feat(plateview): annotate overlap centroids

OpenNest.Core/Diagnostics/OverlapHoverPages.cs

@@ -0,0 +1,120 @@
+using System;
+using System.Collections.Generic;
+using System.Globalization;
+using System.Linq;
+
+namespace OpenNest.Diagnostics;
+
+/// <summary>
+/// Viewport-sized pages of cached overlap details, including continuation pages for a
+/// single long pair. The caller supplies its actual single-line font measurement.
+/// No names or numeric details are elided, and no geometry is queried here.
+/// </summary>
+public sealed class OverlapHoverPages
+{
+    private readonly IReadOnlyList<string>[] pages;
+    private readonly IReadOnlyList<string>[] navigation;
+
+    private OverlapHoverPages(IReadOnlyList<string>[] pages, IReadOnlyList<string>[] navigation,
+        bool needsLargerViewport = false)
+    {
+        this.pages = pages;
+        this.navigation = navigation;
+        NeedsLargerViewport = needsLargerViewport;
+    }
+
+    public IReadOnlyList<string> Lines => PageCount == 0 ? Array.Empty<string>() : pages[PageIndex];
+    public IReadOnlyList<string> NavigationLines => PageCount == 0 ? Array.Empty<string>() : navigation[PageIndex];
+    public int PageIndex { get; private set; }
+    public int PageCount => pages.Length;
+    public bool NeedsLargerViewport { get; }
+
+    public void MovePage(int delta) => PageIndex = (int)System.Math.Clamp((long)PageIndex + delta, 0,
+        System.Math.Max(0, PageCount - 1));
+
+    public static OverlapHoverPages Create(string text, int pairCount, int maxRows,
+        double maxWidth, Func<string, double> measure)
+    {
+        var tooSmall = new OverlapHoverPages([], [], true);
+        if (maxRows < 1 || !double.IsFinite(maxWidth) || maxWidth <= 0)
+            return tooSmall;
+        var lines = Wrap(text, maxWidth, measure);
+        if (lines == null)
+            return tooSmall;
+        if (lines.Count <= maxRows)
+            return new OverlapHoverPages([lines.AsReadOnly()], [Array.Empty<string>()]);
+
+        // Reserve the real, wrapped hint as well as content. Increasing the reserved
+        // rows can increase the page count/digit count, so converge before slicing.
+        for (var hintRows = 2; hintRows < maxRows;)
+        {
+            var contentRows = maxRows - hintRows;
+            var count = (lines.Count - 1) / contentRows + 1;
+            var hints = new IReadOnlyList<string>[count];
+            var requiredHintRows = hintRows;
+            for (var page = 0; page < count; page++)
+            {
+                var hint = Wrap($"Page {page + 1}/{count} · {pairCount} pairs\nPgUp/PgDn", maxWidth, measure);
+                if (hint == null)
+                    return tooSmall;
+                hints[page] = hint.AsReadOnly();
+                requiredHintRows = System.Math.Max(requiredHintRows, hint.Count);
+            }
+            if (requiredHintRows > hintRows)
+            {
+                hintRows = requiredHintRows;
+                continue;
+            }
+            var pages = Enumerable.Range(0, count)
+                .Select(page => (IReadOnlyList<string>)Array.AsReadOnly(lines.Skip(page * contentRows).Take(contentRows).ToArray()))
+                .ToArray();
+            return new OverlapHoverPages(pages, hints);
+        }
+        // There must be room for at least one complete content line AND navigation.
+        return tooSmall;
+    }
+
+    private static List<string> Wrap(string text, double width, Func<string, double> measure)
+    {
+        var lines = new List<string>();
+        foreach (var paragraph in text.Replace("\r\n", "\n").Split('\n'))
+        {
+            if (paragraph.Length == 0)
+            {
+                lines.Add("");
+                continue;
+            }
+            var starts = StringInfo.ParseCombiningCharacters(paragraph).Append(paragraph.Length).ToArray();
+            for (var first = 0; first < starts.Length - 1;)
+            {
+                var low = first;
+                var high = starts.Length - 1;
+                while (low < high)
+                {
+                    var end = low + (high - low + 1) / 2;
+                    if (measure(paragraph[starts[first]..starts[end]]) <= width)
+                        low = end;
+                    else
+                        high = end - 1;
+                }
+                if (low == first)
+                    return null; // Even one grapheme cannot fit; do not silently clip it.
+                var last = low;
+                if (last < starts.Length - 1)
+                {
+                    for (var end = last; end > first; end--)
+                    {
+                        if (char.IsWhiteSpace(paragraph[starts[end - 1]]))
+                        {
+                            last = end;
+                            break;
+                        }
+                    }
+                }
+                lines.Add(paragraph[starts[first]..starts[last]]);
+                first = last;
+            }
+        }
+        return lines;
+    }
+}

