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OpenNest/docs/nesting-engines.md
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ajandClaude Opus 5.5 00acaeaaf1 feat(engine): report best whole-job plans from Rectangles, Circles and Default
Desktop Auto Nest's "Best plan so far" strip now fills in for every built-in
whole-job engine except FlatBar, not only Irregular.

- Rectangles makes one sheet-by-sheet run, so it reports the finished job as
  its one plan, then replays its plate commits (token checked as before).
- Circles reports when a stock-preference run or a tail re-plan beats its
  best result so far.
- Default scores each candidate plan as it ranks results (valid, fewest
  unplaced, lowest cost, candidate order) and reports it only when it beats
  every plan already shown, so a later candidate never shows a worse plan.
  The chosen result is always the last plan reported.
- Shared ReportPlan/SameLayout helpers on CandidateProgress; Irregular uses
  them too. Reporting never changes the search.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
2026-10-18 23:56:38 -04:00

30 KiB

Nesting engines

Whole-job engines implement INestingEngine.Solve(NestJob) and are selected by name through NestingEngineRegistry. Every automatic nesting front end validates engine output the same way; see automatic nesting and validation.

Built-in engines

Engines are named for the jobs they suit, not for how or by whom they were built. Engine code lives in OpenNest.Engine/NestingEngines/<Name>/, its tests in OpenNest.Engine.Tests/NestingEngines/.

Engine Best for Method
Default Any job; used when no engine is named Runs Irregular, Rectangles and Circles, checks each layout with the layout check and keeps the best: valid first, then fewest unplaced parts, then lowest salvage-credited cost; ties keep the earlier engine
Rectangles Plain and near-rectangular plates Each part packed as the box of its material at its minimum-area rotation, using a maximal-rectangles free list; stock chosen sheet by sheet by salvage-credited look-ahead cost
Circles Round parts: blanks, washers, flanges, gears by their tip circle Each part packed as its minimum enclosing circle at centers tangent to two of walls, placed discs and clamp keep-outs, with hexagonal and square lattice seeds; bids only when every part is round; stock chosen as Rectangles does, plus whole-job runs preferring each stock and a tail re-plan
Irregular Irregular profiles No-fit-polygon frontier packing with gap filling and best-fit pairs, six whole-job strategy variants and a tail re-plan
FlatBar Flat bar: parts about as wide as the bar Each stock read as a bar and cut in one row: the CutList cut-list packer and a best-fill search on part lengths less their self-nesting gain, then a slide-left pass that nests shaped ends and refills freed length; stock chosen bar by bar by whole-plan cost
StockLadder Caller-supplied stock ladders Constrained-first fill with equivalent-demand area repacking
Fill, Strip, Vertical Remnant, Horizontal Remnant Single-strategy fills The fixed placement strategies behind interactive fill; Fill is the multi-phase lattice fill (linear, pairs, rectangle best-fit, remainder)

Neither Irregular nor Rectangles wins every job, even within its own lane, so Default runs both rather than choosing by part shape; Rectangles adds little time and is also the fallback when an Irregular layout fails the check. A candidate that throws is skipped. Default routes the whole job: engines cannot share a sheet, so a job mixing plain and irregular parts goes to both engines whole. Circles is a third candidate that bids only on round jobs (see below), so a job mixing round and other parts goes to Irregular and Rectangles.

Rectangles places irregular parts validly, but only as their bounding boxes; it never nests into a notch or hole. Box sides account for how the layout check flattens arcs, so round-edged parts stay valid at box contact.

Best plan so far

Whole-job engines report each better whole-job plan as NestJobStage.PlanImproved with the plan in NestJobProgress.Plan, built without plate commits; desktop Auto Nest shows it as its "Best plan so far" sheet strip (see automatic nesting). Plans are unvalidated proposals with no committed counts, all come before the plate commits, and the last one is the returned layout. Reporting never changes the search: layouts are identical with or without a progress sink.

  • Irregular reports when a strategy variant or the tail re-plan beats its best plan so far.
  • Rectangles makes one sheet-by-sheet run, so it reports the finished job as its one plan.
  • Circles reports when a stock-preference run or a tail re-plan beats its best result so far.
  • Default scores each candidate plan as it ranks results (valid, fewest unplaced, lowest cost, then candidate order) and reports it only when it beats every plan Default has reported, so a later candidate never shows a worse plan after a better one. A candidate result that reports no plans is offered the same way. When the chosen result is not the last plan reported (a candidate's plan can outscore every returned result), Default reports it last.

