Bouncing balls in a heptagon · kimi-k3

Let me build the index.html with a physics simulation. Requirements:

- 20 balls numbered 1-20, compact grid near center, fall under gravity.
- Rotating heptagon, one revolution per 5 seconds, fully visible.
- Ball-ball and ball-wall collisions, moving-wall velocity in bounce, damping/friction.
- Ball angular motion, number rotates with ball.
- Pause/Resume and Reset.
- Stability: contained, no persistent overlap, no unbounded speed.

Plan: canvas, heptagon centered, radius such that it fits canvas with margin. Angular velocity ω = 2π/5 rad/s. For wall collision: closest point on each edge, compute normal, wall velocity at contact point = ω × r (perpendicular). Reflect relative velocity along normal with restitution, tangential friction.

Ball-ball collision: positional correction + impulse with restitution, plus tangential friction to induce spin. Ball spin: angular velocity, torque from friction at contacts.

Physics steps with substeps for stability.

Write code, then test with browser tool.

Let me write it.

Key details:
- dt fixed at 1/120 substeps, 4 substeps per frame.
- gravity 900 px/s².
- ball radius ~18, canvas 800x800, heptagon circumradius ~340.
- initial grid: 5 cols x 4 rows near center, spacing slightly more than 2r.

Wall velocity: v_wall = ω k × p where p is contact point relative to center → v = ω * (-p.y, p.x).

Ball-wall collision: for each edge, compute distance from ball center to segment; if < r, push out along normal (from wall toward ball interior). Ensure normal points inward (toward polygon center). Since polygon is convex and edges ordered CCW, inward normal is... compute and check against center direction.

Actually compute closest point on segment to ball center; normal = (ball - closest)/dist. Relative velocity v_rel = v_ball - v_wall. If v_rel·n < 0, reflect: vn' = -e * vn; tangential: apply friction impulse mu, also change angular velocity.

Ball-ball: standard impulse; tangential friction transfers spin.

Spin also should be damped slightly. Cap speeds.

Let me write the file.

Also wall collision should impart spin from wall friction. Keep simple but visible.

Reset: store initial positions/angles and rotation angle θ0 = 0.

Draw: heptagon edges, balls as circles with number text rotated by ball angle, plus a marker line to show spin.

Write it now.

Initial view good. Let it run a few seconds and check motion frames.

Looks great: heptagon rotates (marker moves), balls fall, collide, numbers rotate with balls. Now test Reset and Pause.

Reset restored the exact initial grid and wall orientation (marker at top, matching the first screenshot). Now test Pause: click Pause button at ~556,10 and take two screenshots to verify frozen.

Pause clicked — button now says "Resume". Verify frozen by taking another screenshot after a delay... screenshot action takes snapshot; let me take another screenshot to confirm scene is identical.

Scene identical — paused works. Resume once and run long to check stability (e.g., 10+ seconds for unbounded speed / escape). Let me click Resume and motion for a long duration, maybe two motion passes.

Stable: balls contained, no persistent overlap visible, numbers spinning at various angles. No console errors. Done. Report.