OpenNest-Engines/OpenNest.Engine.Qwen38FlashNext/Engine/SheetPacker.cs

using System;
using System.Collections.Generic;
using OpenNest.Engine.Jobs;
using OpenNest.Geometry;
using OpenNest.Math;

namespace OpenNest.Engine.Qwen38FlashNext.Engine;

using Math = System.Math;

/// <summary>A committed placement: model, orientation, and origin position on the sheet.</summary>
internal readonly struct PlacedPart
{
    public PlacedPart(PartModel model, OrientationModel orientation, double x, double y)
    {
        Model = model;
        Orientation = orientation;
        X = x;
        Y = y;
    }

    public PartModel Model { get; }
    public OrientationModel Orientation { get; }
    public double X { get; }
    public double Y { get; }
}

internal readonly struct PlacementResult
{
    public PlacementResult(PlacedPart part)
    {
        Part = part;
    }

    public PlacedPart Part { get; }
}

/// <summary>
/// One sheet packed by this engine's own algorithm: bottom-left greedy insertion of
/// convex NFP corner candidates.
/// <para>
/// For each candidate orientation the packer builds a convex No-Fit-Polygon per
/// already-placed part as placedHull (+) disk(spacing) (+) reflect(candidateHull) -
/// a superset of the true NFP because hulls ignore concavities and cutouts, so an
/// anchor outside every NFP plus inside the anchor work-box is always legal ("strict"
/// certification). An anchor inside an NFP is still accepted when the exact material
/// gate says the parts clear: that gate inflates the placed part's material by the
/// spacing (holes shrunk, closed holes treated solid) and tests it against the
/// candidate's raw material with holes subtracted - the same inflation rule the
/// benchmark validator uses, so interlocking concave parts are recovered without ever
/// accepting an overlap or a spacing violation.
/// </para>
/// <para>
/// Candidate anchors are the corner points of the feasible region: the four anchor
/// work-box corners, every NFP vertex, and every NFP-edge/box-line crossing (slides).
/// Candidates are tried in ascending bottom-left order and the first legal one wins.
/// </para>
/// </summary>
internal sealed class SheetPacker
{
    private const int MaxHullVertices = 40;

    private readonly double _workLeft;
    private readonly double _workBottom;
    private readonly double _workRight;
    private readonly double _workTop;

    // Per-placed-part caches (indexed by placement order).
    private readonly List<Bounds> _inflatedBounds = new();
    private readonly List<(Polygon Perimeter, List<Polygon> Holes)> _placedGate = new();

    /// <summary>
    /// Fast-path outlines of the placed parts' gate material in world coordinates,
    /// parallel to <see cref="_placedGate"/> (O(1) translation of the shared per-
    /// orientation template). A <see cref="FastPoly.Clears"/> hit certifies the two
    /// outer shells - hence both materials - are clear and skips the exact
    /// <see cref="Collision"/> gate, which at fine flattening triangulates thousands
    /// of edges per call. Null when the outline has no usable ring.
    /// </summary>
    private readonly List<FastPoly?> _placedGateFast = new();

    // NFP caches: (placedIndex, orientationId) -> forbidden-anchor contour.
    private readonly Dictionary<(int, int), ConvexContour?> _nfpCache = new();
    private readonly Dictionary<OrientationModel, int> _orientationIds = new();

    /// <summary>
    /// Per-orientation cache of NFP/NFP valley anchors (anchors touching two placed
    /// parts at once). A committed part's NFP never changes and <see cref="Placed"/>
    /// only grows, so each (i, j) pair is intersected exactly once per orientation
    /// instead of once per candidate enumeration - the re-sweep was the dominant cost
    /// on crowded sheets (O(placed^2 * edges^2) per insert attempt).
    /// </summary>
    private sealed class ValleyCache
    {
        public int BuiltThrough;
        public readonly List<(double X, double Y)> Valleys = new();
    }

    private readonly Dictionary<OrientationModel, ValleyCache> _valleyCaches = new();
    private readonly Dictionary<OrientationModel, ConvexContour> _reflectedHulls = new();
    private readonly Dictionary<int, ConvexContour> _placedHullDisk = new();
    private ConvexContour? _disk;

