//- Returns -1 or cartesian coordinate component (0=x, 1=y, 2=z) of normal
//  in case of 2D mesh
label twoDNess(const polyMesh& mesh)
{
    const pointField& ctrs = mesh.cellCentres();

    if (ctrs.size() < 2)
    {
        return -1;
    }


    //
    // 1. All cell centres on single plane aligned with x, y or z
    //

    // Determine 3 points to base plane on.
    vector vec10 = ctrs[1] - ctrs[0];
    vec10 /= mag(vec10);

    label otherCellI = -1;

    for (label cellI = 2; cellI < ctrs.size(); cellI++)
    {
        vector vec(ctrs[cellI] - ctrs[0]);
        vec /= mag(vec);

        if (mag(vec & vec10) < 0.9)
        {
            // ctrs[cellI] not in line with n
            otherCellI = cellI;

            break;
        }
    }

    if (otherCellI == -1)
    {
        // Cannot find cell to make decent angle with cell0-cell1 vector.
        // Note: what to do here? All cells (almost) in one line. Maybe 1D case?
        return -1;
    }

    plane cellPlane(ctrs[0], ctrs[1], ctrs[otherCellI]);


    forAll (ctrs, cellI)
    {
        const labelList& cEdges = mesh.cellEdges()[cellI];

        scalar minLen = GREAT;

        forAll (cEdges, i)
        {
            minLen = min(minLen, mesh.edges()[cEdges[i]].mag(mesh.points()));
        }

        if (cellPlane.distance(ctrs[cellI]) > 1E-6*minLen)
        {
            // Centres not in plane
            return  -1;
        }
    }