feat(engine): Opus55 frontier-advance NFP nesting engine

Rename the OpenNest.Engine.Sonnet5 scaffold to OpenNest.Engine.Opus55 and
implement an independent whole-job INestingEngine (no built-in engine,
registry, or best-fit internals are called or copied).

- PartCatalog: snapshot perimeter -> polygon per allowed orientation, with
  adaptive chord tolerance and MBR-aligned rotations for Automatic parts.
- NoFitCache: spacing footprints and cached Clipper2 Minkowski NFPs (convex
  fast path; concave sweep plus both containment terms).
- FrontierPacker: per-(type, orientation) free regions (inner-fit rectangle
  minus NFPs), updated incrementally; gap-fill-largest, else least front
  advance per area^beta.
- Engine: look-ahead stock choice by estimated whole-job net area, six
  deterministic variants, tail re-plan of the last 1-3 sheets.
- Tests judged by OpenNest.Benchmark's NestValidator, including an NFP
  containment regression guard.

P260805-10.nest (219 parts), all 9 stock sizes: 219/219 valid, 27 sheets,
91.7% utilization, ~7 s.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

OpenNest.Engine.Opus55/FrontierPacker.cs

@@ -0,0 +1,272 @@
+using Clipper2Lib;
+using OpenNest.Engine.Jobs;
+using OpenNest.Geometry;
+
+namespace OpenNest.Engine.Opus55;
+
+/// <summary>Direction the packing front sweeps across the sheet (the free strip is left behind it).</summary>
+internal enum PackAxis
+{
+    /// <summary>Front moves in +X; parts settle toward low X, then low Y.</summary>
+    X,
+
+    /// <summary>Front moves in +Y; parts settle toward low Y, then low X.</summary>
+    Y,
+}
+
+internal sealed record Placed(Orientation Orientation, double X, double Y)
+{
+    public double Left => X + Orientation.MinX;
+    public double Right => X + Orientation.MaxX;
+    public double Bottom => Y + Orientation.MinY;
+    public double Top => Y + Orientation.MaxY;
+}
+
+internal sealed record SheetFill(NestPlateStock Stock, IReadOnlyList<Placed> Parts, double PartArea);
+
+/// <summary>
+/// Fills one sheet with a frontier-advance rule over incrementally maintained free regions.
+///
+/// For every (part type, orientation) still in play the packer keeps the exact set of legal
+/// reference points: the inner-fit rectangle of the work area minus the no-fit polygons of
+/// everything already placed. Each placement subtracts one translated NFP from each region,
+/// so regions only shrink, and a region that empties is retired for the rest of the sheet.
+///
+/// Choice rule, applied over all types and orientations at once (not in a fixed order):
+///   1. Gap fill - if any part fits without pushing the packing front forward, place the
+///      largest such part at its lowest such point.
+///   2. Otherwise advance - place the part whose front advance per unit area^beta is smallest,
+///      i.e. the one that buys the most material coverage for the sheet length it consumes.
+/// Parts are never placed in a sequence given up front; the sheet state decides what comes next.
+/// </summary>
+internal sealed class FrontierPacker
+{
+    /// <summary>Slack added around the inner-fit rectangle so zero-width fits survive Clipper;
+    /// chosen points are clamped back, which moves them far less than the clearance margin.</summary>
+    private const double FitSlack = 2e-4;
+
+    private const double Tie = 1e-6;
+
+    private readonly IReadOnlyList<PartType> types;
+    private readonly NoFitCache nfps;
+    private readonly NestPlateStock stock;
+    private readonly PackAxis axis;
+    private readonly double beta;
+    private readonly Box work;
+    private readonly WorkCounter counter;
+
+    public FrontierPacker(IReadOnlyList<PartType> types, NoFitCache nfps, NestPlateStock stock, PackAxis axis, double beta, WorkCounter counter)
+    {
+        this.counter = counter;
+        this.types = types;
+        this.nfps = nfps;
+        this.stock = stock;
+        this.axis = axis;
+        this.beta = beta;
+        work = WorkArea(stock);
+    }
+
+    public static Box WorkArea(NestPlateStock stock)
+    {
+        var left = stock.Quadrant is 1 or 4 ? 0 : -stock.Size.Length;
+        var bottom = stock.Quadrant is 1 or 2 ? 0 : -stock.Size.Width;
+        return new Box(
+            left + stock.EdgeSpacing.Left,
+            bottom + stock.EdgeSpacing.Bottom,
+            stock.Size.Length - stock.EdgeSpacing.Left - stock.EdgeSpacing.Right,
+            stock.Size.Width - stock.EdgeSpacing.Bottom - stock.EdgeSpacing.Top
+        );
+    }
+
+    /// <summary>True when the orientation's bounds fit the work area at all (Box.Length is the X extent).</summary>
+    public static bool Fits(Orientation o, Box work) =>
+        o.Width <= work.Length + 1e-9 && o.Height <= work.Width + 1e-9;
+
+    public SheetFill Fill(IReadOnlyList<int> remaining, CancellationToken token)
+    {
+        var left = remaining.ToArray();
+        var states = new List<Region>();
+        foreach (var type in types)
+        {
+            if (left[type.Index] <= 0)
+                continue;
+            foreach (var o in type.Orientations)
+                if (Fits(o, work))
+                    states.Add(new Region(o, work));
+        }
+
+        var placed = new List<Placed>();
+        var partArea = 0.0;
+        var front = axis == PackAxis.X ? work.Left : work.Bottom;
+
+        while (states.Count > 0)
+        {
+            token.ThrowIfCancellationRequested();
+            var choice = Choose(states, front);
+            if (choice == null)
+                break;
+
+            var (region, point) = choice.Value;
+            var part = new Placed(region.Orientation, point.x, point.y);
+            placed.Add(part);
+            var typeIndex = region.Orientation.TypeIndex;
+            partArea += types[typeIndex].Area;
+            front = System.Math.Max(front, axis == PackAxis.X ? part.Right : part.Top);
+
+            if (--left[typeIndex] == 0)
+                states.RemoveAll(s => s.Orientation.TypeIndex == typeIndex);
+
+            // Each surviving region loses the positions the new part now blocks. Regions are
+            // independent, so they update in parallel without affecting determinism.
+            var snapshot = states.ToArray();
+            counter.Add(snapshot.Length);
+            Parallel.For(
+                0,
+                snapshot.Length,
+                new ParallelOptions { CancellationToken = token },
+                i => snapshot[i].Subtract(nfps.Get(part.Orientation, snapshot[i].Orientation), part.X, part.Y)
+            );
+            states.RemoveAll(s => s.IsEmpty);
+        }
+
+        return new SheetFill(stock, placed, partArea);
+    }
+
+    private (Region, PointD)? Choose(List<Region> states, double front)
+    {
+        Region? bestRegion = null;
+        var bestPoint = default(PointD);
+        var bestFills = false;
+        var bestValue = double.PositiveInfinity;
+        var bestSide = double.PositiveInfinity;
+        var bestLead = double.PositiveInfinity;
+
+        foreach (var region in states)
+        {
+            if (!region.TryLowest(axis, front, out var point, out var advance, out var side, out var lead))
+                continue;
+            var area = types[region.Orientation.TypeIndex].Area;
+            var fills = advance <= Tie;
+            // Gap fill prefers bigger parts (negated area); advance prefers least advance per area.
+            var value = fills ? -area : advance / System.Math.Pow(System.Math.Max(area, 1e-12), beta);
+
+            var better = bestRegion == null
+                || (fills && !bestFills)
+                || (
+                    fills == bestFills
+                    && (
+                        value < bestValue - Tie * System.Math.Max(1, System.Math.Abs(bestValue))
+                        || (
+                            value <= bestValue + Tie * System.Math.Max(1, System.Math.Abs(bestValue))
+                            && (side < bestSide - Tie || (side <= bestSide + Tie && lead < bestLead - Tie))
+                        )
+                    )
+                );
+            if (!better)
+                continue;
+            bestRegion = region;
+            bestPoint = point;
+            bestFills = fills;
+            bestValue = value;
+            bestSide = side;
+            bestLead = lead;
+        }
+
+        return bestRegion == null ? null : (bestRegion, bestPoint);
+    }
+
+    /// <summary>Legal reference points for one orientation on this sheet.</summary>
+    private sealed class Region
+    {
+        private readonly double minX, minY, maxX, maxY;
+        private PathsD free;
+        private RectD bounds;
+
+        public Region(Orientation orientation, Box work)
+        {
+            Orientation = orientation;
+            minX = work.Left - orientation.MinX;
+            maxX = work.Right - orientation.MaxX;
+            minY = work.Bottom - orientation.MinY;
+            maxY = work.Top - orientation.MaxY;
+            // Guard against fits that are infeasible by less than the bounds tolerance.
+            if (maxX < minX)
+                maxX = minX;
+            if (maxY < minY)
+                maxY = minY;
+            free = new PathsD
+            {
+                new PathD
+                {
+                    new(minX - FitSlack, minY - FitSlack),
+                    new(maxX + FitSlack, minY - FitSlack),
+                    new(maxX + FitSlack, maxY + FitSlack),
+                    new(minX - FitSlack, maxY + FitSlack),
+                },
+            };
+            bounds = Clipper.GetBounds(free);
+        }
+
+        public Orientation Orientation { get; }
+        public bool IsEmpty => free.Count == 0;
+
+        public void Subtract(Nfp nfp, double dx, double dy)
+        {
+            if (
+                nfp.Bounds.right + dx < bounds.left
+                || nfp.Bounds.left + dx > bounds.right
+                || nfp.Bounds.bottom + dy < bounds.top
+                || nfp.Bounds.top + dy > bounds.bottom
+            )
+                return;
+            var clip = Clipper.TranslatePaths(nfp.Region, dx, dy);
+            free = Clipper.Difference(free, clip, FillRule.NonZero, NoFitCache.Precision);
+            // Drop numerical dust; a sliver thinner than the precision grid is no real room.
+            free.RemoveAll(p => p.Count < 3);
+            bounds = free.Count == 0 ? default : Clipper.GetBounds(free);
+        }
+
+        /// <summary>
+        /// Best vertex of the free region: least front advance, then lowest cross-axis position,
+        /// then lowest leading edge. Vertices suffice because every score is linear in position.
+        /// </summary>
+        public bool TryLowest(PackAxis axis, double front, out PointD point, out double advance, out double side, out double lead)
+        {
+            point = default;
+            advance = side = lead = double.PositiveInfinity;
+            var found = false;
+            var o = Orientation;
+            foreach (var path in free)
+                foreach (var raw in path)
+                {
+                    var x = System.Math.Clamp(raw.x, minX, maxX);
+                    var y = System.Math.Clamp(raw.y, minY, maxY);
+                    double reach, across, start;
+                    if (axis == PackAxis.X)
+                    {
+                        reach = x + o.MaxX;
+                        across = y + o.MinY;
+                        start = x + o.MinX;
+                    }
+                    else
+                    {
+                        reach = y + o.MaxY;
+                        across = x + o.MinX;
+                        start = y + o.MinY;
+                    }
+                    var adv = System.Math.Max(0, reach - front);
+                    var better = !found
+                        || adv < advance - Tie
+                        || (adv <= advance + Tie && (across < side - Tie || (across <= side + Tie && start < lead - Tie)));
+                    if (!better)
+                        continue;
+                    found = true;
+                    point = new PointD(x, y);
+                    advance = adv;
+                    side = across;
+                    lead = start;
+                }
+            return found;
+        }
+    }
+}

