# Hex smoothing

`nekmeshpy.hexmesh.smoother` moves the vertices of a hex mesh, never its connectivity, under the same
constraints, Laplace smoothing and shape optimizer as the {doc}`quad smoother <../../user/quad_smoother>`
({doc}`user guide <../../user/hex_smoother>`). The pages call the stages directly; in practice the same stages run
as reviewed rounds of a `SmoothSession` (`propose`, then `accept` or `undo`).

```{warning}
Experimental. The hex smoother is native (pure NumPy), moves **vertices only** (on a curved mesh the curved nodes
follow), and has been tested on small meshes (a few hundred hexes). MFEM's TMOP, an optional stage, smooths a curved
mesh as curved ({doc}`../mfem/index`).
```

Each page below is one small example that shows one behaviour. Every page has a 3-D viewer: the input and each result
as variants, a translucent boundary shell and cross-sections coloured by each hex's worst-corner scaled Jacobian.

| page | shows |
|---|---|
| {doc}`methods` | Laplace, the optimizer and the suggested schedule on one perturbed input, boundary frozen |
| {doc}`slide_box` | `boundary="slide"`: face vertices stay on their planes, edge vertices on their lines, corners fixed |
| {doc}`free_boundary` | a free curved wall: `boundary="free"`, `"tangent"`, `"slide"` and an exact cylinder target |
| {doc}`thin_layer` | a designed thin layer, unprotected and kept with `KeepLayer` |
| {doc}`untangle` | inverted hexes repaired by the optimizer's `delta` continuation |

```{toctree}
:maxdepth: 1
:hidden:

methods
slide_box
free_boundary
thin_layer
untangle
```

Every number on these pages is computed by the example script named on the page and written into the page by
`python docs/_ext/gen_smoother_hex_assets.py`; none is typed. The same
thin layer under MFEM's TMOP has a page of its own: {doc}`../mfem/thin_layer`, and a curved bent pipe:
{doc}`../mfem/bent_pipe`.