Retained 3D and n-dimensional projection

RiX keeps three distinct representations instead of treating a display as the mathematical object:

exact n-dimensional geometry -> explicit projection -> retained Scene3D -> Snapshot Graphic or glTF

The bundled nd, scene3d, and gltf plugins implement the first bounded slice of that pipeline. They are browser-safe and opt-in.

Scene3D values

.scene3d.Scene is an immutable output value with schema rix.scene3d@1. Coordinates and 4×4 transforms remain exact RiX integers or rationals until a camera snapshot or target exporter needs numeric coordinates. The internal coordinate convention is right-handed and Z-up.

.Plugin.Load("scene3d");

mesh := .scene3d.Mesh(
    [[0,0,0], [1,0,0], [0,1,0]],
    [[1,2,3]],
    {= color="#275dad", opacity=4/5 }
);
camera := .scene3d.PerspectiveCamera([4,4,3], [0,0,0], {=
    up=[0,0,1], fov=50, near=1/100, far=1000
});
scene := .scene3d.Scene([mesh], {= camera=camera });

Initial constructors are:

Constructor Contract
Scene(children, options?) Retained root with camera, optional lights, and metadata.
Group(children, options?) Ordered retained children.
Transform(children, options?) Exact flat row-major 4×4 matrix, or translate/scale.
Mesh(vertices, triangles, options?) Exact 3-vectors and 1-based triangle indices.
Polyline(points, options?) Exact 3-vectors; closed=1 optionally closes it.
PointCloud(points, options?) Exact 3-vectors with display radius.
Material(options) color, opacity, and wire width hints. A material may be passed in node options.
AmbientLight(color?, intensity?) Retained uniform light contribution.
DirectionalLight(direction, options?) Retained exact direction with hexadecimal color and exact intensity.
PointLight(position, options?) Retained exact position with hexadecimal color and exact intensity.
PerspectiveCamera(position, target, options?) up, degree fov, near, and far.
OrthographicCamera(position, target, options?) Automatic fit, or explicit vertical scale.

The initial schema intentionally contains realized geometry. Parametric and implicit surfaces will be adaptive producers of meshes rather than adding unevaluated functions to interchange files.

Deterministic snapshots

.scene3d.Snapshot projects a retained scene into core .Graphics. Phase 1 implements explicitly named wireframe and lit modes. Wireframe clips perspective segments against the camera’s near/far planes. Lit mode uses deterministic flat Lambert shading and painter’s ordering for mesh triangles; it does not claim certified hidden-surface removal, shadows, triangle clipping, or tessellation.

snapshot := .scene3d.Snapshot(scene, {=
    size=[640,480],
    mode="wireframe"
});
graphic := snapshot["value"];

Lights remain retained scene nodes and affect only an explicitly requested lit snapshot. A wireframe snapshot reports that it ignored present lights instead of silently changing its line rendering.

The result is an adaptive-result map with value, resolved, uncertainty, work, source, and diagnostics. value is a normal Graphic and therefore works unchanged with SVG, Canvas, TikZ, and PNG.

Exact n-dimensional projections

.nd provides Point, Polyline, Polytope, and Hypercube geometry under schema rix.nd@1. A projection is a separate rix.nd.projection@1 value with source/target dimensions, exact matrix, exact offset, method, and provenance. No operation silently discards coordinates.

.Plugin.Load("nd");

tesseract := .nd.Hypercube(4, 2);
rotation := .nd.CayleyRotation(4, 1, 4, 1/3);
xyz := .nd.CoordinateProjection(4, [1,2,3]);
projected := .nd.Project(tesseract, .nd.Compose(xyz, rotation));
scene := .nd.ToScene3D(projected);

Projection(matrix, offset?, options?) constructs an exact affine map. CoordinateProjection(sourceDimension, axes) uses 1-based axes. CayleyRotation(dimension, axis1, axis2, t) uses the rational parameterization cos=(1-t²)/(1+t²) and sin=2t/(1+t²); the core Cayley Infinity value denotes the half-turn. Compose(after, before) means “apply before, then after.” ToScene3D requires dimension 3 and reports an error if the caller has not explicitly projected first.

Projection, slice, fiber, and marginalization remain different notions. This slice implements affine projection; sections/slices and fibers remain future operations and will not be aliases for Project.

glTF export

The gltf renderer accepts Scene3D, converts Z-up coordinates to glTF’s right-handed Y-up convention, and writes glTF 2.0 JSON with an embedded base64 buffer. Mesh triangles, line primitives, point primitives, basic colors, and opacity are exported. Exact positions are rounded to Float32 only here and a gltf-float32-approximation diagnostic records the loss when applicable.

.Plugin.Load("gltf");
result := .gltf.Render(scene);
.Out("scene.gltf", scene);

Phase 1 does not export retained lights, camera nodes, textures, animation, or GLB. glTF line width is not portable and is reported as an informational diagnostic.

Runnable 4D example

From rix/:

bun bin/rix.js --out=tmp/tesseract-out examples/geometry/tesseract.rix

This creates tesseract.svg from a deterministic wireframe snapshot and tesseract.gltf from the same retained 3D scene. The corresponding RiX Web tutorials run the browser-safe parts directly.

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