OpenNest.Engine.Opus55/NoFitCache.cs

@@ -0,0 +1,171 @@
+using System.Collections.Concurrent;
+using Clipper2Lib;
+
+namespace OpenNest.Engine.Opus55;
+
+/// <summary>
+/// Spacing-inflated footprints and the no-fit polygons between them, for one clearance value.
+///
+/// Every placed part owns a footprint: its outline grown by half the required clearance
+/// (plus its own chord tolerance). Two parts respect the clearance exactly when their
+/// footprints do not overlap, so the whole spacing rule reduces to NFP containment.
+/// NFPs are translation-invariant, so each (orientation, orientation) pair is computed once
+/// per job and reused by every sheet, stock trial and strategy variant.
+/// </summary>
+internal sealed class NoFitCache
+{
+    /// <summary>Clipper decimal precision; 1e-4 job units is far below any margin we keep.</summary>
+    public const int Precision = 4;
+
+    private readonly double halfClearance;
+    private readonly ConcurrentDictionary<(int, int), PathD> footprints = new();
+    private readonly ConcurrentDictionary<(int, int, int, int), Lazy<Nfp>> nfps = new();
+
+    public NoFitCache(double clearance)
+    {
+        halfClearance = clearance / 2;
+    }
+
+    public PathD Footprint(Orientation o) =>
+        footprints.GetOrAdd((o.TypeIndex, o.Index), _ => BuildFootprint(o));
+
+    /// <summary>NFP of <paramref name="moving"/> around <paramref name="fixedPart"/> placed at the origin.</summary>
+    public Nfp Get(Orientation fixedPart, Orientation moving) =>
+        nfps.GetOrAdd(
+                (fixedPart.TypeIndex, fixedPart.Index, moving.TypeIndex, moving.Index),
+                _ => new Lazy<Nfp>(() => Build(fixedPart, moving), LazyThreadSafetyMode.ExecutionAndPublication)
+            )
+            .Value;
+
+    private PathD BuildFootprint(Orientation o)
+    {
+        // Miter joins (squared past the limit) always contain the exact round offset, so the
+        // footprint is a superset of "every point within the clearance of the outline".
+        var inflated = Clipper.InflatePaths(
+            new PathsD { o.Outline },
+            halfClearance + o.Tolerance,
+            JoinType.Miter,
+            EndType.Polygon,
+            2.0,
+            Precision,
+            0.0
+        );
+        var best = inflated.OrderByDescending(p => System.Math.Abs(Clipper.Area(p))).First();
+        if (!Clipper.IsPositive(best))
+            best.Reverse();
+        return best;
+    }
+
+    private Nfp Build(Orientation fixedPart, Orientation moving)
+    {
+        var a = Footprint(fixedPart);
+        var b = Footprint(moving);
+        var negB = new PathD(b.Count);
+        foreach (var p in b)
+            negB.Add(new PointD(-p.x, -p.y));
+
+        PathsD region;
+        if (IsConvex(a) && IsConvex(b))
+        {
+            region = new PathsD { ConvexSum(a, negB) };
+        }
+        else
+        {
+            // A (+) P, with P = -B: a reference point the boundary sweep misses puts the moving
+            // copy of B clear of A's boundary, so that copy is inside A, contains A, or misses it.
+            // (A + p0) covers "B inside A" and (P + a0) covers "B swallows A"; both are needed.
+            var sweep = Minkowski.Sum(negB, a, true, Precision);
+            sweep.Add(Clipper.TranslatePath(a, negB[0].x, negB[0].y));
+            sweep.Add(Clipper.TranslatePath(negB, a[0].x, a[0].y));
+            region = Clipper.Union(sweep, new PathsD(), FillRule.NonZero, Precision);
+        }
+        return new Nfp(region, Clipper.GetBounds(region));
+    }
+
+    /// <summary>Minkowski sum of two convex CCW polygons by merging edges in angle order.</summary>
+    private static PathD ConvexSum(PathD a, PathD b)
+    {
+        var ia = LowestIndex(a);
+        var ib = LowestIndex(b);
+        var result = new PathD(a.Count + b.Count);
+        var current = new PointD(a[ia].x + b[ib].x, a[ia].y + b[ib].y);
+        int i = 0, j = 0;
+        while (i < a.Count || j < b.Count)
+        {
+            result.Add(current);
+            var ea = i < a.Count ? Edge(a, ia + i) : default;
+            var eb = j < b.Count ? Edge(b, ib + j) : default;
+            // Both edge sequences start at the lowest vertex, so their angles rise through [0, 2pi).
+            double order;
+            if (i >= a.Count)
+                order = -1;
+            else if (j >= b.Count)
+                order = 1;
+            else
+            {
+                var difference = EdgeAngle(eb) - EdgeAngle(ea);
+                order = System.Math.Abs(difference) < 1e-12 ? 0 : difference;
+            }
+            if (order > 0)
+            {
+                current = new PointD(current.x + ea.x, current.y + ea.y);
+                i++;
+            }
+            else if (order < 0)
+            {
+                current = new PointD(current.x + eb.x, current.y + eb.y);
+                j++;
+            }
+            else
+            {
+                current = new PointD(current.x + ea.x + eb.x, current.y + ea.y + eb.y);
+                i++;
+                j++;
+            }
+        }
+        return result;
+    }
+
+    private static double EdgeAngle(PointD edge)
+    {
+        var angle = System.Math.Atan2(edge.y, edge.x);
+        return angle < 0 ? angle + System.Math.PI * 2 : angle;
+    }
+
+    private static PointD Edge(PathD path, int index)
+    {
+        var from = path[index % path.Count];
+        var to = path[(index + 1) % path.Count];
+        return new PointD(to.x - from.x, to.y - from.y);
+    }
+
+    /// <summary>Lowest (then leftmost) vertex: the start of a CCW edge sequence sorted by angle.</summary>
+    private static int LowestIndex(PathD path)
+    {
+        var best = 0;
+        for (var i = 1; i < path.Count; i++)
+            if (path[i].y < path[best].y || (path[i].y == path[best].y && path[i].x < path[best].x))
+                best = i;
+        return best;
+    }
+
+    private static bool IsConvex(PathD path)
+    {
+        var n = path.Count;
+        if (n < 3)
+            return false;
+        for (var i = 0; i < n; i++)
+        {
+            var a = path[i];
+            var b = path[(i + 1) % n];
+            var c = path[(i + 2) % n];
+            var cross = (b.x - a.x) * (c.y - b.y) - (b.y - a.y) * (c.x - b.x);
+            if (cross < -1e-12)
+                return false;
+        }
+        return true;
+    }
+}
+
+/// <summary>Forbidden reference-point region (interior = overlap, boundary = touching) and its bounds.</summary>
+internal sealed record Nfp(PathsD Region, RectD Bounds);

