Bouncing balls in a heptagon · deepseek-v4.1-flash

Let me build this. I'll create index.html with a canvas-based 2D physics simulation.

Let me plan the physics:
- Heptagon centered in canvas, rotates at 2π/5 rad/s.
- 20 balls numbered 1-20, compact arrangement near center.
- Gravity.
- Ball-ball collision with impulse.
- Ball-wall collision accounting for wall velocity.
- Rotation/spin per ball.

Let me write the code.

Heptagon vertices: center C, radius R. Walls are segments between consecutive vertices. Rotating.

Wall collision: For each ball, for each edge, compute closest point on segment, check distance < radius. But for containment, better compute signed distance to each edge line and push inside. For a convex polygon, the ball must be inside all half-planes. Compute inward normal for each edge. If signed distance (from center of ball to edge line, positive inward) < ball radius, penetration.

For moving wall velocity: The wall point velocity due to rotation of polygon: v = ω × (p - C) = ω * (-(p.y-C.y), (p.x-C.x)) for scalar ω (counterclockwise positive with y down? careful). In screen coords y down, rotation by angle θ using standard cos/sin gives clockwise visual for positive θ. Let's just compute velocity consistently.

Let edge endpoints local rotated positions. The velocity of a point p on rigid body rotating about C with angular velocity ω: v = ω * perp(p - C), where perp(x,y) = (-y, x). This is mathematically consistent regardless of screen orientation.

Collision response: relative velocity of ball w.r.t. wall contact = ballVel + ballAngularContribution? Contact point velocity of ball includes rotation: v_contact = ballVel + ω_ball × r, where r = contact - ballCenter, in 2D = ω_ball * (-r.y, r.x).

Relative normal velocity vrel = (v_contact_ball - v_wall) · n where n is inward normal. Actually we want to resolve if approaching. Let's define n as inward normal (pointing into polygon). Ball approaching wall means vrel · n < 0 (moving outward relative to wall). Penetration = radius - dist.

Impulse: j = -(1+e) * vrel_n / (1/m + (r × n)^2 / I). Apply to ball: v += (j/m)*n; ω += (r × n)*j / I. And subtract wall's contribution by using relative velocity.

Also add positional correction to push ball inside.

Let me define cross product scalar: cross(a,b) = a.x*b.y - a.y*b.x. r × n = r.x*n.y - r.y*n.x.

Ball angular: I = 0.5*m*r^2 for disk.

Let me implement with fixed timestep substeps for stability.

Let's set canvas 800x800. R = 330 maybe. Center 400,400.

Ball radii: vary slightly or uniform. Number 1-20, radius maybe 16-20. Let's do uniform 15? 20 balls radius 15 in compact arrangement. Compact arrangement near center: arrange in concentric rings. e.g. 1 at center, then ring. Let's just do grid spiral with spacing 2*r+small.

Actually compact non-overlapping: place in rows/spiral. Let's do hex packing: positions growing outward, ensure within small region and no overlap.

Simple: place balls on a spiral with increasing radius, spacing so they don't overlap. Place 20 balls: 
- ring 0: 1
- ring 1: 6 around radius 2r
- etc. But simpler: grid 5x4 with spacing 2.2r centered. 5 columns, 4 rows = 20. spacing = 2*r + 2. That's compact and non-overlapping. Region width 5*30=150ish. Fine.

Ball radius 16, spacing 36. Width = 4*36=144, height 3*36=108. Center at canvas center.

Gravity ~ 900 px/s^2.

Damping: linear air drag small, angular damping. Restitution ~0.55, wall friction.

Let me write.

Rendering: draw heptagon, balls as circles with radius line and number rotated by ball.angle. Use save/translate/rotate/fillText.

Let me write the full file.

For rotating number, draw number rotated by ball.angle.

Time: use requestAnimationFrame with dt clamped, substeps.

ω_hept = 2π/5 = 1.2566 rad/s.

Let me be careful about the heptagon orientation reset. Store wallAngle, reset to 0.

