linear_remap.cpp

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#include <iostream>
#include <cmath>

#include "moab/Core.hpp"
#include "moab/Interface.hpp"
#include "moab/IntxMesh/Intx2MeshOnSphere.hpp"
#include "moab/ParallelComm.hpp"
#include "moab/ProgOptions.hpp"
#include "MBParallelConventions.h"
#include "moab/ReadUtilIface.hpp"
#include "MBTagConventions.hpp"

#include "moab/IntxMesh/IntxUtils.hpp"
#include "IntxUtilsCSLAM.hpp"

#include "TestUtil.hpp"

// std::string file_name("./uniform_15.g");
// std::string file_name("./eulerHomme.vtk");

using namespace moab;

// computes cell barycenters in Cartesian X,Y,Z coordinates
void get_barycenters( moab::Interface* mb, moab::EntityHandle set, moab::Tag& planeTag, moab::Tag& barycenterTag );

// computes gnomonic plane for each cell of the Eulerian mesh
void get_gnomonic_plane( moab::Interface* mb, moab::EntityHandle set, moab::Tag& planeTag );

// computes coefficients (A,B,C) for linear reconstruction in gnomonic coordinates: rho(x,y) = Ax +
// By + C
void get_linear_reconstruction( moab::Interface* mb,
                                moab::EntityHandle set,
                                moab::Tag& rhoTag,
                                moab::Tag& planeTag,
                                moab::Tag& barycenterTag,
                                moab::Tag& linearCoefTag );

// evaluates the integral of rho(x,y) over cell, should be equal to cell average rho
void test_linear_reconstruction( moab::Interface* mb,
                                 moab::EntityHandle set,
                                 moab::Tag& rhoTag,
                                 moab::Tag& planeTag,
                                 moab::Tag& barycenterTag,
                                 moab::Tag& linearCoefTag );

// set density function
moab::ErrorCode add_field_value( moab::Interface* mb,
                                 moab::EntityHandle euler_set,
                                 int rank,
                                 moab::Tag& tagTracer,
                                 moab::Tag& tagElem,
                                 moab::Tag& tagArea,
                                 int field_type );

// functions that implement gnomonic projection as in Homme (different from Moab implementation)
int gnomonic_projection_test( const moab::CartVect& pos, double R, int plane, double& c1, double& c2 );
int reverse_gnomonic_projection_test( const double& c1, const double& c2, double R, int plane, moab::CartVect& pos );
void decide_gnomonic_plane_test( const CartVect& pos, int& plane );

double radius = 1.;  // in m:  6371220.

int main( int argc, char* argv[] )
{

    // set up MOAB interface and parallel communication
    MPI_Init( &argc, &argv );
    moab::Core moab;
    moab::Interface& mb = moab;
    moab::ParallelComm mb_pcomm( &mb, MPI_COMM_WORLD );

    // int rank = mb_pcomm->proc_config().proc_rank();
    int rank = mb_pcomm.proc_config().proc_rank();

    // create meshset
    moab::EntityHandle euler_set;
    moab::ErrorCode rval = mb.create_meshset( MESHSET_SET, euler_set );CHECK_ERR( rval );

    // std::stringstream opts;
    // opts <<
    // "PARALLEL=READ_PART;PARTITION;PARALLEL_RESOLVE_SHARED_ENTS;GATHER_SET=0;PARTITION_METHOD=TRIVIAL_PARTITION;VARIABLE=";
    // opts << "PARALLEL=READ_PART;PARTITION;PARALLEL_RESOLVE_SHARED_ENTS";
    std::string fileN = TestDir + "unittest/mbcslam/fine4.h5m";

    rval = mb.load_file( fileN.c_str(), &euler_set );CHECK_ERR( rval );