OpenNest.Engine.Opus55/OpenNest.Engine.Opus55.csproj

@@ -1,13 +1,14 @@
 <Project Sdk="Microsoft.NET.Sdk">
   <PropertyGroup>
     <TargetFramework>net8.0</TargetFramework>
-    <RootNamespace>OpenNest.Engine.Sonnet5</RootNamespace>
+    <RootNamespace>OpenNest.Engine.Opus55</RootNamespace>
-    <AssemblyName>OpenNest.Engine.Sonnet5</AssemblyName>
+    <AssemblyName>OpenNest.Engine.Opus55</AssemblyName>
     <ImplicitUsings>enable</ImplicitUsings>
     <Nullable>enable</Nullable>
   </PropertyGroup>
   <ItemGroup>
     <Compile Remove="tests/**/*.cs" />
+    <InternalsVisibleTo Include="OpenNest.Engine.Opus55.Tests" />
     <ProjectReference Include="../OpenNest.Engine/OpenNest.Engine.csproj" />
   </ItemGroup>
 </Project>

OpenNest.Engine.Opus55/Opus55NestingEngine.cs

@@ -0,0 +1,294 @@
+using System;
+using System.Threading;
+using OpenNest.Engine.Jobs;
+
+namespace OpenNest.Engine.Opus55;
+
+/// <summary>
+/// Frontier-advance NFP packer with look-ahead stock selection.
+///
+/// Per sheet, <see cref="FrontierPacker"/> keeps the exact free region of every
+/// (part type, orientation) as inner-fit rectangle minus no-fit polygons, and repeatedly places
+/// either the largest part that fills a gap behind the packing front, or the part that advances
+/// the front least per unit of area covered. Across sheets, every available stock size is
+/// trial-packed and the one with the lowest estimated whole-job cost (its own net area plus the
+/// remaining demand at the best efficiency seen) is committed. A handful of deterministic
+/// strategy variants (front direction, area exponent) run whole-job, and the cheapest wins.
+///
+/// Fully deterministic: no clocks or randomness influence any decision.
+/// </summary>
+public sealed class Opus55NestingEngine : INestingEngine
+{
+    /// <summary>
+    /// Extra clearance beyond the stock's part spacing, in job units. Validators polygonize arcs
+    /// circumscribed at 0.01 per side, so two tangent true arcs can read as up to 0.02 closer
+    /// than they are; the rest absorbs Clipper's 1e-4 grid and inner-fit clamping.
+    /// </summary>
+    internal const double ClearanceMargin = 0.022;
+
+    /// <summary>Strategy variants, tried in order: (front direction, area exponent beta).</summary>
+    private static readonly (PackAxis Axis, double Beta)[] Variants =
+    {
+        (PackAxis.X, 1.0),
+        (PackAxis.Y, 1.0),
+        (PackAxis.X, 0.5),
+        (PackAxis.Y, 0.5),
+        (PackAxis.X, 1.5),
+        (PackAxis.Y, 1.5),
+    };
+
+    /// <summary>
+    /// Deterministic work budget, in free-region subtractions, after which no further variant
+    /// starts. Keeps big jobs well inside benchmark timeouts without consulting a clock.
+    /// </summary>
+    internal long WorkBudget { get; init; } = 1_500_000;
+
+    public NestJobResult Solve(
+        NestJob job,
+        IProgress<NestJobProgress>? progress = null,
+        CancellationToken token = default
+    )
+    {
+        ArgumentNullException.ThrowIfNull(job);
+        var types = PartCatalog.Build(job);
+        var solver = new Solver(job, types, progress, token);
+
+        // Demand that no offered stock can hold in any allowed orientation is reported unplaced.
+        var demand = new int[types.Count];
+        foreach (var type in types)
+        {
+            var placeable = job.Plates.Any(stock =>
+                stock.Quantity != 0
+                && type.Orientations.Any(o => FrontierPacker.Fits(o, FrontierPacker.WorkArea(stock)))
+            );
+            demand[type.Index] = placeable ? type.Part.Quantity : 0;
+        }
+
+        Plan? best = null;
+        foreach (var (axis, beta) in Variants)
+        {
+            token.ThrowIfCancellationRequested();
+            if (best != null && solver.Work.Value >= WorkBudget)
+                break;
+            var plan = solver.Plan(demand, axis, beta);
+            if (best == null || plan.IsBetterThan(best))
+                best = plan;
+            if (best.Unplaced == 0 && best.Sheets.Count == 0)
+                break;
+        }
+
+        // The last sheets hold the leftovers, which is where waste concentrates; re-plan them.
+        best = solver.ImproveTail(best!, WorkBudget * 2);
+        return BuildResult(job, types, best, progress);
+    }
+
+    /// <summary>Shared state for one solve: job, catalog, NFP caches, effort meter.</summary>
+    private sealed class Solver(
+        NestJob job,
+        IReadOnlyList<PartType> types,
+        IProgress<NestJobProgress>? progress,
+        CancellationToken token
+    )
+    {
+        private const int MaxTail = 3;
+        private readonly Dictionary<double, NoFitCache> caches = new();
+
+        public WorkCounter Work { get; } = new();
+
+        private double Penalty => job.Plates.Count == 0 ? 0 : job.Plates.Max(SheetEconomics.SheetArea);
+
+        public Plan Plan(int[] demand, PackAxis axis, double beta)
+        {
+            var run = Decode(demand, axis, beta, new Dictionary<string, int>(StringComparer.Ordinal), job.Options.MaxPlates, null);
+            var unplaced = types.Sum(t => t.Part.Quantity) - run.Sheets.Sum(s => s.Parts.Count);
+            var reason = run.Reason;
+            if (unplaced > 0 && reason == NestJobStopReason.Completed)
+                reason = NestJobStopReason.NoPlacementFound; // Demand no stock can hold.
+            return new Plan(run.Sheets, run.Net + unplaced * Penalty, unplaced, reason);
+        }
+
+        /// <summary>
+        /// Takes the parts off the last k sheets (k = 1..3) and re-plans just that demand with
+        /// every stock forced as the first sheet, under every variant; the cheapest complete
+        /// re-plan that beats the current tail replaces it. Tails are small and effort is metered.
+        /// </summary>
+        public Plan ImproveTail(Plan plan, long budget)
+        {
+            var sheets = plan.Sheets.ToList();
+            for (var k = 1; k <= System.Math.Min(MaxTail, sheets.Count); k++)
+            {
+                if (Work.Value >= budget)
+                    break;
+                var prefix = sheets.Take(sheets.Count - k).ToList();
+                var tail = sheets.Skip(sheets.Count - k).ToList();
+                var tailParts = tail.Sum(s => s.Parts.Count);
+                var tailNet = tail.Sum(s => SheetEconomics.NetArea(job.Options, s));
+                var tailDemand = new int[types.Count];
+                foreach (var part in tail.SelectMany(s => s.Parts))
+                    tailDemand[part.Orientation.TypeIndex]++;
+                var used = prefix
+                    .GroupBy(s => s.Stock.Id)
+                    .ToDictionary(g => g.Key, g => g.Count(), StringComparer.Ordinal);
+                int? cap = job.Options.MaxPlates is int max ? max - prefix.Count : null;
+
+                Run? bestRun = null;
+                var bestNet = tailNet - 1e-9 * System.Math.Max(1, tailNet);
+                foreach (var (axis, beta) in Variants)
+                    foreach (var first in job.Plates)
+                    {
