Bouncing balls in a heptagon · qwen3.8-max-0902

Let me build this. Single file index.html with canvas, physics.

Design: canvas 800x800. Heptagon radius ~350 centered. Balls radius ~14-16, 20 balls. Gravity 800 px/s². Rotation period 5s → ω = 2π/5.

Collision with moving walls: for each of 7 edges, compute inward normal, penetration, ball velocity relative to wall velocity at contact point (v_wall = ω × r). Reflect normal component with restitution, apply tangential friction, and add spin coupling.

Ball-ball: impulse with restitution and friction affecting angular velocities.

Use substeps for stability, e.g., fixed dt = 1/240 with accumulator.

Position correction to avoid sinking.

Let me write it.

Ball angular: I = 0.5*m*r² for disc.

Friction impulse at ball-ball contact: tangential relative surface velocity = (v_rel · t) + ω_a*r_a + ω_b*r_b ... careful signs.

For ball A and B: contact point. Relative velocity at contact = (vB + ωB × rB_vec) - (vA + ωA × rA_vec). With 2D, ω × r = ω * perp(r) = ω * (-r.y, r.x).

Friction impulse j_t along tangent, clamped by μ*j_n. Apply to both.

Wall: contact point on ball at -n*r (n inward normal). Surface velocity of ball at contact = v + ω × (-n r). Wall velocity at that point = ω_wall × (contactPoint - center). Relative = v_ball_contact - v_wall_contact. Normal component (along inward normal n): vn = rel·n; if vn < 0 (moving into wall), apply normal impulse.

Let me just implement.

Also cap speeds.

Rendering: draw heptagon polygon, balls with circle, radial line marker plus number rotated by angle.

Controls: Pause/Resume, Reset buttons. Maybe also show FPS/status.

Initial arrangement: compact grid near center, non-overlapping, e.g., 5 columns × 4 rows spacing 2r+2.

Reset: restore positions and angle=0, velocities zero, angular zero, time zero.

Let's write the code.

Wall collision handling: iterate over 7 edges; for each edge, get the two vertices, edge direction, inward normal (pointing to center). Compute signed distance from ball center to the edge line: d = dot(c - a, n). If d < r → penetration = r - d. Also need to clamp to segment? For convex polygon inside containment, using infinite lines is fine and simpler; balls stay inside so line-based works.

Push out: c += n * penetration. Then velocity response with wall velocity at contact point p = c - n*r.

wallVel = ω_w × (p - center) = ω_w * (-(p.y-cy), (p.x-cx)).

rel = v - wallVel; vn = rel·n; if vn<0: v -= n*(1+e)*vn. Tangent t = perp(n); vt = rel·t + ω*r... hmm relative surface velocity tangential: vt_rel = rel·t + ω_ball * r (since contact point offset from ball center is -n*r, and ω × (-n r) tangential component: ω*(-n r).x = ω*(-n.y*r)... let's compute: perp(a) = (-a.y, a.x). ω × d = ω*perp(d) = ω*perp(-n*r) = -ω*r*perp(n) = -ω*r*t. So surface velocity of ball at contact = v + (-ω*r*t). Tangential component = rel·t - ω*r.

Friction: to bring this to zero: needed jt such that Δv_t = jt/m (in t direction) and Δω = torque: impulse jt*t applied at contact point d=-n*r from center → torque = cross(d, jt*t) = jt*cross(d,t) = jt*(-n r) cross t → cross(a,b)=a.x*b.y-a.y*b.x; cross(-n r, t) = -r*cross(n,t) = -r*(n.x*t.y - n.y*t.x). With t = perp(n) = (-n.y, n.x): cross(n,t) = n.x*n.x - n.y*(-n.y) = 1. So torque = -jt*r. Δω = -jt*r/I.

We want vt_rel_new = 0: (rel·t + jt/m) - (ω + Δω)*r = vt - ... wait: new tangential surface vel = (rel·t + jt/m) - (ω - jt*r/I)*r = vt_rel + jt/m + jt*r²/I. So jt = -vt_rel / (1/m + r²/I). With I = 0.5*m*r² → r²/I = 2/m → jt = -vt_rel*m/3. Clamp |jt| ≤ μ*|jn| where jn = -(1+e)*vn*m (magnitude of normal impulse). Sign conventions: apply v += jt*t/m, ω -= jt*r/I.

Fine. I'll just write with mass=1.

Ball-ball similar with two bodies.

Let me code it up.

Also add slight air drag and angular damping.

Substeps: 8 per frame maybe, dt clamp.

Write file then test in browser.

There's a leftover weird rotate code (rotate(-b.a); rotate(b.a)) — clean that up. Also remove unused dt param. Let me fix.

Also font size 14 for two-digit numbers in r=15 ball — "20" at 14px bold is ~16px wide, ball diameter 30, ok.

Test in browser.

Initial state looks good: the ball is falling in a compact grid, and the heptagon is rotating (8.4° at t=0.12s... wait, t=0.12s → angle = 72°/s * 0.12 = 8.6°, correct).

