diff --git a/AGENTS.md b/AGENTS.md
index c061d81..49c97fb 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -43,6 +43,7 @@ Domain model, geometry, and CNC primitives organized into namespaces:
 - **Converters** (`Converters/`, `namespace OpenNest.Converters`): Bridges between CNC and Geometry — `ConvertProgram` (CNC→Geometry), `ConvertGeometry` (Geometry→CNC), `ConvertMode` (absolute↔incremental).
 - **Math** (`Math/`, `namespace OpenNest.Math`): `Angle` (radian/degree conversion), `Tolerance` (floating-point comparison), `Trigonometry`, `Generic` (swap utility), `EvenOdd`, `Rounding` (factor-based rounding), `ExpressionEvaluator` (arithmetic expression parser for G-code variable expressions with `$name` references). Note: `OpenNest.Math` shadows `System.Math` — use `System.Math` fully qualified where both are needed.
 - **CNC/CuttingStrategy** (`CNC/CuttingStrategy/`, `namespace OpenNest.CNC`): `ContourCuttingStrategy` orchestrates cut ordering, lead-ins/lead-outs, and tabs. Includes `LeadIn`/`LeadOut` hierarchies (line, arc, clean-hole variants), `Tab` hierarchy (normal, machine, breaker), and `CuttingParameters`/`AssignmentParameters`/`SequenceParameters` configuration.
+- **Diagnostics** (`Diagnostics/`, `namespace OpenNest.Diagnostics`): `PlateOverlapAnalyzer.Capture` owns clean drawing entities and poses; `Analyze` returns read-only world-coordinate, hole-subtracted overlap fragments by input-index pair, with explicit issues for uncheckable inputs. It reuses `Collision.Check` without changing engine overlap semantics. Check `IsComplete` before treating an empty report as clear. See [material-overlap diagnostics](docs/geometry/visual-overlap-check.md) for the API, snapshot ownership, and numeric limits.
 - **Collections** (`Collections/`, `namespace OpenNest.Collections`): `ObservableList<T>`, `DrawingCollection`.
 - **CutOffs** (`namespace OpenNest`): `CutOff` (axis-aligned cut line with position, axis, optional start/end limits), `CutOffAxis` enum (`Horizontal`, `Vertical`), `CutOffSettings` (clearance, overtravel, min segment length, direction), `CutDirection` enum (`TowardOrigin`, `AwayFromOrigin`). Cut-offs generate CNC `Program` objects with trimmed line segments that avoid parts.
 - **Splitting** (`Splitting/`, `namespace OpenNest`): `DrawingSplitter` splits a Drawing into multiple pieces along split lines. `ISplitFeature` strategy pattern with implementations: `StraightSplit` (clean edge), `WeldGapTabSplit` (rectangular tab spacers on one side), `SpikeGrooveSplit` (interlocking spike/V-groove pairs). `AutoSplitCalculator` computes split lines for fit-to-plate and split-by-count modes. Supporting types: `SplitLine`, `SplitParameters`, `SplitFeatureResult`.
diff --git a/OpenNest.Core/Diagnostics/OverlapMaterial.cs b/OpenNest.Core/Diagnostics/OverlapMaterial.cs
new file mode 100644
index 0000000..37f6615
--- /dev/null
+++ b/OpenNest.Core/Diagnostics/OverlapMaterial.cs
@@ -0,0 +1,220 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Threading;
+using OpenNest.Geometry;
+using OpenNest.Math;
+
+namespace OpenNest.Diagnostics;
+
+/// <summary>Request-local, validated single-outer material. Never exposed to report consumers.</summary>
+internal sealed record OverlapMaterial(Polygon Outer, List<Polygon> Holes)
+{
+    internal static OverlapMaterial Read(List<Entity> entities, CancellationToken cancellationToken)
+    {
+        // ShapeBuilder can reverse entities while chaining. Own a fresh copy for each analysis.
+        var shapes = ShapeBuilder.GetShapes(entities.Select(entity => entity.Clone()));
+        if (shapes.Count == 0)
+            throw new ArgumentException("Drawing has no closed material contour.");
+        var polygons = new List<Polygon>();
+        foreach (var shape in shapes)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            ValidateChain(shape);
+            var polygon = shape.ToPolygonWithTolerance(PlateOverlapAnalyzer.ChordTolerance);
+            // The analytic chain was validated above. Normalize its sampled seam (e.g.
+            // sin(2*pi) is not exactly zero), rather than adding a spurious microscopic edge.
+            if (polygon.IsClosed())
+                polygon.Vertices[^1] = polygon.Vertices[0];
+            ValidatePolygon(polygon, cancellationToken);
+            polygons.Add(polygon);
+        }
+        // Sampling can hide a crossing or tangency between curves. Reject native
+        // contour contact before asking the polygon approximation about containment.
+        for (var i = 0; i < shapes.Count; i++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            for (var j = 0; j < i; j++)
+            {
+                shapes[i].Intersects(shapes[j], out var intersections);
+                if (intersections.Count > 0)
+                    throw new ArgumentException("Native material contours cross or touch.");
+            }
+        }
+        var ordered = polygons.OrderByDescending(polygon => Area(polygon.Vertices)).ToList();
+        var outer = ordered[0];
+        var holes = ordered.Skip(1).ToList();
+        for (var i = 0; i < holes.Count; i++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            if (BoundariesTouch(outer, holes[i], cancellationToken)
+                || !Inside(outer, holes[i].Vertices[0]))
+                throw new ArgumentException("Contours must have one outer with strictly internal holes.");
+            for (var j = 0; j < i; j++)
+            {
+                if (BoundariesTouch(holes[i], holes[j], cancellationToken)
+                    || Inside(holes[i], holes[j].Vertices[0])
+                    || Inside(holes[j], holes[i].Vertices[0]))
+                    throw new ArgumentException("Intersecting holes and nested material islands are unsupported.");
+            }
+        }
+        return new OverlapMaterial(outer, holes);
+    }
+
+    internal OverlapMaterial Transform(double rotation, Vector offset) =>
+        new(TransformPolygon(Outer, rotation, offset),
+            Holes.Select(hole => TransformPolygon(hole, rotation, offset)).ToList());
+
+    private static Polygon TransformPolygon(Polygon polygon, double rotation, Vector offset)
+    {
+        var transformed = new Polygon();
+        transformed.Vertices.AddRange(polygon.Vertices.Select(point =>
+            (rotation == 0 ? point : point.Rotate(rotation)) + offset));
+        if (transformed.Vertices.Any(point => !IsFinite(point)))
+            throw new ArithmeticException("Transformed contour has nonfinite coordinates.");
+        transformed.UpdateBounds();
+        if (!double.IsFinite(transformed.BoundingBox.Length)
+            || !double.IsFinite(transformed.BoundingBox.Width))
+            throw new ArithmeticException("Transformed contour bounds overflowed.");
+        var sourceArea = Area(polygon.Vertices);
+        var transformedArea = Area(transformed.Vertices);
+        if (!double.IsFinite(transformedArea) || transformedArea <= Tolerance.Epsilon
+            || System.Math.Abs(sourceArea - transformedArea)
+                > System.Math.Max(Tolerance.Epsilon, sourceArea * 1e-8))
+            throw new ArithmeticException("Coordinate precision cannot preserve the contour area at this pose.");
+        for (var i = 0; i + 1 < transformed.Vertices.Count; i++)
+        {
+            var a = transformed.Vertices[i];
+            var b = transformed.Vertices[i + 1];
+            if (a.X == b.X && a.Y == b.Y)
+                throw new ArithmeticException("Coordinate precision collapsed a contour edge at this pose.");
+        }
+        return transformed;
+    }
+
+    internal static bool IsFinite(Vector point) => double.IsFinite(point.X) && double.IsFinite(point.Y);
+
+    /// <summary>Translation-stable unsigned shoelace area; accepts an explicit closing vertex.</summary>
+    internal static double Area(IReadOnlyList<Vector> vertices)
+    {
+        var twiceArea = 0.0;
+        for (var i = 1; i + 1 < vertices.Count; i++)
+            twiceArea += Cross(vertices[0], vertices[i], vertices[i + 1]);
+        return System.Math.Abs(twiceArea) * 0.5;
+    }
+
+    private static void ValidateChain(Shape shape)
+    {
+        if (!shape.IsClosed())
+            throw new ArgumentException("Material contour is open.");
+        foreach (var entity in shape.Entities)
+        {
+            if (!double.IsFinite(entity.Length) || entity.Length <= 0)
+                throw new ArgumentException("Material contour has a nonfinite or zero-length edge.");
+        }
+        if (shape.Entities.Count == 1 && shape.Entities[0] is Circle circle)
+        {
+            if (!IsFinite(circle.Center) || !double.IsFinite(circle.Radius) || circle.Radius <= 0)
+                throw new ArgumentException("Material circle is invalid.");
+            return;
+        }
+        for (var i = 0; i < shape.Entities.Count; i++)
+        {
+            var end = Endpoints(shape.Entities[i]).End;
+            var start = Endpoints(shape.Entities[(i + 1) % shape.Entities.Count]).Start;
+            // Do not let ShapeBuilder's larger chain tolerance silently repair a broken cut.
