Bouncing balls in a heptagon · qwen3.8-27b

Let's build this simulation. A single index.html that includes canvas, a rotating regular heptagon, 20 numbered balls, gravity, collisions (with moving walls), friction, spin, pause/resume, reset.

Implementation plan:
- Canvas 800x600, heptagon center (400,300), radius about 260, fully visible.
- Balls: radius about 14, placed in a compact grid/spiral around the center.
- Heptagon vertices rotate with angle ω = 2π/5 rad/s.
- Walls: 7 line segments between consecutive vertices. Collision: point-in-polygon / for each ball, find the closest point on each edge and, if distance < r, push out in the direction of the inward normal. Wall velocity at contact point = ω × r_vec (perpendicular direction). Relative velocity = ball_velocity - wall_velocity; if moving toward the wall, reflect using the coefficient of restitution, and add tangential friction.
- Ball-ball: equal mass (or radius-based), impulse resolution with coefficient of restitution and position correction. Tangential friction imparts spin.
- Spin: angular velocity of each ball; draw the number rotated by the ball's angle. Spin from wall friction: change in ω from tangential slip.

Use fixed timestep substeps for stability (e.g., 4 substeps per frame, dt capped).

Alright, let's write the code.

Ball-wall collision details:
- Wall edges from vertices P_i to P_{i+1}. The polygon's interior is around the center C. The inward normal of an edge = the normal pointing toward the center. For each ball, distance from the ball center to the line segment (closest point). If dist < r and the ball is outside… actually, to ensure containment, compute the signed distance: if the ball center is inside the polygon, the closest edge's inward normal points toward the center. Simpler: for each edge, project the ball center onto the line; if the dot product of (ball - closest point) with the outward normal is less than r, collision.

Let's define the outward normal of edge i: n = normalized perpendicular direction pointing away from the center. Compute d = dot(ballPos - closestPoint, n). If d < r and dot(ballPos - edgeCenter, dir) is within the segment range (handled by the closest point), push out: ballPos += (r - d)*n… wait, if d < r the ball is too close to the wall on the outside; penetration = r - d; push in the inward direction = -n. So ballPos -= (r - d)*n? Hmm: n points outward; if d < r the ball is penetrating. Move the ball by -(r-d)*n (inward).

Wall velocity at the contact point Q: v_wall = ω × (Q - C) = ω * (-(Qy-Cy), Qx-Cx) (counterclockwise positive, canvas y is downward — be careful; use v = ω * perp(Q-C), perp(x,y)=(-y,x), which is visually counterclockwise in standard math coords; visually clockwise with canvas y-down, but either way it's fine).

Relative velocity vrel = v_ball - v_wall. vn = dot(vrel, n). If vn < 0 (approaching the wall along the outward normal):
v_ball -= (1+e)*vn*n (outward normal, so if vn<0 it bounces inward). Tangential direction t = perpendicular to n. vt = dot(vrel, t). Apply friction: v_ball -= μ*vt * t * some coefficient (or clamp). Also update spin: ω_ball += (vt * friction factor)/r.

Ball-ball: standard impulse, equal mass (mass ∝ r², but all same r for simplicity). All balls radius 14? 20 balls r=14 in a compact arrangement — no problem.

Spin visualization: rotate the canvas around the ball center by ball.angle and draw the number.

Also add spin from ball-ball collisions: adjust angular velocity from tangential relative slip, small coupling.

Initial placement: 20 balls, compact: arrange in a hexagonal packing pattern: rows 6-5-6-4, or a simple grid 5x4 with spacing slightly larger than 2r, starting from center - offset. Grid 5 columns x 4 rows, spacing 2r+2. Centered on the heptagon's center.

Stability: substep: run physics at a fixed dt = 1/240 (e.g., 4 substeps per 60fps frame), cap the accumulator.

Keep speed bounded: cap max velocity, e=0.5, friction.

Pause/resume button, reset button.

Verification: run in the browser, take screenshots at several points, check the console, press reset.

Let's write the file.

I left a confusing old function `collideWalls` (unused) that contains messy spin lines. Let's delete it to clean things up. Also, I'll delete the placeholder `wallSpin`.

Also, `stepBall` is called before `collideWallsCore` inside `physicsStep` — no problem. However, `physicsStep` references `collideWallsCore` which is defined later — since it's a function declaration, there's no problem.

One concern: the ball is placed near the center, but the heptagon's radius is 280 so there's plenty of room. OK.

Let me run it in the browser and check.

Initial view looks fine: 20 numbered balls inside a 5x4 grid, heptagon fully visible, no console errors (only sandbox-related warnings, unrelated).

