wuwiandClaude Opus 5
e11ad30a63
A slice hooking onto a body two metres to the side flew a closed loop around it forever: 285 frames of the same circuit, never arriving, never falling. A constant turn rate has a constant turn radius (v/w = 2 m), and anything inside that circle cannot be reached however long the ball steers — while the hook pins vy at 0, so nothing else ends it either. A crowd is nothing but close bodies, which made the one place this weapon should shine the one place it hung. The rate is no longer a constant. An arc leaving along the current heading and passing through a body at distance d, bearing a, has radius d/(2 sin a), so the ball needs 2 v sin(a) / d — solved every frame, because the body is walking while the ball travels. sliceTurn stays as the FLOOR, which is what it was always really for: how wide the curl looks when there is room. Turning faster than needed is safe, the aim being re-solved each frame. Two things the maths cannot cover, so they are ruled out instead: a body behind the ball, which no tangent arc reaches at any rate (sliceArc), and a target that walks out of reach mid-hook (sliceHookT, a hard 0.7 s licence to steer). An endless orbit is now impossible by construction rather than by the geometry happening to work out. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>