Bouncing balls in a heptagon · claude-haiku-5.5

I'll plan the setup efficiently: write the file first, then do a quick browser check before reporting back. For the simulation, I'm sketching out a rotating heptagon container with 20 balls, picking a canvas size, center point, radius, and rotation speed, then working out the inradius to size the balls appropriately.

I'm placing the balls in a compact grid near the center using even row spacing to avoid initial overlaps, checking that the arrangement fits within the heptagon's inner boundary. For physics, I'm setting up a fixed timestep with substeps, applying downward gravity, and defining each heptagon edge's outward normal and distance from center so I can detect and resolve wall collisions as the shape rotates.

Working through the collision response: computing the wall's velocity at a contact point from angular velocity, calculating the relative normal velocity between ball and wall, correcting penetration depth, and applying restitution and friction impulses along the tangential direction.

Checking that the normal and tangential relative velocities split cleanly—since the contact offset is parallel to the normal direction, the cross product vanishes, confirming the normal impulse produces zero torque on the ball.

For the tangential direction, computing rc×t gives magnitude r, so the effective tangential mass works out to 1/m + r²/I = 3/m for a uniform disk. I'm setting the tangential impulse as -ut divided by this effective mass, clamped by Coulomb friction (μ·jn), then applying it to update linear velocity and angular velocity via torque = jt·(rc×t) = -r·jt. Now I need to pin down the sign convention for the normal restitution term, where the normal direction points from the ball toward the wall.

Working through the tangential impulse: the effective mass factor comes out to 3jt/m since both linear and rotational contributions add equally (r² jt/I = 2jt/m for a disk), giving jt = -m·ut/3, clamped by friction coefficient times normal impulse. The wall case treats the wall as infinite mass with prescribed velocity, so only the ball's velocity and spin update; for ball-ball collisions the normal impulse applies symmetrically to both.

For the ball-ball tangential impulse I'm deriving the contact geometry: contact points are at ±r along the normal from each center, the tangent vector is the perpendicular of the normal, and each ball's contribution to the effective tangential mass works out to 2/m from translation plus 2/m from rotation, so both balls combined give 6/m total for the inverse effective mass.

Both receiving balls get equal and opposite angular velocity changes, which checks out against the wall-friction formula from earlier. I'm settling on using unit mass with moment of inertia scaled by radius squared, picking damping and restitution coefficients (wall restitution ~0.5, ball-ball ~0.4, friction ~0.3), and planning a fixed timestep with multiple solver iterations plus positional correction to resolve overlaps cleanly.

For the rotating walls, I'm working out the velocity contribution at a contact point from angular velocity, defining edge normals for the heptagon vertices as they rotate, and setting up penetration depth calculations using the inradius and dot product with the normal to detect and resolve wall contacts.

For sizing and setup, I'll fix the canvas at a logical 700x700 with heptagon radius 320 centered at (350,350), scaled via CSS to fit any viewport, use moderate gravity so the drop timing feels natural, and keep everything deterministic — zero initial spin, no randomness, with reset restoring positions, wall angle, and time exactly to their starting state. Now I'm adding exponential velocity damping to the simulation.

I'm defining the physics constants (gravity, friction, restitution, timestep) and planning the state structure for balls and wall rotation, plus pause/resume and reset controls with a small on-screen readout of wall angle and rotation count for verification. Setting up the initialization logic...

Still writing wall-collision solver...

I compute the full contact-point velocity including angular contributions from both ball spin and wall motion, then take its normal component to determine if the ball is approaching the wall. If so, I apply an impulse scaled by the restitution coefficient to reverse the normal velocity, though I need to double check this against the position correction I already applied.

For friction, I use the tangential direction perpendicular to the normal and compute the tangential velocity after the normal impulse, which stays unchanged since the normal impulse only affects velocity along the normal. I clamp the friction impulse by the coefficient of friction times the normal impulse magnitude, then apply it to both the ball's linear velocity and spin, with the spin update accounting for the moment of inertia factor of 2/(m*r). I also note that when the ball is separating from the wall despite penetration, only the positional correction should apply, not a velocity impulse.

I'm now extending this logic to ball-ball collisions, deriving the position correction that pushes both balls apart along the normal direction proportional to their penetration, and computing the relative contact velocity using each ball's linear and angular velocity contributions. I work out the normal impulse formula accounting for both balls having equal mass (giving an effective mass factor of 2), then apply the same tangential friction approach but with an effective mass factor of 6 for the ball-ball case, clamping the impulse by the normal impulse times friction coefficient.

For the angular velocity updates from tangential impulses, I verify the torque arm calculation using the cross product of the contact point vector and tangent direction, confirming it simplifies cleanly to just the ball radius. I also sanity-check the wall-collision case against this same formula to make sure signs are consistent, then move to setting speed caps (linear and angular) and adding exponential velocity damping to keep the simulation stable over time.

Now I'm planning the rendering: each ball gets translated and rotated so its spin is visible via a radial line and a centered number label, and the heptagon boundary is drawn from vertices spaced evenly around the center with the correct inradius. I'm also sizing the canvas responsively, adding on-screen status text for time/wall angle/revolutions/pause state, and making sure reset reinitializes balls and wall without touching pause state, while exposing a simple debug object on the window.

I'm hitting a variable naming collision in solveBalls — I used `j` as both the for-loop index and a const declared inside the loop body, which triggers a "cannot access before initialization" error since the inner const shadows the outer loop variable in the same scope.

I'll rename the inner variable to avoid the TDZ conflict, clean up an unused line, and reload to confirm ball collisions actually run now.

The console error is resolved, and the balls haven't dropped yet at this early timestamp which is expected. The heptagon looks slightly irregular in the screenshot, but that's likely just a rendering quirk since it's actively rotating, and the canvas sizing itself should still be a proper square.

The vertex geometry checks out — vertices placed using the angle offset plus the step rotation, with the inradius calculated from the circumradius and polygon angle, matching correctly. Now I just want to do a quick verification of ball positions after a few seconds and compare against a reset state to confirm the physics is behaving.

The balls look contained and settled, rotating with the wall, with maybe slight overlap but nothing concerning. I should check the Reset and Pause buttons next, keeping things brief.

Pause and Reset both work correctly, with Reset restoring the initial arrangement and wall angle, though the Resume label stays visible since it remains paused afterward. I notice some balls appear to be stacked close together, but I haven't verified if there's actual overlap, so I should be honest about that uncertainty rather than claiming precision.