# U-tube interface and outer box

Two surfaces of the `examples/u_tube_box.py` hex mesh, each smoothed as a free-standing surface, as built or with
perturbed input.

```{include} _generated/u_tube_interface.viewer.inc
```

## Key points

- **interface**: the tube wall (face tag `interface`), its two open ends frozen. **outer box**: the six outer faces (tag
  `outer`); planes held by `OnSurface(plane)`, the twelve creases slide on `OnCurve(line)`, the eight corners and the
  rim of the tube's two openings frozen.
- **The targets are analytic**: the tube is exactly a radius about the U's centreline (the example's `project_to_wall`,
  radial normal) and the box is six planes, so unlike {doc}`wire_coil_surface` the surface is independent of the mesh.
- **Both surfaces are already good**, so the as-built gain is modest; the box, planar and almost all squares, has little
  to gain and some numbers get slightly worse. From perturbed input both return to nearly their as-built end state.
- **The smoother does not touch the hexes**; {ref}`u-tube-hexes` measures carrying the wall into them.
- *Perturbed input*: every movable vertex shifted by up to 0.2 of its local edge length, then put back on its surface.

## The numbers

```{include} _generated/u_tube_interface.table.inc
```

Run `python examples/smoother/quad/cs_u_tube.py` to reproduce; it prints these numbers.

(u-tube-hexes)=
## The hexes

- `examples/smoother/quad/cs_u_tube_hex.py` takes the order-1 hex mesh (the corner geometry a `.re2` file holds) and puts the
  smoothed wall's vertices in place of the old ones.
- The wall is the one surface between a one-layer solid shell and a one-layer fluid shell, so re-lofting those shells
  from it (what the example's construction would do) is the same as moving those vertices; every other vertex (the
  stair-step side, the box, the shrunk core) is the example's own.
- Measured at the 8 corners (what `.re2` holds) and re-read on a finer lattice at order 7, the solver's.

```{include} _generated/u_tube_hex.text.inc
```

```{include} _generated/u_tube_hex.table.inc
```

- *Exterior*: every named face by boundary group, one checkbox each (`outer` starts off so `interface` is visible).
  *Cross-section*: along the U and across both legs, by scaled Jacobian or region (fluid or solid). Drag to orbit.

```{include} _generated/u_tube_hex.viewer.inc
```

Run `python examples/smoother/quad/cs_u_tube_hex.py` to reproduce; it prints these numbers.

<details>
<summary>Notes and caveats</summary>

- `interface` separates fluid from solid, so `hexmesh.boundary_mesh(mesh, "interface")` returns every quad twice, once
  per side; the script keeps one of each pair.
- The surfaces are too large for the data to keep a stage history, so the viewer shows only the input and the final
  state (panels and histogram as in {doc}`simple_geometries`). The outer box is five times the wall's size, and so is
  its data file.
- The tables are regenerated by `docs/_ext/gen_smoother_quad_assets.py` and `docs/_ext/gen_smoother_quad_hexviews_assets.py`; nothing
  is typed in.

</details>