    // Create tag for cell density
    moab::Tag rhoTag = 0;
    rval = mb.tag_get_handle( "Density", 1, moab::MB_TYPE_DOUBLE, rhoTag, moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    moab::Tag rhoNodeTag = 0;
    rval                 = mb.tag_get_handle( "DensityNode", 1, moab::MB_TYPE_DOUBLE, rhoNodeTag,
                                              moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    // Create tag for cell area
    moab::Tag areaTag = 0;
    rval = mb.tag_get_handle( "Area", 1, moab::MB_TYPE_DOUBLE, areaTag, moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    // Create tag for cell barycenters in 3D Cartesian space
    moab::Tag barycenterTag = 0;
    rval                    = mb.tag_get_handle( "CellBarycenter", 3, moab::MB_TYPE_DOUBLE, barycenterTag,
                                                 moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    // Create tag for cell density reconstruction coefficients
    moab::Tag coefRhoTag = 0;
    rval                 = mb.tag_get_handle( "LinearCoefRho", 3, moab::MB_TYPE_DOUBLE, coefRhoTag,
                                              moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    // Create tag for index of gnomonic plane for each cell
    moab::Tag planeTag = 0;
    rval               = mb.tag_get_handle( "gnomonicPlane", 1, moab::MB_TYPE_INTEGER, planeTag,
                                            moab::MB_TAG_CREAT | moab::MB_TAG_DENSE );CHECK_ERR( rval );
    // Set density distributions
    rval = add_field_value( &mb, euler_set, rank, rhoNodeTag, rhoTag, areaTag, 2 );CHECK_ERR( rval );
    // get cell plane
    get_gnomonic_plane( &mb, euler_set, planeTag );

    // get cell barycenters
    get_barycenters( &mb, euler_set, planeTag, barycenterTag );

    // get linear reconstruction
    get_linear_reconstruction( &mb, euler_set, rhoTag, planeTag, barycenterTag, coefRhoTag );

    // test linear reconstruction
    test_linear_reconstruction( &mb, euler_set, rhoTag, planeTag, barycenterTag, coefRhoTag );

    MPI_Finalize();
    return 0;
}

void get_gnomonic_plane( moab::Interface* mb, moab::EntityHandle set, moab::Tag& planeTag )
{
    // get all entities of dimension 2
    // then get the connectivity, etc
    moab::Range cells;
    ErrorCode rval = mb->get_entities_by_dimension( set, 2, cells );
    if( MB_SUCCESS != rval ) return;

    for( Range::iterator it = cells.begin(); it != cells.end(); ++it )
    {
        moab::EntityHandle icell = *it;
        // get the nodes, then the coordinates
        const moab::EntityHandle* verts;
        int num_nodes;
        rval = mb->get_connectivity( icell, verts, num_nodes );
        if( MB_SUCCESS != rval ) return;

        std::vector< double > coords( 3 * num_nodes );
        // get coordinates
        rval = mb->get_coords( verts, num_nodes, &coords[0] );
        if( MB_SUCCESS != rval ) return;

        double centerx = 0;
        double centery = 0;
        double centerz = 0;
        for( int inode = 0; inode < num_nodes; inode++ )
        {
            centerx += coords[inode * 3] / num_nodes;
            centery += coords[inode * 3 + 1] / num_nodes;
            centerz += coords[inode * 3 + 2] / num_nodes;
        }
        double R = std::sqrt( centerx * centerx + centery * centery + centerz * centerz );
        centerx  = centerx / R;
        centery  = centery / R;
        centerz  = centerz / R;
        moab::CartVect center( centerx, centery, centerz );
        R = 1.0;

        int plane = 0;
        moab::IntxUtils::decide_gnomonic_plane( center, plane );
        // decide_gnomonic_plane_test(center,plane);

        rval = mb->tag_set_data( planeTag, &icell, 1, &plane );CHECK_ERR( rval );
    }
    return;
}

void get_barycenters( moab::Interface* mb, moab::EntityHandle set, moab::Tag& planeTag, moab::Tag& barycenterTag )
{
    // get all entities of dimension 2
    moab::Range cells;
    ErrorCode rval = mb->get_entities_by_dimension( set, 2, cells );
    if( MB_SUCCESS != rval ) return;