+            if (!IsFinite(start) || !IsFinite(end) || end.DistanceTo(start) > Tolerance.Epsilon)
+                throw new ArgumentException("Material contour has a gap or invalid endpoint.");
+        }
+    }
+
+    private static (Vector Start, Vector End) Endpoints(Entity entity) => entity switch
+    {
+        Line line => (line.StartPoint, line.EndPoint),
+        Arc arc => (arc.StartPoint(), arc.EndPoint()),
+        _ => throw new ArgumentException("Unsupported material entity."),
+    };
+
+    private static void ValidatePolygon(Polygon polygon, CancellationToken cancellationToken)
+    {
+        var vertices = polygon.Vertices;
+        var area = Area(vertices);
+        if (vertices.Count < 4 || vertices.Any(point => !IsFinite(point))
+            || !double.IsFinite(area) || area <= Tolerance.Epsilon)
+            throw new ArgumentException("Material contour is degenerate or nonfinite.");
+        var count = vertices.Count - 1;
+        for (var i = 0; i < count; i++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            var previous = vertices[(i + count - 1) % count];
+            var current = vertices[i];
+            var next = vertices[i + 1];
+            if (current.X == next.X && current.Y == next.Y)
+                throw new ArgumentException("Material polygon has a zero-length edge.");
+            if (Cross(previous, current, next) == 0
+                && (previous.X - current.X) * (next.X - current.X)
+                    + (previous.Y - current.Y) * (next.Y - current.Y) > 0)
+                throw new ArgumentException("Material polygon has a retraced edge.");
+            for (var j = i + 2; j < count; j++)
+            {
+                if (i == 0 && j == count - 1)
+                    continue;
+                if (SegmentsTouch(vertices[i], vertices[i + 1], vertices[j], vertices[j + 1]))
+                    throw new ArgumentException("Material contour self-intersects or touches itself.");
+            }
+        }
+        // Ear clipping can stop early on unusable geometry. Do not certify that as clear.
+        var local = TransformPolygon(polygon, 0, vertices[0] * -1);
+        var triangulatedArea = Collision.Triangulate(local).Sum(triangle => Area(triangle.Vertices));
+        if (!double.IsFinite(triangulatedArea)
+            || System.Math.Abs(triangulatedArea - area) > System.Math.Max(Tolerance.Epsilon, area * 1e-9))
+            throw new ArgumentException("Material contour could not be completely triangulated.");
+    }
+
+    private static bool BoundariesTouch(Polygon a, Polygon b, CancellationToken cancellationToken)
+    {
+        for (var i = 0; i + 1 < a.Vertices.Count; i++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            for (var j = 0; j + 1 < b.Vertices.Count; j++)
+                if (SegmentsTouch(a.Vertices[i], a.Vertices[i + 1], b.Vertices[j], b.Vertices[j + 1]))
+                    return true;
+        }
+        return false;
+    }
+
+    private static bool SegmentsTouch(Vector a, Vector b, Vector c, Vector d)
+    {
+        var ac = Cross(a, b, c);
+        var ad = Cross(a, b, d);
+        var ca = Cross(c, d, a);
+        var cb = Cross(c, d, b);
+        return ac == 0 && OnSegment(a, b, c) || ad == 0 && OnSegment(a, b, d)
+            || ca == 0 && OnSegment(c, d, a) || cb == 0 && OnSegment(c, d, b)
+            || (ac < 0 && ad > 0 || ac > 0 && ad < 0)
+                && (ca < 0 && cb > 0 || ca > 0 && cb < 0);
+    }
+
+    private static bool OnSegment(Vector a, Vector b, Vector point) =>
+        point.X >= System.Math.Min(a.X, b.X) && point.X <= System.Math.Max(a.X, b.X)
+        && point.Y >= System.Math.Min(a.Y, b.Y) && point.Y <= System.Math.Max(a.Y, b.Y);
+
+    // Boundary contact is rejected before this winding-number test is used for topology.
+    private static bool Inside(Polygon polygon, Vector point)
+    {
+        var winding = 0;
+        for (var i = 0; i + 1 < polygon.Vertices.Count; i++)
+        {
+            var a = polygon.Vertices[i];
+            var b = polygon.Vertices[i + 1];
+            if (a.Y <= point.Y && b.Y > point.Y && Cross(a, b, point) > 0)
+                winding++;
+            else if (a.Y > point.Y && b.Y <= point.Y && Cross(a, b, point) < 0)
+                winding--;
+        }
+        return winding != 0;
+    }
+
+    private static double Cross(Vector a, Vector b, Vector point) =>
+        (b.X - a.X) * (point.Y - a.Y) - (b.Y - a.Y) * (point.X - a.X);
+}
diff --git a/OpenNest.Core/Diagnostics/PlateOverlapAnalyzer.cs b/OpenNest.Core/Diagnostics/PlateOverlapAnalyzer.cs
new file mode 100644
index 0000000..24737c9
--- /dev/null
+++ b/OpenNest.Core/Diagnostics/PlateOverlapAnalyzer.cs
@@ -0,0 +1,201 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Threading;
+using OpenNest.CNC;
+using OpenNest.Converters;
+using OpenNest.Geometry;
+
+namespace OpenNest.Diagnostics;
+
+/// <summary>
+/// Read-only, hole-aware material overlap diagnostics, separate from the engine's boolean checks.
+/// Uses clean drawing outlines, not placed lead-in/tab toolpaths or spacing offsets.
+/// </summary>
+public static class PlateOverlapAnalyzer
+{
+    public const double ChordTolerance = 0.001;
+
+    /// <summary>
+    /// Captures poses and converts each distinct clean source program to owned entities once.
+    /// Inputs must not change during capture. Later analysis never reads live domain objects.