Also need Pause/Resume and Reset buttons.

Let me write code.

signed distance for edge with inward normal: For convex polygon with vertices in order, compute edge from a to b. Inward normal: for CCW ordering... Let's just compute normal and test against center. n = normalize(perp(b-a)); if dot(n, C - a) < 0, flip n. Then dist = dot(ball - a, n) (positive inside). penetration if dist < radius.

Vertices generation: angle_i = wallAngle + i*2π/7, vertex = C + R*(cos, sin). This order is clockwise in screen but fine.

Wall point velocity at contact: v = ω * perp(contact - C).

Closest point on segment: since polygon convex and ball inside, just use... For penetration and contact, use closest point on segment to ball center. Let's compute.

Actually for edge collision it's fine to use closest point.

Resolve each ball against each edge; multiple edges possible near corners.

Let me now write.

Positional correction: ball.pos += n * penetration (fully correct), maybe with slop.

Let me code carefully.

const cx=400, cy=400, R=330. Ball radius 15.

Initial arrangement:
const r=15, gap=4, step=2*r+gap=34.
cols=5, rows=4. startX = cx - (cols-1)*step/2, startY = cy - (rows-1)*step/2.
ball i: col=i%5, row=floor(i/5).

All within center region, non-overlapping.

Reset: reset balls to these positions with zero velocity, angle = 0, wallAngle=0.

Random spin? give small random angular velocity initially 0.

Let me write the physics step function.

function step(dt):
  wallAngle += omega*dt
  compute vertices
  for each ball: v.y += g*dt; apply drag: v *= (1 - linDamp*dt); omega *= (1- angDamp*dt)
  integrate: pos += v*dt
  ball-ball collisions
  ball-wall collisions

Actually collisions should ideally before integrate but fine.

Ball-ball: for each pair, dist < r1+r2. normal n = (b-a)/dist. penetration. positional correction split by mass. relative velocity at contact incl spin. Impulse with restitution and friction.

For simplicity balls equal mass. But let's include mass = r^2.

Let me implement standard.

For ball-ball: contact point ~ a + n*r1. r_a = n*r1, r_b = -n*r2. vrel = (va + ωa × ra) - (vb + ωb × rb). normal component. Apply impulse jn with e. Then friction impulse jt along tangent, clamped by μ*jn.

cross for velocity contribution: ω × r in 2D = ω * (-r.y, r.x).

Let me code helper.

OK writing now.

Let me include substeps: dt clamped to 1/60, do 4 substeps of dt/4.

Let me write the file.

Let me write the file.

Let me test in browser. First inspect and screenshot.

Initial view looks good. The heptagon with 7 sides? Let me count edges: top vertex, then going clockwise... it appears heptagon. Yellow marker at right vertex (i=0 at angle 0). Wait marker should be verts[0] at angle 0 = right side. Yes.

Now let's let it run for a few seconds and check. Use motion or wait. The browser tool likely advances frames. Let me inspect after some time by taking screenshot. Actually each tool call may not advance real time. Let me use motion action which captures frames.

The simulation is working: balls fell, collided, collected at the bottom, and rotate with the heptagon. The heptagon rotation is visible (yellow marker moving). Balls are contained. The spin indicators rotate—hard to tell but visible lines.

However I notice the balls are piling in the lower-left corner. The heptagon rotates and balls settle to the lowest point, which is fine.

Let me check the ball numbers rotating. In frame 4, e.g. ball 1 has "1" rotated. Some numbers visibly rotated. Good.

One concern: balls are quite bunched at the bottom and may be persistently overlapping. The positional correction should handle. Looking at the pile, they look reasonably separated but some might overlap. Let me inspect the current state via JS. But browser tool only has inspect/screenshot etc. Let me use the inspect action to see DOM — not JS eval. Hmm, no JS evaluation tool. Could inject via console? No.

The pile looks okay, not obviously overlapping. Physics seems stable.

