smith

# Form, cut, and thicken

```elixir
Mix.install([{:smith, "~> 0.4.0"}, {:kino, "~> 0.19.0"}])
```

## Before you start

After [extrusion](extrusion.livemd), modify an existing solid: taper its walls, cut it, and reuse a flat section. Then make a thin sleeve from a curved surface.

Run cells in order. Lengths are millimeters and modeling angles are degrees.
Each 3D preview supports orbit, zoom, and fullscreen.


## Draft the walls

The neutral plane fixes the footprint at Z=0. Positive draft removes material in the pull direction, which defaults to the plane normal. Select the four side faces by excluding faces whose normals are parallel to Z. `count: 4` checks the selection before OCCT propagates across any tangent-connected faces.

```elixir
alias Smith.{Assembly, Plane, Selector}

blank = Smith.box(20, 16, 10)
sides = Selector.type(:plane) |> Selector.exclude(Selector.parallel(:z))
tapered = Smith.draft(blank, faces: sides, neutral: :xy, angle: 5, count: 4)

{:ok, result} = Smith.evaluate(tapered)
{:ok, volume} = OCEx.volume(result.shape)
t = :math.tan(5 * :math.pi() / 180)
expected = 20 * 16 * 10 - 36 * t * 100 + 4 / 3 * t * t * 1000
true = abs(volume - expected) < 1.0e-5
Smith.Kino.render(result, label: "1 · Five-degree draft")
```

At height z the rectangle measures `(20 − 2zt) × (16 − 2zt)`. Integrating its area from 0 to 10 gives the volume checked above. Draft supports planar, cylindrical, and conical selected faces. Excessive angles or disappearing faces can fail; the operation does not repair every topology change.

## Keep one side of a cut

The plane normal points toward +Z, so `keep: :negative` retains the material below Z=6. `:positive` keeps the other side. The default, `:both`, preserves both pieces as separate solids without fusing their shared cut face.

```elixir
cut_plane = Plane.xy(z: 6)
tapered_snapshot = Smith.from_result(result)
lower = Smith.split(tapered_snapshot, cut_plane, keep: :negative)
{:ok, lower_result} = Smith.evaluate(lower)
{:ok, volume} = OCEx.volume(lower_result.shape)
expected = 320 * 6 - 36 * t * 36 + 4 / 3 * t * t * 216
true = abs(volume - expected) < 1.0e-5
Smith.Kino.render(lower_result, label: "2 · Lower portion")
```

## Reuse the section

`section` returns the filled planar cross-section, including holes. Disconnected regions remain separate faces. Translate the section to the bed and extrude along a world vector; scalar extrusion is for sketches with a local plane.

```elixir
cross_section = Smith.section(tapered_snapshot, cut_plane)
{:ok, section_result} = Smith.evaluate(cross_section)
{:ok, area} = OCEx.area(section_result.shape)
expected_area = (20 - 12 * t) * (16 - 12 * t)
true = abs(area - expected_area) < 1.0e-5

cap = section_result |> Smith.from_result() |> Smith.translate({0, 0, -6}) |> Smith.extrude({0, 0, 2})
{:ok, cap_result} = Smith.evaluate(cap)
{:ok, volume} = OCEx.volume(cap_result.shape)
true = abs(volume - expected_area * 2) < 1.0e-5
Smith.Kino.render(cap_result, label: "3 · Section extruded into a cap")
```

A missed plane returns an empty compound. Point or edge tangencies do not create a printable section. Check for faces before extruding a section whose position is user-controlled.

## Offset and thicken a curved surface

`surface` selects faces and sews connected boundaries. Here it extracts the cylindrical wall without the end caps. Positive offset follows that wall's outward normal, increasing its radius from 10 to 12. Negative thickening then builds a 1 mm wall toward the inside, from radius 12 to 11. The source cylinder remains unchanged.

```elixir
wall = Smith.cylinder(10, 12) |> Smith.surface(Selector.type(:cylinder))
sleeve = wall |> Smith.offset(2) |> Smith.thicken(-1)
{:ok, sleeve_result} = Smith.evaluate(sleeve)
{:ok, volume} = OCEx.volume(sleeve_result.shape)
true = abs(volume - :math.pi() * (12 * 12 - 11 * 11) * 12) < 1.0e-5
Smith.Kino.render(sleeve_result, label: "4 · Offset sleeve with a one-millimeter wall")
```

`offset` moves surfaces along their normals. Applied to a solid, it expands or contracts its boundary. It does **not** offset a sketch outline within its plane. `thicken` closes a face or open shell into a solid; it rejects a closed shell or an existing solid. To hollow a solid and remove a face, use `Smith.shell/2` instead. Sharp joins accept `join: :arc` or `:intersection`; offset defaults to arc, thickening to intersection. Large distances, narrow gaps, and self-intersections can fail. BREP validity is not proof that every self-intersection is absent.

## Assemble and export

These are three separate samples. Installed positions spread them out for inspection; each part's print placement puts it on the bed. The export verifies each mesh and its STEP round trip before updating the current manifest.

```elixir
samples =
  Assembly.new(:forming)
  |> Assembly.part(:base, lower, print: [on_bed: true])
  |> Assembly.part(:cap, cap, position: {30, 0, 0}, print: [on_bed: true])
  |> Assembly.part(:sleeve, sleeve, position: {70, 8, 0}, print: [on_bed: true])

{:ok, assembly} = Smith.evaluate(samples)
{:ok, files} = Smith.export(assembly, "output/models",
  name: "forming", tolerance: 0.03, angular_tolerance: 0.1)
preview = Smith.Kino.render(assembly, label: "5 · Three printable samples")
Kino.Layout.grid([preview, Kino.Text.new(files.print_pack)])
```

Change the draft angle, cut height, or sleeve thickness and reevaluate dependent cells. Update the formulas along with the dimensions. Mesh and volume checks do not establish strength or fit: inspect the exported parts in your slicer before printing.