+    /// </summary>
+    public static PlateOverlapSnapshot Capture(IReadOnlyList<Part> parts,
+        CancellationToken cancellationToken = default)
+    {
+        ArgumentNullException.ThrowIfNull(parts);
+        cancellationToken.ThrowIfCancellationRequested();
+        var captured = new List<CapturedOverlapPart>();
+        var issues = new List<PlateOverlapIssue>();
+        var sources = new Dictionary<Program, CapturedSource>(ReferenceEqualityComparer.Instance);
+        for (var id = 0; id < parts.Count; id++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            var part = parts[id];
+            if (part?.BaseDrawing?.IsCutOff == true)
+                continue;
+            try
+            {
+                if (part?.BaseDrawing?.Program == null)
+                    throw new ArgumentException("Part has no clean drawing program.");
+                var program = part.BaseDrawing.Program;
+                var rotation = part.Rotation - program.Rotation;
+                var location = part.Location;
+                if (!double.IsFinite(rotation) || !OverlapMaterial.IsFinite(location))
+                    throw new ArgumentException("Part pose must be finite.");
+                if (!sources.TryGetValue(program, out var source))
+                {
+                    try
+                    {
+                        ValidateProgram(program, new HashSet<Program>(ReferenceEqualityComparer.Instance));
+                        // Conversion creates fresh geometry, including expanded shared hole calls;
+                        // no cloning/rotation of a live program or subprogram is necessary.
+                        source = new CapturedSource(ConvertProgram.ToGeometry(program)
+                            .Where(entity => SpecialLayers.IsMaterial(entity.Layer)
+                                && entity.Layer != SpecialLayers.Leadin
+                                && entity.Layer != SpecialLayers.Leadout).ToList(), null);
+                    }
+                    catch (Exception exception) when (IsGeometryFailure(exception))
+                    {
+                        source = new CapturedSource(null, exception.Message);
+                    }
+                    sources.Add(program, source);
+                }
+                if (source.Error != null)
+                    throw new ArgumentException(source.Error);
+                captured.Add(new CapturedOverlapPart(id, part.BaseDrawing.Name,
+                    source.Entities, rotation, location));
+            }
+            catch (Exception exception) when (IsGeometryFailure(exception))
+            {
+                issues.Add(new PlateOverlapIssue(id, null, exception.Message));
+            }
+        }
+        cancellationToken.ThrowIfCancellationRequested();
+        return new PlateOverlapSnapshot(captured, issues);
+    }
+
+    /// <summary>Convenience synchronous capture and analysis of a group of parts.</summary>
+    public static PlateOverlapReport Analyze(IReadOnlyList<Part> parts,
+        CancellationToken cancellationToken = default) =>
+        Analyze(Capture(parts, cancellationToken), cancellationToken);
+
+    /// <summary>
+    /// Returns deterministic pair reports containing closed world-coordinate overlap fragments.
+    /// Cancellation throws and publishes no partial report. Check IsComplete before claiming clear.
+    /// </summary>
+    public static PlateOverlapReport Analyze(PlateOverlapSnapshot snapshot,
+        CancellationToken cancellationToken = default)
+    {
+        ArgumentNullException.ThrowIfNull(snapshot);
+        cancellationToken.ThrowIfCancellationRequested();
+        var issues = snapshot.Issues.ToList();
+        var pairs = new List<PlateOverlapPair>();
+        var prepared = new List<PreparedPart>();
+        var sources = new Dictionary<List<Entity>, PreparedSource>(ReferenceEqualityComparer.Instance);
+        foreach (var part in snapshot.Parts)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            try
+            {
+                if (!sources.TryGetValue(part.Entities, out var source))
+                {
+                    try
+                    {
+                        source = new PreparedSource(OverlapMaterial.Read(part.Entities, cancellationToken), null);
+                    }
+                    catch (Exception exception) when (IsGeometryFailure(exception))
+                    {
+                        source = new PreparedSource(null, exception.Message);
+                    }
+                    sources.Add(part.Entities, source);
+                }
+                if (source.Error != null)
+                    throw new ArgumentException(source.Error);
+                var material = source.Material.Transform(part.Rotation, part.Location);
+                prepared.Add(new PreparedPart(part, material));
+            }
+            catch (Exception exception) when (IsGeometryFailure(exception))
+            {
+                issues.Add(new PlateOverlapIssue(part.Id, null, exception.Message));
+            }
+        }
+
+        var sorted = prepared.OrderBy(part => part.Material.Outer.BoundingBox.Left)
+            .ThenBy(part => part.Input.Id).ToArray();
+        for (var i = 0; i < sorted.Length; i++)
+        {
+            cancellationToken.ThrowIfCancellationRequested();
+            var first = sorted[i];
+            var bounds = first.Material.Outer.BoundingBox;
+            for (var j = i + 1; j < sorted.Length; j++)
+            {
+                cancellationToken.ThrowIfCancellationRequested();
+                var second = sorted[j];
+                var otherBounds = second.Material.Outer.BoundingBox;
+                if (otherBounds.Left >= bounds.Right)
+                    break;
+                if (otherBounds.Bottom >= bounds.Top || bounds.Bottom >= otherBounds.Top)
+                    continue;
+                var a = first.Input.Id < second.Input.Id ? first : second;
+                var b = first.Input.Id < second.Input.Id ? second : first;
+                try
+                {
+                    // Keep pair clipping arithmetic near the parts where possible, then
+                    // restore output to world space. Triangulation itself also uses stable
+                    // local-origin winding so tiny holes in a huge part remain correct.
+                    var origin = a.Material.Outer.Vertices[0];
+                    var localA = a.Material.Transform(0, origin * -1);
+                    var localB = b.Material.Transform(0, origin * -1);
+                    var result = Collision.Check(localA.Outer, localB.Outer, localA.Holes, localB.Holes);
+                    if (!result.Overlaps)
+                        continue;
+                    var regions = result.OverlapRegions.Select(region => new PlateOverlapRegion(
+                        region.Vertices.Select(point => point + origin),
+                        OverlapMaterial.Area(region.Vertices))).ToList();
+                    var area = regions.Sum(region => region.Area);
+                    if (!double.IsFinite(area) || area <= 0)
+                        throw new ArithmeticException("Overlap area is not finite and positive.");
+                    pairs.Add(new PlateOverlapPair(a.Input.Id, b.Input.Id,
+                        a.Input.Name, b.Input.Name, regions));
+                }
