Question 1, Given a triangle, what are the three adjacent triangles?

#include <iostream>
#include <vtkSmartPointer.h>
#include <vtkSphereSource.h>
#include <vtkActor.h>
#include <vtkConeSource.h>
#include <vtkRenderer.h>
#include <vtkRenderWindow.h>
#include <vtkPolyDataMapper.h>
#include <vtkSphereSource.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkProperty.h>
#include <vtkLineSource.h>
#include <vtkCellData.h>
#include <vtkColorTransferFunction.h>
#include <vtkTextSource.h>
#include <vtkTransformPolyDataFilter.h>
#include <vtkCoordinate.h>
#include <vtkPolyDataMapper2D.h>
#include <vtkActor2D.h>
#include <string>
#include <vtkTransform.h>

#define vtkSPtr vtkSmartPointer
#define vtkSPtrNew(Var, Type) vtkSPtr<Type> Var = vtkSPtr<Type>::New();

using namespace std;

void MarkPoint(int index, vtkPolyData *pd, vtkRenderer *render)
{
    cout << "index: " << index << endl;
    vtkSmartPointer<vtkTextSource> text2D =
        vtkSmartPointer<vtkTextSource>::New();
    text2D->SetText( std::to_string( index ).c_str() );

    vtkSmartPointer<vtkTransform> text2DTransform =
        vtkSmartPointer<vtkTransform>::New();
    double *center = pd->GetPoint( index );
    text2DTransform->Translate( center[0], center[1], center[2] );
    text2DTransform->Scale( 0.005, 0.005, 0.005 );

    vtkSmartPointer<vtkTransformPolyDataFilter> text2DDataFilter =
        vtkSmartPointer<vtkTransformPolyDataFilter>::New();
    text2DDataFilter->SetTransform( text2DTransform );
    text2DDataFilter->SetInputConnection( text2D->GetOutputPort() );

    vtkSmartPointer<vtkCoordinate> coords =
        vtkSmartPointer<vtkCoordinate>::New();
    coords->SetCoordinateSystemToWorld();

    vtkSmartPointer<vtkPolyDataMapper2D> text2DMapper =
        vtkSmartPointer<vtkPolyDataMapper2D>::New();
    text2DMapper->SetInputConnection( text2DDataFilter->GetOutputPort() );
    text2DMapper->SetTransformCoordinate( coords );

    vtkSmartPointer<vtkActor2D> text2DActor =
        vtkSmartPointer<vtkActor2D>::New();
    text2DActor->SetMapper( text2DMapper );

    render->AddActor( text2DActor );
}

int main()
{
    vtkSPtrNew( renderer, vtkRenderer );
    vtkSPtrNew( sphere, vtkSphereSource );
    sphere->SetCenter( 0, 0, 0 );
    sphere->SetRadius( 1 );
    sphere->Update();

    vtkPolyData *data = sphere->GetOutput();
    data->BuildCells();
    data->BuildLinks();

    vtkSPtrNew( cellScalars, vtkIntArray );
    cellScalars->SetNumberOfTuples( data->GetNumberOfCells() );
    for( int i = 0; i < data->GetNumberOfCells(); ++i )
    {
        cellScalars->SetTuple1( i, 0 );
    }
    data->GetCellData()->SetScalars( cellScalars );

    // ----------------------- Given a triangle, what are the three adjacent triangles? ---------------------------------
    // GetCellNeighbors: return the shared cell(except parameter cell) by the first point and the other point.
    int seedCellId = 0;
    vtkSPtrNew( ptIds, vtkIdList );
    data->GetCellPoints( seedCellId, ptIds );
    vtkSPtrNew( neiCellIds, vtkIdList );
    for( int i = 0; i < ptIds->GetNumberOfIds(); ++i )
    {
        vtkSPtrNew( ids, vtkIdList );
        ids->InsertNextId( ptIds->GetId( i ) );
        ids->InsertNextId( ptIds->GetId( (i+1)%ptIds->GetNumberOfIds() ) );
        vtkSPtrNew( cellIds, vtkIdList );
        data->GetCellNeighbors( seedCellId, ids, cellIds );
        for( int j = 0; j < cellIds->GetNumberOfIds(); ++j )
        {
            auto cellId = cellIds->GetId( j );
            neiCellIds->InsertUniqueId( cellId );
        }
    }
    // -------------------------------- Finish --------------------------------------