    // set sphere radius to 1
    double R = 1.0;

    for( Range::iterator it = cells.begin(); it != cells.end(); ++it )
    {
        moab::EntityHandle icell = *it;

        // get the nodes
        const moab::EntityHandle* verts;
        int num_nodes;
        rval = mb->get_connectivity( icell, verts, num_nodes );
        if( MB_SUCCESS != rval ) return;

        // get coordinates
        std::vector< double > coords( 3 * num_nodes );
        rval = mb->get_coords( verts, num_nodes, &coords[0] );
        if( MB_SUCCESS != rval ) return;

        // get plane for cell
        int plane = 0;
        rval      = mb->tag_get_data( planeTag, &icell, 1, &plane );
        if( MB_SUCCESS != rval ) return;
        std::vector< double > x( num_nodes );
        std::vector< double > y( num_nodes );
        double area   = 0;
        double bary_x = 0;
        double bary_y = 0;
        for( int inode = 0; inode < num_nodes; inode++ )
        {
            // radius should be 1.0, but divide by it just in case for now
            double rad = sqrt( coords[inode * 3] * coords[inode * 3] + coords[inode * 3 + 1] * coords[inode * 3 + 1] +
                               coords[inode * 3 + 2] * coords[inode * 3 + 2] );
            CartVect xyzcoord( coords[inode * 3] / rad, coords[inode * 3 + 1] / rad, coords[inode * 3 + 2] / rad );
            moab::IntxUtils::gnomonic_projection( xyzcoord, R, plane, x[inode], y[inode] );
            // int dum = gnomonic_projection_test(xyzcoord, R, plane, x[inode],y[inode]);
        }

        for( int inode = 0; inode < num_nodes; inode++ )
        {
            int inode2 = inode + 1;
            if( inode2 >= num_nodes ) inode2 = 0;
            double xmid = 0.5 * ( x[inode] + x[inode2] );
            double ymid = 0.5 * ( y[inode] + y[inode2] );
            double r1   = sqrt( 1 + x[inode] * x[inode] + y[inode] * y[inode] );
            double rm   = sqrt( 1 + xmid * xmid + ymid * ymid );
            double r2   = sqrt( 1 + x[inode2] * x[inode2] + y[inode2] * y[inode2] );
            double hx   = x[inode2] - x[inode];

            area += hx *
                    ( y[inode] / ( r1 * ( 1 + x[inode] * x[inode] ) ) + 4.0 * ymid / ( rm * ( 1 + xmid * xmid ) ) +
                      y[inode2] / ( r2 * ( 1 + x[inode2] * x[inode2] ) ) ) /
                    6.0;

            bary_x += hx *
                      ( x[inode] * y[inode] / ( r1 * ( 1 + x[inode] * x[inode] ) ) +
                        4.0 * xmid * ymid / ( rm * ( 1 + xmid * xmid ) ) +
                        x[inode2] * y[inode2] / ( r2 * ( 1 + x[inode2] * x[inode2] ) ) ) /
                      6.0;

            bary_y += -hx * ( 1.0 / r1 + 4.0 / rm + 1.0 / r2 ) / 6.0;
        }

        bary_x = bary_x / area;
        bary_y = bary_y / area;

        moab::CartVect barycent;
        moab::IntxUtils::reverse_gnomonic_projection( bary_x, bary_y, R, plane, barycent );
        // reverse_gnomonic_projection_test(bary_x, bary_y, R, plane, barycent);
        std::vector< double > barycenter( 3 );
        barycenter[0] = barycent[0];
        barycenter[1] = barycent[1];
        barycenter[2] = barycent[2];

        rval = mb->tag_set_data( barycenterTag, &icell, 1, &barycenter[0] );CHECK_ERR( rval );
    }
    return;
}

void get_linear_reconstruction( moab::Interface* mb,
                                moab::EntityHandle set,
                                moab::Tag& rhoTag,
                                moab::Tag& planeTag,
                                moab::Tag& barycenterTag,
                                moab::Tag& linearCoefTag )
{
    // get all entities of dimension 2
    Range cells;
    ErrorCode rval = mb->get_entities_by_dimension( set, 2, cells );
    if( MB_SUCCESS != rval ) return;

