Tumbler bands.
The rotation that doesn't warp: the cone's own shape, the true diameter, and the level's gravity read.
The band that doesn't wrap
Engraving a flat image onto a cylinder warps it — unless the image was drawn as the cylinder's own shape. A tumbler (or any truncated cone) unrolls to an annular sector: flat radii and a sweep angle, computed from the cup's two diameters and its height. The app does this math; the flat file it outputs cuts true.
Its test example: a cup 90 mm across at the top, 70 at the bottom, 150 tall → outer radius R1 = 676.50 mm, inner R2 = 526.17 mm, sweep 23.947°. Run the same numbers below in the tools.
Which diameter is true?
A flat-band engrave sits size-true at one diameter and stretches in proportion across the band — the levelled tumbler needs no warp. Where that diameter should sit depends on your rig:
| rotary | use |
|---|---|
| Chuck rotary | the middle diameter, (D1+D2)/2 — for a 90→70 cup, true at 80, ±12.5% at the edges |
| Roller rotary | true where the rollers touch — the band's middle by default, adjustable |
xTool's arc
Working in xTool's software? Its Photoshop warp value is a formula, not a guess: 2 × angle − 2.22 (the value's own support article). The app shows it labelled as xTool's.
The level: why the phone knows
The app reads the gravity sensor — deliberately, not the rotation vector, whose magnetometer a steel laser frame disturbs. Smoother with a half-second time constant; it reports tilt = asin(g_y/|g|). For its own zero point: lay the phone, press A, flip it, press B — the true tilt is (A − B)/2 and the phone's offset is (A + B)/2.
The lock band defaults to ±0.2° (settable 0.1–0.5°): a steady tone inside, edge beeps every 100 ms pulling back to 1,000 ms near 3°.
Bent designs export at 254 DPI (0.1 mm) — inside LightBurn's suggested range. The app's honest card: confirm the band's truth with a test engrave on your own rig.