rat_alpha = rel_eps, rat_alphaprev = rel_eps;
#ifdef MOAB_HAVE_MPI
    const char* woptions = "PARALLEL=WRITE_PART";
#else
    const char* woptions = "";
#endif
    std::vector< int > fix_tag( verts.size() );

    rval = mb->tag_get_data( fixed, verts, &fix_tag[0] );
    RC;

#ifdef MOAB_HAVE_MPI
    ParallelComm* pcomm = ParallelComm::get_pcomm( mb, 0 );
    global_rank         = pcomm->rank();
    global_size         = pcomm->size();
#endif

    dbgprint( "-- Starting smoothing cycle --" );
    // perform Laplacian relaxation:
    // 1. setup: set vertex centroids from vertex coords; filter to owned verts; get fixed tags

    // get all verts coords into tag; don't need to worry about filtering out fixed verts,
    // we'll just be setting to their fixed coords
    std::vector< double > verts_o, verts_n;
    verts_o.resize( 3 * verts.size(), 0.0 );
    verts_n.resize( 3 * verts.size(), 0.0 );
    // std::vector vdata(1);
    // vdata[0] = &verts_n[0];
    // const int vdatasize = verts_n.size();
    void* vdata = &verts_n[0];
    rval        = mb->get_coords( verts, &verts_o[0] );
    RC;
    const int nbytes = sizeof( double ) * verts_o.size();

    Tag errt, vpost;
    double def_val[3] = { 0.0, 0.0, 0.0 };
    rval              = mb->tag_get_handle( "error", 1, MB_TYPE_DOUBLE, errt, MB_TAG_CREAT | MB_TAG_DENSE, def_val );
    RC;
    rval = mb->tag_get_handle( "vpos", 3, MB_TYPE_DOUBLE, vpost, MB_TAG_CREAT | MB_TAG_DENSE, def_val );
    RC;
    // rval = mb->tag_set_by_ptr(vpost, verts, vdata); RC;

    if( use_acc )
    {
        verts_acc1.resize( verts_o.size(), 0.0 );
        verts_acc2.resize( verts_o.size(), 0.0 );
        verts_acc3.resize( verts_o.size(), 0.0 );
        memcpy( &verts_acc1[0], &verts_o[0], nbytes );
        memcpy( &verts_acc2[0], &verts_o[0], nbytes );
        memcpy( &verts_acc3[0], &verts_o[0], nbytes );
    }

    // Filter verts down to owned ones and get fixed tag for them
    Range owned_verts, shared_owned_verts;
    if( global_size > 1 )
    {
#ifdef MOAB_HAVE_MPI
        rval = pcomm->filter_pstatus( verts, PSTATUS_NOT_OWNED, PSTATUS_NOT, -1, &owned_verts );MB_CHK_ERR( rval );
#endif
    }
    else
        owned_verts = verts;

#ifdef MOAB_HAVE_MPI
    // Get shared owned verts, for exchanging tags
    rval = pcomm->get_shared_entities( -1, shared_owned_verts, 0, false, true );MB_CHK_ERR( rval );
    // Workaround: if no shared owned verts, put a non-shared one in the list, to prevent exchanging
    // tags for all shared entities
    if( shared_owned_verts.empty() ) shared_owned_verts.insert( *verts.begin() );
#endif

#ifdef WRITE_DEBUG_FILES
    {
        // output file, using parallel write
        std::stringstream sstr;
        sstr << "LaplacianSmootherIterate_0.h5m";
        rval = mb->write_file( sstr.str().c_str(), NULL, woptions );
        RC;
    }
#endif

    bool check_metrics = true;
    VerdictWrapper vw( mb );
    vw.set_size( 1. );  // for relative size measures; maybe it should be user input

    double mxdelta = 0.0, global_max = 0.0;
    // 2. for num_its iterations:
    for( int nit = 0; nit < num_its; nit++ )
    {

        mxdelta = 0.0;