    // set sphere radius to 1
    double R = 1;

    // Get coefficients of reconstruction (in cubed-sphere coordinates)
    // rho(x,y) = Ax + By + C
    for( Range::iterator it = cells.begin(); it != cells.end(); ++it )
    {
        moab::EntityHandle icell = *it;

        // get the nodes, then the coordinates
        const moab::EntityHandle* verts;
        int num_nodes;
        rval = mb->get_connectivity( icell, verts, num_nodes );
        if( MB_SUCCESS != rval ) return;

        moab::Range adjacentEdges;
        rval = mb->get_adjacencies( &icell, 1, 1, true, adjacentEdges );CHECK_ERR( rval );
        // int num_edges = adjacentEdges.size();

        // get adjacent cells from edges
        moab::Range adjacentCells;
        rval = mb->get_adjacencies( adjacentEdges, 2, true, adjacentCells, Interface::UNION );
        if( MB_SUCCESS != rval ) return;
        // get plane for cell
        int plane = 0;
        rval      = mb->tag_get_data( planeTag, &icell, 1, &plane );CHECK_ERR( rval );

        std::vector< double > dx( adjacentCells.size() - 1 );
        std::vector< double > dy( adjacentCells.size() - 1 );
        std::vector< double > dr( adjacentCells.size() - 1 );
        double bary_x;
        double bary_y;

        // get barycenter of cell where reconstruction occurs
        std::vector< double > barycent( 3 );
        rval = mb->tag_get_data( barycenterTag, &icell, 1, &barycent[0] );CHECK_ERR( rval );
        CartVect barycenter( barycent[0], barycent[1], barycent[2] );
        double cellbaryx = 0;
        double cellbaryy = 0;
        moab::IntxUtils::gnomonic_projection( barycenter, R, plane, cellbaryx, cellbaryy );
        // int rc = gnomonic_projection_test(barycenter, R, plane, cellbaryx, cellbaryy);

        // get density value
        double rhocell = 0;
        rval           = mb->tag_get_data( rhoTag, &icell, 1, &rhocell );CHECK_ERR( rval );

        // get barycenters of surrounding cells
        std::vector< double > cell_barys( 3 * adjacentCells.size() );
        rval = mb->tag_get_data( barycenterTag, adjacentCells, &cell_barys[0] );CHECK_ERR( rval );

        // get density of surrounding cells
        std::vector< double > rho_vals( adjacentCells.size() );
        rval = mb->tag_get_data( rhoTag, adjacentCells, &rho_vals[0] );CHECK_ERR( rval );

        std::size_t jind = 0;
        for( std::size_t i = 0; i < adjacentCells.size(); i++ )
        {

            if( adjacentCells[i] != icell )
            {
                CartVect bary_xyz( cell_barys[i * 3], cell_barys[i * 3 + 1], cell_barys[i * 3 + 2] );
                moab::IntxUtils::gnomonic_projection( bary_xyz, R, plane, bary_x, bary_y );
                // rc = gnomonic_projection_test(bary_xyz, R, plane, bary_x, bary_y);

                dx[jind] = bary_x - cellbaryx;
                dy[jind] = bary_y - cellbaryy;
                dr[jind] = rho_vals[i] - rhocell;

                jind++;
            }
        }

        std::vector< double > linearCoef( 3 );
        if( adjacentCells.size() == 5 )
        {

