Write high-order elements to VTK files about omega2d HOT 4 OPEN

After generating test files for Lagrange elements of order 2 and 3 (9 and 16 points, respectively), I learned that ParaView 5.5.0 and 5.8.0 can read them. The elements can be automatically subdivided for smoother surface rendering as well. This looks nice. But contours are still terrible. In fact, they are even worse for these Lagrangian HO elements than for the standard bicubic quads! The contour lines are still jagged, and do not even fall onto the non-subdivided surface (i.e. some run beneath the surface and some above). It is essentially unusable.

<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian" header_type="UInt32">
    <UnstructuredGrid>
        <Piece NumberOfPoints="16" NumberOfCells="1">
            <Points>
                <DataArray NumberOfComponents="3" Name="position" type="Float32" format="ascii"> 0.15 0.1 0.0 0.85 0.1 0.0 0.95 0.9 0.0 0.05 0.9 0.0 0.35 0.11 0.0 0.55 0.11 0.0 0.88 0.35 0.0 0.92 0.65 0.0 0.35 0.92 0.0 0.65 0.92 0.0 0.12 0.35 0.0 0.08 0.65 0.0 0.35 0.36 0.05 0.58 0.36 0.05 0.35 0.67 0.05 0.62 0.67 0.05 </DataArray>
            </Points>
            <Cells>
                <DataArray Name="connectivity" type="Int32" format="ascii"> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 </DataArray>
                <DataArray Name="offsets" type="Int32" format="ascii"> 16 </DataArray>
                <DataArray Name="types" type="UInt8" format="ascii"> 70 </DataArray>
            </Cells>
            <PointData Scalars="density">
                <DataArray Name="density" type="Float32" format="ascii"> 0.2 0.3 0.7 0.5 0.23 0.27 0.4 0.5 0.57 0.62 0.3 0.4 0.4 0.45 0.45 0.5 </DataArray>
            </PointData>
        </Piece>
    </UnstructuredGrid>
</VTKFile>```

from omega2d.

My conclusion is that, given the current state, we should internally subdivide our HO elements into linear quads at higher resolution than the Legendre or Lagrange points themselves, and just write a larger number of VTK_QUAD elements into our vtu files.

from omega2d.

AH! I spoke/wrote too soon. These higher-order elements are useful, but one must first "Tesselate" the elements, then apply Contour.

from omega2d.

Old-style bicubic quads are now supported as measurement features and writing to vtu with 4ad8bae
Not closing this issue because we still do not support the arbitrary-order Lagrange elements (but is that necessary?)

from omega2d.