Eight workings behind the bench's numbers — drawn once, worked plain, every line sourced.
The drawn workings
The beam burns a strip of material on both sides of every cut path — cut parts land small, cut holes land big, by the same strip. Measure it before you design anything that fits. Cut N squares of side S, push them end to end, and read the true total M: the pushed row comes up N·K short, so one square's share falls straight out — K = S − M / N.
The default pair is ten squares of 20 mm — a 200 mm drawn line is a long enough ruler. The app's own example measures 198.4 and lands K = 0.16 mm.
Every edge of a cut loses K/2 to the beam. Give LightBurn that number as the kerf offset and it moves closed paths the way the loss went: outward on outer shapes, inward on holes — exactly the material the cut removes, so drawn lines stay drawn sizes.
With an offset in, a slot meant for clearance c draws at T + c and the machine handles the beam. With the offset off, you bake the kerf into the drawing yourself: the slot draws at T + c − K, a tab grows by K.
No clearance default exists: zero is a press fit, and the gauge measures everything looser. Cut the printed plate — ten slots from T − 0.25 to T + 0.20 mm in 0.05 steps, cut with the offset off, teeth 4 mm, slots 10 mm deep, plate 22 mm tall, the digits stroked on a score layer in seven segments. Press your test tooth through until one slot holds a light pinch.
That slot is the answer. The gauge was cut by the same beam with no offset, so every slot opens at its drawn width + K — which lands your clearance at c = the slot that fit + K − T. Caliper the sheet first: ply sold as 3 mm varies by a few tenths (3 ± 0.2 mm on the maker's own spec, and '3 mm' Baltic birch in the US is often 1/8").
Pick the odd finger count n — three or more — that brings edge / n closest to the target width; ties go to more fingers. Odd counts put both ends of an edge on one panel, so corners belong wholly to one piece: front and back own the corners, left and right own the ends of their edges. Each finger boundary moves c/4, which lands a finger c narrower than its gap — the slack lives inside the joint and the box's outer size stays untouched.
On an axis walled at both ends, outside = inside + 2T — and that's the whole arithmetic. A 100 mm edge at the 10 mm target works out to eleven fingers of 9.0909 mm.
The lattice bends because the material between slit ends twists. Fenner's analysis: a link w wide on T sheet, twisted by θ, spans w·cos θ + T·sin θ — a span that may grow by at most the kerf — so the links you need are bend ÷ θ. His example: 3 mm sheet, links 3 mm wide, 0.2 mm kerf, a 90° bend — 23 links. The bend's radius works as lattice length ÷ bend: 69 mm over 90° is about 44 mm.
Lay the rows out the common way: even rows run whole slits and leave bridges at the edges; odd rows sit offset by half and run off the edges. Slit 20 mm and bridge 3 mm are starting points, not tested values — tune them on scraps, and keep 15 mm of solid sheet at each end of a test strip.
What a beam can eat follows its wavelength, so a setting doesn't jump laser types — the app refuses to convert one. CO₂ runs 10.6 µm (some tubes 9.3–9.4 µm; the lens table assumes 10.6), and its light is what cuts clear acrylic. The blue diode, about 450 nm, cuts wood and dark acrylic — the maker setting tables live on diode machines — but clear acrylic passes its light straight through. Fiber runs 1.064 µm, metal marking's band.
Two habits ride along. Enter a diode module's optical watts — modules are sold by electrical input, several times the light out. And the never-cut list — PVC, vinyl, polycarbonate, ABS, HDPE, the foams, fiberglass and FR4 — holds for every beam type; its one-liner lives in the glossary.
Fold a whole setting into one figure: E = W · (p/100) · N/v — the joules each millimetre of travel receives. Worked example: 20 W at 80% over 10 mm/s = 1.6 J/mm. The app shows the fire caution at 1 J/mm or more in one pass, raw or converted — because slow, powerful settings are the likeliest to catch fire (Thunder Laser's and Trotec's fire pages, Stanford's laser-cutter guidance).
The number-line tells the story: engraving sits near zero — 0.01 J/mm at 250 mm/s — while a 10 W diode cutting at 5 mm/s runs 2 J/mm. The converter keeps the energy as it trades speed for power: at the target's top speed it lowers power, at its floor it adds passes, up to ten.
Nesting on a photo of the real bed starts with one ruler: a bank card — 85.60 × 53.98 mm everywhere on Earth (ISO's ID-1). Lay it down, shoot the bed top-down at 5 px/mm, and the four marked corners give the photo-to-bed transform — a normalised direct linear transform that un-tilts the picture. A synthetic tilted photo comes back within 0.2 mm, and turns snap to 15°.
The marks police themselves: refused when they cross, sit near edge-on (tilt-sine under 0.04), crowd closer than 8 px, or leave the map ill-conditioned — reshoot, don't force it. The honest limit: verified against synthetic tilts so far; the spec's own note allows a millimetre or two on a real photo, more near the edges and with a card.