Plug-ins may report plans the same way; FlatBar, StockLadder and the fixed-strategy engines do not.

Interactive Fill shows its rectangle best-fit (box packing) layout before the best-fit pair phase, whose first computation for a drawing can take a minute, so Accept is available at once. The box layout is only a fallback: the strategies still run in their usual order and a completed fill picks the same winner as without it. While the pairs are computed the progress detail reads "Computing best-fit pairs (may take a minute)...". Accepting or stopping stops waiting for the pair computation, which finishes in the background and is cached for the next fill.

On a plate with clamps, interactive Fill (Fill Area and filling from a part) fills as if the clamps were absent, then drops every part that enters a clamp keep-out or sits too close to an existing part, and a whole copy of a multi-part group when any member does. Packing around the clamps usually gives a worse layout than losing the few parts on them. When every clamp in the fill area lies on one edge, Fill also fills the area with that edge moved just past the clamp keep-outs, as a larger edge spacing would, and keeps whichever layout the strategy ranks better (a tie keeps the dropped-parts layout). Small parts usually win by dropping, large parts by moving past the strip. The second fill reuses the cached best-fit pairs. Progress previews are filtered by the same check and never fall below the first layout, so a preview accepted early is clamp-clear. When a quantity is requested and copies were dropped, the fill asks for that many more, up to two more times. Pack and whole-plate Nest still pack only into the clamp-free areas.

Interactive/full-area box packing uses the same 90% work-area slack allowance as Rectangles. A free box may absorb a slightly oversized side only at its right/top edge when that edge coincides with the plate work-area boundary. Internal leftover edges keep the strict packing tolerance, and actual part dimensions still determine spacing away from the plate boundary.

Irregular keeps nominal orientation bounds for line-only outlines, so an allowed rotation can fit exactly between the configured plate-edge gaps. These bounds use original rotated line endpoints, retaining material extents even when polygon cleanup discards short-edge chains. Curved outlines retain conservative flattening-error padding. This does not relax part-spacing footprints, no-fit polygons or layout validation tolerances; a part extending beyond the accepted work-area bounds remains invalid.

Irregular fills gaps and open notches using outer profiles; it does not yet place parts inside enclosed cutouts. For a part with two or more copies it also offers its best-fit pairs (two copies interlocked, as the Best Fit viewer shows them) alongside the single copies, and places a pair where both members' free regions allow it. Each pair's internal spacing is re-checked with the layout check before it is offered, and only rotations the part's policy allows are used. A pair may introduce legal rotations beyond the sampled single poses; these remain eligible even when none of the sampled singles fits the stock. Both members block space separately, leaving their notches and intervening gaps available for later parts. A concave footprint is split once into convex pieces (ear clipping, then merging across every diagonal whose removal keeps both ends convex, all decided with exact integer cross products on the Clipper lattice); each concave no-fit polygon is the union of the pairwise convex sums of the two footprints' pieces, which is the same filled Minkowski sum the edge-pair sweep gives, at a fraction of the union's cost for outlines with many vertices. A footprint the clipper cannot decompose (self-touching, zero-area runs) keeps the single boundary/containment union. Any remaining numerical hole is filled only when its entire ring is certified to lie in forbidden space, preserving genuine enclosed placement pockets without changing spacing tolerances.

The pairs and the Fill blocks below read each part through one private drawing per part geometry, owned by the engine instance: pairs and blocks share it, and so do a pipeline's cutout trial and its ordinary solve. The best-fit search itself runs once per part geometry and spacing in the whole process: every drawing reconstructed from job geometry (DrawingJobMapper.CreateDrawing) takes its unfiltered candidates from a pool in BestFitCache keyed by the snapshot's exact content (mode and every motion value, bit for bit) and the spacing, so a repeated or re-tuned Auto Nest of the same drawings, a fresh engine instance, another engine or the cutout pre-pass skips the search and offers the same pairs. Candidates depend on the program geometry and spacing alone, so a pooled set is the set the search would produce and placements are unchanged. The pool keeps the 512 most recently used sets (BestFitCache.SharedCapacity), outlives the private drawings (Invalidate releases a drawing's entry, not the pool) and is in-memory only: the sets saved in a .nest file belong to the caller's drawings and are not consulted here.

