FA-87179 / Physics integrator stability / Member archive

Hemisphere canonicalization negates only the scalar part · case 04

Quaternions with negative w are turned into a different rotation.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

solve(q, omega, dt, steps): orientation quaternion [w,x,y,z], world-frame angular velocity omega. Each step q += 0.5*dt*(0,omega) (x) q (Hamilton product, omega on the left), then renormalize to unit length. Return q with w>=0 (negate all components otherwise), rounded to 6.

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.720466, -0.308046, 0.553475, 0.282316]`	`[0.720466, 0.308046, -0.553475, -0.282316]`	Failed

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