> ## 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.

# Paths, sweeps, and lofts

> Create exact bounded ruled lofts and line, circular-arc, or composite path sweeps.

Lofts and sweeps are exact OCCT features in 0.1. Their admitted grammar is
intentionally narrower than a general-purpose surface modeler so each accepted
case has explicit validation and volume checks.

## Ruled solid loft

```ts theme={"system"}
const lower = cad.sketch("lower", plane.xy(), (sketch) =>
  sketch.profile(
    sketch.rectangle("lower-outline", { width: mm(40), height: mm(30) }),
  ),
);

const upper = cad.sketch(
  "upper",
  plane.xy(vec3(mm(0), mm(0), mm(50))),
  (sketch) =>
    sketch.profile(
      sketch.rectangle("upper-outline", { width: mm(20), height: mm(15) }),
    ),
);

const loft = cad.loft("loft", [lower, upper], { ruled: true });
```

The current document grammar requires at least two distinct, ordered,
hole-free profiles on compatible parallel principal planes. Interpolation is
ruled; smooth, guided, open, and holed lofts remain future contracts.

## Polyline path

```ts theme={"system"}
const path = cad.polylinePath("path", [
  vec3(mm(0), mm(0), mm(0)),
  vec3(mm(20), mm(0), mm(0)),
  vec3(mm(20), mm(20), mm(0)),
]);
```

Paths are first-class nodes, not sketch profiles. The polyline must be open and
simple; repeated points and redundant collinear vertices are rejected.

## Three-point circular arc

```ts theme={"system"}
const arc = cad.circularArcPath("bend", {
  start: vec3(mm(0), mm(0), mm(0)),
  through: vec3(mm(7.071), mm(2.929), mm(0)),
  end: vec3(mm(10), mm(10), mm(0)),
});
```

`through` lies on the desired arc. It is not a Bézier control point. The three
points must define one conditioned arc below a full turn.

## Composite line/arc route

```ts theme={"system"}
const route = cad.compositePath("route", {
  start: vec3(mm(0), mm(0), mm(0)),
  segments: [
    { kind: "line", end: vec3(mm(5), mm(0), mm(0)) },
    {
      kind: "circularArc",
      through: vec3(mm(8.535), mm(1.465), mm(0)),
      end: vec3(mm(10), mm(5), mm(0)),
    },
    { kind: "line", end: vec3(mm(10), mm(10), mm(0)) },
  ],
});
```

A composite has at least two segments and at least one arc. Segments connect by
construction because each begins at the previous end. Arc junctions must be
forward G1 tangent; line-line junctions use right-corner semantics.

## Sweep a profile

The profile plane must be seated at the path start with its normal parallel to
the initial tangent:

```ts theme={"system"}
const section = cad.sketch("section", plane.yz(), (sketch) =>
  sketch.profile(
    sketch.rectangle("section-outline", { width: mm(2), height: mm(2) }),
  ),
);

const swept = cad.sweep("swept", section, route, {
  frame: "corrected-frenet",
  transition: "right-corner",
});
```

Those option values are currently the only admitted frame and transition
contracts; omitting them selects the same defaults.

## Clearance and conditioning

InvariantCAD validates more than path syntax. It checks the full profile
envelope against arc radius, remote path returns, adjacent curvature
neighborhoods, native transfer floors, and numerical conditioning. Composite
results are checked against an analytic transported-centroid volume oracle.

The important user-facing rule is simple: the complete cross-section needs
physical clearance around every bend and between remote path segments.
Shrinking only a nominal width while leaving an off-center profile can still be
invalid.

For exact tolerances, major-arc restrictions, centered-profile stock-runtime
behavior, and the owned-facade refinements, read the
[complete guide](/reference/complete-guide#exact-path-sweeps).

## Not yet supported

* closed or full-circle path documents
* Bézier, B-spline, and helix paths
* guided or variable-section sweeps
* arbitrary transition and frame modes
* holed sweep profiles
* general smooth surfacing

Rejected input receives a structured diagnostic; it is not silently
approximated with a different feature.