Function wanderSpherical

Spherical wander (WP-8.2): steer toward a target that jitters on a sphere in a heading-aligned frame.

angle     += uniform(−jitter · dt, +jitter · dt)   (draw 1 of 2)
elevation += uniform(−jitter · dt, +jitter · dt)   (draw 2 of 2)
elevation  = clamp(elevation, −π/2, +π/2)
frame      = orthonormal(forward = velocity, up ≈ +Y)   // Gram-Schmidt
centre     = position + forward · distance
target     = centre + radius · (
               cos(el)·cos(az) · forward +
               sin(el)         · up +
               cos(el)·sin(az) · right
             )
result     = seek(target)
Copy

The frame is built from the agent's velocity: forward is the unit velocity, up is world +Y with its forward component removed (Gram-Schmidt), and right = forward × up. A zero (or degenerate) velocity falls back to +X forward, +Y up; a velocity parallel to +Y retries the hint with +Z, then +X.

Determinism — two draws (WP-8.2)

Exactly two draws from random per call, always, in that order: azimuth then elevation. Planar wander stays one draw, so a stream that used to feed wander cannot be replayed through this function and expected to match. Two agents seeded alike still trace identical 3D paths. tests/steering.test.ts asserts both the draw count and the bit-identity.

Elevation is clamped to [−π/2, π/2] rather than wrapped: wrapping through a pole would flip the azimuth's meaning and produce a discontinuous jump. Azimuth wraps to [−π, π) like wander.