When remaining demand exceeds two, Irregular also offers Fill patterns as optional multi-member candidates, not as solid bounding boxes or a whole-job Fill fallback. It searches the empty work area and physical leftover space for up to two high-area rectangles. Occupied outlines are expanded by part spacing before rectangle search. Each sheet prepares blocks initially and after its first placement, for up to four high-demand-area types; each type has at most eight new Fill preparations per spacing per solve. Repeated rectangles reuse private drawing/candidate caches. Quantity-one and quantity-two requests never run block Fill.

Block members are trimmed to remaining demand, mapped back to source-frame rotations, and checked for legal rotations and internal material clearance before competing with singles and pairs. Group-only rotations do not expand the single-part rotation choices. Placement intersects all member free regions and subtracts each placed member separately, preserving usable gaps. A failed or invalid Fill proposal leaves singles and pairs available. Large enclosed-pocket blocks remain pending the hole-geometry integration; containment cutting order and shop-use safety acceptance remain separate sequencer/verification work.

Flat bar

FlatBar treats each stock's long work-area axis as the bar's length and lays parts in a single row along it, so it is a one-dimensional cut list. Each part's length is its material extent at the shortest rotation whose cross extent fits the bar's width; a part that fits no bar is unplaced. Lengths carry one part spacing each, like a saw kerf.

Parts with shaped ends nest into their neighbours. FlatBar measures each part's self-nesting gain once per stock by laying three copies the way the layout pass will and averaging the two joints (so a part that only nests every other copy is not over-credited), and packs each copy at its length less that gain; the first copy of each run pays the gain back.

Bar by bar, every available stock offers two candidate bars: the fullest bar of the CutList packer (first-fit decreasing plus its swap optimization, or an exhaustive fewest-bars search for 25 items or fewer) and the fullest single bar a bounded subset-sum search can fill from the remaining demand. Lower priority numbers pack first in both. Each candidate is laid out, then the rest of the demand is priced at the cheaper of each stock's cut-list plan and its repeated best fills. The winner has the fewest unplaced parts of the most urgent tier, then the fewest unplaced parts, then the lowest salvage-credited cost. Searches stop at counted node budgets, so results are deterministic.

The layout pass starts each part box-to-box after the previous one and slides it back with the Compactor push, trying each of its shortest rotations (so mitred ends nest by turning alternate parts). Every slid pose is confirmed with NestLayoutCheck.Clears and backed off until it passes; box-to-box always passes. Parts whose outline fills their box skip the slide. A packed part that does not fit after all returns to the demand, and length freed at the end of a run is refilled from it.

Limits: one part per position across the width, so narrow parts waste the rest of it; clamp zones that reach the row block their whole clearance-expanded length; FlatBar is not a Default candidate and must be selected by name.

Rectangular clamp zones

Whole-job Rectangles and Irregular exclude each stock's rectangular clamp zones, expanded on all sides by its bottom edge spacing. Part spacing is not added to clamp clearance. Default runs and validates both lanes as usual. Empty clamp collections leave the existing packing path unchanged; clamps never become requested or placed parts.

Every Plate, including plates the engine builds from stock, stores clamp zones relative to the sheet's lower-left corner; NestPlateStock.ClampZones carries them in the signed placement frame of part coordinates. Code that compares a plate's zones with parts, cuts or motions maps them through ClampZoneFrame.ToPlacement, which reproduces the stock's zones exactly; reading Plate.ClampZones bounds directly is wrong in quadrants 2-4.

Irregular prepares static rectangle obstacles and their cached no-fit polygons once per stock per solve, separately from the part-spacing cache. Every orientation's initial free region excludes these obstacles, including extra orientations introduced by pairs or Fill blocks. Blocks still size their proposals from work-area/placed-part rectangles; member free regions determine whether the whole proposal can actually fit around clamps. Open notches and material between clamps remain available. Inflated synthetic rectangles are enclosed on the existing clipping grid before NFP preparation, retaining at least one grid interval per axis so positive sub-grid clamps cannot disappear. Existing arc/grid safety margins, covered-hole certification and cancellation apply without relaxed tolerances.

Rectangles blocks each clamp's keep-out out of its free list. When part spacing is so large that the spacing-adjusted block would invert, it blocks a zero-width line at the clamp edge facing the sheet interior instead: parts on that side keep the exact clearance and the unavoidable extra exclusion falls toward the nearer sheet edge. Keep-outs narrower than 0.001" on either axis are judged by a tolerance-free rectangle test (KeepOutOverlap) in layout validation, interactive fill and the overlap check, so they can neither crash validation nor be called clear.

