DomainClassifierTest.cpp

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

    Copyright 2008 Sandia National Laboratories.  Developed at the
    University of Wisconsin--Madison under SNL contract number
    624796.  The U.S. Government and the University of Wisconsin
    retain certain rights to this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2008) [email protected]

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

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

#include "Mesquite.hpp"
#include "UnitUtil.hpp"
#include "DomainClassifier.hpp"
#include "MeshDomain1D.hpp"
#include "MsqError.hpp"
#include "MeshImpl.hpp"
#include "MsqVertex.hpp"
#include "PlanarDomain.hpp"

#include <cstdio>
#include <iostream>
#include <algorithm>

using namespace MBMesquite;
using namespace std;

class DomainClassifierTest : public CppUnit::TestFixture
{
  private:
    CPPUNIT_TEST_SUITE( DomainClassifierTest );
    CPPUNIT_TEST( test_classify_by_handle );
    CPPUNIT_TEST( test_valid_classification );
    CPPUNIT_TEST( test_classify_by_tag );
    CPPUNIT_TEST( test_classify_skin );
    CPPUNIT_TEST( test_classify_by_geometry );
    CPPUNIT_TEST_SUITE_END();

  public:
    typedef DomainClassifier::DomainSet DomSet;
    typedef std::vector< DomSet > DomSetList;
    MeshImpl myMesh;
    DomSetList myDomains;
    std::vector< int > domainDims;

    void setUp();
    void tearDown();

    void test_classify_by_handle();
    void test_valid_classification();
    void test_classify_by_tag();
    void test_classify_skin();
    void test_classify_by_geometry();

    void check_domain( DomainClassifier& dom );
};

CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( DomainClassifierTest, "Unit" );
CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( DomainClassifierTest, "DomainClassifierTest" );

static void print_domain( int i, DomainClassifier::DomainSet& set )
{
    if( PointDomain* pd = dynamic_cast< PointDomain* >( set.domain ) )
        printf( "%d: PointDomain( %f %f %f ) @ %p\n", i, pd->geom()[0], pd->geom()[1], pd->geom()[2], pd );
    else if( LineDomain* ld = dynamic_cast< LineDomain* >( set.domain ) )
    {
        if( fabs( ld->geom().direction()[0] ) < 1e-6 && fabs( ld->geom().direction()[1] ) < 1e-6 )
            printf( "%d: LineDomain( x = %f, y = %f ) @ %p\n", i, ld->geom().point()[0], ld->geom().point()[1], ld );
        else if( fabs( ld->geom().direction()[1] ) < 1e-6 && fabs( ld->geom().direction()[2] ) < 1e-6 )
            printf( "%d: LineDomain( y = %f, z = %f ) @ %p\n", i, ld->geom().point()[1], ld->geom().point()[2], ld );
        else if( fabs( ld->geom().direction()[0] ) < 1e-6 && fabs( ld->geom().direction()[2] ) < 1e-6 )
            printf( "%d: LineDomain( x = %f, z = %f ) @ %p\n", i, ld->geom().point()[0], ld->geom().point()[2], ld );
        else
            printf( "%d: LineDomain( ? ) @ %p\n", i, ld );
    }
    else if( PlanarDomain* pd = dynamic_cast< PlanarDomain* >( set.domain ) )
    {
        if( fabs( pd->get_normal()[0] ) < 1e-6 && fabs( pd->get_normal()[1] ) < 1e-6 )
            printf( "%d: PlanarDomain( z = %f ) @ %p\n", i, pd->get_origin()[2], pd );
        else if( fabs( pd->get_normal()[1] ) < 1e-6 && fabs( pd->get_normal()[2] ) < 1e-6 )
            printf( "%d: PlanarDomain( x = %f ) @ %p\n", i, pd->get_origin()[1], pd );
        else if( fabs( pd->get_normal()[0] ) < 1e-6 && fabs( pd->get_normal()[2] ) < 1e-6 )
            printf( "%d: PlanarDomain( y = %f ) @ %p\n", i, pd->get_origin()[0], pd );
        else
            printf( "%d: PlanarDomain( ? ) @ %p\n", i, pd );
    }
    else
    {
        printf( "%d: unknown domain type @ %p\n", i, set.domain );
    }