+                        token.ThrowIfCancellationRequested();
+                        var run = Decode(tailDemand, axis, beta, used, cap, first);
+                        if (run.Sheets.Sum(s => s.Parts.Count) != tailParts || run.Net >= bestNet)
+                            continue;
+                        bestRun = run;
+                        bestNet = run.Net;
+                    }
+
+                if (bestRun == null)
+                    continue;
+                sheets = prefix.Concat(bestRun.Sheets).ToList();
+                plan = plan with { Sheets = sheets.ToList(), Cost = plan.Cost - (tailNet - bestRun.Net) };
+            }
+            return plan;
+        }
+
+        private NoFitCache CacheFor(NestPlateStock stock)
+        {
+            var clearance = System.Math.Max(0, stock.PartSpacing) + ClearanceMargin;
+            if (!caches.TryGetValue(clearance, out var cache))
+                caches[clearance] = cache = new NoFitCache(clearance);
+            return cache;
+        }
+
+        /// <summary>
+        /// Greedy sheet-by-sheet decode. <paramref name="usedBefore"/> seeds finite-stock
+        /// accounting, <paramref name="sheetCap"/> bounds the sheets this run may add, and
+        /// <paramref name="first"/>, when set, forces the stock of the first sheet.
+        /// </summary>
+        private Run Decode(
+            int[] demand,
+            PackAxis axis,
+            double beta,
+            IReadOnlyDictionary<string, int> usedBefore,
+            int? sheetCap,
+            NestPlateStock? first
+        )
+        {
+            var remaining = (int[])demand.Clone();
+            var used = job.Plates.ToDictionary(s => s.Id, s => usedBefore.GetValueOrDefault(s.Id), StringComparer.Ordinal);
+            var sheets = new List<SheetFill>();
+            var net = 0.0;
+            NestJobStopReason reason;
+
+            while (true)
+            {
+                if (remaining.All(r => r == 0))
+                {
+                    reason = NestJobStopReason.Completed;
+                    break;
+                }
+                if (sheetCap is int cap && sheets.Count >= cap)
+                {
+                    reason = NestJobStopReason.PlateLimitReached;
+                    break;
+                }
+
+                var trials = new List<(SheetFill Fill, double Net)>();
+                foreach (var stock in job.Plates)
+                {
+                    token.ThrowIfCancellationRequested();
+                    if (sheets.Count == 0 && first != null && !ReferenceEquals(stock, first))
+                        continue;
+                    if (stock.Quantity is int available && used[stock.Id] >= available)
+                        continue;
+                    progress?.Report(new NestJobProgress(NestJobStage.EvaluatingCandidate, stock.Id, sheets.Count, 0, 0));
+                    var packer = new FrontierPacker(types, CacheFor(stock), stock, axis, beta, Work);
+                    var fill = packer.Fill(remaining, token);
+                    if (fill.Parts.Count > 0)
+                        trials.Add((fill, SheetEconomics.NetArea(job.Options, fill)));
+                }
+
+                if (trials.Count == 0)
+                {
+                    var exhausted = job.Plates.Any(s => s.Quantity is int q && used[s.Id] >= q);
+                    reason = exhausted ? NestJobStopReason.StockExhausted : NestJobStopReason.NoPlacementFound;
+                    break;
+                }
+
+                // Look-ahead: charge whatever a trial leaves behind at the best efficiency any trial
+                // achieved, so a sheet that finishes the job competes fairly with a denser partial one.
+                var remainingArea = types.Sum(t => remaining[t.Index] * t.Area);
+                var bestRatio = trials.Min(t => t.Net / System.Math.Max(t.Fill.PartArea, 1e-12));
+                var chosen = trials
+                    .Select((t, order) => (t.Fill, t.Net, order, Estimate: t.Net + System.Math.Max(0, remainingArea - t.Fill.PartArea) * bestRatio))
+                    .OrderBy(t => t.Estimate)
+                    .ThenByDescending(t => t.Fill.Parts.Count)
+                    .ThenBy(t => t.order)
+                    .First();
+
+                sheets.Add(chosen.Fill);
+                net += chosen.Net;
+                used[chosen.Fill.Stock.Id]++;
+                foreach (var part in chosen.Fill.Parts)
+                    remaining[part.Orientation.TypeIndex]--;
+            }
+
+            return new Run(sheets, net, reason);
+        }
+    }
+
+    private sealed record Run(IReadOnlyList<SheetFill> Sheets, double Net, NestJobStopReason Reason);
+
+    private static NestJobResult BuildResult(
+        NestJob job,
+        IReadOnlyList<PartType> types,
+        Plan plan,
+        IProgress<NestJobProgress>? progress
+    )
+    {
+        var placed = new int[types.Count];
+        var plates = new List<NestJobPlateResult>(plan.Sheets.Count);
+        var committedParts = 0;
+        foreach (var sheet in plan.Sheets)
+        {
+            var placements = sheet.Parts.Select(p =>
+            {
+                var type = types[p.Orientation.TypeIndex];
+                return new NestJobPlacement(type.Part.Id, placed[type.Index]++, p.X, p.Y, p.Orientation.Rotation);
+            });
+            plates.Add(new NestJobPlateResult(plates.Count, sheet.Stock, placements.ToList()));
+            committedParts += sheet.Parts.Count;
+            progress?.Report(new NestJobProgress(NestJobStage.PlateCommitted, sheet.Stock.Id, plates.Count - 1, plates.Count, committedParts));
+        }
+
+        var fulfillment = types.Select(t => new PartFulfillment(t.Part.Id, t.Part.Quantity, placed[t.Index], t.Part.Quantity - placed[t.Index]));
+        var usage = job.Plates.Select(stock =>
+        {
+            var count = plan.Sheets.Count(s => ReferenceEquals(s.Stock, stock));
+            return new StockUsage(stock.Id, count, stock.Quantity - count);
+        });
+        var status = plan.Unplaced == 0 ? NestJobStatus.Complete : NestJobStatus.Incomplete;
+        return new NestJobResult(status, plan.Reason, plates, fulfillment.ToList(), usage.ToList());
+    }
+
+    private sealed record Plan(IReadOnlyList<SheetFill> Sheets, double Cost, int Unplaced, NestJobStopReason Reason)
+    {
+        public bool IsBetterThan(Plan other)
+        {
+            if (Unplaced != other.Unplaced)
+                return Unplaced < other.Unplaced;
+            var scale = System.Math.Max(1, System.Math.Max(Cost, other.Cost));
+            if (System.Math.Abs(Cost - other.Cost) > 1e-9 * scale)
+                return Cost < other.Cost;
+            return Sheets.Count < other.Sheets.Count;
+        }
+    }
+}
+
+/// <summary>Deterministic effort meter shared by all packers in one solve.</summary>
+internal sealed class WorkCounter
+{
+    private long value;
+    public long Value => Interlocked.Read(ref value);
+    public void Add(long amount) => Interlocked.Add(ref value, amount);
+}