+                catch (Exception exception) when (IsGeometryFailure(exception))
+                {
+                    issues.Add(new PlateOverlapIssue(a.Input.Id, b.Input.Id, exception.Message));
+                }
+            }
+        }
+        cancellationToken.ThrowIfCancellationRequested();
+        return new PlateOverlapReport(pairs.OrderBy(pair => pair.PartAId)
+            .ThenBy(pair => pair.PartBId).ToList(), issues.OrderBy(issue => issue.PartAId)
+            .ThenBy(issue => issue.PartBId).ToList());
+    }
+
+    private static bool IsGeometryFailure(Exception exception) => exception is
+        ArgumentException or InvalidOperationException or NotSupportedException or ArithmeticException;
+
+    private static void ValidateProgram(Program program, HashSet<Program> visiting)
+    {
+        if (program == null || !visiting.Add(program) || visiting.Count > 64)
+            throw new ArgumentException("Missing, recursive, or excessively nested subprogram.");
+        foreach (var code in program.Codes)
+        {
+            if (code == null)
+                throw new ArgumentException("Program contains a missing instruction.");
+            if (code is Motion motion && !OverlapMaterial.IsFinite(motion.EndPoint)
+                || code is ArcMove arc && !OverlapMaterial.IsFinite(arc.CenterPoint))
+                throw new ArgumentException("Program coordinates must be finite.");
+            if (code is SubProgramCall call)
+            {
+                if (!OverlapMaterial.IsFinite(call.Offset) || !double.IsFinite(call.Rotation))
+                    throw new ArgumentException("Subprogram pose must be finite.");
+                ValidateProgram(call.Program, visiting);
+            }
+        }
+        visiting.Remove(program);
+    }
+
+    private sealed record CapturedSource(List<Entity> Entities, string Error);
+    private sealed record PreparedSource(OverlapMaterial Material, string Error);
+    private sealed record PreparedPart(CapturedOverlapPart Input, OverlapMaterial Material);
+}
diff --git a/OpenNest.Core/Diagnostics/PlateOverlapReport.cs b/OpenNest.Core/Diagnostics/PlateOverlapReport.cs
new file mode 100644
index 0000000..891f8d7
--- /dev/null
+++ b/OpenNest.Core/Diagnostics/PlateOverlapReport.cs
@@ -0,0 +1,88 @@
+using System.Collections.Generic;
+using System.Linq;
+using OpenNest.Geometry;
+
+namespace OpenNest.Diagnostics;
+
+/// <summary>An owned diagnostic result. An empty Pairs list is clear only if IsComplete is true.</summary>
+public sealed class PlateOverlapReport
+{
+    internal PlateOverlapReport(List<PlateOverlapPair> pairs, List<PlateOverlapIssue> issues)
+    {
+        Pairs = pairs.AsReadOnly();
+        Issues = issues.AsReadOnly();
+    }
+
+    public IReadOnlyList<PlateOverlapPair> Pairs { get; }
+    public IReadOnlyList<PlateOverlapIssue> Issues { get; }
+    public bool IsComplete => Issues.Count == 0;
+    public double ChordTolerance => PlateOverlapAnalyzer.ChordTolerance;
+}
+
+/// <summary>Shared material for two input positions, ordered by zero-based input index.</summary>
+public sealed class PlateOverlapPair
+{
+    private readonly Box bounds;
+
+    internal PlateOverlapPair(int partAId, int partBId, string partAName, string partBName,
+        List<PlateOverlapRegion> regions)
+    {
+        PartAId = partAId;
+        PartBId = partBId;
+        PartAName = partAName;
+        PartBName = partBName;
+        Regions = regions.AsReadOnly();
+        Area = regions.Sum(region => region.Area);
+        var points = regions.SelectMany(region => region.Vertices).ToArray();
+        var left = points.Min(point => point.X);
+        var bottom = points.Min(point => point.Y);
+        bounds = new Box(left, bottom, points.Max(point => point.X) - left,
+            points.Max(point => point.Y) - bottom);
+    }
+
+    public int PartAId { get; }
+    public int PartBId { get; }
+    public string PartAName { get; }
+    public string PartBName { get; }
+    /// <summary>Convex fragments, not connected islands; no mutable kernel polygons are exposed.</summary>
+    public IReadOnlyList<PlateOverlapRegion> Regions { get; }
+    public double Area { get; }
+    /// <summary>A fresh world-coordinate bounds copy.</summary>
+    public Box Bounds => new(bounds.X, bounds.Y, bounds.Length, bounds.Width);
+}
+
+/// <summary>A positive-area, hole-subtracted convex polygon in world coordinates.</summary>
+public sealed class PlateOverlapRegion
+{
+    internal PlateOverlapRegion(IEnumerable<Vector> vertices, double area)
+    {
+        Vertices = System.Array.AsReadOnly(vertices.ToArray());
+        Area = area;
+    }
+
+    /// <summary>Read-only vertices with an exactly repeated closing vertex.</summary>
+    public IReadOnlyList<Vector> Vertices { get; }
+    public double Area { get; }
+}
+
+/// <summary>An input or pair that could not be checked. IDs are zero-based input positions.</summary>
+public sealed record PlateOverlapIssue(int PartAId, int? PartBId, string Message);
+
+/// <summary>
+/// Owned clean geometry and poses. Capture while inputs are stable, then analyze on a worker.
+/// No live Part, Drawing, Program, or subprogram is retained.
+/// </summary>
+public sealed class PlateOverlapSnapshot
+{
+    internal PlateOverlapSnapshot(List<CapturedOverlapPart> parts, List<PlateOverlapIssue> issues)
+    {
+        Parts = parts.AsReadOnly();
+        Issues = issues.AsReadOnly();
+    }
+
+    internal IReadOnlyList<CapturedOverlapPart> Parts { get; }
+    internal IReadOnlyList<PlateOverlapIssue> Issues { get; }
+}
+
+internal sealed record CapturedOverlapPart(int Id, string Name, List<Entity> Entities,
+    double Rotation, Vector Location);
diff --git a/OpenNest.Core/Geometry/ConvexDecomposition.cs b/OpenNest.Core/Geometry/ConvexDecomposition.cs
index f2e51a6..6c3e078 100644
--- a/OpenNest.Core/Geometry/ConvexDecomposition.cs
+++ b/OpenNest.Core/Geometry/ConvexDecomposition.cs
@@ -148,14 +148,12 @@ namespace OpenNest.Geometry
         /// </summary>
         private static double SignedArea(List<Vector> verts)
         {
+            // World-coordinate products can erase the sign of a small polygon's area
+            // far from the origin, leaving CW outlines/holes untriangulated. Measure
+            // relative to a vertex, just as the clipping kernel measures its fragments.
             var area = 0.0;
-
-            for (var i = 0; i < verts.Count; i++)
-            {
-                var j = (i + 1) % verts.Count;
-                area += verts[i].X * verts[j].Y;
-                area -= verts[j].X * verts[i].Y;
-            }
+            for (var i = 1; i + 1 < verts.Count; i++)
+                area += Cross(verts[0], verts[i], verts[i + 1]);
 
             return area * 0.5;
         }
diff --git a/OpenNest.Tests/Diagnostics/PlateOverlapAnalyzerTests.cs b/OpenNest.Tests/Diagnostics/PlateOverlapAnalyzerTests.cs
new file mode 100644
index 0000000..0cd5a64
--- /dev/null
+++ b/OpenNest.Tests/Diagnostics/PlateOverlapAnalyzerTests.cs
@@ -0,0 +1,444 @@
+using OpenNest.CNC;
+using OpenNest.Diagnostics;
+using OpenNest.Geometry;
+using OpenNest.Shapes;
+
+namespace OpenNest.Tests.Diagnostics;
+
+public class PlateOverlapAnalyzerTests
+{
+    [Fact]
+    public void Analyze_ReturnsOwnedWorldPolygonsForEachOverlappingPair()
+    {
+        var parts = new[] { Rectangle(0, 0, 1, 1), Rectangle(0.5, 0, 1, 1) };
+
+        var report = PlateOverlapAnalyzer.Analyze(parts);