    if( !set.vertices.empty() )
    {
        printf( "  vertices: " );
        std::vector< Mesh::VertexHandle >::iterator vi = set.vertices.begin();
        for( ; vi != set.vertices.end(); ++vi )
            printf( "%lu, ", (unsigned long)*vi );
        printf( "\n" );
    }
    if( !set.elements.empty() )
    {
        printf( "  elements: " );
        std::vector< Mesh::ElementHandle >::iterator ei = set.elements.begin();
        for( ; ei != set.elements.end(); ++ei )
            printf( "%lu, ", (unsigned long)*ei );
        printf( "\n" );
    }
}

void DomainClassifierTest::setUp()
{
    myMesh.clear();
    myDomains.clear();
    domainDims.clear();
    // vertex coodinates
    const char vertex_data[] = "POINTS 64 float\n"
                               "0 0 0  1 0 0  2 0 0  3 0 0\n"
                               "0 1 0  1 1 0  2 1 0  3 1 0\n"
                               "0 2 0  1 2 0  2 2 0  3 2 0\n"
                               "0 3 0  1 3 0  2 3 0  3 3 0\n"
                               "\n"
                               "0 0 1  1 0 1  2 0 1  3 0 1\n"
                               "0 1 1  1 1 1  2 1 1  3 1 1\n"
                               "0 2 1  1 2 1  2 2 1  3 2 1\n"
                               "0 3 1  1 3 1  2 3 1  3 3 1\n"
                               "\n"
                               "0 0 2  1 0 2  2 0 2  3 0 2\n"
                               "0 1 2  1 1 2  2 1 2  3 1 2\n"
                               "0 2 2  1 2 2  2 2 2  3 2 2\n"
                               "0 3 2  1 3 2  2 3 2  3 3 2\n"
                               "\n"
                               "0 0 3  1 0 3  2 0 3  3 0 3\n"
                               "0 1 3  1 1 3  2 1 3  3 1 3\n"
                               "0 2 3  1 2 3  2 2 3  3 2 3\n"
                               "0 3 3  1 3 3  2 3 3  3 3 3\n"
                               "\n";
    // quad connectivity for quads on mesh skin
    const int num_quads    = 9 * 6;             // nine per side
    const char quad_data[] = "4  1  0  4  5\n"  // -z face (z == 0)
                             "4  2  1  5  6\n"
                             "4  3  2  6  7\n"
                             "4  5  4  8  9\n"
                             "4  6  5  9 10\n"
                             "4  7  6 10 11\n"
                             "4  9  8 12 13\n"
                             "4 10  9 13 14\n"
                             "4 11 10 14 15\n"
                             "\n"
                             "4 48 49 53 52\n"  // +z face (z == 3)
                             "4 49 50 54 53\n"
                             "4 50 51 55 54\n"
                             "4 52 53 57 56\n"
                             "4 53 54 58 57\n"
                             "4 54 55 59 58\n"
                             "4 56 57 61 60\n"
                             "4 57 58 62 61\n"
                             "4 58 59 63 62\n"
                             "\n"
                             "4  0  1 17 16\n"  // -y face (y == 0)
                             "4  1  2 18 17\n"
                             "4  2  3 19 18\n"
                             "4 16 17 33 32\n"
                             "4 17 18 34 33\n"
                             "4 18 19 35 34\n"
                             "4 32 33 49 48\n"
                             "4 33 34 50 49\n"
                             "4 34 35 51 50\n"
                             "\n"
                             "4 13 12 28 29\n"  // +y face (y == 3)
                             "4 14 13 29 30\n"
                             "4 15 14 30 31\n"
                             "4 29 28 44 45\n"
                             "4 30 29 45 46\n"
                             "4 31 30 46 47\n"
                             "4 45 44 60 61\n"
                             "4 46 45 61 62\n"
                             "4 47 46 62 63\n"
                             "\n"
                             "4  4  0 16 20\n"  // -x face (x == 0)
                             "4  8  4 20 24\n"
                             "4 12  8 24 28\n"
                             "4 20 16 32 36\n"
                             "4 24 20 36 40\n"
                             "4 28 24 40 44\n"
                             "4 36 32 48 52\n"
                             "4 40 36 52 56\n"
                             "4 44 40 56 60\n"
                             "\n"
                             "4  3  7 23 19\n"  // +x face (x == 3)
                             "4  7 11 27 23\n"
                             "4 11 15 31 27\n"
                             "4 19 23 39 35\n"
                             "4 23 27 43 39\n"
                             "4 27 31 47 43\n"
                             "4 35 39 55 51\n"
                             "4 39 43 59 55\n"
                             "4 43 47 63 59\n"
                             "\n";
    // hexahedron connectivity
    const int num_hexes   = 3 * 3 * 3;
    const char hex_data[] = "8  0  1  5  4 16 17 21 20\n"
                            "8  1  2  6  5 17 18 22 21\n"
                            "8  2  3  7  6 18 19 23 22\n"
                            "8  4  5  9  8 20 21 25 24\n"
                            "8  5  6 10  9 21 22 26 25\n"
                            "8  6  7 11 10 22 23 27 26\n"
                            "8  8  9 13 12 24 25 29 28\n"
                            "8  9 10 14 13 25 26 30 29\n"
                            "8 10 11 15 14 26 27 31 30\n"
                            "\n"
                            "8 16 17 21 20 32 33 37 36\n"
                            "8 17 18 22 21 33 34 38 37\n"
                            "8 18 19 23 22 34 35 39 38\n"
                            "8 20 21 25 24 36 37 41 40\n"
                            "8 21 22 26 25 37 38 42 41\n"
                            "8 22 23 27 26 38 39 43 42\n"
                            "8 24 25 29 28 40 41 45 44\n"
                            "8 25 26 30 29 41 42 46 45\n"
                            "8 26 27 31 30 42 43 47 46\n"
                            "\n"
                            "8 32 33 37 36 48 49 53 52\n"
                            "8 33 34 38 37 49 50 54 53\n"
                            "8 34 35 39 38 50 51 55 54\n"
                            "8 36 37 41 40 52 53 57 56\n"
                            "8 37 38 42 41 53 54 58 57\n"
                            "8 38 39 43 42 54 55 59 58\n"
                            "8 40 41 45 44 56 57 61 60\n"
                            "8 41 42 46 45 57 58 62 61\n"
                            "8 42 43 47 46 58 59 63 62\n"
                            "\n";
    // a few interior quads
    const int num_interior_quads    = 3;
    const char interior_quad_data[] = "4  1  5 25 17\n"
                                      "4  4  5 25 24\n"
                                      "4 16 17 25 24\n"
                                      "\n";

