Function buildExtrude

Sweep a 2D polygon cross-section along a 3D centreline path, producing extruded geometry.

Useful for beams, mouldings, conduit, gutters, parapets, stair stringers — anything with a constant cross-section along a curve.

The cross-section lies in the plane perpendicular to the path's tangent at each path vertex. The local frame (N, B) is computed via parallel transport along the path so the cross-section doesn't twist between vertices.

Conventions

• shape is a flat array [x0, y0, x1, y1, ...] defining the cross-section in its local plane. List vertices CCW (viewed from +T) so face normals point outward. For closed shapes the last vertex implicitly connects back to the first — don't repeat the first vertex.
• path is a flat array [x0, y0, z0, x1, y1, z1, ...] defining the 3D centreline.
• closedShape (default true) controls whether the cross-section closes into a loop. Open shapes produce a swept strip and never get caps.
• closedPath (default false) controls whether the path itself closes into a loop. Closed paths skip caps.
• caps (default true) fills the start and end with the cross-section polygon when both closedShape is true and closedPath is false. The cap triangulation is a simple fan from vertex 0; convex shapes work, non-convex shapes produce overlapping triangles and should not be capped via this builder.

Sharp corners on the path bevel the cross-section (the per-vertex tangent averages the incoming and outgoing edge directions); for cleaner mitres pre-process the path to insert duplicated vertices at the corners with the desired offset.

Usage

// 0.2 × 0.2 square beam swept along an L-bend in the XY plane.
const result = buildExtrude({
  shape: [-0.1, -0.1,  0.1, -0.1,  0.1, 0.1,  -0.1, 0.1],
  path:  [0, 0, 0,  1, 0, 0,  1, 1, 0]
});
if (result.ok) {
  const geometry = result.value;
  // Pass to sceneModel.createGeometry(...)
} else {
  console.error("Error creating extrusion:", result.error);
}
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