OpenNest.Engine.Opus55/PartCatalog.cs

@@ -0,0 +1,274 @@
+using Clipper2Lib;
+using OpenNest.Converters;
+using OpenNest.Engine.Jobs;
+using OpenNest.Engine.Jobs.Adapters;
+using OpenNest.Geometry;
+
+namespace OpenNest.Engine.Opus55;
+
+/// <summary>
+/// One allowed pose of a part type: its rotation, its polygonized outline at that rotation
+/// (reference point = snapshot origin), and the outline's conservative bounds.
+/// </summary>
+internal sealed class Orientation
+{
+    public required int TypeIndex { get; init; }
+    public required int Index { get; init; }
+    public required double Rotation { get; init; }
+
+    /// <summary>CCW outline whose every point lies within <see cref="Tolerance"/> of the true perimeter.</summary>
+    public required PathD Outline { get; init; }
+
+    /// <summary>Chord deviation used for arcs; footprints are grown by it to stay conservative.</summary>
+    public required double Tolerance { get; init; }
+
+    /// <summary>Outline bounds grown by the tolerance, so they contain the true perimeter.</summary>
+    public required double MinX { get; init; }
+    public required double MinY { get; init; }
+    public required double MaxX { get; init; }
+    public required double MaxY { get; init; }
+
+    public double Width => MaxX - MinX;
+    public double Height => MaxY - MinY;
+}
+
+internal sealed class PartType
+{
+    public required int Index { get; init; }
+    public required NestJobPart Part { get; init; }
+    public required double Area { get; init; }
+    public required IReadOnlyList<Orientation> Orientations { get; init; }
+}
+
+/// <summary>
+/// Converts job snapshots into the polygon world the packer works in. Parts whose geometry
+/// cannot be read are kept with no orientations, so they surface as unplaced instead of
+/// failing the whole job.
+/// </summary>
+internal static class PartCatalog
+{
+    /// <summary>Finest chord deviation of the working outline from true arcs, in job units.</summary>
+    public const double ChordTolerance = 0.002;
+
+    /// <summary>Outline vertex count above which arcs are polygonized more coarsely (NFP cost is ~n*m).</summary>
+    private const int TargetVertices = 64;
+
+    /// <summary>Hard cap on distinct orientations evaluated per part type.</summary>
+    private const int MaxOrientations = 8;
+
+    private const double TwoPi = System.Math.PI * 2;
+
+    public static IReadOnlyList<PartType> Build(NestJob job)
+    {
+        // Fewer orientations per type for jobs with many distinct parts; every (type, rotation)
+        // pair costs a feasible-region update per placement.
+        var perType = System.Math.Clamp(48 / System.Math.Max(1, job.Parts.Count), 2, MaxOrientations);
+        var types = new List<PartType>(job.Parts.Count);
+        for (var index = 0; index < job.Parts.Count; index++)
+        {
+            var part = job.Parts[index];
+            Shape? perimeter;
+            try
+            {
+                perimeter = ReadPerimeter(part.Geometry);
+            }
+            catch (Exception ex) when (ex is ArgumentException or NotSupportedException or InvalidOperationException)
+            {
+                perimeter = null;
+            }
+
+            if (perimeter == null)
+            {
+                types.Add(new PartType { Index = index, Part = part, Area = 0, Orientations = [] });
+                continue;
+            }
+
+            var angles = CandidateAngles(part.Rotation, perimeter, perType);
+            var tolerance = ChooseTolerance(perimeter);
+            var orientations = new List<Orientation>();
+            var signatures = new List<string>();
+            foreach (var angle in angles)
+            {
+                var outline = Polygonize(perimeter, angle, tolerance);
+                if (outline.Count < 3)
+                    continue;
+                // Point-symmetric parts (rectangles, discs...) look identical at several angles;
+                // evaluating duplicates only costs time.
+                var signature = Signature(outline);
+                if (signatures.Contains(signature))
+                    continue;
+                signatures.Add(signature);
+                orientations.Add(MakeOrientation(index, orientations.Count, angle, outline, tolerance));
+            }
+
+            var area = orientations.Count == 0 ? 0 : System.Math.Abs(Clipper.Area(orientations[0].Outline));
+            types.Add(new PartType { Index = index, Part = part, Area = area, Orientations = orientations });
+        }
+        return types;
+    }
+
+    private static Shape? ReadPerimeter(PartGeometrySnapshot geometry)
+    {
+        var entities = ConvertProgram
+            .ToGeometry(DrawingJobMapper.ToProgram(geometry))
+            .Where(e => !ReferenceEquals(e.Layer, SpecialLayers.Rapid))
+            .ToList();
+        if (entities.Count == 0)
+            return null;
+        var profile = new ShapeProfile(entities);
+        return profile.Perimeter is { } perimeter && perimeter.Area() > 1e-9 ? perimeter : null;
+    }
+
+    /// <summary>
+    /// Coarsens arc polygonization (up to 0.1% of the part size) until the outline is small
+    /// enough for cheap Minkowski sums. Lines are always exact, so only arc-heavy parts pay.
+    /// </summary>
+    private static double ChooseTolerance(Shape perimeter)
+    {
+        var box = perimeter.BoundingBox;
+        var cap = System.Math.Max(ChordTolerance, 0.001 * System.Math.Max(box.Width, box.Length));
+        var tolerance = ChordTolerance;
+        while (tolerance * 2 <= cap && perimeter.ToPolygonWithTolerance(tolerance).Vertices.Count > TargetVertices)
+            tolerance *= 2;
+        return tolerance;
+    }
+
+    private static PathD Polygonize(Shape perimeter, double angle, double tolerance)
+    {
+        var shape = (Shape)perimeter.Clone();
+        if (angle != 0)
+            shape.Rotate(angle);
+        var polygon = shape.ToPolygonWithTolerance(tolerance);
+        var path = new PathD(polygon.Vertices.Count);
+        foreach (var v in polygon.Vertices)
+        {
+            if (path.Count > 0 && System.Math.Abs(path[^1].x - v.X) < 1e-9 && System.Math.Abs(path[^1].y - v.Y) < 1e-9)
+                continue;
+            path.Add(new PointD(v.X, v.Y));
+        }
+        if (path.Count > 1 && System.Math.Abs(path[0].x - path[^1].x) < 1e-9 && System.Math.Abs(path[0].y - path[^1].y) < 1e-9)
+            path.RemoveAt(path.Count - 1);
+        if (!Clipper.IsPositive(path))
+            path.Reverse();
+        return path;
+    }
+
+    private static Orientation MakeOrientation(int typeIndex, int index, double angle, PathD outline, double tolerance)
+    {
+        var bounds = Clipper.GetBounds(outline);
+        return new Orientation
+        {
+            TypeIndex = typeIndex,
+            Index = index,
+            Rotation = angle,
+            Outline = outline,
+            Tolerance = tolerance,
+            MinX = bounds.left - tolerance,
+            MinY = bounds.top - tolerance, // Clipper RectD: top is the minimum Y.
+            MaxX = bounds.right + tolerance,
+            MaxY = bounds.bottom + tolerance,
+        };
+    }
+
+    private static string Signature(PathD outline)
+    {
+        var bounds = Clipper.GetBounds(outline);
+        var points = outline
+            .Select(p => (System.Math.Round(p.x - bounds.left, 5), System.Math.Round(p.y - bounds.top, 5)))
+            .OrderBy(p => p.Item1)
+            .ThenBy(p => p.Item2)
+            .Select(p => $"{p.Item1:R},{p.Item2:R}");
+        return string.Join(";", points);
+    }
+
+    /// <summary>
+    /// Rotations to try, all satisfying the part's policy. Automatic parts get the four
+    /// right angles plus the two orientations that align their minimum-area bounding
+    /// rectangle with the sheet axes.
+    /// </summary>
+    internal static List<double> CandidateAngles(RotationPolicy policy, Shape perimeter, int limit)
+    {
+        var raw = new List<double>();
+        switch (policy.Kind)
+        {
+            case RotationPolicyKind.Fixed:
+                raw.Add(policy.Start);
+                if (policy.Allow180Equivalent)
+                    raw.Add(policy.Start + System.Math.PI);
+                break;
+
+            case RotationPolicyKind.BoundedSweep:
+                {
+                    var steps = (int)System.Math.Floor((policy.End - policy.Start) / policy.Step + 1e-9);
+                    var samples = System.Math.Min(steps + 1, policy.Allow180Equivalent ? System.Math.Max(1, limit / 2) : limit);
+                    for (var i = 0; i < samples; i++)
+                    {
+                        var k = samples == 1 ? 0 : (int)System.Math.Round(i * (double)steps / (samples - 1));
+                        raw.Add(policy.Start + k * policy.Step);
+                        if (policy.Allow180Equivalent)
+                            raw.Add(policy.Start + k * policy.Step + System.Math.PI);
+                    }
+                    break;
+                }
+
+            default:
+                {
+                    var rightAngles = new[] { 0, System.Math.PI / 2, System.Math.PI, System.Math.PI * 1.5 };
+                    var aligned = AlignedAngle(perimeter);
+                    raw.Add(0);
+                    raw.Add(System.Math.PI / 2);
+                    if (aligned is double a)
+                    {
+                        raw.Add(Normalize(a));
+                        raw.Add(Normalize(a + System.Math.PI / 2));
+                    }
+                    raw.Add(System.Math.PI);
+                    raw.Add(System.Math.PI * 1.5);
+                    if (aligned is double b)
+                    {
+                        raw.Add(Normalize(b + System.Math.PI));
+                        raw.Add(Normalize(b + System.Math.PI * 1.5));
+                    }
+                    break;
+                }
+        }
+
+        var result = new List<double>();
+        foreach (var angle in raw)
+        {
+            if (!policy.Allows(angle))
+                continue;
+            if (result.Any(existing => SameTurn(existing, angle)))
+                continue;
+            result.Add(angle);
+            if (result.Count >= limit)
+                break;
+        }
+        return result;
+    }
+
+    private static double? AlignedAngle(Shape perimeter)
+    {
+        var polygon = perimeter.ToPolygonWithTolerance(ChordTolerance * 5);
+        if (polygon.Vertices.Count < 3)
+            return null;
+        var mbr = RotatingCalipers.MinimumBoundingRectangle(polygon.Vertices);
+        var angle = Normalize(-mbr.Angle) % (System.Math.PI / 2);
+        // Already axis-aligned (within ~0.05°): the right angles cover it.
+        if (angle < 1e-3 || System.Math.PI / 2 - angle < 1e-3)
+            return null;
+        return angle;
+    }
+
+    private static double Normalize(double angle)
+    {
+        var value = angle % TwoPi;
+        return value < 0 ? value + TwoPi : value;
+    }
+
+    private static bool SameTurn(double a, double b)
+    {
+        var delta = System.Math.Abs(Normalize(a - b));
+        return delta < 1e-9 || TwoPi - delta < 1e-9;
+    }
+}