    // Uniform spatial grid over placed parts' inflated bounds: IsLegal only tests the
    // parts whose cells touch the candidate's cells, so legality stays near-constant
    // as a sheet fills instead of scanning every placed part.
    private readonly double _cellSize;
    private readonly int _gridCols;
    private readonly int _gridRows;
    private readonly List<int>[] _grid;

    private SheetPacker(NestPlateStock stock, PartPreparation prep, int stockIndex)
    {
        Stock = stock;
        StockIndex = stockIndex;
        Preparation = prep;
        Spacing = stock.PartSpacing;
        var work = stock.WorkArea;
        _workLeft = work.Left;
        _workBottom = work.Bottom;
        _workRight = work.Right;
        _workTop = work.Top;
        WorkWidth = _workRight - _workLeft;
        WorkHeight = _workTop - _workBottom;

        // Cells roughly the size of a mid-range part: a candidate usually touches 2-6.
        _cellSize = System.Math.Max(1.0, System.Math.Min(WorkWidth, WorkHeight) / 12.0);
        _gridCols = System.Math.Max(1, (int)System.Math.Ceiling(WorkWidth / _cellSize));
        _gridRows = System.Math.Max(1, (int)System.Math.Ceiling(WorkHeight / _cellSize));
        _grid = new List<int>[_gridCols * _gridRows];
        for (var i = 0; i < _grid.Length; i++)
            _grid[i] = new List<int>();
    }

    public static SheetPacker Create(NestPlateStock stock, PartPreparation prep, int stockIndex) =>
        new(stock, prep, stockIndex);

    public NestPlateStock Stock { get; }
    public int StockIndex { get; }
    public PartPreparation Preparation { get; }
    public double Spacing { get; }
    public double WorkWidth { get; }
    public double WorkHeight { get; }

    public List<PlacedPart> Placed { get; } = new();

    public bool IsFull => Placed.Count >= MaxPartsPerSheet;

    /// <summary>
    /// Safety cap on parts per sheet: real sheets never exceed this, and it bounds
    /// per-insert NFP work and the validator's area budget on pathological jobs.
    /// </summary>
    public const int MaxPartsPerSheet = 500;

    /// <summary>True when the part's bounds can never fit this sheet in any orientation.</summary>
    public bool CanEverFit(PartModel model)
    {
        foreach (var angle in PartPreparation.CandidateAngles(model))
        {
            var orientation = Preparation.Oriented(model, angle, 0);
            if (Stock.Fits(orientation.Width, orientation.Height))
                return true;
        }
        return false;
    }

    internal long DiagInsertAttempts;
    internal long DiagCandidateChecks;
    internal long DiagGateCalls;
    internal long DiagConvexRejections;
    internal long DiagFastClears;
    internal long DiagFastNull;
    internal long DiagFastOverlapWithHoles;
    internal long DiagFastOverlaps;
    internal long DiagFastUnknowns;

    public string DiagStats() =>
        $"inserts={DiagInsertAttempts} checks={DiagCandidateChecks} gates={DiagGateCalls} " +
        $"convexRej={DiagConvexRejections} fastClear={DiagFastClears} fastOver={DiagFastOverlaps} fastUnk={DiagFastUnknowns} fastNull={DiagFastNull} fastOverHoles={DiagFastOverlapWithHoles} triNull={DiagTriNull} triNullOut={DiagTriNullOut} triFallback={DiagTriFallback}";

    /// <summary>
    /// Greedily insert an instance: best (bottom-left) legal corner over all candidate
    /// orientations. Returns false (and changes nothing) when no legal position exists.
    /// </summary>
    public bool TryInsert(PartModel model, out PlacementResult result)
    {
        result = default;
        var bestScore = double.MaxValue;
        PlacedPart? best = null;
        DiagInsertAttempts++;

        foreach (var angle in PartPreparation.CandidateAngles(model))
        {
            var orientation = Preparation.Oriented(model, angle, Spacing);
            if (orientation.Width > WorkWidth + 1e-9 || orientation.Height > WorkHeight + 1e-9)
                continue;

            foreach (var (x, y) in OrderedCandidates(orientation))
            {
                var score = Score(orientation, x, y);
                if (score >= bestScore)
                    continue; // no later candidate (same sort) can beat it
                if (!IsLegal(orientation, x, y))
                    continue;
                bestScore = score;
                best = new PlacedPart(model, orientation, x, y);
                break; // first legal in ascending-score order is this orientation's best
            }
        }

        if (best == null)
            return false;

