fidget-cube.md

Rhino-derived fidget cube

The editable model is in fidget-shapes.gid, available as Examples → Fidget Shapes (Command+3 / Ctrl+3). The cube is the last list item. The standalone fidget-cube.gid remains a regression and performance fixture. Its source is a no-argument Grap function; the body constructs ordinary Fidget fields through existing library functions. There is no cube primitive in the evaluator or Fidget adapter. Its inline preview uses mesh rendering at depth 5. The implicit model is unchanged; preview 3d remains available for voxel-rendered comparison.

Reference

The reference is the owner's rhino-cube-plugin checkout at commit 1fe8fbc (2025-06-08), especially:

• src/models/ShinyCube.cs: size, chamfer size, and depth.
• src/ShinyCubeRhino.cs: six quadratic surface patches and twelve planar chamfers.
• src/commands/CreateShinyCubeCommand.cs: defaults 1, 0.1, and 0.5.

The older rhino-cube checkout has the same underlying surface construction, but the plugin contains the later model and machining work. This port concerns the part's shape only; it does not port tools, toolpaths, machine kinematics, or G-code. Neither external checkout is needed to load the example.

Rhino's NurbsSurface.CreateFromPoints uses control points, not interpolation points. With three points and degree two in each direction, each face is a tensor-product quadratic Bézier patch. Only its middle control point moves inward. At the patch center its weight is (1/2) × (1/2) = 1/4, so a control depth of 0.5 produces a surface depression of 0.125. The example deliberately preserves this distinction.

Field construction

Let s be size, c chamfer, and d control-point depth. The bindings compute:

h = s / 2
a = h - c
D = d / 4
L = s - c
q(t) = max(0, 1 - (t / a)²)

One opposing face pair is:

face(n, u, v) = |n| - h + D q(u) q(v)

On the top face this gives z = h - D(1 - (x/a)²)(1 - (y/a)²) within the square [-a,a]²: the Rhino quadratic patch, not a spherical approximation. Clamping each factor to zero extends the field outside that square without introducing another depression beyond the face. Chamfer constraints trim that extension; it does not add exposed flat strips to the part.

An opposing set of chamfer planes is:

chamfer(u, v) = |u| + |v| - L

The full field is the maximum of the three face-pair fields (one per normal axis) and the three chamfer-pair fields (xy, xz, yz). Negative is inside. These give six concave faces and twelve hexagonal chamfers. Three chamfers meet at each corner (±(h-c/2), ±(h-c/2), ±(h-c/2)); there is no additional triangular corner face or rounding.

This is an implicit field with the intended boundary, not an exact signed distance function. Fidget can render it as a field; its numeric magnitude must not be mistaken for distance when building offsets or cutter clearance.

Units, editing, and checks

The source keeps the Rhino program's numbers and model units. There is no unit type or conversion in this example. The viewport uses explicit −0.6…0.6 bounds and receives the pane's actual width and height; those viewing bounds do not rescale the part. Larger dimensional edits may require zooming out or changing the bounds.

The ordinary geometric regime requires s > 0, 0 ≤ c < s/2, and a depth small enough that neighboring face patches do not cross. The example does not constrain scrubbing or implement a general CAD parameter-validity system. Degenerate dimensions and excessive depth are not certified solids.

Tests evaluate the actual Grap example, compare sampled boundaries against an independent evaluation of Rhino's nine-control-point patches on all six faces, check the twelve chamfers and their corner joins, and vary the dimensions. The frame tests separately send the generated field through the real Fidget preview and check that it produces a visible surface. The text fixture also round-trips and has no orphaned definitions.