ArchLang

27. Net internal area beside the centreline area ​

  • Status: Accepted
  • Date: 2026-10
  • Relates to: ADR 0022 (decide geometry exactly where the inputs allow), ADR 0008 (describe() reports facts)
  • Scope: describe() gains rooms[].net_area_m2, totals.net_floor_area_m2 and, on a schedule rooms plan, schedule[].net_area_m2; the drawn ROOM SCHEDULE gains a NET AREA column. No language syntax, no change to lint(), area_m2 unchanged.

Context ​

A room is drawn on wall centrelines, so area_m2 runs to the middle of every wall round it. That is the right figure for a plan's geometry, and two consumers depend on it byte for byte: the dataset deduplicates rows by describe() (dataset/dedup.ts) and the fidelity eval scores room areas (eval/fidelity.ts). It is not the figure a buyer, a brief or a building code means by "room area". They mean the floor between the walls. On a typical flat that is about 8% less: the agent-UX audit plan reports 65.00 m² on centrelines and about 60.0 m² net.

An agent reading describe() could only estimate the difference. The owner decided (agent-reach decision 2, 2026-10-13) that describe() gains a new field net_area_m2, area_m2 stays as it is, and the byte-identity law tables are re-measured once, with this reason written down. The same record adds a condition: if net area cannot be computed exactly from the room's shape for wall-less edges or curved rooms, the field ships only for the cases it can state exactly, and no copy calls an approximate figure a measurement.

Decision ​

1. Net area is the room's floor that no wall stands on.

net_area = area(room) − area(room ∩ ⋃ wall bands)

The room is its own shape (a rectangle, a room polygon's ring, a room circle), never its bounding box. A wall's band is the solid the drawing draws for it before any opening is cut, built by wallBand() in src/geometry/band.ts, the same builder the wall joinery uses: its two faces at ± half its thickness, a square cap at a free end, a mitre at each joint (bevelled past the stroke's mitre limit), and true concentric arcs on a curved run.

The first version of this rule inset only the edges that had a wall centreline ON them. That missed every wall standing on a floor any other way, and the shipped corpus has them: examples/hexagon-pavilion.arch's 1200 mm drum is tangent to the inner edge of all six wedge galleries, so its outer half-band covers about 1.5 m² of each (15.09 → 13.55 m², 11.97 → 10.52 m²). The figure is now what the drawing shows. What follows from the definition:

  • A wall on the room's edge takes half of itself (each wall its own thickness). A shared partition takes half from each room either side. This is the old inset, and on every room where the old rule was right the two give the same number (see Consequences).
  • A wall standing on the floor takes what it stands on: a drum tangent to a room, a bay curving into it, a wall whose centreline is off the edge, a wall across or inside the room.
  • A wall's free end is drawn square-capped, half its thickness past the end, and the cap stands on whatever floor is there. Where a thicker wall ends on an edge beside a thinner one, its cap takes a little more than the thinner wall's inset.
  • A joint is drawn mitred, so at an inside (reflex) corner of one wall run the corner square is wall. Two separate walls meeting there are square-capped, and their caps cover the same square.
  • An edge with no wall loses nothing, and a door or window does not cut the band: the threshold inside a wall's thickness is not floor.
  • A circle is cut by whatever band crosses it: a concentric arc wall walled all round by one thickness leaves π(r − t/2)², and a straight wall tangent to it takes the circular segment its band covers.

2. Exact, or omitted. The area of room ∩ ⋃ bands is computed by Green's theorem on its boundary. Every edge of the room and of every band whose box meets the room's box (straight lines and true arcs) is split at every crossing with every other, in closed form (src/geometry/intersect.ts). A piece lies on the boundary of the covered region exactly when one side of it is in the room and in a band and the other side is not. Each such piece adds ½∮(x dy − y dx) in closed form: a line by its two ends, an arc by its ends, centre and swept angle. A piece that two edges share is counted once. No tessellation, no sampling and no bounding box enters the figure. On a rectilinear plan every crossing is an exact vertical × horizontal intersection, so the sum is exact in floating point. An arc piece reads its angle through Math.atan2, which is not exactly rounded across engines, so a room crossed by a curved band may differ in the last ulps between platforms, far below the 0.01 m² it is printed to.