            // compute normal equations matrix
            double N11 = dx[1] * dx[1] + dx[2] * dx[2] + dx[3] * dx[3] + dx[0] * dx[0];
            double N22 = dy[1] * dy[1] + dy[2] * dy[2] + dy[3] * dy[3] + dy[0] * dy[0];
            double N12 = dx[1] * dy[1] + dx[2] * dy[2] + dx[3] * dy[3] + dx[0] * dy[0];

            // rhs
            double Rx = dx[1] * dr[1] + dx[2] * dr[2] + dx[3] * dr[3] + dx[0] * dr[0];
            double Ry = dy[1] * dr[1] + dy[2] * dr[2] + dy[3] * dr[3] + dy[0] * dr[0];

            // determinant
            double Det = N11 * N22 - N12 * N12;

            // solution
            linearCoef[0] = ( Rx * N22 - Ry * N12 ) / Det;
            linearCoef[1] = ( Ry * N11 - Rx * N12 ) / Det;
            linearCoef[2] = rhocell - linearCoef[0] * cellbaryx - linearCoef[1] * cellbaryy;
        }
        else
        {
            // default to first order
            linearCoef[0] = 0.0;
            linearCoef[1] = 0.0;
            linearCoef[2] = rhocell;
            std::cout << "Need 4 adjacent cells for linear reconstruction! \n";
        }

        rval = mb->tag_set_data( linearCoefTag, &icell, 1, &linearCoef[0] );CHECK_ERR( rval );
    }
    return;
}

void test_linear_reconstruction( moab::Interface* mb,
                                 moab::EntityHandle set,
                                 moab::Tag& rhoTag,
                                 moab::Tag& planeTag,
                                 moab::Tag& barycenterTag,
                                 moab::Tag& linearCoefTag )
{
    // get all entities of dimension 2
    Range cells;
    ErrorCode rval = mb->get_entities_by_dimension( set, 2, cells );
    if( MB_SUCCESS != rval ) return;

    // set sphere radius to 1
    double R = 1;

    // For get coefficients for reconstruction (in cubed-sphere coordinates)
    for( Range::iterator it = cells.begin(); it != cells.end(); ++it )
    {
        moab::EntityHandle icell = *it;

        // get the nodes, then the coordinates
        const moab::EntityHandle* verts;
        int num_nodes;
        rval = mb->get_connectivity( icell, verts, num_nodes );
        if( MB_SUCCESS != rval ) return;

        // get coordinates
        std::vector< double > coords( 3 * num_nodes );
        rval = mb->get_coords( verts, num_nodes, &coords[0] );
        if( MB_SUCCESS != rval ) return;

        // get plane for cell
        int plane = 0;
        rval      = mb->tag_get_data( planeTag, &icell, 1, &plane );CHECK_ERR( rval );

        // get vertex coordinates projections
        std::vector< double > x( num_nodes );
        std::vector< double > y( num_nodes );
        for( int inode = 0; inode < num_nodes; inode++ )
        {
            double rad = sqrt( coords[inode * 3] * coords[inode * 3] + coords[inode * 3 + 1] * coords[inode * 3 + 1] +
                               coords[inode * 3 + 2] * coords[inode * 3 + 2] );
            CartVect xyzcoord( coords[inode * 3] / rad, coords[inode * 3 + 1] / rad, coords[inode * 3 + 2] / rad );
            moab::IntxUtils::gnomonic_projection( xyzcoord, R, plane, x[inode], y[inode] );
            // int dum = gnomonic_projection_test(xyzcoord, R, plane, x[inode],y[inode]);
        }

        double area  = 0;
        double int_x = 0;
        double int_y = 0;
        for( int inode = 0; inode < num_nodes; inode++ )
        {
            int inode2 = inode + 1;
            if( inode2 >= num_nodes ) inode2 = 0;
            double xmid = 0.5 * ( x[inode] + x[inode2] );
            double ymid = 0.5 * ( y[inode] + y[inode2] );
            double r1   = sqrt( 1 + x[inode] * x[inode] + y[inode] * y[inode] );
            double rm   = sqrt( 1 + xmid * xmid + ymid * ymid );
            double r2   = sqrt( 1 + x[inode2] * x[inode2] + y[inode2] * y[inode2] );
            double hx   = x[inode2] - x[inode];

