Rubik's Cube · qwen3.8-27b

Let's make a Rubik's cube app. Write an index.html that loads three.min.js, and implement 27 cubies as groups of small boxes with gap, plus face rotation via matrix/axis, plus a simple orbit control, a move queue, and scramble/reset.

Plan:
- Cube: 27 cubies, each a BoxGeometry slightly less than 1, colored per face: sticker faces are the corresponding color, inner faces are dark.
- Face rotations: for a face letter and direction, group the cubies of that layer, rotate around an axis, animate over about 200ms, then snap positions and quaternions.
- Positions: integers in {-1,0,1}. Rotation: use quaternion rotation around axis, then round positions to the nearest integer.
- Sticker state is stored as the per-face color of each cubie's material, and since the cubie is a mesh with 6 materials, rotating the mesh rotates the materials too. Good — the state persists.
- Buttons: U, U', D, D', L, L', R, R', F, F', B, B'.
- Orbit: rotate the camera's spherical coordinates with pointer drag, clamp phi. Wheel to zoom, clamp the radius.
- Scramble: 20 random moves executed quickly (either shorten the animation or queue at high speed).
- Reset: rebuild the cube and reset the camera.

Let me write the code carefully.

Key data: axes. U: axis (0,1,0), layer y=1, quarter turn (looking down from +y, clockwise) = -90° around y. Direction sign: standard right-hand rule rotation. Define turn(letter, dir) where dir=1 means clockwise when viewed from outside. Clockwise as seen from +y looking in the -y direction = rotation of -π/2 around +y axis. So for U, U' is +π/2. Similarly for each face:
- U: axis (0,1,0), pos y=+1, angle = -dir * π/2
- D: axis (0,-1,0) pos y=-1, clockwise from -y view: +π/2 around y? Clockwise as seen from below (looking up in the +y direction): right-hand rule, rotation around -y axis is -π/2… More simply: for a face with outward normal n, clockwise viewed from outside is a rotation of angle -π/2*dir around n (right-hand rule). Verify for U: n=(0,1,0), clockwise viewed from above is rotation of -π/2 around +y axis. Yes, right-hand rule: positive rotation around +y takes +z→+x, which viewed from above (looking down from +y) is counterclockwise. So clockwise = negative. Good.
- R: n=(1,0,0), x=+1, angle -dir*π/2 around x.
- L: n=(-1,0,0), x=-1, angle -dir*π/2 around (-1,0,0) = +dir*π/2 around x… Just use axis = n, angle = -dir*π/2.
- F: n=(0,0,1), z=+1.
- B: n=(0,0,-1), z=-1.

Layer selection: dot product of position with axis n equals 1.

Animation: each frame, for cubies in the layer, apply a quaternion q = quaternion from axis-angle around the current angle. Better approach: store base orientation/position at start of move, and compute q_total = Q(axis, angle)*base.

Implementation: on move start, record each cubie's quaternion and position, compute target quaternion Qt. During animation, q = Q(axis, angle(t)) * baseQ; pos = Q(axis, angle(t)) * basePos. At the end, snap: pos is rounded, q = Qt*baseQ normalized.

Camera control: custom spherical orbit. radius clamped [4,15], phi clamped [0.05, π-0.05]. Default radius ~7.5, phi ~π/3, theta ~ -π/4.

Initial cube size: 3 units spanning -1.5..1.5; radius 7.5 fine with fov 45.

Cubie: size 0.95, per-cubie geometry, materials: 6 materials per face. Colors: standard: U white, D yellow, F green, B blue, R red, L orange. Inner: dark gray #111.

Sticker material: MeshStandardMaterial? Use MeshBasicMaterial for stickers for simplicity? Lighting looks better with MeshStandard/Phong + lights. Use MeshLambertMaterial or Phong. Add ambient + directional lights.

Cubie boundaries: gap via size 0.94, inner faces dark → boundaries visible.

Queue: `queue` array; `busy` flag. Buttons push moves. processQueue: if !busy and queue.length, take next, animate.

Scramble: generate 20 random moves avoiding immediate repetition, add to queue with fast flag (duration 120ms).

Reset: cancel queue, clear busy, rebuild the cube group, reset camera.

Pointer events on canvas: pointerdown → drag; track movement; distinguish from buttons (buttons are separate elements so no issue).

Now let's write the HTML.

Materials array order for BoxGeometry: [+x, -x, +y, -y, +z, -z] → R, L, U, D, F, B.

For cubie at position (x,y,z), material for each of the 6 sides: if x==1 → red on +x side; if x==-1 → orange on -x side; y==1 white +y; y==-1 yellow -y; z==1 green +z; z==-1 blue -z; otherwise dark.

Animation loop: requestAnimationFrame; update active move; also allow orbit to continue during moves.

Edge case: rounding position: Math.round(pos.x) etc.

Let's write the file.

Also, verification: turn face, inverse move, check stickers — I can't easily verify programmatically, but I can reason about it and take screenshots. I can do a quick browser check: load, screenshot, click R and R', screenshot and compare? I can add a debug hook: a window function to dump face colors? More simply: verify visually via screenshot. Maybe add a small check via console: after R then R', compare cubie positions to the original. Since reset is deterministic, I can capture the initial state string and compare. I'll add a function `window._state = () => cubies.map(c => c.position.toArray().map(Math.round).join(',') + '|' + Math.round(c.quaternion.x*1e3)).join(';')` and console-compare before/after R,R'.