OpenNest.Core/Diagnostics/OverlapPairPresentation.cs

@@ -0,0 +1,46 @@
+using System;
+using System.Collections.Generic;
+using System.Globalization;
+using System.Linq;
+using OpenNest.Geometry;
+
+namespace OpenNest.Diagnostics;
+
+/// <summary>Read-only pair presentation; no geometry preparation or collision queries.</summary>
+public static class OverlapPairPresentation
+{
+    public static string Label(PlateOverlapPair pair) => $"{pair.PartAId + 1}/{pair.PartBId + 1}";
+
+    public static string Details(PlateOverlapPair pair, Units capturedUnits, IFormatProvider provider = null)
+    {
+        var units = UnitsHelper.GetShortString(capturedUnits);
+        return $"Pair {Label(pair)}: {pair.PartAName} / {pair.PartBName}\n"
+            + $"Shared area ≈ {Number(pair.Area, provider)} {units}²\n"
+            + $"Centroid: ({Number(pair.Centroid.X, provider)}, {Number(pair.Centroid.Y, provider)}) {units}";
+    }
+
+    // Significant figures adapt to scale: a positive sliver must never read as zero.
+    public static string Number(double value, IFormatProvider provider = null) =>
+        value.ToString("G6", provider ?? CultureInfo.CurrentCulture);
+
+    public static double MarkerHalfSize(int deviceDpi) => 6.0 * deviceDpi / 96;
+    public static double HitRadius(int deviceDpi) => 10.0 * deviceDpi / 96;
+
+    /// <summary>
+    /// Projects cached centroids into a screen-pixel coordinate space. The pointer must
+    /// use that same space; view zoom never scales the DPI-adjusted hit radius.
+    /// Coincident or nearby markers return every matching pair in stable ID order.
+    /// </summary>
+    public static IReadOnlyList<PlateOverlapPair> HitTest(IEnumerable<PlateOverlapPair> pairs,
+        Func<Vector, Vector> worldToScreen, Vector pointer, int deviceDpi)
+    {
+        var radius = HitRadius(deviceDpi);
+        return pairs.Where(pair =>
+        {
+            var center = worldToScreen(pair.Centroid);
+            var dx = pointer.X - center.X;
+            var dy = pointer.Y - center.Y;
+            return dx * dx + dy * dy <= radius * radius;
+        }).OrderBy(pair => pair.PartAId).ThenBy(pair => pair.PartBId).ToArray();
+    }
+}

OpenNest.Core/Diagnostics/OverlapReportState.cs

@@ -2,7 +2,7 @@ using System.Collections.Generic;
 
 namespace OpenNest.Diagnostics;
 
-public enum OverlapDisplayMode { Off, Areas }
+public enum OverlapDisplayMode { Off, Areas, Centroids, Both }
 public enum OverlapCheckStatus { NotChecked, Checking, Current, Incomplete, Failed, Canceled, Stale }
 
 /// <summary>UI-thread lifecycle policy, independent of workers, GDI and view transforms.</summary>
@@ -34,7 +34,8 @@ public sealed class OverlapReportState
     {
         Clear(OverlapCheckStatus.Checking);
         stamp = OverlapGeometryStamp.Capture(plate);
-        DisplayMode = OverlapDisplayMode.Areas;
+        if (DisplayMode == OverlapDisplayMode.Off)
+            DisplayMode = OverlapDisplayMode.Areas;
         return Generation;
     }
 