Note that the canvas is taller than the viewport (760px). The screenshot shows a cropped view. No problem.

Let's sample a few moments: take screenshots after a few seconds, check the collision, then Reset and compare with the initial state. Use motion or screenshots with delays. The browser tool's "motion" captures frames. Let's take screenshots at intervals. Can't directly sleep, but does the browser's motion action capture over time? For now let's take screenshots after a few actions.

Check: after about 3 seconds, the ball should be at the bottom and colliding. Take a screenshot.

The simulation is working: the ball falls, rolls along the rotating wall, contacts are counted, and the numbers rotate (the numbers appear tilted at various angles). The wall angle advances at 72°/s. Max speed stays within limits (about 250–320). The ball is contained within the lower region.

Observations:
- The ball is being carried along by the rotating wall — good.
- Numbers rotate with the ball — verifiable in the frame (tilted numbers).
- The ball appears to be resting on the bottom edge; no problem.

Concerns: The canvas is 760px tall, and the bottom is cut off in the viewport screenshot; but the canvas fits within the page (scrollable). The task says "keep it fully visible" regarding the heptagon — the heptagon is fully inside the canvas (R_POLY=340, canvas 760 → margin 40). Good.

Next, test pause/resume and reset. Click pause, take a screenshot, click resume, then reset and compare with the initial state.

Also, verify stability over the long term: run for about 30 seconds and check that max speed doesn't diverge and that the ball stays inside. Can I evaluate via the console? The browser tool doesn't have evaluate. I can check the HUD values in the DOM text. Let me run motion again later.

First: pause test.

Pause is working (PAUSED, button shows "Resume"). Next, click Reset and compare with the initial view. After that, click Resume.

Reset restored the exact initial grid and wall orientation (vertex on top, angle 0.0°), matching the first screenshot. Good.

Minor point: the HUD's "contacts=11" is stale after reset (contactsThisStep isn't reset). Trivial, but reset it to 0 in reset(). Also, after reset while paused, the HUD displays t=0.00s — good.

Next, resume and run a longer stability check (about 20-30 seconds of simulation). Also confirm that the ball stays contained and the speed is bounded. First fix the contacts reset, then reload, resume (running by default), and sample the motion again after some time.

Also, the canvas is 760px tall, and the page might scroll; the heptagon is fully visible within the canvas. No problem.

Another improvement: the numbers on the ball rotate — verified in the frame.

Edit: add contactsThisStep = 0 to reset().

Reload and run for about 25 seconds of simulation time, then check the HUD (max velocity, containment). The motion tool only captures about 2 seconds. To let more time pass, I can insert waits between calls. Each browser call has some latency. Maybe I can use bash's sleep between browser calls? The simulation runs in real time inside the browser page. I can call bash sleep 20 and then take a screenshot.

After reloading, it's running again. Let it run for about 25 seconds, then take a screenshot to verify long-term stability (containment, bounded velocity, no persistent heavy overlap).

Wait — is the browser page running while I'm sleeping? The browser tool probably keeps the page alive between calls. Let me take a screenshot.

At t=33.6s: max velocity ~286-329 (bounded, roughly the scale of the terminal velocity from wall-driven motion), balls are contained at the bottom, contacts=13, fps 60. Stable.

Check the bottom of the canvas — balls near the bottom edge; the canvas is 760 tall, heptagon inradius = R_POLY*cos(π/7) ≈ 340*0.9009 ≈ 306; center 380 → lowest point is 380+340=720 < 760. No problem.

Another check: balls aren't persistently overlapping — in the screenshot they look separated/stacked without issue.

Also, verify that the numbers rotate with the balls over time: compare the orientation of the same ball between frames — in previous frames, tilted numbers were visible. Good.

Remaining: confirm that Resume works after Pause (previously clicked Pause → button became Resume; then clicked Reset while paused; then reloaded). Let's do a simple test: click Pause, then click Resume, and confirm that t advances.

Currently in a paused state at t=43.44s. Click Resume and confirm that t progresses (either use motion, or take another screenshot after a brief action).

Resume works: state is RUNNING, angle advances (247.5° → 247.8° between captures), max speed is non-zero.

All required behaviors verified:
- 20 numbered balls, compact non-overlapping grid at start, falling under gravity ✓
- Heptagon rotates at 72°/s (360°/5s): confirmed angle progression matches t (e.g., t=0.11s → 7.8°; t=33.59s → 258.3° ≈ (33.59*72)%360 = 2418.5%360 = 258.5 ✓). Fully displayed within the canvas ✓
- Custom ball-ball and ball-wall collisions, wall velocity in restitution response, friction/damping ✓ (balls get carried/rolled by the rotating walls)
- Angular motion: numbers tilt/rotate together with the balls, spin indicator line ✓
- Stability: over 43 seconds, speed stays bounded (≤ ~330), balls stay inside, no persistent overlap ✓
- Pause/resume ✓, reset restores the exact grid and 0° orientation ✓

Console: only sandbox iframe warnings from the harness, no page errors.

Done. Reporting.