+
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Empty(report.Issues);
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal((0, 1), (pair.PartAId, pair.PartBId));
+        Assert.Equal(0.5, pair.Area, 9);
+        Assert.NotEmpty(pair.Regions);
+        Assert.All(pair.Regions, region =>
+        {
+            Assert.True(region.Area > 0);
+            Assert.Equal(region.Vertices[0], region.Vertices[^1]);
+            Assert.All(region.Vertices, point =>
+            {
+                Assert.InRange(point.X, 0.5, 1);
+                Assert.InRange(point.Y, 0, 1);
+            });
+        });
+        Assert.Equal(pair.Area, pair.Regions.Sum(r => r.Area), 9);
+        Assert.Equal((0.5, 0.0, 1.0, 1.0),
+            (pair.Bounds.Left, pair.Bounds.Bottom, pair.Bounds.Right, pair.Bounds.Top));
+    }
+
+    [Fact]
+    public void Analyze_FullContainmentDoesNotRequireCrossingPoints()
+    {
+        var pair = Assert.Single(PlateOverlapAnalyzer.Analyze(new[]
+        {
+            Rectangle(0, 0, 4, 4), Rectangle(1, 1, 1, 1)
+        }).Pairs);
+        Assert.Equal(1, pair.Area, 9);
+    }
+
+    [Theory]
+    [InlineData(2, 0)]
+    [InlineData(1, 0)]
+    [InlineData(1, 1)]
+    public void Analyze_DisjointAndBoundaryOnlyContactAreClear(double x, double y)
+    {
+        var report = PlateOverlapAnalyzer.Analyze(new[]
+        {
+            Rectangle(0, 0, 1, 1), Rectangle(x, y, 1, 1)
+        });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_EmptyAndSinglePartAreComplete()
+    {
+        foreach (var parts in new[] { Array.Empty<Part>(), new[] { Rectangle(0, 0, 1, 1) } })
+        {
+            var report = PlateOverlapAnalyzer.Analyze(parts);
+            Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+            Assert.Empty(report.Pairs);
+        }
+    }
+
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void Analyze_SubtractsHolesOfEitherOperand(bool swap)
+    {
+        var frame = WithContours(Square(0, 0, 4), Square(1, 1, 2));
+        var insert = Rectangle(1.5, 1.5, 1, 1);
+        var report = PlateOverlapAnalyzer.Analyze(swap ? new[] { insert, frame } : new[] { frame, insert });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Empty(report.Pairs);
+
+        insert.Location = new Vector(0.5, 1.5);
+        report = PlateOverlapAnalyzer.Analyze(swap ? new[] { insert, frame } : new[] { frame, insert });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(0.5, Assert.Single(report.Pairs).Area, 9);
+    }
+
+    [Fact]
+    public void Analyze_SubtractsBothPartsHolesWithoutDuplicatingArea()
+    {
+        var a = WithContours(Square(0, 0, 4), Square(0.5, 0.5, 1));
+        var b = WithContours(Square(0, 0, 4), Square(2, 2, 1));
+        var report = PlateOverlapAnalyzer.Analyze(new[] { a, b });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(14, Assert.Single(report.Pairs).Area, 8);
+    }
+
+    [Fact]
+    public void Analyze_ConcaveIntersectionKeepsDisconnectedFragments()
+    {
+        var u = WithContours(new[]
+        {
+            new Vector(0, 0), new Vector(3, 0), new Vector(3, 3), new Vector(2, 3),
+            new Vector(2, 1), new Vector(1, 1), new Vector(1, 3), new Vector(0, 3)
+        });
+        var report = PlateOverlapAnalyzer.Analyze(new[] { u, Rectangle(0, 2, 3, 1) });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(2, pair.Area, 8);
+        Assert.All(pair.Regions, region => Assert.True(
+            region.Vertices.All(p => p.X <= 1) || region.Vertices.All(p => p.X >= 2)));
+    }
+
+    [Theory]
+    [InlineData(0, 0)]
+    [InlineData(1000000000, 1000000000)]
+    [InlineData(-1000000000, -1000000000)]
+    public void Analyze_ReversedWindingAndLargeTranslationPreserveArea(double x, double y)
+    {
+        var a = WithContours(Square(0, 0, 1).Reverse().ToArray());
+        var b = Rectangle(0, 0, 1, 1);
+        a.Location = new Vector(x, y);
+        b.Location = new Vector(x + 0.5, y);
+        var report = PlateOverlapAnalyzer.Analyze(new[] { a, b });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(0.5, pair.Area, 7);
+        Assert.Equal(x + 0.5, pair.Bounds.Left, 7);
+        Assert.Equal(y + 1, pair.Bounds.Top, 7);
+    }
+
+    [Fact]
+    public void Analyze_UsesBaselineAdjustedCleanDrawingPose()
+    {
+        var drawing = Rectangle(0, 0, 2, 1).BaseDrawing;
+        drawing.Program.Rotate(System.Math.PI / 2);
+        var part = new Part(drawing);
+        part.Rotate(System.Math.PI / 2);
+        part.Location = new Vector(10, 10);
+        var report = PlateOverlapAnalyzer.Analyze(new[] { part, Rectangle(8, 9, 2, 1) });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(2, Assert.Single(report.Pairs).Area, 8);
+    }
+
+    [Fact]
+    public void Analyze_CircularHoleIsNotSolidMaterial()
+    {
+        var ring = new Part(new RingShape { OuterDiameter = 10, InnerDiameter = 7 }.GetDrawing());
+        var disk = new Part(new CircleShape { Diameter = 6 }.GetDrawing());
+        ring.Location = new Vector(-36.8, 5.4);
+        disk.Location = new Vector(-36.7, 5.4);
+        var report = PlateOverlapAnalyzer.Analyze(new[] { ring, disk });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_KeepsInputIndicesAndDeterministicOrderWhileSkippingCutoffs()
+    {
+        var cutoff = Rectangle(0, 0, 1, 1);
+        cutoff.BaseDrawing.IsCutOff = true;
+        var drawing = Rectangle(0, 0, 1, 1).BaseDrawing;
+        var parts = new[] { new Part(drawing), cutoff, new Part(drawing), new Part(drawing) };
+        var report = PlateOverlapAnalyzer.Analyze(parts);
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(new[] { (0, 2), (0, 3), (2, 3) },
+            report.Pairs.Select(p => (p.PartAId, p.PartBId)));
+        Assert.All(report.Pairs, p => Assert.Equal(1, p.Area, 9));
+    }
+
+    [Fact]
+    public void Analyze_SweepMatchesAnalyticalExhaustiveRectanglePairs()
+    {
+        var random = new Random(928);
+        var parts = Enumerable.Range(0, 40)
+            .Select(_ => Rectangle(random.Next(-10, 10), random.Next(-10, 10), 3, 2)).ToArray();
+        var expected = new List<(int, int, double)>();
+        for (var a = 0; a < parts.Length; a++)
+            for (var b = a + 1; b < parts.Length; b++)
+            {
+                var dx = System.Math.Min(parts[a].Right, parts[b].Right)
+                    - System.Math.Max(parts[a].Left, parts[b].Left);
+                var dy = System.Math.Min(parts[a].Top, parts[b].Top)
+                    - System.Math.Max(parts[a].Bottom, parts[b].Bottom);
+                if (dx > 0 && dy > 0)
+                    expected.Add((a, b, dx * dy));
+            }
+        var report = PlateOverlapAnalyzer.Analyze(parts);
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(expected.Select(pair => (pair.Item1, pair.Item2)),
+            report.Pairs.Select(pair => (pair.PartAId, pair.PartBId)));
+        foreach (var (expectedPair, actualPair) in expected.Zip(report.Pairs))
+            Assert.Equal(expectedPair.Item3, actualPair.Area, 9);
+    }
+
+    [Theory]
+    [InlineData("open")]
+    [InlineData("empty")]
+    [InlineData("nan")]
+    [InlineData("infinite-pose")]
+    [InlineData("disjoint-outers")]
+    [InlineData("nested-island")]
+    [InlineData("crossing-holes")]
+    [InlineData("self-crossing")]
+    public void Analyze_InvalidPartMakesReportIncompleteButRetainsKnownOverlaps(string invalid)
+    {
+        var bad = Rectangle(0, 0, 1, 1);