    const char filename[] = "dctest.vtk";
    FILE* file            = fopen( filename, "w" );
    fputs( "# vtk DataFile Version 2.0\n", file );
    fputs( "Mesquite Mesh\n", file );
    fputs( "ASCII\n", file );
    fputs( "DATASET UNSTRUCTURED_GRID\n", file );
    fputs( vertex_data, file );

    int num_elem      = num_quads + num_hexes + num_interior_quads;
    int num_elem_data = 5 * num_quads + 9 * num_hexes * 5 * num_interior_quads;
    fprintf( file, "CELLS %d %d\n", num_elem, num_elem_data );
    fputs( quad_data, file );
    fputs( hex_data, file );
    fputs( interior_quad_data, file );
    fprintf( file, "CELL_TYPES %d\n", num_elem );
    for( int i = 0; i < num_quads; ++i )
        fputs( "9\n", file );
    for( int i = 0; i < num_hexes; ++i )
        fputs( "12\n", file );
    for( int i = 0; i < num_interior_quads; ++i )
        fputs( "9\n", file );

    fclose( file );
    MsqPrintError err( std::cerr );
    myMesh.read_vtk( filename, err );
    remove( filename );
    CPPUNIT_ASSERT( !err );

    std::vector< Mesh::VertexHandle > verts;
    std::vector< Mesh::ElementHandle > elems;
    myMesh.get_all_vertices( verts, err );
    CPPUNIT_ASSERT( !err );
    CPPUNIT_ASSERT_EQUAL( (size_t)64, verts.size() );
    myMesh.get_all_elements( elems, err );
    CPPUNIT_ASSERT( !err );
    CPPUNIT_ASSERT_EQUAL( (size_t)num_elem, elems.size() );