            area += hx *
                    ( y[inode] / ( r1 * ( 1 + x[inode] * x[inode] ) ) + 4.0 * ymid / ( rm * ( 1 + xmid * xmid ) ) +
                      y[inode2] / ( r2 * ( 1 + x[inode2] * x[inode2] ) ) ) /
                    6.0;

            int_x += hx *
                     ( x[inode] * y[inode] / ( r1 * ( 1 + x[inode] * x[inode] ) ) +
                       4.0 * xmid * ymid / ( rm * ( 1 + xmid * xmid ) ) +
                       x[inode2] * y[inode2] / ( r2 * ( 1 + x[inode2] * x[inode2] ) ) ) /
                     6.0;

            int_y += -hx * ( 1.0 / r1 + 4.0 / rm + 1.0 / r2 ) / 6.0;
        }

        // get linear coeficients
        std::vector< double > rho_coefs( 3 );
        rval = mb->tag_get_data( linearCoefTag, &icell, 1, &rho_coefs[0] );CHECK_ERR( rval );

        // get barycenters
        std::vector< double > bary( 3 );
        rval = mb->tag_get_data( barycenterTag, &icell, 1, &bary[0] );CHECK_ERR( rval );
        double bary_x;
        double bary_y;
        CartVect bary_xyz( bary[0], bary[1], bary[2] );
        moab::IntxUtils::gnomonic_projection( bary_xyz, R, plane, bary_x, bary_y );
        // int rc = gnomonic_projection_test(bary_xyz, R, plane, bary_x, bary_y);

        // get cell average density
        double cell_rho;
        rval = mb->tag_get_data( rhoTag, &icell, 1, &cell_rho );CHECK_ERR( rval );

        // ave rho = \int rho^h(x,y) dV / area = (\int (Ax + By + C) dV) / area
        double rho_test1 = ( rho_coefs[0] * int_x + rho_coefs[1] * int_y + rho_coefs[2] * area ) / area;

        // ave rho = A*bary_x + B*bary_y + C
        double rho_test2 = rho_coefs[0] * bary_x + rho_coefs[1] * bary_y + rho_coefs[2];

        std::cout << cell_rho << "  " << rho_test1 << "  " << rho_test2 << "  " << cell_rho - rho_test1 << "\n";
    }
    return;
}

int reverse_gnomonic_projection_test( const double& c1, const double& c2, double R, int plane, CartVect& pos )
{

    double x = c1;
    double y = c2;
    double r = sqrt( 1.0 + x * x + y * y );

    switch( plane )
    {

        case 1: {
            pos[0] = R / r * R;
            pos[1] = R / r * x;
            pos[2] = R / r * y;
            break;
        }
        case 2: {
            pos[0] = -R / r * x;
            pos[1] = R / r * R;
            pos[2] = R / r * y;
            break;
        }
        case 3: {
            pos[0] = -R / r * R;
            pos[1] = -R / r * x;
            pos[2] = R / r * y;
            break;
        }
        case 4: {
            pos[0] = R / r * x;
            pos[1] = -R / r * R;
            pos[2] = R / r * y;
            break;
        }
        case 5: {
            pos[0] = R / r * y;
            pos[1] = R / r * x;
            pos[2] = -R / r * R;
            break;
        }
        case 6: {
            pos[0] = -R / r * y;
            pos[1] = R / r * x;
            pos[2] = R / r * R;
            break;
        }
    }

    return 0;  // no error
}

void decide_gnomonic_plane_test( const CartVect& pos, int& plane )
{

    // This is from early version of Homme vorticity calculation in parvis
    // Poles are reversed from Homme and Iulian version.