    MarkPoint( ptIds->GetId( 0 ), data, renderer );
    MarkPoint( ptIds->GetId( 1 ), data, renderer );
    MarkPoint( ptIds->GetId( 2 ), data, renderer );

    cellScalars->SetTuple1( 0, 1 );
    for( int i = 0; i < neiCellIds->GetNumberOfIds(); ++i )
    {
        auto cellId = neiCellIds->GetId( i );
        cellScalars->SetTuple1( cellId, 2 );
    }

    vtkSPtrNew( lut, vtkColorTransferFunction );
    lut->SetClamping( 0 );
    double colors[4][3] = { {199, 21, 133}, { 139, 0, 0 }, {85, 107, 47}, { 123, 104, 238 } };
    for( int i = 0; i < 4; ++i )
    {
        lut->AddRGBPoint( i, colors[i][0]/255.0, colors[i][1]/255.0, colors[i][2]/255.0 );
    }

    vtkSPtrNew( mapper, vtkPolyDataMapper );
    mapper->SetInputData( data );
    mapper->SetScalarModeToUseCellData();
    mapper->SetLookupTable( lut );
    mapper->SetScalarRange( 0, 3 );

    vtkSPtrNew( sphereActor, vtkActor );
    sphereActor->SetMapper( mapper );

    renderer->AddActor( sphereActor );
    renderer->SetBackground( 0, 0, 0 );

    vtkSPtrNew( renderWindow, vtkRenderWindow );
    renderWindow->AddRenderer( renderer );

    vtkSPtrNew( renderWindowInteractor, vtkRenderWindowInteractor );
    renderWindowInteractor->SetRenderWindow( renderWindow );

    renderer->ResetCamera();
    renderWindow->Render();
    renderWindowInteractor->Start();
    return 0;
}

Question 2, Given an edge, which two triangles share it?

    // ---------------------- Given an edge, which two triangles share it? ----------------------
    int seedCellId = 0;
    vtkSPtrNew( ptIds, vtkIdList );
    data->GetCellPoints( seedCellId, ptIds );
    vtkSPtrNew( neiCellIds, vtkIdList );;
    auto pId0 = ptIds->GetId( 0 );
    auto pId1 = ptIds->GetId( 1 );
    data->GetCellEdgeNeighbors( seedCellId, pId0, pId1, neiCellIds );
    // -------------------------------- Finish --------------------------------------

    MarkPoint( ptIds->GetId( 0 ), data, renderer );
    MarkPoint( ptIds->GetId( 1 ), data, renderer );

    cellScalars->SetTuple1( seedCellId, 1 );
    for( int i = 0; i < neiCellIds->GetNumberOfIds(); ++i )
    {
        auto cellId = neiCellIds->GetId( i );
        cellScalars->SetTuple1( cellId, 2 );
    }

Question 3, Given a vertex, which faces share it?