        // 2a. Apply Laplacian Smoothing Filter to Mesh
        if( use_hc )
        {
            rval = hcFilter( mb, pcomm, verts, dim, fixed, verts_o, verts_n, alpha, beta );
            RC;
        }
        else
        {
            rval = laplacianFilter( mb, pcomm, verts, dim, fixed, verts_o, verts_n );
            RC;
        }

        if( check_metrics )
        {
            bool smooth_success = true;
            std::vector< double > coords;
            double jac    = 0.0;
            int num_nodes = 0;
            for( unsigned ic = 0; ic < cells.size(); ++ic )
            {
                EntityHandle ecell = cells[ic];
                EntityType etype   = mb->type_from_handle( ecell );
                Range everts;
                rval = mb->get_connectivity( &ecell, 1, everts, num_nodes );
                RC;
                coords.resize( num_nodes * 3, 0.0 );
                for( int iv = 0; iv < num_nodes; ++iv )
                {
                    const int offset = mb->id_from_handle( everts[iv] ) * 3;
                    for( int ii = 0; ii < 3; ++ii )
                        coords[iv * 3 + ii] = verts_n[offset + ii];
                }
                rval = vw.quality_measure( ecell, MB_SHAPE, jac, num_nodes, etype, &coords[0] );
                RC;
                if( jac < 1e-8 )
                {
                    dbgprint( "Inverted element " << ic << " with jacobian = " << jac << "." );
                    smooth_success = false;
                    break;
                }
            }

            if( !smooth_success )
            {
                verts_o.swap( verts_n );
                dbgprint( "Found element inversions during smoothing. Stopping iterations." );
                break;
            }
        }

        if( use_acc )
        {

            // if (acc_method < 5 || nit <= 3) {
            //   memcpy( &verts_acc1[0], &verts_acc2[0], nbytes );
            //   memcpy( &verts_acc2[0], &verts_acc3[0], nbytes );
            //   memcpy( &verts_acc3[0], &verts_n[0],    nbytes );
            // }

            rat_alphaprev = rat_alpha;
            for( unsigned i = 0; i < verts_n.size(); ++i )
            {
                rat_alpha =
                    std::max( rat_alpha,
                              std::abs( ( verts_acc3[i] - verts_acc2[i] ) * ( verts_acc2[i] - verts_acc1[i] ) ) /
                                  ( ( verts_acc2[i] - verts_acc1[i] ) * ( verts_acc2[i] - verts_acc1[i] ) ) );
            }
            rat_theta = std::abs( rat_alpha / rat_alphaprev - 1.0 );