    //  Now has been changed for consistency

    double X = pos[0];
    double Y = pos[1];
    double Z = pos[2];
    double R = sqrt( X * X + Y * Y + Z * Z );
    X        = X / R;
    Y        = Y / R;
    Z        = Z / R;

    if( ( Y < X ) & ( Y > -X ) )
    {
        if( Z > X )
        {
            plane = 6;
        }
        else if( Z < -X )
        {
            plane = 5;
        }
        else
        {
            plane = 1;
        }
    }
    else if( ( Y > X ) & ( Y < -X ) )
    {
        if( Z > -X )
        {
            plane = 6;
        }
        else if( Z < X )
        {
            plane = 5;
        }
        else
        {
            plane = 3;
        }
    }
    else if( ( Y > X ) & ( Y > -X ) )
    {
        if( Z > Y )
        {
            plane = 6;
        }
        else if( Z < -Y )
        {
            plane = 5;
        }
        else
        {
            plane = 2;
        }
    }
    else if( ( Y < X ) & ( Y < -X ) )
    {
        if( Z > -Y )
        {
            plane = 6;
        }
        else if( Z < Y )
        {
            plane = 5;
        }
        else
        {
            plane = 4;
        }
    }
    else
    {
        if( fabs( X ) < Z )
        {
            plane = 6;
        }
        else if( Z < -fabs( X ) )
        {
            plane = 5;
        }
        else if( ( X > 0 ) & ( Y > 0 ) )
        {
            plane = 1;
        }
        else if( ( X < 0 ) & ( Y > 0 ) )
        {
            plane = 2;
        }
        else if( ( X < 0 ) & ( Y < 0 ) )
        {
            plane = 3;
        }
        else
        {
            plane = 4;
        }
    }

    return;
}

moab::ErrorCode add_field_value( moab::Interface* mb,
                                 moab::EntityHandle euler_set,
                                 int /*rank*/,
                                 moab::Tag& tagTracer,
                                 moab::Tag& tagElem,
                                 moab::Tag& tagArea,
                                 int field_type )
{

    /*
     * get all plys first, then vertices, then move them on the surface of the sphere
     *  radius is 1., most of the time
     *
     */
    moab::Range polygons;
    moab::ErrorCode rval = mb->get_entities_by_dimension( euler_set, 2, polygons );
    if( MB_SUCCESS != rval ) return rval;

    moab::Range connecVerts;
    rval = mb->get_connectivity( polygons, connecVerts );
    if( MB_SUCCESS != rval ) return rval;

    void* data;  // pointer to the LOC in memory, for each vertex
    int count;

    rval = mb->tag_iterate( tagTracer, connecVerts.begin(), connecVerts.end(), count, data );CHECK_ERR( rval );
    // here we are checking contiguity
    assert( count == (int)connecVerts.size() );
    double* ptr_DP = (double*)data;
    // lambda is for longitude, theta for latitude
    // param will be: (la1, te1), (la2, te2), b, c; hmax=1, r=1/2
    // nondivergent flow, page 5, case 1, (la1, te1) = (M_PI, M_PI/3)
    //                                    (la2, te2) = (M_PI, -M_PI/3)
    //                 la1,    te1    la2    te2     b     c  hmax  r
    if( field_type == 1 )  // quasi smooth
    {
        double params[] = { 5 * M_PI / 6.0, 0.0, 7 * M_PI / 6, 0.0, 0.1, 0.9, 1., 0.5 };
        for( Range::iterator vit = connecVerts.begin(); vit != connecVerts.end(); ++vit )
        {
            moab::EntityHandle oldV = *vit;
            moab::CartVect posi;
            rval = mb->get_coords( &oldV, 1, &( posi[0] ) );CHECK_ERR( rval );

            moab::IntxUtils::SphereCoords sphCoord = moab::IntxUtils::cart_to_spherical( posi );

            ptr_DP[0] = IntxUtilsCSLAM::quasi_smooth_field( sphCoord.lon, sphCoord.lat, params );

