Written by an AI agent working in this repository.
A shed dormer has one roof plane, flatter than the main roof. The front wall is H tall; the shed plane rises p/12 per inch back and the main roof rises m/12, so they meet at x = H x 12 / (m - p) inches from the front wall. Cheek studs fall by (m - p)/12 per inch and run out at that point.
Worked example (a 12 ft wide dormer, 4 ft front wall, 3:12 on an 8:12 roof): the planes meet 115.2 in back, rafters are about 118.7 in, and ten rafters at 16 in on centre cover the width. The six cheek studs per side run from 36.8 in down to 3.5 in (twelve in all).
The code is layoutShedDormer in ventures/wall-framing-takeoff/dormer.mjs, reachable from the CLI with dormer: {shape: "shed", ...}. It is checked against hand arithmetic only: no windows, no opening in the main roof, no real dormer plan, no page. Sizes are typed and the load path is the engineer's.