            if( nit > 3 && ( nit % nacc ) && rat_theta < 1.0 )
            {

                if( acc_method == 1 )
                { /* Method 2 from ACCELERATION OF VECTOR SEQUENCES:
                     http://onlinelibrary.wiley.com/doi/10.1002/cnm.1630020409/pdf */
                    double vnorm = 0.0, den, acc_alpha = 0.0, acc_gamma = 0.0;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        den = ( verts_acc3[i] - 2.0 * verts_acc2[i] + verts_acc1[i] );
                        vnorm += den * den;
                        acc_alpha += ( verts_acc3[i] - verts_acc2[i] ) * ( verts_acc3[i] - verts_acc2[i] );
                        acc_gamma += ( verts_acc2[i] - verts_acc1[i] ) * ( verts_acc2[i] - verts_acc1[i] );
                    }
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        verts_n[i] = verts_acc2[i] + ( acc_gamma * ( verts_acc3[i] - verts_acc2[i] ) -
                                                       acc_alpha * ( verts_acc2[i] - verts_acc1[i] ) ) /
                                                         vnorm;
                    }
                }
                else if( acc_method == 2 )
                { /* Method 3 from ACCELERATION OF VECTOR SEQUENCES:
                     http://onlinelibrary.wiley.com/doi/10.1002/cnm.1630020409/pdf */
                    double vnorm = 0.0, num = 0.0, den = 0.0, mu = 0.0;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        num +=
                            ( verts_acc3[i] - verts_acc2[i] ) * ( verts_acc3[i] - 2.0 * verts_acc2[i] + verts_acc1[i] );
                        den = ( verts_acc3[i] - 2.0 * verts_acc2[i] + verts_acc1[i] );
                        vnorm += den * den;
                    }
                    mu = num / vnorm;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        verts_n[i] = verts_acc3[i] + mu * ( verts_acc2[i] - verts_acc3[i] );
                    }
                }
                else if( acc_method == 3 )
                { /* Method 5 from ACCELERATION OF VECTOR SEQUENCES:
                     http://onlinelibrary.wiley.com/doi/10.1002/cnm.1630020409/pdf */
                    double num = 0.0, den = 0.0, mu = 0.0;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        num += ( verts_acc3[i] - verts_acc2[i] ) * ( verts_acc2[i] - verts_acc1[i] );
                        den +=
                            ( verts_acc2[i] - verts_acc1[i] ) * ( verts_acc3[i] - 2.0 * verts_acc2[i] + verts_acc1[i] );
                    }
                    mu = num / den;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        verts_n[i] = verts_acc3[i] - mu * ( verts_acc3[i] - verts_acc2[i] );
                    }
                }
                else if( acc_method == 4 )
                { /* Method 8 from ACCELERATION OF VECTOR SEQUENCES:
                     http://onlinelibrary.wiley.com/doi/10.1002/cnm.1630020409/pdf */
                    double num = 0.0, den = 0.0, lambda = 0.0;
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        num += ( verts_acc3[i] - verts_acc2[i] ) * ( verts_acc3[i] - verts_acc2[i] );
                        den += ( verts_acc2[i] - verts_acc1[i] ) * ( verts_acc2[i] - verts_acc1[i] );
                    }
                    lambda = std::sqrt( num / den );
                    for( unsigned i = 0; i < verts_n.size(); ++i )
                    {
                        verts_n[i] = verts_acc3[i] - lambda / ( lambda - 1.0 ) * ( verts_acc3[i] - verts_acc2[i] );
                    }
                }
                else if( acc_method == 5 )
                { /* Minimum polynomial extrapolation of vector sequenes :
                     https://en.wikipedia.org/wiki/Minimum_polynomial_extrapolation */
                    /* Pseudo-code
                          U=x(:,2:end-1)-x(:,1:end-2);
                          c=-pinv(U)*(x(:,end)-x(:,end-1));
                          c(end+1,1)=1;
                          s=(x(:,2:end)*c)/sum(c);
                    */
                    Matrix U( verts_n.size(), 2 );
                    Vector res( verts_n.size() );
                    for( unsigned ir = 0; ir < verts_n.size(); ir++ )
                    {
                        U( ir, 0 ) = verts_acc2[ir] - verts_acc1[ir];
                        U( ir, 1 ) = verts_acc3[ir] - verts_acc2[ir];
                        res[ir]    = -( verts_n[ir] - verts_acc3[ir] );
                    }
                    // U.print();
                    // Vector acc = QR(U).solve(res);
                    Vector acc    = solve( U, res );
                    double accsum = acc[0] + acc[1] + 1.0;
                    for( unsigned ir = 0; ir < verts_n.size(); ir++ )
                    {
                        verts_n[ir] = ( verts_acc1[ir] * acc[0] + verts_acc2[ir] * acc[1] + verts_acc3[ir] ) / accsum;
                    }

                    memcpy( &verts_acc1[0], &verts_acc2[0], nbytes );
                    memcpy( &verts_acc2[0], &verts_acc3[0], nbytes );
                    memcpy( &verts_acc3[0], &verts_n[0], nbytes );
                }
                else
                {
                    int offset = 0;
                    for( Range::const_iterator vit = verts.begin(); vit != verts.end(); ++vit, offset += 3 )
                    {
                        // if !fixed
                        if( fix_tag[offset / 3] ) continue;

                        CartVect num1 = ( CartVect( &verts_acc3[offset] ) - CartVect( &verts_acc2[offset] ) );
                        CartVect num2 = ( CartVect( &verts_acc3[offset] ) - 2.0 * CartVect( &verts_acc2[offset] ) +
                                          CartVect( &verts_acc1[offset] ) );

                        num1.scale( num2 );
                        const double mu = num1.length_squared() / num2.length_squared();