Desktop clamp editing, the stock-size resolution of a nest's clamp rail, last-resort clamp removal and the other clamp-aware tools are described in automatic nesting. Other engines and plug-ins have not gained clamp-aware placement from this change.

Repeating completed layouts

Rectangles and Irregular can skip repeated sheet searches after selecting one nonempty layout whose normal sheet search has completed. The repeat count includes the first physical copy and is limited by the scarcest requirement on that layout, remaining finite stock and the remaining physical MaxPlates allowance. Parts absent from the layout keep their demand. A salvage-worthy offcut does not prevent repetition: completion means the engine found no further supported requested placement, not that no geometric packing exists.

Fast-forwarding applies only while exactly one stock entry remains available. Different stock IDs count as alternatives even at identical dimensions. Irregular's forced-first-stock tail trial still counts all remaining stock entries, not just that trial's restricted shortlist; it commits the forced first sheet once when alternatives remain and resumes ordinary stock selection. Candidates that cannot pass the existing candidate validator retain ordinary one-sheet allocation. Cancellation never certifies a layout and is checked during physical-copy expansion.

Both engines continue automatically with residual demand in the same solve, including when a layout's repeat count is one. There is no per-layout stop, confirmation or opt-in mode. Rectangles retains both Global/Ordered packing modes and its priority guard. Irregular retains demand-dependent singles, pairs and blocks, variant ordering and its existing work-budget semantics; saved work can allow additional variants to run, so this is not a promise of historical pose equality.

Raw NestJobResult output remains one entry per physical sheet, with fresh placements and unique instance indices, physical stock usage and physical progress counts. Irregular also retains each physical copy in its working plan: its last-one-to-three-sheet improvement can return the removed tail's finite stock, repack that demand, and replace just those copies while keeping the prefix. Default inherits these fast paths by running the two engines; other engines and external plug-ins keep their existing search behavior. Quantity-bearing presentation is a separate validated-pipeline representation; repeating does not bypass whole-job validation or change cutting programs.

Circles

Circles (OpenNest.Engine/NestingEngines/Circles/) packs every part as its minimum enclosing circle (CirclePacking/Item): the circle covers the layout check's outward-flattened perimeter, so packing is never more lenient than the check. When any readable part fills less than 0.8 of that circle (a square fills 0.64, a gear about 0.85), it returns everything unplaced without reporting progress, and Default discards it at almost no cost. Holes are not used here; rings in rings come from the cutout pre-pass, which hands the engine each nested chain as its outer frame.

Each disc goes, lower priority number first and then largest first, to the best feasible center tangent to two of: the work-area walls, placed discs, and clamp zones grown by the bottom-edge clearance (square-cornered, as the layout check grows them). Discs keep the part spacing plus twice NestTolerances.ValidationOutline between them. Bottom-left fills rows and left-bottom fills columns; each also runs seeded with a hexagonal lattice of the type with the most remaining area, and bottom-left runs over a square lattice too, which wins when only a few discs span the sheet. A disc with no feasible tangent center for one radius is skipped for that radius and larger ones. Sheets and stock are chosen by the loop Rectangles uses (NestingEngines/SheetByStock): salvage-credited look-ahead cost, priority first, and repeated completed layouts. That per-sheet estimate can take a large sheet first and still need a second, so Circles runs the whole job once with a free stock choice and once preferring each offered stock, and keeps the best result as Default ranks candidates (valid, fewest unplaced, lowest cost). The last sheet, and the last two sheets together, are then re-packed onto each single stock and replaced when that lowers the whole job's cost, so a small remainder does not finish on a large sheet.

Filling cutouts

Every whole-job NestPipeline.Run (desktop Auto Nest, Console, MCP and API) first places parts inside other parts' enclosed cutouts, before the selected engine, so every engine benefits and none needs to know about holes. The steps below prepare frame-plus-insert bundles; the engine places each bundle's frame as an ordinary part and never sees its reserved inserts.

