Keep the offsets when placing monitors from the system layout

[mgth]

Two monitors side by side with the second hanging 219 px higher came out stacked a whole screen height apart. Two separate faults, and between them they are why the first layout a user is shown never matched what Place from windows config gave them a moment later.

Measured on a real desktop — two 1440p panels, the second 219 px up, and a 1280×720 TV:

	before	after
second panel	−340.0 mm (a full screen height: stacked above)	−51.7 mm

219 × 340 / 1440 = 51.7 is the answer.

The offset was never computed

The placement rules only ever recognised exact equalities — edge against edge, or tops/bottoms matching to the pixel. A monitor adjacent on one axis but offset by an arbitrary amount on the other matched the adjacency rule and none of the alignment ones, so it kept whatever coordinate it happened to have and the compact pass shoved it somewhere.

ForceCompact ran inside the walk

Every monitor not yet reached is still stacked at the origin, so compacting mid-walk resolves overlaps against screens that have no position yet — and pushes the ones just placed correctly out of the way.

That is the whole of why running the placement twice gave a better answer than running it once: the second pass started from a layout already spread out, so the same compacts found nothing to do. The button was never better than the startup path; it just ran second. One compact at the end, which is what catches monitors with no adjacency at all.

The rule, and a wrong turn worth recording

The new perpendicular rule is the exact inverse of PixelLocationSolver: the physical midpoint of the shared span projects to the same pixel on both monitors. So apply to system and place from system round-trip instead of drifting further apart on each pass — asserted on the real desktop:

MAIN: system (0,0)       -> solved (0,0)
SIDE: system (2560,-219) -> solved (2560,-219)
TV:   system (5120,0)    -> solved (5120,-0)

Taking that midpoint in pixel space is closed-form and tempting, and it round-trips perfectly until two monitors have very different pitches — which is the case this file exists for. The TV drifted 115 px. In millimetre space, as the inverse takes it, the shared span depends on the position being solved for; it is settled by iterating from the pixel-space estimate, which is already the answer whenever the two spans cover each other.

One existing assertion changed

SystemPlacement_SideBySidePixels_StaysSideBySideInMm wanted three monitors bottom-aligned while spanning identical pixel rows. Their tops match exactly as much as their bottoms do, and a 920 mm panel cannot have both — the choice was arbitrary, and that arrangement did not survive a round trip. The TV is now centred on what it shares with its neighbour.

Tests

Six new (PlaceFromSystemTests): the offset itself, placing twice landing where placing once did — on a simple row and on the real desktop — pixel order, contact, and the round trip. 111 in the DisplayLayout suite; 129 + 60 + 5 elsewhere, 56 Rust.