OpenNest.Engine.Opus55/README.md

@@ -0,0 +1,95 @@
+# OpenNest.Engine.Opus55
+
+An independent whole-job `INestingEngine`: **frontier-advance NFP packing with look-ahead
+stock selection**. It does not call, wrap, or select over any built-in engine
+(`StockLadderNestingEngine`, `FixedStrategyNestingEngine` strategies, `PlateNesterFactory`,
+`NestingEngineRegistry`), nor the removed `OpenNest.Engine/Nfp` bottom-left-fill/annealing code.
+Every placement decision (which part, which rotation, where, on which sheet) comes from the logic below.
+
+## Algorithm
+
+**1. Geometry (`PartCatalog`, `NoFitCache`)**
+- Each part's outer perimeter is polygonized with a known chord tolerance (0.002 by default,
+  coarsened for arc-heavy parts until the outline is ≤ ~64 vertices, capped at 0.1% of part size).
+- Candidate rotations come from the part's `RotationPolicy`: for `Automatic`, the four right
+  angles plus the two orientations that axis-align the minimum-area bounding rectangle
+  (`RotatingCalipers`); for sweeps, up to 8 evenly spaced legal steps. Point-symmetric duplicates are dropped.
+- Each orientation gets a **footprint**: outline inflated (miter joins, so it contains the exact
+  round offset) by `(spacing + 0.022) / 2 + chordTolerance`. Two parts respect the spacing
+  when their footprints don't overlap. The 0.022 covers validators that polygonize arcs
+  circumscribed at 0.01 per side, plus Clipper's 1e-4 grid.
+- **No-fit polygons** between footprints come from Clipper2 Minkowski sums: an O(n+m)
+  edge merge for convex pairs, and for concave pairs the boundary sweep ∪ (A + p₀) ∪ (−B + a₀).
+  The last two terms cover "B inside A" and "B swallows A". NFPs are cached per orientation pair.
+
+**2. Sheet filling (`FrontierPacker`)**
+- For every (part type, orientation) still in play, the packer keeps the exact **free region** of
+  legal reference points: the inner-fit rectangle minus the NFPs of everything placed. Each
+  placement subtracts one translated NFP from each region (in parallel, which stays deterministic).
+  Regions only shrink, and an empty region is retired for the rest of the sheet.
+- At every step all remaining types × orientations compete (there is no fixed placement sequence):
+  1. **Gap fill:** if any part fits without pushing the packing front forward, place the
+     *largest* such part at its lowest point.
+  2. **Advance:** otherwise place the part with the least front advance per `area^β`, i.e. the
+     most material coverage for the sheet length it consumes.
+- The front sweeps along X or Y, which leaves one full-width offcut strip for salvage credit.
+
+**3. Whole job (`Opus55NestingEngine`, `SheetEconomics`)**
+- Sheet by sheet, every available stock size is trial-filled. The trial with the lowest
+  *estimated whole-job cost* (its net area, plus the remaining demand priced at the best
+  efficiency any trial achieved) is committed. This lets a sheet that finishes the job beat a
+  denser partial one.
+- Net area = sheet area − `SalvageRate` × the largest qualifying full-width/full-length edge
+  offcut. This is the objective the benchmark scores.
+- Six strategy variants (front axis X/Y × β ∈ {1, 0.5, 1.5}) each run whole-job, and the cheapest
+  plan wins (fewest unplaced, then cost, then sheets). A **tail re-plan** then re-decodes the
+  parts on the last 1–3 sheets with each stock forced first, and keeps any strictly cheaper result.
+- **Deterministic:** no clock or randomness affects decisions. Effort is capped by a
+  count-based work budget (free-region subtractions), not wall time.
+
+## Layout
+
+| File | Role |
+|---|---|
+| `Opus55NestingEngine.cs` | `Solve()`: demand filtering, variants, stock look-ahead, tail re-plan, result assembly |
+| `FrontierPacker.cs` | One-sheet fill: free regions and the gap-fill/advance choice rule |
+| `NoFitCache.cs` | Spacing footprints and cached NFPs (Clipper2 Minkowski) |
+| `PartCatalog.cs` | Snapshot → perimeter polygon per allowed orientation |
+| `SheetEconomics.cs` | Net-area objective with salvage credit |
+| `tests/` | xUnit suite. Layouts are judged by `OpenNest.Benchmark.NestValidator` |
+
+## Build / test
+
+```bash
+dotnet build OpenNest.Engine.Opus55/OpenNest.Engine.Opus55.csproj -c Release
+dotnet test  OpenNest.Engine.Opus55/tests/OpenNest.Engine.Opus55.Tests.csproj
+```
+
+This project is intentionally **outside** `OpenNest.sln`, the same pattern as the
+`OpenNest.Engine.Aurora` plugin. It's discovered at runtime as a plugin.
+
+## Benchmark
+
+```bash
+dotnet build OpenNest.Benchmark/OpenNest.Benchmark.csproj -c Release
+mkdir -p OpenNest.Benchmark/bin/Release/net8.0/Engines
+cp OpenNest.Engine.Opus55/bin/Release/net8.0/OpenNest.Engine.Opus55.dll OpenNest.Benchmark/bin/Release/net8.0/Engines/
+dotnet OpenNest.Benchmark/bin/Release/net8.0/OpenNest.Benchmark.dll <path-to-.nest-or-manifest-or-folder>
+```
+
+The engine reports as `Opus55NestingEngine`.
+
+## Known limitations
+
+- **No part-in-part:** holes are treated as solid, so small parts never nest inside cutouts.
+- **Clearance padding:** gaps are ~0.022 (plus up to the chord tolerance) wider than the
+  required spacing, to stay valid under circumscribed-polygon validators. That's negligible in mm
+  and about 0.02" in inches. The constants are absolute and assume job units near inch/mm scale.
+- **Rotation coverage:** `Automatic` parts try at most 8 orientations (fewer when a job has many
+  distinct parts: `48 / partCount`, minimum 2). Free-angle rotations aren't explored beyond the MBR alignment.
+- **Greedy core:** there is no order/permutation search. The variants and tail re-plan are the only
+  search, and density on small mixed jobs trails what an interlocking-pair filler can reach.
+- **`NestJobPart.Priority` is ignored**, and progress reports only `EvaluatingCandidate`
+  per trial and `PlateCommitted` at the end, with no finer-grained progress.
+- Parts whose geometry has no readable closed perimeter, or that fit no offered stock at any
+  allowed rotation, are reported unplaced (`NoPlacementFound`) instead of failing the job.

OpenNest.Engine.Opus55/SheetEconomics.cs

@@ -0,0 +1,41 @@
+using OpenNest.Engine.Jobs;
+
+namespace OpenNest.Engine.Opus55;
+
+/// <summary>
+/// The objective the engine optimizes: sheet area consumed, less the salvage credit for the
+/// single largest full-width or full-length edge offcut the job's options allow. Packing toward
+/// one edge (see <see cref="PackAxis"/>) is what makes that offcut large.
+/// </summary>
+internal static class SheetEconomics
+{
+    public static double SheetArea(NestPlateStock stock) => stock.Size.Width * stock.Size.Length;
+
+    public static double NetArea(NestJobOptions options, SheetFill fill)
+    {
+        var area = SheetArea(fill.Stock);
+        var minimum = options.MinimumSalvageDimension;
+        if (options.SalvageRate <= 0 || minimum <= 0 || fill.Parts.Count == 0)
+            return area;
+
+        var work = FrontierPacker.WorkArea(fill.Stock);
+        var gap = fill.Stock.PartSpacing;
+        var left = fill.Parts.Min(p => p.Left);
+        var right = fill.Parts.Max(p => p.Right);
+        var bottom = fill.Parts.Min(p => p.Bottom);
+        var top = fill.Parts.Max(p => p.Top);
+        var offcuts = new[]
+        {
+            // Box.Length is the X extent, Box.Width the Y extent.
+            (work.Length, bottom - work.Bottom - gap),
+            (work.Length, work.Top - top - gap),
+            (left - work.Left - gap, work.Width),
+            (work.Right - right - gap, work.Width),
+        };
+        var salvage = 0.0;
+        foreach (var (a, b) in offcuts)
+            if (a >= minimum && b >= minimum)
+                salvage = System.Math.Max(salvage, a * b);
+        return area - options.SalvageRate * salvage;
+    }
+}

OpenNest.Engine.Opus55/tests/NoFitCacheTests.cs

@@ -0,0 +1,68 @@
+using System.Linq;
+using Clipper2Lib;
+using OpenNest.CNC;
+using OpenNest.Engine.Jobs;
+using OpenNest.Geometry;
+
+namespace OpenNest.Engine.Opus55.Tests;
+
+public class NoFitCacheTests
+{
+    [Theory]
+    [InlineData(0.0, 0.0)] // B's corner at A's corner: B covers A completely.
+    [InlineData(-5.0, -5.0)] // A deep inside B.
+    [InlineData(2.0, 0.5)] // Partial overlap.
+    public void ForbidsEveryOverlappingOffsetIncludingContainment(double dx, double dy)
+    {
+        var (small, big) = Orientations();
+        var nfp = new NoFitCache(0.1).Get(small, big);
+
+        Assert.True(Forbidden(nfp, new PointD(dx, dy)), $"offset ({dx}, {dy}) should be forbidden");
+    }
+
+    [Theory]
+    [InlineData(4.0, 0.0)] // Beside A, clear by more than the clearance.
+    [InlineData(0.0, -21.0)] // Below A.
+    [InlineData(-21.0, 0.0)] // Left of A.
+    public void AllowsClearOffsets(double dx, double dy)
+    {
+        var (small, big) = Orientations();
+        var nfp = new NoFitCache(0.1).Get(small, big);
+
+        Assert.False(Forbidden(nfp, new PointD(dx, dy)), $"offset ({dx}, {dy}) should be free");
+    }
+
+    /// <summary>A = 3x3 L (concave), B = 20x20 square; both at rotation 0 with origin at the lower-left.</summary>
+    private static (Orientation Small, Orientation Big) Orientations()
+    {
+        var job = new NestJob(
+            new[]
+            {
+                new NestJobPart("small", Snapshot((0, 0), (3, 0), (3, 1), (1, 1), (1, 3), (0, 3)), 1, 0, RotationPolicy.Fixed(0)),
+                new NestJobPart("big", Snapshot((0, 0), (20, 0), (20, 20), (0, 20)), 1, 0, RotationPolicy.Fixed(0)),
+            },
+            new[] { new NestPlateStock("s", new Size(100, 100)) }
+        );
+        var types = PartCatalog.Build(job);
+        return (types[0].Orientations.Single(), types[1].Orientations.Single());
+    }
+
+    private static bool Forbidden(Nfp nfp, PointD point)
+    {
+        var winding = 0;
+        foreach (var path in nfp.Region)
+            if (Clipper.PointInPolygon(point, path) == PointInPolygonResult.IsInside)
+                winding += Clipper.IsPositive(path) ? 1 : -1;
+        return winding != 0;
+    }
+
+    private static PartGeometrySnapshot Snapshot(params (double X, double Y)[] points)
+    {
+        var program = new Program();
+        program.Codes.Add(new RapidMove(points[0].X, points[0].Y));
+        foreach (var (x, y) in points.Skip(1))
+            program.Codes.Add(new LinearMove(x, y));
+        program.Codes.Add(new LinearMove(points[0].X, points[0].Y));
+        return PartGeometrySnapshot.FromProgram(program);
+    }
+}

