Project curves onto surfaces

Projection transfers boundary curves to target surfaces, similar to casting the outline of a shape onto another surface. Start with workplanes and sketches. It does not intersect filled sketch material with a body. Use it to place an outline on a face, measure a curve on a curved surface, or create a planar profile for another operation. Coordinates stay in world space.

Parallel projection

alias Smith.{Plane, Selector, Sketch}

source = Sketch.circle(4, on: Plane.xy(z: 12))
inclined = Plane.new(normal: {1, 0, 1}, x_direction: {1, 0, -1})
target = Sketch.rectangle(30, 30, on: inclined)
outline = Smith.project(source, target, direction: {0, 0, -1})
{:ok, projected} = Smith.evaluate(outline)
{:ok, [_wire]} = OCEx.wires(projected.shape)

The source circle lies above the target plane z = -x. Its projection is an ellipse on that plane. The direction is normalized, so its magnitude does not set a travel distance. Parallel projection is bidirectional: changing {0,0,-1} to {0,0,1} does not select a different side.

Fill a planar outline

profile = Smith.face(outline)
{:ok, face_result} = Smith.evaluate(profile)
{:ok, area} = OCEx.area(face_result.shape)
true = abs(area - 16 * :math.pi() * :math.sqrt(2)) < 1.0e-6

part = profile |> Smith.extrude({0, 0, 3})
{:ok, result} = Smith.evaluate(part)
{:ok, volume} = OCEx.volume(result.shape)
true = abs(volume - 48 * :math.pi()) < 1.0e-6

face/1 accepts one closed planar wire. It preserves world placement and returns a face recipe that composes with extrusion, revolution, and Boolean operations. It does not guess which projected boundaries are holes or pick one of several surface hits. Multiple wires return :wrong_shape_type, open wires return :open_wire, and nonplanar boundaries cannot be filled by this operation.

Project through a point

enlarged = Sketch.circle(2, on: Plane.xy(z: 5))
  |> Smith.project(Sketch.rectangle(20, 20), from: {0, 0, 10})
  |> Smith.face()
{:ok, enlarged_result} = Smith.evaluate(enlarged)
{:ok, area} = OCEx.area(enlarged_result.shape)
true = abs(area - 16 * :math.pi()) < 1.0e-6

This conical projection follows half-rays from the point through the source. The target is twice as far from the point as the source plane, so the radius doubles from 2 to 4 mm. Targets between the point and source can also be hit; targets behind the point are excluded. Source curves passing through the point, or other degenerate configurations, may fail.

Exactly one of :direction and :from is required. There is no implicit view direction or perspective point.

Choose the target surface

body = Smith.box(20, 20, 4, align: {:center, :center, :min})
top = Smith.surface(body, Selector.facing(:z))
top_outline = Smith.project(source, top, direction: {0, 0, -1})
{:ok, top_result} = Smith.evaluate(top_outline)
{:ok, [_wire]} = OCEx.wires(top_result.shape)

Projecting onto the whole box instead would retain both the top and bottom hits. Projection does not sort intersections by distance or choose a visible surface. Selecting target faces first makes that choice explicit. Native targets may be faces, shells, solids, or compounds of those types; free edges are rejected.

Curved surfaces and clipping

wall = Smith.cylinder(5, 10) |> Smith.surface(Selector.type(:cylinder))
curves = Smith.line({-3, -10, 5}, {3, -10, 5})
  |> Smith.project(wall, direction: {0, 1, 0})
{:ok, curves_result} = Smith.evaluate(curves)
{:ok, wires} = OCEx.wires(curves_result.shape)
2 = length(wires)
{:ok, length} = OCEx.length(curves_result.shape)
true = abs(length - 20 * :math.asin(3 / 5)) < 1.0e-5

The line produces an arc on each side of the cylinder. Inspect them with Smith.edges/2, Smith.inspect_edges/2, or OCEx.edge_sample/2. The projected curves remain exact native geometry; this operation does not use a mesh.

Target boundaries and holes clip curves, so a closed source can yield open or disconnected results. A sketch contributes all its boundary wires, including holes. A completely enclosing outline that misses the target boundary does not fill the target. A missed or failed source boundary returns :projection_failed; collections fail if any boundary fails. Successful partial intersections remain valid output. If a swept source curve lies on a target surface, the intersection is not an isolated curve: OCCT can return boundaries of the coincident region. Avoid coincident or tangent configurations when a unique projected curve is needed.

Preview and export

Kino renders faces and solids as triangle surfaces, and wire-only results as sampled curves. Preview each stage or inspect exact geometry with curve queries. Wires can be exported as BREP/STEP through OCEx, but printable STL/3MF require solid geometry.

{:ok, files} = Smith.export(result, "output", name: "projected-cap", on_bed: true,
  angular_tolerance: 0.1)
true = files.verification.mesh.watertight

The projection Livebook shows these stages and exports a two-part print pack. Orthographic drawings and hidden-line removal are separate operations; this API projects source curves onto supplied target geometry.