Tilt data is unstable when the pen is nearly vertical
Aliases: tilt jitter · near-vertical · gimbal singularity · tilt noise
What it is
When the pen is nearly upright, tilt nears zero and the shaft’s projection on the screen shrinks to a point. Azimuth is then geometrically undefined, and the tilt estimate itself drowns in noise: the sensor’s lateral component is tiny, so a little jitter makes reported tilt and azimuth thrash. Near-vertical is a common writing grip, so this is not an edge-case bug; it is a structural weakness of the pose channel.
Why it happens
Tilt is estimated from the ratio of a lateral field (or accelerometer horizontal) to the axial component. Near upright that ratio is extremely noise-sensitive, the analogue of a gimbal singularity: the degree of freedom around the normal collapses in the projection. An EMR coil couples most strongly when vertical and has the weakest lateral gradient; capacitive electrode asymmetry likewise shrinks. Reported tilt then hops in a 0–10° band, and azimuth may swing half a turn in a few frames. If the brush turns those values into a footprint ellipse, centre-stroke writing breathes in width and a chisel twists for no reason. Engineering uses a dead band, hysteresis, and freeze: below a tilt threshold, lock the footprint to a disk or freeze the last valid azimuth; leaving the band uses hysteresis so the value does not oscillate on the threshold. Filtering damps jitter, but a heavy low-pass lags a real sweep of the pen.
Studying it
Sweep tilt from 0° to 60° on a jig, logging variance of reported tilt/azimuth and azimuth wrap-arounds. Then have people write in a natural grip and draw side-strokes, comparing footprint stability in the near-vertical band with clearly laid-down strokes.
Independent variables: tilt, dead-band threshold, azimuth freeze, filter cutoff. Dependent measures: azimuth wrap count, coefficient of variation of width, facing lag introduced by freeze, and “the line is shaking” ratings.
Do not measure pose accuracy only at a 45° side-stroke; that is where the channel is at its best.
Where it stops holding
Deliberate side-stroke painting leaves the vertical region and instability stops dominating. Inertial fusion (in-pen IMU) can help in motion, but a still upright pen still lacks a lateral signal. Too large a dead band treats a shallow side-stroke as centre-stroke and dulls chisel tools. Children hold more upright, so the dead-band policy should be more conservative than an illustration default.
Applying it
- Give tilt a hysteretic upright dead band: a disk or frozen azimuth inside, side-stroke ellipse only outside.
- Do not rotate a chisel from raw near-vertical azimuth; the jump is more visible than a small bias.
- Make the threshold adjustable: smaller for calligraphy, larger for handwriting defaults.
- How to check: write a passage upright—width should not breathe with micro-shake. Then lay the pen outside the band for a side-stroke; the chisel should lock on after exit rather than flicker on the threshold.