        Commit(best.Value);
        result = new PlacementResult(best.Value);
        return true;
    }

    private double Score(OrientationModel orientation, double x, double y) =>
        x + orientation.MinX + (y + orientation.MinY) * 1.0001;

    /// <summary>
    /// Corner candidates in deterministic ascending bottom-left order: anchor work-box
    /// corners, NFP vertices, and NFP-edge/box-line crossings.
    /// </summary>
    private List<(double x, double y)> OrderedCandidates(OrientationModel orientation)
    {
        var boxLeft = _workLeft - orientation.MinX;
        var boxRight = _workRight - orientation.MaxX;
        var boxBottom = _workBottom - orientation.MinY;
        var boxTop = _workTop - orientation.MaxY;

        var seen = new HashSet<(long, long)>();
        var candidates = new List<(double, double)>(128);

        // Math.Clamp throws when min > max, and a part that fits the work area to
        // within floating-point noise can invert the anchor box by ~1e-14. Order the
        // bounds so a degenerate box collapses to its single legal point.
        var anchorMinX = Math.Min(boxLeft, boxRight);
        var anchorMaxX = Math.Max(boxLeft, boxRight);
        var anchorMinY = Math.Min(boxBottom, boxTop);
        var anchorMaxY = Math.Max(boxBottom, boxTop);

        void Add(double x, double y)
        {
            if (x < anchorMinX - 1e-9 || x > anchorMaxX + 1e-9 || y < anchorMinY - 1e-9 || y > anchorMaxY + 1e-9)
                return;
            x = Math.Clamp(x, anchorMinX, anchorMaxX);
            y = Math.Clamp(y, anchorMinY, anchorMaxY);
            if (!seen.Add(((long)Math.Round(x * 1e6), (long)Math.Round(y * 1e6))))
                return;
            candidates.Add((x, y));
        }

        Add(boxLeft, boxBottom);
        Add(boxRight, boxBottom);
        Add(boxLeft, boxTop);
        Add(boxRight, boxTop);

        for (var i = 0; i < Placed.Count; i++)
        {
            var nfp = NfpFor(i, orientation);
            if (nfp == null)
                continue;
            var n = nfp.Count;
            for (var v = 0; v < n; v++)
                Add(nfp.X(v), nfp.Y(v));
            // Slides: NFP edges crossing the anchor box border lines.
            for (var v = 0; v < n; v++)
            {
                var ax = nfp.X(v);
                var ay = nfp.Y(v);
                var bx = nfp.X((v + 1) % n);
                var by = nfp.Y((v + 1) % n);
                CrossLine(ax, ay, bx, by, boxLeft, true, Add);
                CrossLine(ax, ay, bx, by, boxRight, true, Add);
                CrossLine(ax, ay, bx, by, boxBottom, false, Add);
                CrossLine(ax, ay, bx, by, boxTop, false, Add);
            }
        }

        // Valleys between two neighbors: NFP/NFP edge intersections are the anchors
        // where the candidate touches two placed parts at once - the classic
        // bottom-left stable corners the single-NFP candidates cannot produce.
        foreach (var (vx, vy) in ValleysFor(orientation))
            Add(vx, vy);

        candidates.Sort(
            (p, q) =>
            {
                var byY = p.Item2.CompareTo(q.Item2);
                return byY != 0 ? byY : p.Item1.CompareTo(q.Item1);
            }
        );
        return candidates;
    }

    /// <summary>
    /// Cached NFP/NFP valley anchors for one orientation, extended in place with the
    /// pairs involving placements committed since the last call. Each (i, j) pair is
    /// intersected once per orientation for the packer's lifetime.
    /// </summary>
    private List<(double X, double Y)> ValleysFor(OrientationModel orientation)
    {
        if (!_valleyCaches.TryGetValue(orientation, out var cache))
        {
            cache = new ValleyCache();
            _valleyCaches[orientation] = cache;
        }