Wait — the heptagon seems to have already rotated a bit? In the initial frame, the top vertex is... the first vertex is at angle -π/2 (top). In the image, the top vertex is slightly tilted to the left, meaning the simulation has already run a bit. No problem.

Take a few more screenshots and check the falling motion, rotation, and ball behavior. Wait a bit (screenshot again).

The screenshot looks the same as the previous one — suspicious. The ball is still in the initial grid position, and the heptagon is in the same orientation too. The simulation isn't moving? Or was the screenshot taken from a cached frame? Let me check if the animation is working — maybe the screenshot tool is capturing a new frame each time. Same image means it's possible the simulation is frozen (e.g., an exception inside the rAF loop?). The console only showed warnings. Let me look into the DOM/console to check for errors, and try evaluating state.

Actually, it might be that an error is occurring in physicsStep after the first draw. Let me check the console messages with the browser's inspect feature.

The simulation is running: the balls have fallen, are stuck on the left/bottom wall, the heptagon has rotated, and the balls are rotating together with it (the cluster moved along with the rotating wall). The numbers are rotating along with the balls (e.g., "15", "16" are upside down).

Wait—the balls on the upper left (17, 12) and top (11, 13)? They're floating on the upper edge—this might be because the wall is rotating and carrying them away, or due to a collision glitch. Balls 11 and 13 are near the top vertex. It seems like they're sliding along the edge, but... it's plausible.

Let me take another screenshot and observe, then pause, then reset, and verify that reset restores the state.

The image is identical to the previous one (at the inspect point)—strange, considering 2.5 seconds have passed. Could it be that the screenshot tool is displaying a cached/detached frame? Or has the simulation stopped? The status still shows "running". Both screenshots are pixel-for-pixel identical, but considering that the heptagon rotates one revolution in 5 seconds, that shouldn't be possible.

Could it be that the screenshot tool is returning the same attached image from the same frame? Both were labeled "Frame 1, +0ms". It's possible the tool only captures one frame at reload time. Let me call screenshot one more time to check.

The simulation is progressing: the heptagon has rotated further, the balls are being carried along by the rotating wall, and no persistent overlap is observed. The numbers are rotating together with the balls.

Next, test Reset: click the Reset button and compare with the initial frame.

The Reset click didn't visually reset — the balls are still scattered. Did the click miss the button? The button is at (389,731) in the 1200x800 viewport… In the screenshot, the Reset button is around x=389, y=731 — yeah, it looks right. But the screenshot was captured in the same frame before the click effect? "Frame 1, +0ms" suggests the screenshot is from the same moment. Maybe the click registered but the image was captured instantly, showing the state before the click? No — if Reset was applied, the balls should be in the center. The balls are still in the lower region, so either the click didn't hit or the capture was before the click.

Let me click again and then wait a bit before taking the screenshot.

Reset hasn't happened yet — the ball is still scattered around the perimeter. Hmm. Maybe the click isn't landing on the button (coordinate offset?). The Reset button is at roughly (389, 731) in the displayed 1200x800 image. In the screenshot, the button is around x=615/1200*... wait, the image is 1200x800 and the canvas region is 180..820 in image coordinates. The Reset button appears at about x=631 in image pixels? Let me check: in the last image, "Reset" is at roughly x=615-650, y=731. No actually, the image is 1200 wide, and the button appears to be around x=631. I clicked at (389,731), but that was based on a previous image that was 800 wide? The first screenshot was 800x640? No — the initial screenshot was 1200x800 with the button around x=389? In the initial screenshot (which looks 800x640), Reset was at x=389. But later images are 1200x800 with Reset at x=631.

The browser tool says the viewport is 1200×800. So I should click at (631, 731).

The reset worked — the ball returned to the initial 5×4 grid, the status changed to "running (reset)", and the heptagon's orientation returned close to the initial state (there's been a slight rotation since the reset. The wall has been rotated a bit — since the reset sets wallAngle=0, that's not a problem). The arrangement matches the initial view.

Next I'll test Pause: click Pause (543,731), take a screenshot, verify that the state is stationary, then Resume.

The button changed to "Resume", and the status is "paused". The balls were frozen partway through the fall (they fell and bounced along the upper-left edge). I'll confirm that pause keeps things frozen: take another screenshot after a short wait and compare that it's identical. Then click Resume.

The images are identical — confirming that the pause is holding its state. Next, I'll click Resume to restore.

Resume is working (status is "running", button shows "Pause", and the scene has progressed slightly — the heptagon has rotated a bit further). Everything's working fine.

Quick sanity check: no errors in the console (only unrelated sandbox warnings). All the necessary behaviors have been verified. One more thing: checking whether the long-term stability/velocity limits are fine — I observed multiple moments, and the balls are settling against the wall, with no blow-ups or overlaps.

Done. I'll report back.