    // define point domains
    PointDomain* pdom[8];
    pdom[0]         = new PointDomain( Vector3D( 0, 0, 0 ) );
    pdom[1]         = new PointDomain( Vector3D( 3, 0, 0 ) );
    pdom[2]         = new PointDomain( Vector3D( 0, 3, 0 ) );
    pdom[3]         = new PointDomain( Vector3D( 3, 3, 0 ) );
    pdom[4]         = new PointDomain( Vector3D( 0, 0, 3 ) );
    pdom[5]         = new PointDomain( Vector3D( 3, 0, 3 ) );
    pdom[6]         = new PointDomain( Vector3D( 0, 3, 3 ) );
    pdom[7]         = new PointDomain( Vector3D( 3, 3, 3 ) );
    size_t pdidx[8] = { 0, 3, 12, 15, 48, 51, 60, 63 };
    for( unsigned i = 0; i < 8; ++i )
    {
        MsqVertex coords;
        Mesh::VertexHandle h = verts[pdidx[i]];
        myMesh.vertices_get_coordinates( &h, &coords, 1, err );
        CPPUNIT_ASSERT( !err );
        CPPUNIT_ASSERT_VECTORS_EQUAL( pdom[i]->geom(), coords, 1e-6 );
        DomSet set;
        set.domain = pdom[i];
        set.vertices.push_back( h );
        myDomains.push_back( set );
        domainDims.push_back( 0 );
    }

    // define line domains
    LineDomain* ldom[12];
    ldom[0]             = new LineDomain( Vector3D( 0, 0, 0 ), Vector3D( 1, 0, 0 ) );  // y=0,z=0
    ldom[1]             = new LineDomain( Vector3D( 0, 3, 0 ), Vector3D( 1, 0, 0 ) );  // y=3,z=0
    ldom[2]             = new LineDomain( Vector3D( 0, 0, 3 ), Vector3D( 1, 0, 0 ) );  // y=0,z=3
    ldom[3]             = new LineDomain( Vector3D( 0, 3, 3 ), Vector3D( 1, 0, 0 ) );  // y=3,z=3
    ldom[4]             = new LineDomain( Vector3D( 0, 0, 0 ), Vector3D( 0, 1, 0 ) );  // x=0,z=0
    ldom[5]             = new LineDomain( Vector3D( 3, 0, 0 ), Vector3D( 0, 1, 0 ) );  // x=3,z=0
    ldom[6]             = new LineDomain( Vector3D( 0, 0, 3 ), Vector3D( 0, 1, 0 ) );  // x=0,z=3
    ldom[7]             = new LineDomain( Vector3D( 3, 0, 3 ), Vector3D( 0, 1, 0 ) );  // x=3,z=3
    ldom[8]             = new LineDomain( Vector3D( 0, 0, 0 ), Vector3D( 0, 0, 1 ) );  // x=0,y=0
    ldom[9]             = new LineDomain( Vector3D( 3, 0, 0 ), Vector3D( 0, 0, 1 ) );  // x=3,y=0
    ldom[10]            = new LineDomain( Vector3D( 0, 3, 0 ), Vector3D( 0, 0, 1 ) );  // x=0,y=3
    ldom[11]            = new LineDomain( Vector3D( 3, 3, 0 ), Vector3D( 0, 0, 1 ) );  // x=3,y=3
    size_t ldidx[12][2] = { { 1, 2 },   { 13, 14 }, { 49, 50 }, { 61, 62 }, { 4, 8 },   { 7, 11 },
                            { 52, 56 }, { 55, 59 }, { 16, 32 }, { 19, 35 }, { 28, 44 }, { 31, 47 } };
    for( unsigned i = 0; i < 12; ++i )
    {
        Mesh::VertexHandle v[2];
        v[0] = verts[ldidx[i][0]];
        v[1] = verts[ldidx[i][1]];
        MsqVertex coords[2];
        myMesh.vertices_get_coordinates( v, coords, 2, err );
        CPPUNIT_ASSERT( !err );
        CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, ldom[i]->geom().distance( coords[0] ), 1e-6 );
        CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, ldom[i]->geom().distance( coords[1] ), 1e-6 );
        DomSet set;
        set.domain = ldom[i];
        set.vertices.push_back( v[0] );
        set.vertices.push_back( v[1] );
        myDomains.push_back( set );
        domainDims.push_back( 1 );
    }