        var count = Placed.Count;
        for (var j = cache.BuiltThrough; j < count; j++)
        {
            var nfpB = NfpFor(j, orientation);
            if (nfpB == null)
                continue;
            for (var i = 0; i < j; i++)
            {
                var nfpA = NfpFor(i, orientation);
                if (nfpA == null || !nfpA.Bounds.Intersects(nfpB.Bounds))
                    continue;
                var na = nfpA.Count;
                var nb = nfpB.Count;
                for (var va = 0; va < na; va++)
                {
                    var a0x = nfpA.X(va);
                    var a0y = nfpA.Y(va);
                    var a1x = nfpA.X((va + 1) % na);
                    var a1y = nfpA.Y((va + 1) % na);
                    for (var vb = 0; vb < nb; vb++)
                    {
                        var b0x = nfpB.X(vb);
                        var b0y = nfpB.Y(vb);
                        var b1x = nfpB.X((vb + 1) % nb);
                        var b1y = nfpB.Y((vb + 1) % nb);
                        if (
                            Math.Max(a0x, a1x) < Math.Min(b0x, b1x)
                            || Math.Max(b0x, b1x) < Math.Min(a0x, a1x)
                            || Math.Max(a0y, a1y) < Math.Min(b0y, b1y)
                            || Math.Max(b0y, b1y) < Math.Min(a0y, a1y)
                        )
                            continue;
                        var r = SegmentIntersect(
                            a0x, a0y, a1x, a1y,
                            b0x, b0y, b1x, b1y
                        );
                        if (r.HasValue)
                            cache.Valleys.Add((r.Value.X, r.Value.Y));
                    }
                }
            }
        }
        cache.BuiltThrough = count;
        return cache.Valleys;
    }

    /// <summary>Proper or endpoint intersection of two segments, if any.</summary>
    private static Vector? SegmentIntersect(
        double ax,
        double ay,
        double bx,
        double by,
        double cx,
        double cy,
        double dx,
        double dy
    )
    {
        var rx = bx - ax;
        var ry = by - ay;
        var sx = dx - cx;
        var sy = dy - cy;
        var denom = rx * sy - ry * sx;
        if (Math.Abs(denom) < 1e-12)
            return null; // parallel
        var t = ((cx - ax) * sy - (cy - ay) * sx) / denom;
        var u = ((cx - ax) * ry - (cy - ay) * rx) / denom;
        if (t < -1e-9 || t > 1 + 1e-9 || u < -1e-9 || u > 1 + 1e-9)
            return null;
        return new Vector(ax + t * rx, ay + t * ry);
    }

    private static void CrossLine(
        double ax,
        double ay,
        double bx,
        double by,
        double at,
        bool vertical,
        Action<double, double> add
    )
    {
        var (ua, ub) = vertical ? (ax, bx) : (ay, by);
        if (ua == ub)
            return;
        var t = (at - ua) / (ub - ua);
        if (t < 0 || t > 1)
            return;
        var along = vertical ? ay + (by - ay) * t : ax + (bx - ax) * t;
        if (vertical)
            add(at, along);
        else
            add(along, at);
    }

    private void Commit(PlacedPart part)
    {
        Placed.Add(part);
        var pad = Spacing;
        _inflatedBounds.Add(
            new Bounds(
                part.X + part.Orientation.MinX - pad,
                part.Y + part.Orientation.MinY - pad,
                part.X + part.Orientation.MaxX + pad,
                part.Y + part.Orientation.MaxY + pad
            )
        );

        // Gate geometry: material inflated by spacing (holes shrunk) when positive,
        // raw material at zero spacing; already in world coordinates.
        var gatePerimeter = part.Orientation.InflatedPerimeter ?? part.Orientation.Perimeter;
        var gateHoles = part.Orientation.InflatedPerimeter != null
            ? part.Orientation.InflatedHoles
            : part.Orientation.Holes;
        var worldPerimeter = (Polygon)gatePerimeter.Clone();
        worldPerimeter.Offset(part.X, part.Y);
        worldPerimeter.UpdateBounds();
        var worldHoles = new List<Polygon>(gateHoles.Count);
        foreach (var hole in gateHoles)
        {
            var h = (Polygon)hole.Clone();
            h.Offset(part.X, part.Y);
            h.UpdateBounds();
            worldHoles.Add(h);
        }
        _placedGate.Add((worldPerimeter, worldHoles));
        _placedGateFast.Add(part.Orientation.GateFast?.Translated(part.X, part.Y));

