> ## Documentation Index
> Fetch the complete documentation index at: https://invariant-cad.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Primitives and transforms

> Create boxes, cylinders, cones, spheres, and parameterized transform chains.

## Primitives

```ts theme={"system"}
const box = cad.box("box", {
  size: vec3(mm(40), mm(20), mm(8)),
  center: true,
});

const cylinder = cad.cylinder("cylinder", {
  height: mm(30),
  radius: mm(10),
  center: true,
  segments: 96,
});

const cone = cad.cylinder("cone", {
  height: mm(30),
  radius: mm(12),
  radiusTop: mm(4),
});

const sphere = cad.sphere("sphere", {
  radius: mm(10),
  segments: 64,
});
```

`segments` controls tessellation where a backend uses it. It does not turn an
exact OCCT circle into a polygon; exact kernels can preserve analytic surfaces
while using the value for mesh extraction where applicable.

All size, height, and radius expressions must resolve to finite valid geometry.
The evaluator rejects zero or negative dimensions before asking a kernel to
construct the shape.

## One transform

```ts theme={"system"}
const moved = cad.translate(
  "moved",
  box,
  vec3(mm(100), mm(0), mm(25)),
);

const turned = cad.rotate(
  "turned",
  moved,
  angleVec3(deg(0), deg(0), deg(90)),
);
```

Convenience methods are available for translation, Euler rotation, nonuniform
scale, and mirror.

## Ordered transform chain

Use `cad.transform` when operation order must be explicit:

```ts theme={"system"}
const placed = cad.transform("placed", box, [
  tf.scale(scalarVec3(2, 1, 1)),
  tf.rotate(angleVec3(deg(0), deg(0), deg(90))),
  tf.translate(vec3(mm(100), mm(5), mm(0))),
]);
```

Operations execute in authored order. Reordering scale, rotation, and
translation generally changes the result and therefore changes effective
feature hashes.

## Mirror

```ts theme={"system"}
const mirrored = cad.mirror(
  "mirrored",
  placed,
  scalarVec3(1, 0, 0),
);
```

The vector is the mirror-plane normal. It must resolve to a usable finite
direction. A zero normal is invalid.

## Topology through transforms

Transforms create a new feature node, but semantic topology can retain origin
and modification lineage when the selected backend provides it. Query for
`modifiedBy(transform)` and combine it with the original feature source rather
than using a post-transform coordinate alone.

Nonuniform scale changes metric geometry and may change analytic surface kinds.
Persistent matching therefore depends on compatible evidence and the declared
topology protocol, not merely on the fact that a transform node exists.