            ptr_DP++;  // increment to the next node
        }
    }
    else if( 2 == field_type )  // smooth
    {
        moab::CartVect p1, p2;
        moab::IntxUtils::SphereCoords spr;
        spr.R   = 1;
        spr.lat = M_PI / 3;
        spr.lon = M_PI;
        p1      = moab::IntxUtils::spherical_to_cart( spr );
        spr.lat = -M_PI / 3;
        p2      = moab::IntxUtils::spherical_to_cart( spr );
        //                  x1,    y1,     z1,    x2,   y2,    z2,   h_max, b0
        double params[] = { p1[0], p1[1], p1[2], p2[0], p2[1], p2[2], 1, 5. };
        for( Range::iterator vit = connecVerts.begin(); vit != connecVerts.end(); ++vit )
        {
            moab::EntityHandle oldV = *vit;
            moab::CartVect posi;
            rval = mb->get_coords( &oldV, 1, &( posi[0] ) );CHECK_ERR( rval );

            moab::IntxUtils::SphereCoords sphCoord = moab::IntxUtils::cart_to_spherical( posi );

            ptr_DP[0] = IntxUtilsCSLAM::smooth_field( sphCoord.lon, sphCoord.lat, params );

            ptr_DP++;  // increment to the next node
        }
    }
    else if( 3 == field_type )  // slotted
    {
        //                   la1, te1,   la2, te2,       b,   c,   r
        double params[] = { M_PI, M_PI / 3, M_PI, -M_PI / 3, 0.1, 0.9, 0.5 };  // no h_max
        for( Range::iterator vit = connecVerts.begin(); vit != connecVerts.end(); ++vit )
        {
            moab::EntityHandle oldV = *vit;
            moab::CartVect posi;
            rval = mb->get_coords( &oldV, 1, &( posi[0] ) );CHECK_ERR( rval );

            moab::IntxUtils::SphereCoords sphCoord = moab::IntxUtils::cart_to_spherical( posi );

            ptr_DP[0] = IntxUtilsCSLAM::slotted_cylinder_field( sphCoord.lon, sphCoord.lat, params );
            ;

            ptr_DP++;  // increment to the next node
        }
    }
    else if( 4 == field_type )  // constant = 1
    {
        for( Range::iterator vit = connecVerts.begin(); vit != connecVerts.end(); ++vit )
        {
            /* moab::EntityHandle oldV = *vit;
             moab::CartVect posi;
             rval = mb->get_coords(&oldV, 1, &(posi[0]));

             moab::IntxUtils::SphereCoords sphCoord = moab::IntxUtils::cart_to_spherical(posi);*/

            ptr_DP[0] = 1.0;

            ptr_DP++;  // increment to the next node
        }
    }
    // add average value for quad/polygon (average corners)
    // do some averages

    Range::iterator iter = polygons.begin();
    while( iter != polygons.end() )
    {
        rval = mb->tag_iterate( tagElem, iter, polygons.end(), count, data );CHECK_ERR( rval );
        double* ptr = (double*)data;

        rval = mb->tag_iterate( tagArea, iter, polygons.end(), count, data );CHECK_ERR( rval );
        double* ptrArea = (double*)data;
        for( int i = 0; i < count; i++, ++iter, ptr++, ptrArea++ )
        {
            const moab::EntityHandle* conn = NULL;
            int num_nodes                  = 0;
            rval                           = mb->get_connectivity( *iter, conn, num_nodes );CHECK_ERR( rval );
            if( num_nodes == 0 ) return MB_FAILURE;
            std::vector< double > nodeVals( num_nodes );
            double average = 0.;
            rval           = mb->tag_get_data( tagTracer, conn, num_nodes, &nodeVals[0] );CHECK_ERR( rval );
            for( int j = 0; j < num_nodes; j++ )
                average += nodeVals[j];
            average /= num_nodes;
            *ptr = average;
        }
    }

    return MB_SUCCESS;
}