        GridAdd(Placed.Count - 1, _inflatedBounds[^1]);
    }

    // ---- uniform spatial grid (cell -> placed indices) --------------------------

    private void GridAdd(int placedIndex, in Bounds bounds)
    {
        var c0 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MinX - _workLeft) / _cellSize),
            0,
            _gridCols - 1
        );
        var c1 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MaxX - _workLeft) / _cellSize),
            0,
            _gridCols - 1
        );
        var r0 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MinY - _workBottom) / _cellSize),
            0,
            _gridRows - 1
        );
        var r1 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MaxY - _workBottom) / _cellSize),
            0,
            _gridRows - 1
        );
        for (var r = r0; r <= r1; r++)
            for (var c = c0; c <= c1; c++)
                _grid[r * _gridCols + c].Add(placedIndex);
    }

    private readonly HashSet<int> _nearScratch = new();

    private HashSet<int> Near(in Bounds bounds)
    {
        _nearScratch.Clear();
        var c0 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MinX - _workLeft) / _cellSize),
            0,
            _gridCols - 1
        );
        var c1 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MaxX - _workLeft) / _cellSize),
            0,
            _gridCols - 1
        );
        var r0 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MinY - _workBottom) / _cellSize),
            0,
            _gridRows - 1
        );
        var r1 = System.Math.Clamp(
            (int)System.Math.Floor((bounds.MaxY - _workBottom) / _cellSize),
            0,
            _gridRows - 1
        );
        for (var r = r0; r <= r1; r++)
            for (var c = c0; c <= c1; c++)
                foreach (var index in _grid[r * _gridCols + c])
                    _nearScratch.Add(index);
        return _nearScratch;
    }

    /// <summary>
    /// Legality of one anchor. Outside every overlapping NFP is strict certification;
    /// inside one still passes when the exact material gate clears (interlocking
    /// concaves and cutouts that the convex NFP cannot represent).
    /// </summary>
    private bool IsLegal(OrientationModel orientation, double x, double y)
    {
        if (
            x + orientation.MinX < _workLeft - 1e-9
            || x + orientation.MaxX > _workRight + 1e-9
            || y + orientation.MinY < _workBottom - 1e-9
            || y + orientation.MaxY > _workTop + 1e-9
        )
            return false;

        var pad = Spacing;
        var candidate = new Bounds(
            x + orientation.MinX - pad,
            y + orientation.MinY - pad,
            x + orientation.MaxX + pad,
            y + orientation.MaxY + pad
        );

        // World-space candidate material, built at most once per anchor and only when
        // a convex-NFP hit actually needs the exact gate; freed with the anchor.
        (Polygon Perimeter, List<Polygon> Holes)? gate = null;

        foreach (var i in Near(candidate))
        {
            var bounds = _inflatedBounds[i];
            if (
                candidate.MinX >= bounds.MaxX
                || candidate.MaxX <= bounds.MinX
                || candidate.MinY >= bounds.MaxY
                || candidate.MaxY <= bounds.MinY
            )
                continue;

            // Fast rejection: outside the hull-based NFP the placed and candidate
            // HULLS are at least spacing apart, and hulls contain materials, so the
            // materials clear - a valid certification for any shape, holed or
            // concave. Inside the NFP decides nothing by itself (the hull sum
            // over-approximates for concaves and holes), but when both materials are
            // convex solids with uncapped hulls the sum is exact (modulo the
            // circumscribed disk's chord error, which only ever rejects a hair too
            // much), so interior means overlap. Everything else pays the exact
            // material gate.
            DiagCandidateChecks++;
            var nfp = NfpFor(i, orientation);
            if (nfp == null)
            {
                if (!TryPairVerdict(orientation, x, y, i, out var nullNfpOverlap))
                {
                    DiagGateCalls++;
                    gate ??= BuildCandidateGate(orientation, x, y);
                    nullNfpOverlap = MaterialOverlap(gate.Value, orientation, x, y, i);
                }
                if (nullNfpOverlap)
                    return false;
                continue;
            }
            if (!nfp.ContainsPoint(x, y))
                continue; // outside the conservative forbidden sum: certified clear
            if (
                orientation.IsConvexSolid
                && Placed[i].Orientation.IsConvexSolid
                && orientation.Hull.Count <= MaxHullVertices
                && Placed[i].Orientation.Hull.Count <= MaxHullVertices
            )
            {
                DiagConvexRejections++;
                return false; // exact convex-convex NFP interior: overlap
            }