OpenNest.Engine.Opus55/tests/OpenNest.Engine.Opus55.Tests.csproj

@@ -13,7 +13,9 @@
   </ItemGroup>
   <ItemGroup>
     <Using Include="Xunit" />
-    <ProjectReference Include="../OpenNest.Engine.Sonnet5.csproj" />
+    <ProjectReference Include="../OpenNest.Engine.Opus55.csproj" />
     <ProjectReference Include="../../OpenNest.Engine/OpenNest.Engine.csproj" />
+    <!-- The benchmark's NestValidator is the arbiter the engine is scored by. -->
+    <ProjectReference Include="../../OpenNest.Benchmark/OpenNest.Benchmark.csproj" />
   </ItemGroup>
 </Project>

OpenNest.Engine.Opus55/tests/Opus55NestingEngineTests.cs

@@ -0,0 +1,283 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using OpenNest.Benchmark;
+using OpenNest.CNC;
+using OpenNest.Engine.Jobs;
+using OpenNest.Engine.Jobs.Adapters;
+using OpenNest.Geometry;
+
+namespace OpenNest.Engine.Opus55.Tests;
+
+public class Opus55NestingEngineTests
+{
+    [Fact]
+    public void RectanglesFitOnOneSheetWithSpacing()
+    {
+        var job = Job(new[] { Part("rect", Rectangle(10, 5), 12) }, new[] { Stock("sheet", 48, 96, spacing: 0.25) });
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+        Assert.Single(result.Plates);
+        Assert.Equal(12, result.Plates[0].Placements.Count);
+    }
+
+    [Theory]
+    [InlineData(1)]
+    [InlineData(2)]
+    [InlineData(3)]
+    [InlineData(4)]
+    public void MixedArcAndConcavePartsAreValidInEveryQuadrant(int quadrant)
+    {
+        var job = Job(
+            new[]
+            {
+                Part("disc", Disc(3), 10),
+                Part("ell", LShape(12, 8, 4), 10),
+                Part("tri", Triangle(9, 6), 10),
+                Part("slot", Obround(10, 3), 6),
+            },
+            new[] { Stock("sheet", 40, 60, spacing: 0.5, edge: new Spacing(0.5, 0.5, 0.5, 0.5), quadrant: quadrant) }
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+    }
+
+    [Fact]
+    public void ZeroSpacingStillKeepsPartsApartForValidation()
+    {
+        var job = Job(new[] { Part("disc", Disc(2), 30), Part("rect", Rectangle(7, 3), 20) }, new[] { Stock("sheet", 30, 40) });
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+    }
+
+    [Fact]
+    public void LargeAndSmallConcavePartsShareASheet()
+    {
+        // End-to-end companion to NoFitCacheTests' containment cases (the precise regression guard).
+        var job = Job(
+            new[] { Part("small", LShape(3, 3, 1), 6), Part("big", Rectangle(20, 20), 2) },
+            new[] { Stock("sheet", 25, 45, spacing: 0.25) }
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+    }
+
+    [Fact]
+    public void PicksTheCheaperSheetWhenItHoldsEverything()
+    {
+        var job = Job(
+            new[] { Part("square", Rectangle(10, 10), 4) },
+            new[] { Stock("big", 60, 120, spacing: 0.25), Stock("small", 25, 25, spacing: 0.25) }
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+        Assert.Equal("small", Assert.Single(result.Plates).StockId);
+    }
+
+    [Fact]
+    public void SpillsOntoAdditionalSheets()
+    {
+        var job = Job(new[] { Part("rect", Rectangle(20, 10), 25) }, new[] { Stock("sheet", 30, 50, spacing: 0.5) });
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Complete, result.Status);
+        Assert.True(result.Plates.Count > 1);
+        Assert.Equal(25, result.Plates.Sum(p => p.Placements.Count));
+        var indices = result.Plates.SelectMany(p => p.Placements).Select(p => p.InstanceIndex).OrderBy(i => i);
+        Assert.Equal(Enumerable.Range(0, 25), indices);
+    }
+
+    [Fact]
+    public void RespectsFixedAndBoundedRotationPolicies()
+    {
+        var fixedPolicy = RotationPolicy.Fixed(0);
+        var sweep = RotationPolicy.BoundedSweep(0, System.Math.PI / 2, System.Math.PI / 4);
+        var job = Job(
+            new[]
+            {
+                Part("fixed", LShape(10, 6, 3), 8, fixedPolicy),
+                Part("swept", Triangle(8, 5), 8, sweep),
+            },
+            new[] { Stock("sheet", 40, 60, spacing: 0.25) }
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        foreach (var placement in result.Plates.SelectMany(p => p.Placements))
+        {
+            var policy = placement.PartId == "fixed" ? fixedPolicy : sweep;
+            Assert.True(policy.Allows(placement.Rotation), $"{placement.PartId} at {placement.Rotation}");
+        }
+    }
+
+    [Fact]
+    public void OversizedPartIsReportedUnplacedWithoutBlockingOthers()
+    {
+        var job = Job(
+            new[] { Part("huge", Rectangle(100, 100), 1), Part("small", Rectangle(5, 5), 3) },
+            new[] { Stock("sheet", 20, 20) }
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStatus.Incomplete, result.Status);
+        Assert.Equal(NestJobStopReason.NoPlacementFound, result.StopReason);
+        Assert.Equal(1, result.Fulfillment.Single(f => f.PartId == "huge").Unplaced);
+        Assert.Equal(3, result.Fulfillment.Single(f => f.PartId == "small").Placed);
+    }
+
+    [Fact]
+    public void StopsWhenFiniteStockRunsOut()
+    {
+        var job = Job(new[] { Part("rect", Rectangle(9, 9), 20) }, new[] { Stock("sheet", 20, 20, quantity: 2) });
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Equal(NestJobStopReason.StockExhausted, result.StopReason);
+        Assert.Equal(2, result.Plates.Count);
+        var usage = Assert.Single(result.StockUsage);
+        Assert.Equal(2, usage.Used);
+        Assert.Equal(0, usage.Remaining);
+    }
+
+    [Fact]
+    public void HonorsMaxPlates()
+    {
+        var job = Job(
+            new[] { Part("rect", Rectangle(9, 9), 20) },
+            new[] { Stock("sheet", 20, 20) },
+            new NestJobOptions(maxPlates: 1)
+        );
+
+        var result = new Opus55NestingEngine().Solve(job);
+
+        AssertValid(job, result);
+        Assert.Single(result.Plates);
+        Assert.Equal(NestJobStopReason.PlateLimitReached, result.StopReason);
+    }
+
+    [Fact]
+    public void IsDeterministic()
+    {
+        NestJob Build() =>
+            Job(
+                new[] { Part("disc", Disc(2.5), 12), Part("ell", LShape(9, 7, 3), 12), Part("tri", Triangle(7, 7), 12) },
+                new[] { Stock("a", 30, 45, spacing: 0.3), Stock("b", 40, 40, spacing: 0.3) }
+            );
+
+        var first = new Opus55NestingEngine().Solve(Build());
+        var second = new Opus55NestingEngine().Solve(Build());
+
+        Assert.Equal(Describe(first), Describe(second));
+    }
+
+    [Fact]
+    public void HasPublicParameterlessConstructorForPluginDiscovery()
+    {
+        var engine = Activator.CreateInstance(typeof(Opus55NestingEngine));
+        Assert.IsAssignableFrom<INestingEngine>(engine);
+    }
+
+    // ---- helpers -------------------------------------------------------------------------
+
+    private static string Describe(NestJobResult result) =>
+        string.Join(
+            "|",
+            result.Plates.Select(p =>
+                p.StockId + ":" + string.Join(",", p.Placements.Select(x => $"{x.PartId}#{x.InstanceIndex}@{x.X:R},{x.Y:R},{x.Rotation:R}"))
+            )
+        );
+
+    private static void AssertValid(NestJob job, NestJobResult result)
+    {
+        var materialized = NestResultMaterializer.Materialize(job, result);
+        var runs = materialized.Nest.Plates.Select(plate => (Plate: plate, Parts: plate.Parts.ToList())).ToList();
+        var requirements = job.Parts.ToDictionary<NestJobPart, Drawing, (string Name, int Quantity)>(
+            p => materialized.DrawingsByPartId[p.Id],
+            p => (p.Id, p.Quantity),
+            ReferenceEqualityComparer.Instance
+        );
+        var validation = NestValidator.Validate(runs, requirements);
+        NestValidator.ValidateAgainstJob(job, result, job.Parts.ToDictionary(p => p.Id, p => p.Id), validation);
+        Assert.True(validation.Valid, string.Join(Environment.NewLine, validation.Violations));
+
+        foreach (var f in result.Fulfillment)
+            Assert.Equal(f.Requested, f.Placed + f.Unplaced);
+    }
+
+    private static NestJob Job(NestJobPart[] parts, NestPlateStock[] stock, NestJobOptions? options = null) =>
+        new(parts, stock, options);
+
+    private static NestJobPart Part(string id, Program program, int quantity, RotationPolicy? rotation = null) =>
+        new(id, PartGeometrySnapshot.FromProgram(program), quantity, 0, rotation);
+
+    /// <param name="width">Y extent.</param>
+    /// <param name="length">X extent.</param>
+    private static NestPlateStock Stock(
+        string id,
+        double width,
+        double length,
+        double spacing = 0,
+        Spacing edge = default,
+        int quadrant = 1,
+        int? quantity = null
+    ) => new(id, new Size(width, length), quantity, spacing, edge, quadrant);
+
+    private static Program Polyline(params (double X, double Y)[] points)
+    {
+        var program = new Program();
+        program.Codes.Add(new RapidMove(points[0].X, points[0].Y));
+        foreach (var (x, y) in points.Skip(1))
+            program.Codes.Add(new LinearMove(x, y));
+        program.Codes.Add(new LinearMove(points[0].X, points[0].Y));
+        return program;
+    }
+
+    private static Program Rectangle(double w, double h) => Polyline((0, 0), (w, 0), (w, h), (0, h));
+
+    private static Program Triangle(double w, double h) => Polyline((0, 0), (w, 0), (w * 0.3, h));
+
+    private static Program LShape(double w, double h, double t) => Polyline((0, 0), (w, 0), (w, t), (t, t), (t, h), (0, h));
+
+    private static Program Disc(double r)
+    {
+        var program = new Program();
+        program.Codes.Add(new RapidMove(r, 0));
+        program.Codes.Add(new ArcMove(-r, 0, 0, 0, RotationType.CCW));
+        program.Codes.Add(new ArcMove(r, 0, 0, 0, RotationType.CCW));
+        return program;
+    }
+
+    /// <summary>Stadium: two semicircular ends joined by straight sides, offset from the origin.</summary>
+    private static Program Obround(double length, double width)
+    {
+        var r = width / 2;
+        var program = new Program();
+        program.Codes.Add(new RapidMove(1 + r, 1));
+        program.Codes.Add(new LinearMove(1 + length - r, 1));
+        program.Codes.Add(new ArcMove(1 + length - r, 1 + width, 1 + length - r, 1 + r, RotationType.CCW));
+        program.Codes.Add(new LinearMove(1 + r, 1 + width));
+        program.Codes.Add(new ArcMove(1 + r, 1, 1 + r, 1 + r, RotationType.CCW));
+        return program;
+    }
+}

