# OpenNest.Engine.Rectangles

A whole-job `INestingEngine` for the **rectangle lane**: jobs whose parts are plain or
near-rectangular plates. Every part is nested as the axis-aligned box of its material at its
minimum-area rotation(s), packed with a **maximal-rectangles** free list
(Jylänki, *A Thousand Ways to Pack the Bin*, 2010).

For these parts the box wastes almost nothing, and exact box packing is both denser and far
faster than contour-sliding engines. Irregular parts are still placed validly, but only as their
bounding boxes: nothing is nested into another part's notch or hole. Use a general engine
(Opus55, Gpt6Astra) for irregular work.

## Algorithm

**1. Boxes (`BoxCatalog`)**
- Rotations come from the host's `RotationCandidates.ForShape` (the policy angles plus, for
  `Automatic`, the minimum-bounding-rectangle alignment). Only the rotations whose box area is
  within 1e-6 of the minimum are kept, with duplicate box shapes removed. A 10 x 4 plate drawn at
  30° is squared up; a fixed-rotation part keeps its one angle.
- Bounds use material contours only (rapids and scribe/etch excluded), like the layout check.
- **Curved extremes:** the layout check circumscribes arcs and snaps to a 1e-4 grid, so a disc
  or obround reads slightly larger than its true arc. Each box side takes the check's own
  outline (`ClipperBridge.OffsetForValidation`) plus one grid unit wherever that outline sticks
  out by more than a quarter of `NestTolerances.SpacingSlack`. Straight-edged parts are unchanged
  and still pack at exactly the part spacing.

**2. One sheet (`MaxRectsSheet`, `SheetPacker`)**
- Boxes and the work area are grown by the part spacing on their right/top sides, so touching
  grown boxes are exactly one spacing apart and the last box can touch the work-area edge.
- The free list keeps every maximal empty rectangle; placing a box splits each free rectangle it
  hits and prunes the contained ones.
- Six placement rules: best short side, best long side, best area, bottom-left, left-bottom and
  contact point. Two pick modes: *global* (each step places whichever remaining box scores best
  anywhere) and *ordered* (priority, then largest box first, each type filled until it stops
  fitting). Lower priority numbers are always served first.

**3. Whole job (`RectanglesNestingEngine`)**
- Sheet by sheet, every available stock is packed under all 12 rule/mode pairs. The candidate with
  the lowest estimated whole-job cost wins: its salvage-credited `NestJobCost.NetSheetArea`, plus
  the remaining demand priced at the best net-area-per-part-area ratio any candidate reached. A
  candidate that leaves more of the most urgent priority tier unplaced never wins.
- Deterministic: no clocks or randomness; the only stop besides completion is the host token.

## Results

`OpenNest.Benchmark`, `--min-salvage-dimension 12`, each file's own sheet sizes, `--parallel 3`
(times are under that load). Synthetic results only here; the real-part corpus stays local.

Local corpus of converted 2026 production nests (file names and parts stay out of this repo):

| Lane | Jobs | Engine | Valid | Total cost | Time |
|---|---|---|---|---|---|
| Every part plain or near-rectangular | 91 | **Rectangles** | 91 | 333,081 | 5.9 s |
| | | Gpt6Astra | 89 | 332,153 | 169.5 s |
| | | Opus55 | 91 | 332,925 | 13.7 s |
| | | StockLadder | 89 | 337,641 | 36.0 s |
| Every part fills ≥ 90% of its box | 77 | **Rectangles** | 77 | 641,637 | 19.1 s |
| | | Gpt6Astra | 76 | 651,514 | 195.6 s |
| | | StockLadder | 76 | 671,590 | 93.4 s |
| | | Opus55 | 76 | 693,972 | 31.8 s |

Rectangles never leaves a part unplaced that another engine placed. Its losses are a handful of
multi-sheet jobs where the sheet-by-sheet greedy choice commits to a worse sheet mix (see Next).

`tests/` (27 tests): contract, starter and engine tests, including an 80-job sweep of discs,
rings, obrounds and triangles at four spacings that failed 16–50 jobs before the curved-extreme
rule.

## Next

- Multi-sheet jobs: the sheet-by-sheet greedy choice loses to whole-plan search on a few jobs.
  Re-plan the last sheets and try whole-job variants, as Opus55 does.
- Guillotine-only mode for shears and for cut-off-friendly layouts.
- Exhaustive search for small jobs (one or two part types).