            // Cheap world-bbox test against the placed gate material before paying
            // for candidate gate construction or the clipper.
            if (
                !_placedGate[i]
                    .Perimeter.BoundingBox
                    .Intersects(orientation.Perimeter.BoundingBox.Translate(x, y))
            )
                continue;

            // Fast shell relation against the placed gate outline: a certified clear
            // skips the exact gate entirely (no Polygon clones, no triangulation), a
            // certified overlap rejects without it. Hole-bearing pairs and touches fall
            // through to the exact gate.
            if (TryPairVerdict(orientation, x, y, i, out var fastOverlap))
            {
                if (fastOverlap)
                    return false;
                continue;
            }

            DiagGateCalls++;
            gate ??= BuildCandidateGate(orientation, x, y);
            if (MaterialOverlap(gate.Value, orientation, x, y, i))
                return false;
        }
        return true;
    }

    /// <summary>
    /// Fast outer-shell relation for one (candidate, placed) pair against the placed
    /// part's spacing-inflated gate outline, deciding whether the exact material gate
    /// must run. A CERTIFIED verdict skips it: disjoint shells mean no material overlap
    /// (holes only remove material), and a shell crossing/containment between two
    /// hole-free polygons IS a positive-area material overlap. Hole-bearing pairs whose
    /// shells overlap and near-degenerate touches fall through to the exact gate.
    /// </summary>
    private bool TryPairVerdict(
        OrientationModel orientation,
        double x,
        double y,
        int placedIndex,
        out bool overlap
    )
    {
        overlap = false;
        var placedFast = _placedGateFast[placedIndex];
        var candidateFast = orientation.PerimeterFast;
        if (placedFast == null || candidateFast == null)
        {
            DiagFastNull++;
            return false;
        }

        var relation = FastPoly.Relate(candidateFast.Translated(x, y), placedFast);
        if (relation == FastPoly.FastRelation.Overlap)
            DiagFastOverlapWithHoles++;
        switch (relation)
        {
            case FastPoly.FastRelation.Clear:
                DiagFastClears++;
                return true; // certified clear (spacing included in the placed gate)
            case FastPoly.FastRelation.Overlap
                when orientation.Holes.Count == 0 && _placedGate[placedIndex].Holes.Count == 0:
                DiagFastOverlaps++;
                overlap = true; // certified overlap: shells share area, nothing to subtract
                return true;
            default:
                DiagFastUnknowns++;
                return false; // exact gate must decide
        }
    }

    internal static bool VerifyFastClear { get; set; }

    internal long DiagFastClearMismatch;
    internal long DiagTriMismatch;
    internal long DiagTriNull;
    internal long DiagTriNullOut;
    internal long DiagTriFallback;

    /// <summary>
    /// Exact clearance gate against one placed part: placed gate material (inflated by
    /// spacing when positive) versus the candidate's raw material with holes subtracted.
    /// </summary>
    private bool MaterialOverlap(
        (Polygon Perimeter, List<Polygon> Holes) gate,
        OrientationModel orientation,
        double x,
        double y,
        int placedIndex
    )
    {
        var placed = _placedGate[placedIndex];
        if (!placed.Perimeter.BoundingBox.Intersects(orientation.Perimeter.BoundingBox.Translate(x, y)))
            return false;

        if (!gate.Perimeter.BoundingBox.Intersects(placed.Perimeter.BoundingBox))
            return false;

        var placedPart = Placed[placedIndex];

        // Allocation-free path: both sides carry cached triangulations in their local
        // frames, so the test clips triangles with the anchors as plain translations.
        var candTris = orientation.MaterialTris;
        var placedTris = placedPart.Orientation.GateTris;
        if (candTris == null || placedTris == null)
            DiagTriNull++;
        if (candTris != null && placedTris != null)
        {
            var cached = candTris.HasOverlap(
                placedTris, x, y, placedPart.X, placedPart.Y
            );
            if (cached.HasValue)
            {
                if (VerifyFastClear)
                {
                    var truth = Collision.HasOverlap(
                        gate.Perimeter, placed.Perimeter, gate.Holes, placed.Holes
                    );
                    if (truth != cached.Value)
                    {
                        DiagTriMismatch++;
                        System.IO.File.AppendAllText(
                            "/tmp/triset_mismatch.log",
                            $"cached={cached.Value} truth={truth} candAng={orientation.Angle:F4} at ({x:F8},{y:F8}) " +
                            $"placedAng={placedPart.Orientation.Angle:F4} at ({placedPart.X:F8},{placedPart.Y:F8}) " +
                            $"candTris={candTris} candVerts={orientation.Perimeter.Vertices.Count} holes={orientation.Holes.Count} " +
                            $"placedVerts={placedPart.Orientation.Perimeter.Vertices.Count} placedHoles={placedPart.Orientation.Holes.Count}\n"
                        );
                    }
                }
                return cached.Value;
            }
            DiagTriNullOut++;
            // Scratch overflow: fall through to the Polygon gate.
        }
        DiagTriFallback++;