+        switch (invalid)
+        {
+            case "open": bad.BaseDrawing.Program.Codes.RemoveAt(bad.BaseDrawing.Program.Codes.Count - 1); break;
+            case "empty": bad.BaseDrawing.Program.Codes.Clear(); break;
+            case "nan": ((LinearMove)bad.BaseDrawing.Program.Codes[1]).EndPoint = new Vector(double.NaN, 0); break;
+            case "infinite-pose": bad.Location = new Vector(double.PositiveInfinity, 0); break;
+            case "disjoint-outers": bad = WithContours(Square(0, 0, 1), Square(3, 3, 1)); break;
+            case "nested-island": bad = WithContours(Square(0, 0, 6), Square(1, 1, 4), Square(2, 2, 1)); break;
+            case "crossing-holes": bad = WithContours(Square(0, 0, 6), Square(1, 1, 3), Square(2, 2, 3)); break;
+            case "self-crossing": bad = WithContours(new[] { new Vector(0, 0), new Vector(3, 3), new Vector(0, 3), new Vector(2, 0) }); break;
+        }
+        var report = PlateOverlapAnalyzer.Analyze(new[] { Rectangle(0, 0, 1, 1), bad, Rectangle(0, 0, 1, 1) });
+        Assert.False(report.IsComplete);
+        var issue = Assert.Single(report.Issues);
+        Assert.Equal(1, issue.PartAId);
+        Assert.Null(issue.PartBId);
+        Assert.False(string.IsNullOrWhiteSpace(issue.Message));
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal((0, 2), (pair.PartAId, pair.PartBId));
+    }
+
+    [Fact]
+    public void Capture_IsIndependentOfLaterDrawingPoseAndCollectionChanges()
+    {
+        var a = Rectangle(0, 0, 1, 1);
+        var b = new Part(a.BaseDrawing, new Vector(0.5, 0));
+        var parts = new List<Part> { a, b };
+        var snapshot = PlateOverlapAnalyzer.Capture(parts);
+        a.BaseDrawing.Program.Codes.Clear();
+        b.Location = new Vector(100, 100);
+        parts.Clear();
+        var first = PlateOverlapAnalyzer.Analyze(snapshot);
+        var second = PlateOverlapAnalyzer.Analyze(snapshot);
+        Assert.True(first.IsComplete);
+        Assert.Equal(0.5, Assert.Single(first.Pairs).Area, 9);
+        Assert.Equal(0.5, Assert.Single(second.Pairs).Area, 9);
+    }
+
+    [Fact]
+    public void Analyze_IgnoresPlacedCuttingProgramAndDoesNotMutateParts()
+    {
+        var a = Rectangle(0, 0, 1, 1);
+        var b = Rectangle(0.5, 0, 1, 1);
+        Assert.True(a.RestoreLeadInProgram(Rectangle(100, 100, 4, 4).Program, locked: true));
+        var program = a.Program;
+        var source = a.BaseDrawing.Program;
+        var sourceText = source.ToString();
+        var placedText = program.ToString();
+        var bounds = a.BoundingBox;
+        var location = a.Location;
+        var rotation = a.Rotation;
+        var report = PlateOverlapAnalyzer.Analyze(new[] { a, b });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(0.5, Assert.Single(report.Pairs).Area, 9);
+        Assert.Same(program, a.Program);
+        Assert.Same(source, a.BaseDrawing.Program);
+        Assert.Equal(sourceText, source.ToString());
+        Assert.Equal(placedText, program.ToString());
+        Assert.Same(bounds, a.BoundingBox);
+        Assert.Equal(location, a.Location);
+        Assert.Equal(rotation, a.Rotation);
+        Assert.True(a.HasManualLeadIns);
+        Assert.True(a.LeadInsLocked);
+    }
+
+    [Fact]
+    public void Analyze_IgnoresScribeRapidAndLeadPathsInCleanSource()
+    {
+        var a = Rectangle(0, 0, 1, 1);
+        foreach (var layer in new[] { LayerType.Scribe, LayerType.Leadin, LayerType.Leadout })
+        {
+            a.BaseDrawing.Program.Codes.Add(new RapidMove(new Vector(0, 0)));
+            a.BaseDrawing.Program.Codes.Add(new LinearMove(new Vector(10, 10)) { Layer = layer });
+        }
+        var report = PlateOverlapAnalyzer.Analyze(new[] { a, Rectangle(5, 5, 1, 1) });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_ReportCollectionsAndBoundsCannotBeMutated()
+    {
+        var report = PlateOverlapAnalyzer.Analyze(new[] { Rectangle(0, 0, 1, 1), Rectangle(0, 0, 1, 1) });
+        var pair = Assert.Single(report.Pairs);
+        Assert.Throws<NotSupportedException>(() => ((IList<PlateOverlapPair>)report.Pairs).Clear());
+        Assert.Throws<NotSupportedException>(() => ((IList<PlateOverlapRegion>)pair.Regions).Clear());
+        var region = pair.Regions[0];
+        Assert.Throws<NotSupportedException>(() => ((IList<Vector>)region.Vertices)[0] = new Vector(99, 99));
+        pair.Bounds.X = 99;
+        Assert.Equal(0, pair.Bounds.X);
+    }
+
+    [Fact]
+    public async Task Capture_SharedHoleSubprogramsAreOwnedAndReusableAcrossWorkers()
+    {
+        var source = Rectangle(0, 0, 10, 10).BaseDrawing;
+        var hole = Rectangle(0, 0, 1, 1).BaseDrawing.Program;
+        hole.Mode = Mode.Incremental;
+        source.Program.SubPrograms[-1] = hole;
+        source.Program.Codes.Add(new SubProgramCall { Id = -1, Program = hole, Offset = new Vector(2, 2) });
+        source.Program.Codes.Add(new SubProgramCall { Id = -1, Program = hole, Offset = new Vector(6, 2) });
+        source.Program.Rotate(System.Math.PI / 2);
+        var placed = new Part(source);
+        placed.Rotate(System.Math.PI / 2);
+        placed.Location = new Vector(20, 20);
+        var parts = new[] { placed, Rectangle(10, 10, 10, 10) };
+        var before = source.Program.Codes.Select(code => code.ToString()).ToArray();
+        var holeBefore = hole.Codes.Select(code => code.ToString()).ToArray();
+        var snapshot = PlateOverlapAnalyzer.Capture(parts);
+        Assert.Equal(before, source.Program.Codes.Select(code => code.ToString()));
+        Assert.Equal(holeBefore, hole.Codes.Select(code => code.ToString()));
+        foreach (var call in source.Program.Codes.OfType<SubProgramCall>())
+            call.Offset = new Vector(100, 100);
+        hole.Codes.Clear();
+        source.Program.Codes.Clear();
+        var reports = await Task.WhenAll(Enumerable.Range(0, 4).Select(_ =>
+            Task.Run(() => PlateOverlapAnalyzer.Analyze(snapshot))));
+        foreach (var report in reports)
+        {
+            Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+            Assert.Equal(98, Assert.Single(report.Pairs).Area, 8);
+        }
+    }
+
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void Capture_InvalidSubprogramGraphIsIncompleteRatherThanRecursive(bool missing)
+    {
+        var part = Rectangle(0, 0, 1, 1);
+        var call = new SubProgramCall();
+        if (!missing)
+            call.Program = part.BaseDrawing.Program;
+        part.BaseDrawing.Program.Codes.Add(call);
+        var report = PlateOverlapAnalyzer.Analyze(new[] { part });
+        Assert.False(report.IsComplete);
+        Assert.Single(report.Issues);
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_NullArgumentsThrowAndNullEntriesAreIssues()
+    {
+        Assert.Throws<ArgumentNullException>(() => PlateOverlapAnalyzer.Capture(null!));
+        Assert.Throws<ArgumentNullException>(() => PlateOverlapAnalyzer.Analyze((PlateOverlapSnapshot)null!));
+        var report = PlateOverlapAnalyzer.Analyze(new Part[] { null! });
+        Assert.False(report.IsComplete);
+        Assert.Single(report.Issues);
+        Assert.Empty(report.Pairs);
+    }
+
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void Analyze_HugeOuterWithSmallClockwisePartIsOrderIndependent(bool swap)
+    {
+        var outer = Rectangle(0, 0, 1e9, 1e9);
+        var small = WithContours(Square(0, 0, 1).Reverse().ToArray());