                        verts_n[offset + 0] =
                            verts_acc3[offset + 0] + mu * ( verts_acc2[offset + 0] - verts_acc3[offset + 0] );
                        verts_n[offset + 1] =
                            verts_acc3[offset + 1] + mu * ( verts_acc2[offset + 1] - verts_acc3[offset + 1] );
                        verts_n[offset + 2] =
                            verts_acc3[offset + 2] + mu * ( verts_acc2[offset + 2] - verts_acc3[offset + 2] );
                    }
                }
            }
            memcpy( &verts_acc1[0], &verts_acc2[0], nbytes );
            memcpy( &verts_acc2[0], &verts_acc3[0], nbytes );
            memcpy( &verts_acc3[0], &verts_n[0], nbytes );
        }

        // 2b. foreach owned vertex: compute change in coordinate norm
        for( unsigned v = 0; v < verts.size(); ++v )
        {
            double delta    = ( CartVect( &verts_n[3 * v] ) - CartVect( &verts_o[3 * v] ) ).length();
            mxdelta         = std::max( delta, mxdelta );
            EntityHandle vh = verts[v];
            rval            = mb->tag_set_data( errt, &vh, 1, &mxdelta );
            RC;
        }

        // global reduce for maximum delta, then report it
        global_max = mxdelta;
#ifdef MOAB_HAVE_MPI
        if( global_size > 1 ) MPI_Allreduce( &mxdelta, &global_max, 1, MPI_DOUBLE, MPI_MAX, pcomm->comm() );
#endif

        if( !( nit % report_its ) )
        {
            dbgprint( "\tIterate " << nit << ": Global Max delta = " << global_max << "." );
        }

#ifdef WRITE_DEBUG_FILES
        {
            // write the tag back onto vertex coordinates
            rval = mb->set_coords( verts, &verts_n[0] );
            RC;
            // output VTK file for debugging purposes
            std::stringstream sstr;
            sstr << "LaplacianSmootherIterate_" << nit + 1 << ".h5m";
            rval = mb->write_file( sstr.str().c_str(), NULL, woptions );
            RC;
        }
#endif

#ifdef MOAB_HAVE_MPI
        // 2c. exchange tags on owned verts
        if( global_size > 1 )
        {
            rval = mb->tag_set_data( vpost, owned_verts, vdata );
            RC;
            rval = pcomm->exchange_tags( vpost, shared_owned_verts );
            RC;
        }
#endif

        if( global_max < rel_eps )
            break;
        else
        {
            std::copy( verts_n.begin(), verts_n.end(), verts_o.begin() );
        }
    }

    // write the tag back onto vertex coordinates
    rval = mb->set_coords( verts, &verts_n[0] );
    RC;

    dbgprint( "-- Final iterate error = " << global_max << ".\n" );
    return MB_SUCCESS;
}

/*
  Standard Laplacian Smooth Filter

  Additional references: http://www.doc.ic.ac.uk/~gr409/thesis-MSc.pdf
*/
ErrorCode laplacianFilter( Core* mb,
                           moab::ParallelComm* pcomm,
                           moab::Range& verts,
                           int dim,
                           Tag fixed,
                           std::vector< double >& verts_o,
                           std::vector< double >& verts_n,
                           bool use_updated )
{
    ErrorCode rval;
    std::vector< int > fix_tag( verts.size() );
    double* data;

    memcpy( &verts_n[0], &verts_o[0], sizeof( double ) * verts_o.size() );

    if( use_updated )
        data = &verts_n[0];
    else
        data = &verts_o[0];

    // filter verts down to owned ones and get fixed tag for them
    Range owned_verts;
    if( pcomm->size() > 1 )
    {
#ifdef MOAB_HAVE_MPI
        rval = pcomm->filter_pstatus( verts, PSTATUS_NOT_OWNED, PSTATUS_NOT, -1, &owned_verts );
        if( rval != MB_SUCCESS ) return rval;
#endif
    }
    else
        owned_verts = verts;

    rval = mb->tag_get_data( fixed, owned_verts, &fix_tag[0] );
    RC;

    int vindex = 0;
    for( Range::const_iterator vit = owned_verts.begin(); vit != owned_verts.end(); ++vit, vindex++ )
    {
        // if !fixed
        if( fix_tag[vindex] ) continue;

        const int index = verts.index( *vit ) * 3;

        moab::Range adjverts, adjelems;
        // Find the neighboring vertices (1-ring neighborhood)
        rval = mb->get_adjacencies( &( *vit ), 1, dim, false, adjelems );
        RC;
        rval = mb->get_connectivity( adjelems, adjverts );
        RC;
        adjverts.erase( *vit );

        const int nadjs = adjverts.size();
        if( nadjs )
        {
            double delta[3] = { 0.0, 0.0, 0.0 };