        return Preparation.MaterialOverlapMemo(
            placedPart.Orientation,
            placedPart.X,
            placedPart.Y,
            orientation,
            x,
            y,
            () => Collision.HasOverlap(
                gate.Perimeter,
                placed.Perimeter,
                gate.Holes,
                placed.Holes
            )
        );
    }

    private (Polygon, List<Polygon>) BuildCandidateGate(OrientationModel orientation, double x, double y)
    {
        var perimeter = (Polygon)orientation.Perimeter.Clone();
        perimeter.Offset(x, y);
        perimeter.UpdateBounds();
        var holes = new List<Polygon>(orientation.Holes.Count);
        foreach (var hole in orientation.Holes)
        {
            var h = (Polygon)hole.Clone();
            h.Offset(x, y);
            h.UpdateBounds();
            holes.Add(h);
        }
        return (perimeter, holes);
    }

    private int OrientationId(OrientationModel orientation)
    {
        if (!_orientationIds.TryGetValue(orientation, out var id))
        {
            id = _orientationIds.Count;
            _orientationIds[orientation] = id;
        }
        return id;
    }

    /// <summary>
    /// Convex NFP of forbidden anchors: placedHull (+) disk(spacing) (+) reflect(candidateHull).
    /// </summary>
    private ConvexContour? NfpFor(int placedIndex, OrientationModel orientation)
    {
        var key = (placedIndex, OrientationId(orientation));
        if (_nfpCache.TryGetValue(key, out var cached))
            return cached;

        ConvexContour? result;
        try
        {
            if (!_placedHullDisk.TryGetValue(placedIndex, out var placedDisk))
            {
                var placed = Placed[placedIndex];
                var hull = placed.Orientation.Hull;
                var capped = CapHull(hull, placed.X, placed.Y);
                var placedHull = ConvexContour.FromVertices(capped);
                placedDisk = Spacing > Tolerance.Epsilon
                    ? NfpGeometry.Minkowski(placedHull, Disk())
                    : placedHull;
                _placedHullDisk[placedIndex] = placedDisk;
            }
            if (!_reflectedHulls.TryGetValue(orientation, out var reflected))
            {
                var capped = CapHull(orientation.Hull, 0, 0);
                reflected = NfpGeometry.Reflect(ConvexContour.FromVertices(capped));
                _reflectedHulls[orientation] = reflected;
            }
            result = NfpGeometry.Minkowski(placedDisk, reflected);
        }
        catch (Exception)
        {
            // A degenerate Minkowski sum removes the fast rejection for this pair;
            // the material gate still enforces correctness.
            result = null;
        }
        _nfpCache[key] = result;
        return result;
    }

    /// <summary>
    /// Bounded-size convex SUPERSET of <paramref name="hull"/> (translated by dx/dy).
    /// When the hull is dense, keep every k-th vertex, then shift each chord's
    /// supporting line outward by the chord's maximum sagitta (the largest distance of
    /// any dropped vertex to its chord). Every dropped vertex lies within the sagitta
    /// of its chord, so the offset half-plane intersection contains the original hull
    /// and the NFP built from it stays a conservative superset of the forbidden anchors.
    /// </summary>
    private static List<Vector> CapHull(List<Vector> hull, double dx, double dy)
    {
        var n = hull.Count;
        var shifted = new List<Vector>(n);
        for (var i = 0; i < n; i++)
            shifted.Add(new Vector(hull[i].X + dx, hull[i].Y + dy));
        if (n <= MaxHullVertices)
            return shifted;