+        small.Location = new Vector(999999998, 999999998);
+        var report = PlateOverlapAnalyzer.Analyze(swap ? new[] { small, outer } : new[] { outer, small });
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        Assert.Equal(1, Assert.Single(report.Pairs).Area, 8);
+    }
+
+    [Fact]
+    public void Analyze_TranslationThatCollapsesMaterialIsIncompleteNotClear()
+    {
+        var report = PlateOverlapAnalyzer.Analyze(new[]
+        {
+            Rectangle(1e16, 1e16, 1, 1), Rectangle(1e16, 1e16, 1, 1)
+        });
+        Assert.False(report.IsComplete);
+        Assert.Equal(new[] { 0, 1 }, report.Issues.Select(issue => issue.PartAId));
+        Assert.Empty(report.Pairs);
+    }
+
+    [Theory]
+    [InlineData(9.0)]
+    [InlineData(9.0002)]
+    public void Analyze_NativeCircularHoleContactCannotBeHiddenByTessellation(double y)
+    {
+        var source = Rectangle(0, 0, 10, 10).BaseDrawing;
+        source.Program.Codes.Add(new RapidMove(new Vector(6, y)));
+        source.Program.Codes.Add(new ArcMove(new Vector(6, y), new Vector(5, y), RotationType.CCW));
+        var report = PlateOverlapAnalyzer.Analyze(new[] { new Part(source) });
+        Assert.False(report.IsComplete);
+        Assert.Single(report.Issues);
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_SubChordThinRingIsExplicitlyUncheckableNotClear()
+    {
+        const double radius = 4.995098381203606;
+        var ring = new Part(new RingShape
+        {
+            OuterDiameter = 2 * (radius + 0.0001),
+            InnerDiameter = 2 * (radius - 0.0001)
+        }.GetDrawing());
+        var report = PlateOverlapAnalyzer.Analyze(new[] { ring });
+        Assert.False(report.IsComplete);
+        Assert.Single(report.Issues);
+        Assert.Empty(report.Pairs);
+    }
+
+    [Fact]
+    public void Analyze_CancellationThrowsInsteadOfPublishingPartialClear()
+    {
+        var parts = new[] { Rectangle(0, 0, 1, 1), Rectangle(0, 0, 1, 1) };
+        var snapshot = PlateOverlapAnalyzer.Capture(parts);
+        using var cancellation = new CancellationTokenSource();
+        cancellation.Cancel();
+        Assert.Throws<OperationCanceledException>(() => PlateOverlapAnalyzer.Capture(parts, cancellation.Token));
+        Assert.Throws<OperationCanceledException>(() => PlateOverlapAnalyzer.Analyze(snapshot, cancellation.Token));
+    }
+
+    private static Part Rectangle(double x, double y, double width, double height) =>
+        new(WithContours(new[] { new Vector(0, 0), new Vector(width, 0),
+            new Vector(width, height), new Vector(0, height) }).BaseDrawing, new Vector(x, y));
+
+    private static Vector[] Square(double x, double y, double size) =>
+        new[] { new Vector(x, y), new Vector(x + size, y), new Vector(x + size, y + size), new Vector(x, y + size) };
+
+    private static Part WithContours(params Vector[][] contours)
+    {
+        var program = new Program(Mode.Absolute);
+        foreach (var contour in contours)
+        {
+            program.Codes.Add(new RapidMove(contour[0]));
+            foreach (var point in contour.Skip(1).Append(contour[0]))
+                program.Codes.Add(new LinearMove(point));
+        }
+        return new Part(new Drawing("same name", program));
+    }
+}
diff --git a/OpenNest.Tests/Geometry/CollisionTranslationTests.cs b/OpenNest.Tests/Geometry/CollisionTranslationTests.cs
new file mode 100644
index 0000000..501ea14
--- /dev/null
+++ b/OpenNest.Tests/Geometry/CollisionTranslationTests.cs
@@ -0,0 +1,70 @@
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.Geometry;
+
+public class CollisionTranslationTests
+{
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void Check_ContainedClockwisePolygonFarFromOriginDoesNotDependOnOperandOrder(bool swap)
+    {
+        var outer = Square(0, 0, 1e9);
+        var small = Square(999999998, 999999998, 1);
+        small.Reverse();
+
+        var result = swap ? Collision.Check(small, outer) : Collision.Check(outer, small);
+
+        Assert.True(result.Overlaps);
+        // Do not use Polygon.Area here: this test isolates triangulation, not that legacy API.
+        Assert.Equal(1, result.OverlapRegions.Sum(StableArea), 8);
+    }
+
+    [Fact]
+    public void Check_ClockwiseHoleFarFromOriginIsSubtracted()
+    {
+        var outer = Square(0, 0, 1e9);
+        var hole = Square(999999998, 999999998, 1);
+        hole.Reverse();
+        var insert = Square(999999998.25, 999999998.25, 0.5);
+
+        var result = Collision.Check(outer, insert, new List<Polygon> { hole });
+
+        Assert.False(result.Overlaps);
+        Assert.Empty(result.OverlapRegions);
+    }
+
+    [Theory]
+    [InlineData(1000000000)]
+    [InlineData(-1000000000)]
+    public void Triangulate_ClockwiseTranslatedUnitSquareHasFullArea(double offset)
+    {
+        var polygon = Square(offset, offset, 1);
+        polygon.Reverse();
+        var triangles = ConvexDecomposition.Triangulate(polygon);
+        Assert.Equal(2, triangles.Count);
+        Assert.Equal(1, triangles.Sum(StableArea), 8);
+    }
+
+    private static Polygon Square(double x, double y, double size)
+    {
+        var polygon = new Polygon();
+        polygon.Vertices.AddRange(new[] { new Vector(x, y), new Vector(x + size, y),
+            new Vector(x + size, y + size), new Vector(x, y + size), new Vector(x, y) });
+        polygon.UpdateBounds();
+        return polygon;
+    }
+
+    private static double StableArea(Polygon polygon)
+    {
+        var area = 0.0;
+        var origin = polygon.Vertices[0];
+        for (var i = 1; i + 1 < polygon.Vertices.Count; i++)
+        {
+            var a = polygon.Vertices[i] - origin;
+            var b = polygon.Vertices[i + 1] - origin;
+            area += a.X * b.Y - a.Y * b.X;
+        }
+        return System.Math.Abs(area) / 2;
+    }
+}
diff --git a/README.md b/README.md
index 02aa9d7..1666e6b 100644
--- a/README.md
+++ b/README.md
@@ -72,7 +72,7 @@ Layouts are validated (bounds, spacing, quantity, rotation, stock match); invali
 | Project | Purpose |
 |---------|---------|
 | **OpenNest** | WinForms desktop app |
-| **OpenNest.Core** | Domain model, geometry, CNC primitives |
+| **OpenNest.Core** | Domain model, geometry, CNC primitives; [material-overlap diagnostics](docs/geometry/visual-overlap-check.md) |
 | **OpenNest.Engine** | Nesting algorithms and whole-job contracts |
 | **OpenNest.IO** | DXF/DWG, `.nest`, G-code, BOM I/O; CAD import |
 | **OpenNest.Console** | Headless batch nesting |
diff --git a/docs/geometry/visual-overlap-check.md b/docs/geometry/visual-overlap-check.md
new file mode 100644
index 0000000..bbf99e6
--- /dev/null
+++ b/docs/geometry/visual-overlap-check.md
@@ -0,0 +1,140 @@
+# Material-overlap polygon diagnostics
+
+`OpenNest.Diagnostics.PlateOverlapAnalyzer` in OpenNest.Core checks a group of placed
+parts and returns the shared polygon areas for each overlapping pair. This is the
+cross-platform analysis foundation for a future PlateView overlay; it does not add
+a menu command, painting, centroids, or freshness management yet. Existing
+`Part.Intersects`, `PartOverlapChecker`, `Plate.HasOverlappingParts`, engine
+validators, and CLI entry points are unchanged. A separate shared-triangulator fix
+uses translation-stable winding, correcting missed clockwise outlines/holes far
+from the origin without changing contact or fragment-area tolerance policies.