            // Add the vertices and divide by the number of vertices
            for( int j = 0; j < nadjs; ++j )
            {
                const int joffset = verts.index( adjverts[j] ) * 3;
                delta[0] += data[joffset + 0];
                delta[1] += data[joffset + 1];
                delta[2] += data[joffset + 2];
            }

            verts_n[index + 0] = delta[0] / nadjs;
            verts_n[index + 1] = delta[1] / nadjs;
            verts_n[index + 2] = delta[2] / nadjs;
        }
    }

    return MB_SUCCESS;
}

/*
  HC (Humphrey’s Classes) Smooth Algorithm - Reduces Shrinkage of Laplacian Smoother

  Link:
  http://informatikbuero.com/downloads/Improved_Laplacian_Smoothing_of_Noisy_Surface_Meshes.pdf

  Where sv - original points
      pv - previous points,
      alpha [0..1] influences previous points pv, e.g. 0
      beta  [0..1] e.g. > 0.5
*/
ErrorCode hcFilter( Core* mb,
                    moab::ParallelComm* pcomm,
                    moab::Range& verts,
                    int dim,
                    Tag fixed,
                    std::vector< double >& verts_o,
                    std::vector< double >& verts_n,
                    double alpha,
                    double beta )
{
    ErrorCode rval;
    std::vector< double > verts_hc( verts_o.size() );
    std::vector< int > fix_tag( verts.size() );

    // Perform Laplacian Smooth
    rval = laplacianFilter( mb, pcomm, verts, dim, fixed, verts_o, verts_n );
    RC;

    // Compute Differences
    for( unsigned index = 0; index < verts_o.size(); ++index )
    {
        verts_hc[index] = verts_n[index] - ( alpha * verts_n[index] + ( 1.0 - alpha ) * verts_o[index] );
    }

    // filter verts down to owned ones and get fixed tag for them
    Range owned_verts;
#ifdef MOAB_HAVE_MPI
    if( pcomm->size() > 1 )
    {
        rval = pcomm->filter_pstatus( verts, PSTATUS_NOT_OWNED, PSTATUS_NOT, -1, &owned_verts );
        if( rval != MB_SUCCESS ) return rval;
    }
    else
#endif
        owned_verts = verts;

    rval = mb->tag_get_data( fixed, owned_verts, &fix_tag[0] );
    RC;

    int vindex = 0;
    for( Range::const_iterator vit = owned_verts.begin(); vit != owned_verts.end(); ++vit, vindex++ )
    {
        // if !fixed
        if( fix_tag[vindex] ) continue;

        const int index = verts.index( *vit ) * 3;

        moab::Range adjverts, adjelems;
        // Find the neighboring vertices (1-ring neighborhood)
        rval = mb->get_adjacencies( &( *vit ), 1, dim, false, adjelems );
        RC;
        rval = mb->get_connectivity( adjelems, adjverts );
        RC;
        adjverts.erase( *vit );

        const int nadjs = adjverts.size();
        double delta[3] = { 0.0, 0.0, 0.0 };

        for( int j = 0; j < nadjs; ++j )
        {
            const int joffset = verts.index( adjverts[j] ) * 3;
            delta[0] += verts_hc[joffset + 0];
            delta[1] += verts_hc[joffset + 1];
            delta[2] += verts_hc[joffset + 2];
        }

        verts_n[index + 0] -= beta * verts_hc[index + 0] + ( ( 1.0 - beta ) / nadjs ) * delta[0];
        verts_n[index + 1] -= beta * verts_hc[index + 1] + ( ( 1.0 - beta ) / nadjs ) * delta[1];
        verts_n[index + 2] -= beta * verts_hc[index + 2] + ( ( 1.0 - beta ) / nadjs ) * delta[2];
    }

    return MB_SUCCESS;
}