CutoutLatticeFill (OpenNest.Engine/Jobs/Cutouts/) fills one closed cutout with copies of one part. It runs Fill over the cutout's bounds plus one part step on every side, then shifts that lattice across a grid of offsets of up to half a step each way. At each offset it keeps the copies whose spacing-grown outline lies inside the cutout, using the part's inner-fit region of the inscribed, flattened cutout, and the offset keeping the most copies wins. Every returned pose is then checked against the frame and the other copies with NestLayoutCheck.Clears, the test the layout check uses. The method suits many small copies in a large cutout; a few large inserts are meant for no-fit-polygon placement. Fill can return different, equally scored lattices on repeated calls for some parts, so results are not yet guaranteed identical between runs.

The internal CutoutRouter can propose copies from the shifted lattice, then search bounded inner-fit/NFP sample points for remaining copies and other insert requirements. It keeps original requirement IDs, reindexes accepted copies and checks clearance against the frame and every previously accepted insert. Lattice shifts account for occupied poses before quantity trimming; a pre-fill work limit declines giant grids and lets bounded NFP sampling try instead. A null NFP proposal is not proof of geometric impossibility. No material-area ratio cutoff rejects a possible placement: the measured 0.10 and 0.35 ratios guide search order only. Below 0.10 it starts with Fill for three or more copies; between 0.10 and 0.35 it compares Fill-plus-NFP with NFP-only counts; above 0.35 it tries NFP first, then Fill if demand remains, taking the higher-count valid proposal. An 0.20 NFP-only rule would lose a second 4-inch square in a 10-inch round hole. Six geometry-only, anonymized real-job probes and neutral ring fixtures informed the search-order hints; these limited cases are not a global density guarantee.

When the cutout is one circle and every insert fills at least 0.8 of its enclosing circle (discs, washers, gears by their tip circle), CutoutCirclePacker first packs the whole insert list as discs: largest first, at centers tangent to two of the hole wall and the placed discs, or at the hole's center. It tries a center-out pass, so a single insert sits concentric, and a wall-first pass, which reaches the optimal counts for up to nine equal discs. Each gap is the spacing plus twice NestTolerances.ValidationOutline, and every pose passes NestLayoutCheck. Its result is the router's proposal for that hole: the lattice and NFP searches never placed more there and were slow on round inserts, most of all when demand exceeds what fits. CutoutPipelinePrepass builds quantity-one proxy instances for eligible closed-cutout frames. It considers legal frame rotations without outer-perimeter symmetry reduction, shifts insert rotation policies into the local frame, and reserves certified router poses by original requirement ID. It can fill multiple holes and repeated/different frame requirements; inserts with a different priority stay independent, and a hole smaller in area than an insert's outline (a bolt hole) is not searched for it. Frames are bundled smallest first, so a larger frame's round cutout can take, through CutoutCirclePacker only, a round part with its own cutouts (a washer with an empty bore) or an earlier bundle as one insert: a flange holds a washer that holds a smaller washer that holds a slug. Chains stop at four parts deep (CutoutPipelinePrepass.MaxLevels). Lattice and NFP proposals never take such inserts, since they could seat a part in a ring's bore or over a nested bundle's reserved inserts; non-round frames with cutouts stay independent. A frame's proposals are compared by physical parts placed, a nested bundle counting its frame and contents, and ties keep the flat router's proposal. It uses the largest offered spacing for every bundle because the current job contract cannot condition insert demand on the stock selected later. Remaining demand is offered to the selected engine once. Only actually placed proxies expand, recursively, to original frame and insert identities. An unplaced proxy's reservations, including every nested frame and insert, return to the original unplaced demand; they cannot be packed retroactively in that same solve. Engine indices and metadata are checked, then every physical pose, stock, rotation, quantity and fulfillment is independently validated before binding caller drawings. Forged or geometrically invalid composites return no bindable plates even with invalid-result consent. Candidate evaluation progress is forwarded with unverified proxy commitment counts zeroed; transformed proxy commits are hidden. Physical commits are reported only after physical validation. Preparation is bounded to 32 bundles and 16 base sweep-angle samples per frame (automatic quarter-turns are all retained); remaining copies stay ordinary requirements. Within one preparation, geometry reads and NestLayoutCheck.Clears answers are replayed (CutoutMemo: same geometry, bit-identical poses), so repeated frame instances and frame angles do not repeat that check, its main cost; layouts are the same as without the replay. A hole's proposal is also replayed whenever the same frame, hole and offered inserts (ids, remaining quantities and frame-local rotation policies) come up again: automatic-rotation inserts ask the same question at every frame angle, and a second instance of the frame asks it again until the first instance's inserts change the remaining demand. The lattice and NFP searches prepare the frame's and the occupants' validation outlines once per search (NestLayoutCheck.Prepare) and test each candidate against the small occupants before the frame, so a crowded window no longer re-outlines and re-triangulates the frame at every candidate; the answers are those of the pairwise check. Fixed legal proxy orientations are a conservative search choice, not full engine choice among all legal orientations; unsupported bundles remain ordinary independent requirements.