        // Chord (v_i, v_{i+k}) for i in steps of k, with each chord's outward shift:
        // the max perpendicular distance from any vertex it spans to the chord line.
        var k = (int)Math.Ceiling(n / (double)MaxHullVertices);
        var lines = new List<(double ax, double ay, double bx, double by, double shift)>();
        for (var i = 0; i < n; i += k)
        {
            var a = shifted[i];
            var b = shifted[(i + k) % n];
            var span = Math.Min(k, n - i);
            var sagitta = 0.0;
            var length = Math.Sqrt((b.X - a.X) * (b.X - a.X) + (b.Y - a.Y) * (b.Y - a.Y));
            if (length > 1e-12)
                for (var j = 1; j < span; j++)
                {
                    var p = shifted[i + j];
                    var distance = Math.Abs(Cross(a.X, a.Y, b.X, b.Y, p)) / length;
                    if (distance > sagitta)
                        sagitta = distance;
                }
            lines.Add((a.X, a.Y, b.X, b.Y, sagitta));
        }

        // Sutherland-Hodgman from a generous bounding box; the interior of each chord
        // is the CCW left side, shifted outward (left) by the sagitta.
        var minX = double.MaxValue;
        var minY = double.MaxValue;
        var maxX = double.MinValue;
        var maxY = double.MinValue;
        foreach (var v in shifted)
        {
            if (v.X < minX)
                minX = v.X;
            if (v.X > maxX)
                maxX = v.X;
            if (v.Y < minY)
                minY = v.Y;
            if (v.Y > maxY)
                maxY = v.Y;
        }
        var margin = Math.Max(1.0, Math.Max(maxX - minX, maxY - minY));
        var polygon = new List<Vector>
        {
            new(minX - margin, minY - margin),
            new(maxX + margin, minY - margin),
            new(maxX + margin, maxY + margin),
            new(minX - margin, maxY + margin),
        };

        foreach (var (ax, ay, bx, by, shift) in lines)
        {
            if (polygon.Count == 0)
                return shifted; // degenerate; fall back to full hull
            // Shift the line perpendicular away from the interior (CCW: interior is left).
            var edgeX = bx - ax;
            var edgeY = by - ay;
            var length = Math.Sqrt(edgeX * edgeX + edgeY * edgeY);
            if (length <= 1e-12)
                continue;
            var nx = edgeY / length;
            var ny = -edgeX / length;
            var ox = ax + nx * shift;
            var oy = ay + ny * shift;
            var input = polygon;
            polygon = new List<Vector>();
            for (var i = 0; i < input.Count; i++)
            {
                var current = input[i];
                var next = input[(i + 1) % input.Count];
                var currentInside = Cross(ox, oy, ox + edgeX, oy + edgeY, current) >= 0;
                var nextInside = Cross(ox, oy, ox + edgeX, oy + edgeY, next) >= 0;
                if (currentInside)
                {
                    polygon.Add(current);
                    if (!nextInside)
                        polygon.Add(Intersect(ox, oy, ox + edgeX, oy + edgeY, current, next));
                }
                else if (nextInside)
                {
                    polygon.Add(Intersect(ox, oy, ox + edgeX, oy + edgeY, current, next));
                }
            }
        }

        return polygon.Count >= 3 ? polygon : shifted;
    }

    private static double Cross(double ax, double ay, double bx, double by, Vector p) =>
        (bx - ax) * (p.Y - ay) - (by - ay) * (p.X - ax);

    private static Vector Intersect(
        double ax,
        double ay,
        double bx,
        double by,
        Vector p,
        Vector q
    )
    {
        var dx1 = bx - ax;
        var dy1 = by - ay;
        var dx2 = q.X - p.X;
        var dy2 = q.Y - p.Y;
        var cross = dx1 * dy2 - dy1 * dx2;
        if (Math.Abs(cross) < 1e-300)
            return p;
        var t = ((p.X - ax) * dy2 - (p.Y - ay) * dx2) / cross;
        return new Vector(ax + t * dx1, ay + t * dy1);
    }

    private ConvexContour Disk() =>
        // Circumscribed so the polygon contains the true spacing disk: the NFP stays a
        // conservative superset of the forbidden-anchor region.
        _disk ??= ConvexContour.Disk(Spacing / Math.Cos(Math.PI / 24), 24);
}