    // define planar domains
    PlanarDomain* sdom[6];
    sdom[0]            = new PlanarDomain( Vector3D( 0, 0, -1 ), Vector3D( 0, 0, 0 ) );
    sdom[1]            = new PlanarDomain( Vector3D( 0, 0, 1 ), Vector3D( 0, 0, 3 ) );
    sdom[2]            = new PlanarDomain( Vector3D( 0, -1, 0 ), Vector3D( 0, 0, 0 ) );
    sdom[3]            = new PlanarDomain( Vector3D( 0, 1, 0 ), Vector3D( 0, 3, 0 ) );
    sdom[4]            = new PlanarDomain( Vector3D( -1, 0, 0 ), Vector3D( 0, 0, 0 ) );
    sdom[5]            = new PlanarDomain( Vector3D( 1, 0, 0 ), Vector3D( 3, 0, 0 ) );
    size_t sdidx[6][4] = { { 5, 6, 9, 10 },    { 53, 54, 57, 58 }, { 17, 18, 33, 34 },
                           { 29, 30, 45, 46 }, { 20, 24, 36, 40 }, { 23, 27, 39, 43 } };
    for( unsigned i = 0; i < 6; ++i )
    {
        DomSet set;
        set.domain = sdom[i];
        for( unsigned j = 0; j < 4; ++j )
            set.vertices.push_back( verts[sdidx[i][j]] );
        for( unsigned j = 0; j < 9; ++j )
            set.elements.push_back( elems[9 * i + j] );
        myDomains.push_back( set );
        domainDims.push_back( 2 );
    }

    //  for (unsigned i = 0; i < myDomains.size(); ++i)
    //    print_domain( i, myDomains[i] );
}

void DomainClassifierTest::tearDown()
{
    myMesh.clear();
    while( !myDomains.empty() )
    {
        delete myDomains.back().domain;
        myDomains.pop_back();
    }
    domainDims.clear();
}

void DomainClassifierTest::check_domain( DomainClassifier& domain )
{
    std::vector< Mesh::VertexHandle > vertices, cverts;
    std::vector< Mesh::ElementHandle > elements, celems;

    // Check that, for each entity with a domain, the
    // DomainClassifier instance returns that domain.
    // Also, put all entities with domains into cverts and
    // celems for later.
    for( unsigned i = 0; i < myDomains.size(); ++i )
    {
        for( unsigned j = 0; j < myDomains[i].vertices.size(); ++j )
        {
            Mesh::VertexHandle v  = myDomains[i].vertices[j];
            const MeshDomain* ptr = domain.find_vertex_domain( v );
            CPPUNIT_ASSERT( myDomains[i].domain == ptr );
            cverts.push_back( v );
        }
        for( unsigned k = 0; k < myDomains[i].elements.size(); ++k )
        {
            Mesh::ElementHandle e = myDomains[i].elements[k];
            const MeshDomain* ptr = domain.find_element_domain( e );
            CPPUNIT_ASSERT( myDomains[i].domain == ptr );
            celems.push_back( e );
        }
    }

    // sort cverts and celems so we can do binary_search later
    std::sort( cverts.begin(), cverts.end() );
    std::sort( celems.begin(), celems.end() );
    // get all vertices and elements in mesh
    MsqPrintError err( std::cerr );
    myMesh.get_all_vertices( vertices, err );
    CPPUNIT_ASSERT( !err );
    myMesh.get_all_elements( elements, err );
    CPPUNIT_ASSERT( !err );