    // ---------------------------- Given a vertex, which faces share it? ---------------------------------
    int seedPtId = 0;
    vtkIdType ncells;
    vtkIdType* neiCellIds;
    data->GetPointCells( seedPtId, ncells, neiCellIds );
    // ------------------------------------- Finish ------------------------------------

    cout << "neiCellIds count: " << ncells << endl;
    MarkPoint( seedPtId, data, renderer );

    for( int i = 0; i < ncells; ++i )
    {
        cellScalars->SetTuple1( neiCellIds[i], i+1 );
    }

    vtkSPtrNew( lut, vtkColorTransferFunction );
    lut->SetClamping( 0 );
    double colors[9][3] = { {199, 21, 133}, { 139, 0, 0 }, {85, 107, 47}, { 123, 104, 238 },
                            {0, 228, 225},{ 47, 79, 79}, { 72, 209, 204}, { 255, 255, 0 },
                            { 255, 255, 255 }};
    for( int i = 0; i < 9; ++i )
    {
       lut->AddRGBPoint( i, colors[i][0]/255.0, colors[i][1]/255.0, colors[i][2]/255.0 );
    }

Question 4, Given a vertex, which edges share it?

    // ------------------------------- Given a vertex, which edges share it? --------------------------------------------
    int seedPtId = 0;
    vtkIdType ncells;
    vtkIdType* neiCellIds;
    data->GetPointCells( seedPtId, ncells, neiCellIds );
    std::vector<vtkSmartPointer<vtkIdList>> edgePtIds;
    for( int i = 0; i < ncells; ++i )
    {
        vtkCell *cell = data->GetCell( neiCellIds[i] );
        for( int j = 0; j < cell->GetNumberOfEdges(); ++j )
        {
            vtkCell *edge = cell->GetEdge( j );
            cout << edge->GetPointId( 0 ) << ", " << edge->GetPointId( 1 ) << endl;
            if( edge->GetPointId( 0 ) == seedPtId || edge->GetPointId( 1 ) == seedPtId )
            {
                vtkSmartPointer<vtkIdList> linePtIds = vtkSmartPointer<vtkIdList>::New();
                linePtIds->InsertNextId( edge->GetPointId( 0 ) );
                linePtIds->InsertNextId( edge->GetPointId( 1 ) );

                bool hasSameEdge = false;
                for( int k = 0; k < edgePtIds.size(); ++k )
                {
                    auto edgePtId0 = edgePtIds[k]->GetId( 0 );
                    auto edgePtId1 = edgePtIds[k]->GetId( 1 );
                    if( (edgePtId0 == edge->GetPointId( 0 ) && edgePtId1 == edge->GetPointId( 1 )) ||
                        (edgePtId0 == edge->GetPointId( 1 ) && edgePtId1 == edge->GetPointId( 0 )) )
                    {
                        hasSameEdge = true;
                    }
                }

                if( !hasSameEdge )
                {
                    edgePtIds.push_back( linePtIds );
                }
            }
        }
    }
    // ------------------------------- Finish --------------------------------------------

    MarkPoint( seedPtId, data, renderer );

    vtkSPtrNew(points, vtkPoints);
    vtkSPtrNew(cells, vtkCellArray);
    double bds[6];
    data->GetBounds(bds);
    vtkSPtrNew(pointsLocator, vtkPointLocator);
    pointsLocator->InitPointInsertion(points, bds);
    cout << "edges count : " << edgePtIds.size() << endl;
    for( int i = 0; i < edgePtIds.size(); ++i )
    {
        vtkIdType newcell[2];
        double tmp[3];
        for( int j = 0; j < 2; ++j )
        {
            auto id = edgePtIds[i]->GetId( j );
            data->GetPoint( id, tmp );
            pointsLocator->InsertUniquePoint(tmp, newcell[j]);
        }
        cells->InsertNextCell( 2, newcell );
    }
    vtkSPtrNew(linesPd, vtkPolyData);
    linesPd->SetPoints(points);
    linesPd->SetLines(cells);
    linesPd->Modified();

    vtkSPtrNew( lineMapper, vtkPolyDataMapper );
    lineMapper->SetInputData( linesPd );

    vtkSPtrNew( lineActor, vtkActor );
    lineActor->SetMapper( lineMapper );
    lineActor->GetProperty()->SetColor( 1, 0, 0 );
    lineActor->GetProperty()->SetLineWidth( 2 );

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