Let me test Pause/Resume and Reset by clicking. First let me screenshot the current, then click Pause and verify state stays. Actually let's click reset and compare to initial. I'll click reset, then screenshot.

Note the buttons. Let me click Reset and check wall orientation returns to initial (yellow marker at right).

Let me do click on Reset button coordinates. Button location near bottom center. From the initial 1200x800 screenshot, controls around y=752? Actually canvas 800x800 rendered at scale. The wrap is centered. Buttons were not visible in screenshot (cut off). The screenshot shows canvas filling most. The buttons are below at y~790 maybe cut. Let me inspect DOM already shows Pause/Reset/running.

Clicking may be tricky if off-screen. Let me use key? No. Let me instead rely on structure. Actually I can check reset behavior by clicking at coordinates. In screenshot, the canvas spans x 200-1000, y 0-800 approximately. Buttons below are cut off. The viewport 1200x800, canvas 800 tall + title + controls exceeds 800, so controls off-screen. That's a layout concern but functional.

Let me scroll down to see controls. Use scroll action delta 300. Then screenshot.

Still doesn't scroll because body overflow hidden. Controls inaccessible in viewport. That's a usability issue but the app still functions; buttons exist. The task says provide Pause/Resume and Reset. They should be reachable. Since body overflow hidden and wrap is 100vh centered, content overflows top and bottom? The title is visible, canvas visible, controls below cut. Let me fix layout so everything fits: scale canvas via CSS to max height. Set canvas CSS max-height, and wrap with padding. Use canvas style width/height auto based on viewport.

Better: make canvas responsive: CSS `height: min(70vh, 800px); width: auto;` Actually canvas attribute 800x800; CSS set width/height to min(72vh, 90vw). Then controls fit.

Let me update CSS: `canvas { width: min(78vh, 92vw); height: min(78vh, 92vw); }` and wrap uses height 100vh with justify center, gap smaller. Title small. That should fit title + canvas + controls.

Actually with 800px tall viewport, 78vh = 624 canvas, plus title ~20 + controls ~40 + gaps = ~700, fits.

Let me edit CSS. Also remove overflow hidden? Keep hidden but fit.

Let me update.

Oops the oldText I targeted was the first block, but I included a large block. Let me verify the edit applied correctly - it said replaced 1 block. Let me read the CSS region.

Good. Now reload and test, including reset by clicking. Let me reload and screenshot.

Now controls visible. Initial arrangement matches exactly the first initial view (yellow marker right, balls grid). Good.

Now let me test Pause, then reset. Let me click Pause at approx (513,718). Then wait/motion and see if it freezes. Then click Reset and compare.

Let me first let it run a bit, then click reset. Actually to test reset I need it to have moved. Let me do motion to advance, then click reset, then screenshot.

Simulation runs stably, rotates, balls contained, numbers spin. Now test pause and reset.

Click Pause at (513,718).

Paused works. Now click Resume, then Reset. Let me click Reset directly (521,718). Actually test resume first quickly, then reset. I'll just click Reset to verify restore. But requirement: Pause/Resume and Reset. Let me click Resume then reset.

Click Resume (516,718). Then Reset. I'll batch? They are dependent but I can do two calls. Let me click Resume.

Resume works (status running, ball positions slightly changed from paused frame). Now click Reset and verify restore to initial grid + marker right.

Reset restored exactly the initial arrangement and wall orientation (yellow marker at right). 

Let me verify no persistent overlap / runaway speed. The pile looks reasonable. One thing: in the first motion sequence, balls seemed to settle into the corner, but the heptagon rotation continuously stirs them, so they stay dynamic. Good.

Let me do a quick check to ensure balls don't escape over time. Motion frames showed contained. Good enough.

I could add a small JS check but no eval tool. The behavior looks solid.

One issue: the "visible ball contacts produce bounce responses" — motion showed balls colliding and scattering. Good.

I'm within budget. Final report.

Let me double check the file has no syntax errors — console only shows sandbox warning, no errors. Good.

Final file present at /tmp/job-7D58iK/index.html.