NestPipeline.Run keeps a bundled trial that is valid and complete. Otherwise it also runs the ordinary solve of the same job (with last-resort clamp removal, which the bundled trial does not offer) and returns:

  • the ordinary solve when the trial was refused, with the refusal on NestPipelineResult.RefusedCutoutTrial (never in Violations, since the refused trial has no bindable plates);
  • the ordinary solve when the trial was incomplete and the valid ordinary solve places more physical parts;
  • otherwise the incomplete trial, which is a keepable layout like any other incomplete result.

So a job with cutouts may take up to two engine solves; a job without eligible frames takes one, exactly as before. Expanded sheets list each frame's inserts immediately before the frame, at every level (innermost first), so the committed part order cuts every insert before the cutout that would release its slug. Leads are not changed: pre-post verification still warns when a host's hole lead or an insert's lead meets the other part, or when a later reorder (by hand or Auto Sequence) puts the host first (see pre-post verification); Plan Cutting cuts each insert before its frame and refuses a kept order that does not. Engine benchmarks call engines directly and do not run this pre-pass; internal NestPipeline.RunWithoutCutouts is the ordinary-solve baseline for tests.

Renamed engines

The registry maps names used by earlier releases (the first two shipped as plug-ins) so saved desktop selections, scripts and API requests keep working:

Old name Now
Opus55NestingEngine Irregular
RectanglesNestingEngine Rectangles

In v0.3.0 and earlier, Default was the multi-phase fill engine now named Fill. Default now names the choosing engine above, so saved selections, scripts and API requests that name it get that engine. Fill-strategy calls (interactive fill, PlateFillService, console fill without --autonest, MCP fill tools) still read Default as Fill.

Gpt6Astra and Qwen38FlashNext are no longer shipped and have no alias. A saved selection of either falls back to the default engine with the usual status-bar warning.

Changing an engine

Use the engine benchmarking guide for the command, candidate-sheet controls, and comparison procedure.

  • A change lands only when it beats the engine's current result on OpenNest.Benchmark for the jobs that engine targets, with every layout valid. Report cost, validity, unplaced parts and time.
  • Placement must be deterministic: no clocks, unseeded randomness or environment variables. Budget work by counting it; wall time may stop work only through the cancellation token.
  • Keep each engine's tests passing, including EngineContractTests<TEngine> (quadrants, overflow, priority, cancellation, stock and plate limits, determinism). Every layout in those tests is checked with NestLayoutCheck, the benchmark's validator.
  • Engines may share code. Move a helper into shared Engine code when a second engine needs it, rather than copying it.

Plug-ins

External engines still load from an Engines/ folder beside the desktop, console, MCP or benchmark executable. A plug-in implements INestingEngine with a public parameterless constructor and registers under its CLR type name. A plug-in whose name matches a built-in engine, or a renamed engine's old name, is skipped: a leftover OpenNest.Engine.Opus55.dll cannot shadow Irregular. Leftover Gpt6Astra or Qwen38FlashNext DLLs still load as ordinary plug-ins until deleted.

Cost basis and heuristic limits

NestPlateStock.Cost is nullable, immutable and per physical sheet. Every available stock must have a finite positive cost, or all must omit it. Omitted costs preserve area scoring. The original constructor and area-valued NetSheetArea and obsolete EstimateNetArea APIs retain their units. NetSheetCost applies proportional salvage to explicit costs; geometric area still controls fit, utilization and material ordering.

Rectangles uses net cost in sheet trials and remaining-material estimates. Irregular uses it in look-ahead, strategy comparison and equivalent-demand tail replacement. StockLadder ranks net cost per placed material area and uses total net cost for consolidation. Default compares valid equally fulfilled results by generic job score. Fixed Fill/Strip/remnant strategies rank priority fulfillment first, then net cost for priced stock (gross area for legacy unpriced stock), then existing stable ties. None guarantees globally optimal purchasing or explores every combination of patterns.