OpenNest.Engine.Sonnet5/README.md

@@ -1,57 +0,0 @@
-# OpenNest.Engine.Sonnet5
-
-An independent `INestingEngine` implementation — **not** a wrapper, ensemble, or
-selector over OpenNest's built-in engines (`StockLadderNestingEngine`,
-`FixedStrategyNestingEngine` "Default"/"Strip"/"Vertical Remnant"/"Horizontal Remnant`,
-or anything reachable through `PlateNesterFactory`/`NestingEngineRegistry`).
-`Solve()` must never call, instantiate, or otherwise delegate a placement decision
-to one of those.
-
-## Allowed building blocks
-
-Low-level geometry/data-structure primitives are fair game — they are not nesting
-strategies:
-
-- `OpenNest.Core` geometry: `Polygon`, `Shape`, `BoundingBox`, `Vector`, `Box`,
-  `ConvexHull`, `ConvexDecomposition`, `RotatingCalipers`, `Collision` (overlap/spacing
-  checks), `NoFitPolygon`, `ShapeProfile`, `SpatialQuery`.
-- `OpenNest.Engine` support types if useful: `PartBoundary`, `RotationAnalysis`,
-  `AngleCandidateBuilder` — the *decision logic* using them must be your own (don't just
-  call `BestFitFinder`/`PairEvaluator`/`RotationSlideStrategy`, which are the existing
-  best-fit engine's internals).
-
-## What to fill in
-
-`Sonnet5NestingEngine.cs` — implement `Solve()`. Pick and document an actual
-placement strategy (NFP-based sliding placement, skyline/shelf packer,
-simulated-annealing/genetic layout search, guillotine-cut packer,
-physics/gravity-settling, etc). It's fine to be simpler or worse than the built-in
-engines to start; it must not be the same algorithm re-derived through indirection.
-
-## Build
-
-```bash
-dotnet build OpenNest.Engine.Sonnet5/OpenNest.Engine.Sonnet5.csproj
-```
-
-This project is intentionally **outside** `OpenNest.sln` (same pattern as the
-`OpenNest.Engine.Aurora` plugin) — it's discovered at runtime as a plugin, not built
-as part of the main solution.
-
-## Try it out with the benchmark
-
-`OpenNest.Benchmark` auto-loads plugin engines from an `Engines/` folder next to its
-own build output:
-
-```bash
-dotnet build OpenNest.Engine.Sonnet5/OpenNest.Engine.Sonnet5.csproj -c Release
-dotnet build OpenNest.Benchmark/OpenNest.Benchmark.csproj -c Release
-
-mkdir -p OpenNest.Benchmark/bin/Release/net8.0/Engines
-cp OpenNest.Engine.Sonnet5/bin/Release/net8.0/OpenNest.Engine.Sonnet5.dll    OpenNest.Benchmark/bin/Release/net8.0/Engines/
-
-dotnet OpenNest.Benchmark/bin/Release/net8.0/OpenNest.Benchmark.dll <path-to-.nest-or-folder>
-```
-
-Your engine will show up in the report under its CLR type name (`Sonnet5NestingEngine`),
-competing on equal footing against the built-in engines.

OpenNest.Engine.Sonnet5/Sonnet5NestingEngine.cs

@@ -1,41 +0,0 @@
-using System;
-using System.Threading;
-using OpenNest.Engine.Jobs;
-
-namespace OpenNest.Engine.Sonnet5;
-
-/// <summary>
-/// TODO: name and describe the actual placement strategy here (e.g. "skyline packer with
-/// greedy shelf assignment", "NFP-based sliding placement with simulated-annealing order
-/// search", etc). This must be an independently designed algorithm — see README.md.
-/// </summary>
-public sealed class Sonnet5NestingEngine : INestingEngine
-{
-    public NestJobResult Solve(
-        NestJob job,
-        IProgress<NestJobProgress>? progress = null,
-        CancellationToken token = default
-    )
-    {
-        ArgumentNullException.ThrowIfNull(job);
-
-        // TODO: implement independent placement logic here.
-        //
-        // Do NOT call NestingEngineRegistry.Create(...), PlateNesterFactory, or any
-        // FixedStrategyNestingEngine / StockLadderNestingEngine instance from inside this
-        // method. Decide placements yourself using OpenNest.Core / OpenNest.Geometry
-        // primitives (Polygon, NoFitPolygon, Collision, ConvexHull, RotatingCalipers, etc).
-        //
-        // job.Parts        -> requested parts (PartGeometrySnapshot geometry, quantity, priority, rotation policy)
-        // job.Plates        -> candidate stock sheets (size, spacing, quadrant, quantity)
-        // job.Options       -> job-wide options
-        //
-        // Return a NestJobResult built from NestJobPlateResult (one per used sheet, holding
-        // ordered NestJobPlacement values), PartFulfillment (requested vs placed per part id),
-        // and StockUsage (sheets used per stock id).
-
-        throw new NotImplementedException(
-            "Sonnet5 nesting engine placement logic not yet implemented."
-        );
-    }
-}

OpenNest.Engine.Sonnet5/tests/Sonnet5NestingEngineTests.cs

@@ -1,20 +0,0 @@
-using System;
-using System.Collections.Generic;
-using OpenNest.Engine.Jobs;
-using OpenNest.Geometry;
-
-namespace OpenNest.Engine.Sonnet5.Tests;
-
-public class Sonnet5NestingEngineTests
-{
-    [Fact]
-    public void SolveReturnsAResultForASingleSimplePart()
-    {
-        // TODO: replace with a real fixture once Solve() is implemented — this only
-        // proves the plumbing (project reference, constructor, interface) is wired up.
-        var engine = new Sonnet5NestingEngine();
-
-        Assert.NotNull(engine);
-        Assert.IsAssignableFrom<INestingEngine>(engine);
-    }
-}