+
+## Synchronous use
+
+```csharp
+using OpenNest.Diagnostics;
+
+var report = PlateOverlapAnalyzer.Analyze(parts, cancellationToken);
+var areas = report.Pairs.SelectMany(pair => pair.Regions).ToList();
+
+foreach (var pair in report.Pairs)
+{
+    // IDs are zero-based positions in the original input list, including skipped cutoffs.
+    Console.WriteLine($"{pair.PartAId} / {pair.PartBId}: {pair.Area}");
+    foreach (var region in pair.Regions)
+    {
+        // region.Vertices: closed, read-only world-coordinate polygon
+        // region.Area: positive shared material area, in model units squared
+    }
+}
+
+// An empty list alone does not mean the whole group was checked successfully.
+if (!report.IsComplete)
+    foreach (var issue in report.Issues)
+        Console.WriteLine($"Uncheckable input/pair {issue.PartAId} / {issue.PartBId}: {issue.Message}");
+```
+
+`Pairs` is ordered by `(PartAId, PartBId)`, with `PartAId < PartBId`. Drawing names
+are captured as labels, not used as identity. Repeated instances and different
+drawings with the same name remain distinct. Callers should pass each physical
+instance once; duplicate input entries are distinct positions in the group.
+`pair.Bounds` returns a fresh world-coordinate bounding box; collections and
+vertices cannot mutate the snapshot, report, or live geometry.
+
+## Capture once, analyze off-thread
+
+```csharp
+// UI thread, while parts/drawings are stable:
+var snapshot = PlateOverlapAnalyzer.Capture(parts, cancellationToken);
+
+// Worker thread, no access to live Part/Drawing/Program objects:
+var report = await Task.Run(
+    () => PlateOverlapAnalyzer.Analyze(snapshot, cancellationToken),
+    cancellationToken);
+```
+
+Capture converts each distinct clean source program by reference identity once
+into owned entities, including expanded shared hole-subprogram calls, and copies
+input IDs, names, locations, and baseline-adjusted rotations. This is intentionally
+not a `Program.Clone` dependency: conversion itself creates fresh geometry without
+mutating the source or re-aligning shared subprograms. Capture has synchronous
+conversion cost; callers must not mutate inputs while capture runs.
+
+Analysis clones captured entities before chaining, prepares polygons once per
+source, then prepares each pose. An X-sorted bounds sweep prunes separated pairs.
+It invokes the existing hole-aware `Collision.Check` once per candidate pair,
+without an earlier boolean collision pass. Pairs are rebased near the origin for
+clipping/triangulation and restored to world coordinates; area calculation uses
+translated-origin products to avoid cancellation far from the origin. Snapshots
+can be reused and analyzed concurrently. Callers own freshness checks and must
+not publish results after geometry changes or after a newer request supersedes them.
+
+Cancellation throws `OperationCanceledException`; it never returns a partial
+all-clear. Checks occur between source/pose preparation, validation loops, and
+candidate pairs, and before return. An individual conversion, polygonization,
+triangulation, or `Collision.Check` call is not internally interruptible.
+
+## Material contract
+
+- Material comes from `Part.BaseDrawing.Program`, transformed by
+  `part.Rotation - drawing.Program.Rotation`, then `part.Location`. Applied or
+  restored lead-ins, lead-outs, and tabs in `Part.Program` do not redefine material.
+- Cutoff parts are skipped. Scribe, rapid, lead-in, and lead-out layers in the clean
+  source do not define material; ordinary cut/default/display contours do.
+- The caller chooses the group. Preview parts are not intrinsically distinguishable
+  from committed parts here; a PlateView caller must supply committed parts only.
+- Valid material has one simple closed outer contour and strictly internal,
+  mutually disjoint holes. Open, empty, degenerate, self-intersecting, nonfinite,
+  disconnected-outer, touching-hole, intersecting-hole, or nested-island geometry
+  produces an issue. Native contour intersections are checked before polygonal
+  containment, so sampling cannot hide a circular-hole crossing or tangency.
+  A gap above `Tolerance.Epsilon` is not silently welded closed.
+  Open cut marks are conservatively uncheckable; mark them as Scribe instead.
+- Some valid curved geometry, such as sub-chord-width thin rings whose sampled
+  contours cross, is uncheckable at this fixed tolerance and returns incomplete
+  rather than clear. No automatic healing or adaptive refinement is performed.
+  Poses that collapse edges or materially change area through floating-point
+  rounding are also incomplete, even when all coordinates remain finite.
+- Expected geometry failures produce issues with original input indices and
+  preserve overlaps found among other valid parts. Unexpected failures propagate.
+  A report with any issue has `IsComplete == false`, even if `Pairs` is empty.
+- No part, drawing, quantity, pose, cutting state, or selection is modified.
+
+## Interpretation and limits
+
+Regions are the kernel's convex, hole-subtracted fragments, not merged connected
+islands. Fill the fragments for a visual overlay; do not outline triangulation
+seams as physical boundaries. Areas within one pair may be summed. Areas across
+pairs are not a union: three coincident parts produce three overlapping pairs,
+so summing all pair areas double-counts shared plate locations.
+
+Full containment and coincident parts are detected without relying on crossing
+points. Edge/corner contact with no positive shared material is not overlap.
+There are no spacing offsets, plate-edge checks, cut-path crossing checks, automatic
+repairs, export blocks, or machining-validity guarantees.
+
+Arc/circle flattening uses a chord tolerance of `0.001` model units (also exposed
+as `report.ChordTolerance`). Curved overlaps and topology are therefore polygonal
+approximations. The unchanged collision kernel applies dimensional bounds and
+fragment-area thresholds using `Tolerance.Epsilon` (`0.00001`); sufficiently small
+slivers are below its reporting policy. Floating-point coordinates still have
+finite resolution. Contact and fragment thresholds are unchanged; only the shared
+triangulator's winding arithmetic was stabilized in the prerequisite fix.
+
+Next integration/hardening: add PlateView request generations and stale-result
+invalidation before rendering; measure real-plate capture/analysis cost and
+cancellation latency before adding cached triangulations or background capture;
+add area-weighted centroids separately if the UI needs them.
+
+## Verification
+
+`OpenNest.Tests/Diagnostics/PlateOverlapAnalyzerTests.cs` exercises analytical
+rectangle regions/areas, containment and contact, both operands' holes, concave
+and disconnected intersections, curves, baseline rotation, large translations,
+deterministic pair ordering against an exhaustive rectangle oracle, invalid
+inputs, snapshot isolation, read-only output, cutting-program independence, and
+cancellation. Run:
+
+```sh
+dotnet test OpenNest.Tests/OpenNest.Tests.csproj --filter FullyQualifiedName~PlateOverlapAnalyzerTests
+```