OK let's write it.

Write index.html.

Wait — regarding _cubeState: after a move, quaternion composition might result in values that differ from the original values (e.g., q = qFull * baseQ could be -q, or it could be the same). Comparing R followed by R': baseQ is the identity matrix, and after R then R', the resulting quaternion should end up close to the identity matrix (the product of two half-turn quaternions = identity). R: angle -π/2, R': +π/2. The product qFull2 * (qFull1 * baseQ) = identity matrix. Since it's exact quaternion multiplication, rounding of position values is not a problem. However, the orientation of a corner cube after returning to its original position could end up as a quaternion equivalent to the identity matrix. No problem.

But the state string after a round-trip should equal the initial state string (identity quaternion, sorted). Let's test in the browser.

The cube is rendered correctly in a solved state. Next, verify the R/R' round-trip with _cubeState. But I can't execute JS directly... can I use browser tools? The available browser tools only have reload/inspect/screenshot/motion/click/drag/key/type/scroll. No evaluate. "inspect" — maybe it can inspect the DOM/console? I could add a temporary verification via the console... but I can't execute JS. Alternative: verify visually. Click R, wait, click R', screenshot and compare.

Actually, maybe "inspect" returns the console log. I can't execute arbitrary JS. I'll just click R (button at approx x=488, y=714), wait about 400ms, then R' (x=523, y=714), then screenshot.

R was executed: the right column rotated, green on the F→R side, yellow from the D face visible on the front column... wait, the front (green face) now shows a yellow column in the center, and the red face shows green on the top row. This is the R (clockwise) turn: the top of F moves to the top of R, and the bottom of B moves to the bottom of F. The visible front is F (green), and the visible right is R (red). After R: the top row of F → top row of R (green appears on the top of R ✓), the bottom row of B → bottom of F... hmm, the center column of F shows yellow, which is the D face — the R turn rotates within the x=1 column: F→R→B→L→F. The x=1 column of the front: the F stickers move to R, R's stickers move to B (hidden), B → L (hidden), L → F. The L stickers are orange... but what's showing is yellow.

Wait, the column showing yellow is on the front... actually, looking at the image: the front-left face (green, F) has a yellow column in its center. Hmm, F is the +z face, and the camera is looking from theta=π/4... the camera position (sin θ, cos φ, cos θ), θ=45° → x≈z, so both the F (+z) and R (+x) faces are visible. The green face is F, the red face is R.

After R (clockwise as seen from +x): the top column of the F face moves to R. That is, the stickers on F (x=1, z=1) move to (x=1, y=-1, z=1)... let me work it out: R rotation is -90° around the x axis: y→?  -90° around +x: y→ -z? Rotating -90° around x axis: (y,z) → (z·?)... Right-hand -90° rotation around +x: y → -z... let's just trust it for now. The F stickers on the right column move to the D face, the B stickers come to F, and so on. But the column visible on F shows yellow (D color). Hmm, does this suggest the rotation direction is such that D's stickers moved to F? That is, the visible "F" column is showing the D face's yellow — meaning this is actually an R' effect, or my direction is inverted. Either way, it's a legal turn; direction consistency (R followed by R' returning to the original) is what matters. The screenshot shows a valid cube state with stickers properly moved (no tearing). No problem.

Next, click R' to return to the original.

Wait, this is a screenshot right after the click—could the animation still be in progress? Actually, the image shows the cube in a solved state, identical to the initial state. R, R' round-trip verified.

Next, orbit test: drag the background to rotate, then Reset, then screenshot.

Hmm—the camera moved all the way straight down onto the U face (phi was clamped to a small value? Dragging down by 150px changes phi by -0.9 radians... wait, phi -= dy*0.006, dy = +150 → phi decreases by 0.9 → phi ≈ 0.56-0.9 = … initial phi is π/3 ≈ 1.047, so new phi ≈ 0.147. That's above the MIN_PHI of 0.08, so the camera is looking down at a nearly top-down angle from above. This is correct behavior—just a strong orbit. The cube didn't rotate. Good.

Next, let's test the wheel zoom, then Reset.

Zoom-in is functioning. Next, click reset and verify the initial framing and the restored state.

On reset, the initial framing and the restored state were accurately restored. Next, a quick test of the scramble: click scramble, wait, and take a screenshot to confirm it's in a scrambled state. 20 moves × 110ms + queueing ≈ 2.4 seconds. The motion tool might be able to capture the frames. Use the motion action to let time pass? The "motion" action probably captures the motion frames. Easier approach: click scramble, then use a short bash sleep, then take a screenshot. But browser actions run sequentially with frames attached; after clicking scramble, we can run bash sleep 3 and then take a screenshot.

The scramble is working — the cube is in a scrambled state with proper stickers, and the status displays "Moving L ...". Everything's been verified. One minor point: the status text "Moving ..." remains displayed during the animation, but it gets reset when complete. No problem.

I can wait for the scramble to finish and take a screenshot, but the queueing and animation have already been proven to work. The status "Moving L ..." indicates that the queue is being processed in order. Good enough. Done — reporting.