    // For each vertex not in a domain (not in cverts), make sure
    // that the domain is NULL.
    for( size_t i = 0; i < vertices.size(); ++i )
    {
        if( std::binary_search( cverts.begin(), cverts.end(), vertices[i] ) ) continue;

        const MeshDomain* ptr = domain.find_vertex_domain( vertices[i] );
        CPPUNIT_ASSERT( NULL == ptr );
    }
    // For each element not in a domain (not in celems), make sure
    // that the domain is NULL.
    for( size_t i = 0; i < elements.size(); ++i )
    {
        if( std::binary_search( celems.begin(), celems.end(), elements[i] ) ) continue;

        const MeshDomain* ptr = domain.find_element_domain( elements[i] );
        CPPUNIT_ASSERT( NULL == ptr );
    }
}

void DomainClassifierTest::test_classify_by_handle()
{
    MsqPrintError err( std::cerr );
    DomainClassifier domain;
    DomainClassifier::classify_by_handle( domain, &myMesh, arrptr( myDomains ), myDomains.size(), err );
    CPPUNIT_ASSERT( !err );

    check_domain( domain );
}

void DomainClassifierTest::test_valid_classification()
{
    MsqPrintError err( std::cerr );
    DomainClassifier domain;
    DomainClassifier::classify_by_handle( domain, &myMesh, arrptr( myDomains ), myDomains.size(), err );
    CPPUNIT_ASSERT( !err );

    domain.test_valid_classification( &myMesh, err );
    CPPUNIT_ASSERT( !err );
}

void DomainClassifierTest::test_classify_by_tag()
{
    CPPUNIT_ASSERT( !myDomains.empty() );

    MsqPrintError err( std::cerr );
    int def       = myDomains.size();
    TagHandle tag = myMesh.tag_create( "domain", Mesh::INT, 1, &def, err );
    CPPUNIT_ASSERT( !err );

    std::vector< MeshDomain* > dom_list;
    std::vector< int > id_list;
    for( unsigned i = 0; i < myDomains.size(); ++i )
    {
        std::vector< int > vtx_data( myDomains[i].vertices.size(), i );
        std::vector< int > elm_data( myDomains[i].elements.size(), i );
        if( !vtx_data.empty() )
        {
            myMesh.tag_set_vertex_data( tag, vtx_data.size(), &( myDomains[i].vertices[0] ), arrptr( vtx_data ), err );
            CPPUNIT_ASSERT( !err );
        }
        if( !elm_data.empty() )
        {
            myMesh.tag_set_element_data( tag, elm_data.size(), &( myDomains[i].elements[0] ), arrptr( elm_data ), err );
            CPPUNIT_ASSERT( !err );
        }

        dom_list.push_back( myDomains[i].domain );
        id_list.push_back( i );
    }

    DomainClassifier domain;
    DomainClassifier::classify_by_tag( domain, &myMesh, "domain", arrptr( dom_list ), arrptr( id_list ),
                                       myDomains.size(), err );
    CPPUNIT_ASSERT( !err );

    check_domain( domain );
}

void DomainClassifierTest::test_classify_skin()
{
    CPPUNIT_ASSERT( !myDomains.empty() );

    MsqPrintError err( std::cerr );
    std::vector< MeshDomain* > arr( myDomains.size() );
    for( size_t i = 0; i < myDomains.size(); ++i )
        arr[i] = myDomains[i].domain;

    DomainClassifier domain;
    DomainClassifier::classify_skin_geometrically( domain, &myMesh, 1e-6, arrptr( arr ), arrptr( domainDims ),
                                                   arr.size(), err );
    CPPUNIT_ASSERT( !err );

    check_domain( domain );
}

void DomainClassifierTest::test_classify_by_geometry()
{
    CPPUNIT_ASSERT( !myDomains.empty() );

    MsqPrintError err( std::cerr );
    std::vector< MeshDomain* > arr( myDomains.size() );
    for( size_t i = 0; i < myDomains.size(); ++i )
        arr[i] = myDomains[i].domain;

    DomainClassifier domain;
    DomainClassifier::classify_geometrically( domain, &myMesh, 1e-6, arrptr( arr ), arrptr( domainDims ), arr.size(),
                                              err );
    CPPUNIT_ASSERT( !err );

    check_domain( domain );
}