The figure is omitted (no net_area_m2 on the room) rather than approximated in two named cases:

  • The room's box meets more than MAX_NET_CURVES (2,000) room and band edges. The pair loop is quadratic in them, and the cap bounds it. No shipped room reaches 140.
  • The boundary integral is not finite, or falls outside [−ε, area + ε] with ε = 10⁻⁹ · area + 10⁻³ mm². That is the signature of a configuration the split did not resolve. No shipped room triggers it.

When any room's figure is omitted, totals.net_floor_area_m2 is omitted too (never a sum over a subset), and so are the room schedule's net subtotal and TOTAL. The omitted cell is drawn -, the table's ASCII mark for "no value" (the DOOR & WINDOW SCHEDULE's HAND column uses it). describe() has no notes channel, so the absent key is the signal. Within ε, the result is clamped to [0, area] so that net <= area holds to the last bit. The clamp removes float noise and nothing else: the corpus test reads the unclamped figure and finds it inside [0, area] on every room.

3. Implementation. src/analyze/net-area.ts (netAreaBands, roomNetAreaMm2, netAreaDetail), re-exported from src/analyze.ts beside roomAreaMm2. describe() builds a storey's bands once and measures every room against them. Inside compile(), a schedule rooms plan measures the same rooms for its table. The drawing budget is charged first (src/draw-budget.ts) with a count that builds no band: each room's edges times the wall segments whose box meets it. The public roomSchedule() measures net area only when it is given the walls; without them its rows carry no net figure at all, never one equal to area_m2.

4. What reports it.

  • describe().rooms[].net_area_m2: 2 dp, <= area_m2, equal to it when no wall touches the room. Absent when omitted.
  • describe().totals.net_floor_area_m2: the sum of the rooms' rounded figures, the way floor_area_m2 sums theirs. Absent when any room's is.
  • describe().schedule[].net_area_m2 on a schedule rooms plan.
  • The drawn ROOM SCHEDULE's NET AREA column, with its subtotals and TOTAL. The centreline column is labelled AREA (CENTRELINE, m²) and the new one NET AREA (m²). These are the owner's "Area (centreline)" and "Net area" in the table's capitals, with the unit kept. The AREA column widens to hold its label. The NO. and NAME cells keep their place; the AREA cells and totals move right with the column's right edge.

lint() does not read net area. The minimum-area rules stay on area_m2, so no diagnostic moves. Zones, the caption and Plan JSON are unchanged.

Consequences ​

  • Every describe() payload gains the fields, so every byte-identity row that digests describe() moved. They were re-measured once, with the reason written in each table's header (test/byte-identity-baseline.ts, "EVERY row re-measured, once"). The switch from the edge inset to the band rule moved six more plans, each named with its rooms in "Six plans re-measured again": hexagon-pavilion, tiny-house, aquarium, hillside-villa, materials and townhouse. A hybrid run of the law tests, with the earlier describe(), shows that nothing else moved.
  • On the red-team's constructed rooms (32 of its 36 resolve as written), the band rule gives the edge inset's number to the square millimetre wherever the inset was right (13 rooms): walls on the edge, shared partitions, a T, collinear runs, reversed runs, reflex joints and a U. It differs where a band stands on the floor (an intrusion, a through-wall, an offset wall, a free end's cap), and on a thin oblique room where the old insets crossed and were clamped to zero. In every one of the 32 it agrees with the grid oracle.
  • Every schedule rooms sheet's room schedule is wider, by the NET AREA column and by what the AREA column grew to hold its label. A legend, door & window schedule or notes table to its right moves right by that width. No page size in the corpus moved.
  • area_m2 remains the centreline figure, so dataset/dedup.ts and eval/fidelity.ts read the same numbers as before.
  • test/net-area.test.ts holds every corpus room to a grid oracle (test/net-area-oracle.ts) within the oracle's own error bound. The oracle shares only the band and the room's own area with the code. The same test shows the oracle rejects the old inset-only figure on hexagon-pavilion, so an intrusion like that one cannot hide again.
  • The D4 equivariance oracle (test/d4-oracle.ts) holds net area invariant under every turn and mirror of a placed plan.
  • The measurement is quadratic in the band edges near one room. It is capped per room by MAX_NET_CURVES and, inside compile(), charged to the drawing budget before it runs. describe() has no budget, so there the cost is that cap times the number of rooms; compile charges it only under schedule rooms, and in practice the hosted Worker's CPU cap bounds it.