OpenNest.Core/Diagnostics/PlateOverlapAnalyzer.cs

@@ -150,14 +150,26 @@ public static class PlateOverlapAnalyzer
                     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.");
+                    // Evaluate every hole-subtracted fragment before restoring world space.
+                    // A failed moment must make this pair incomplete, never an origin marker.
+                    var moments = new List<PolygonAreaMoments>();
+                    var regions = new List<PlateOverlapRegion>();
+                    foreach (var region in result.OverlapRegions)
+                    {
+                        cancellationToken.ThrowIfCancellationRequested();
+                        if (!PolygonAreaMoments.TryCompute(region.Vertices, out var fragment))
+                            throw new ArithmeticException("Overlap fragment area moments are invalid.");
+                        moments.Add(fragment);
+                        regions.Add(new PlateOverlapRegion(region.Vertices.Select(point => point + origin),
+                            fragment.Area));
+                    }
+                    if (!PolygonAreaMoments.TryCombine(moments, out var combined))
+                        throw new ArithmeticException("Combined overlap area moments are invalid.");
+                    var centroid = combined.Centroid + origin;
+                    if (!OverlapMaterial.IsFinite(centroid))
+                        throw new ArithmeticException("Overlap centroid is not finite in world coordinates.");
                     pairs.Add(new PlateOverlapPair(a.Input.Id, b.Input.Id,
-                        a.Input.Name, b.Input.Name, regions));
+                        a.Input.Name, b.Input.Name, regions, centroid));
                 }
                 catch (Exception exception) when (IsGeometryFailure(exception))
                 {

OpenNest.Core/Diagnostics/PlateOverlapReport.cs

@@ -25,7 +25,7 @@ public sealed class PlateOverlapPair
     private readonly Box bounds;
 
     internal PlateOverlapPair(int partAId, int partBId, string partAName, string partBName,
-        List<PlateOverlapRegion> regions)
+        List<PlateOverlapRegion> regions, Vector centroid)
     {
         PartAId = partAId;
         PartBId = partBId;
@@ -33,6 +33,7 @@ public sealed class PlateOverlapPair
         PartBName = partBName;
         Regions = regions.AsReadOnly();
         Area = regions.Sum(region => region.Area);
+        Centroid = centroid;
         var points = regions.SelectMany(region => region.Vertices).ToArray();
         var left = points.Min(point => point.X);
         var bottom = points.Min(point => point.Y);
@@ -47,6 +48,11 @@ public sealed class PlateOverlapPair
     /// <summary>Convex fragments, not connected islands; no mutable kernel polygons are exposed.</summary>
     public IReadOnlyList<PlateOverlapRegion> Regions { get; }
     public double Area { get; }
+    /// <summary>
+    /// Finite world-coordinate area centroid of all shared material, after hole subtraction.
+    /// This can lie outside disconnected or concave shared material. Returned by value.
+    /// </summary>
+    public Vector Centroid { get; }
     /// <summary>A fresh world-coordinate bounds copy.</summary>
     public Box Bounds => new(bounds.X, bounds.Y, bounds.Length, bounds.Width);
 }

OpenNest.Core/Geometry/PolygonAreaMoments.cs

@@ -0,0 +1,101 @@
+using System.Collections.Generic;
+
+namespace OpenNest.Geometry;
+
+/// <summary>
+/// Positive area and area centroid of a simple polygon, independent of winding.
+/// Moments are evaluated about a nearby origin rather than the world origin.
+/// </summary>
+public readonly struct PolygonAreaMoments
+{
+    private PolygonAreaMoments(double area, Vector centroid)
+    {
+        Area = area;
+        Centroid = centroid;
+    }
+
+    public double Area { get; }
+    public Vector Centroid { get; }
+
+    /// <summary>
+    /// Accepts an open vertex list or an exactly repeated closing vertex. Returns false
+    /// for degenerate or nonfinite moments; does not validate polygon topology.
+    /// </summary>
+    public static bool TryCompute(IReadOnlyList<Vector> vertices, out PolygonAreaMoments moments)
+    {
+        moments = default;
+        if (vertices == null || vertices.Count < 3)
+            return false;
+        foreach (var point in vertices)
+            if (!IsFinite(point))
+                return false;
+
+        var origin = vertices[0];
+        var count = vertices.Count;
+        if (vertices[count - 1].X == origin.X && vertices[count - 1].Y == origin.Y)
+            count--;
+        if (count < 3)
+            return false;
+
+        var twiceArea = 0.0;
+        var momentX = 0.0;
+        var momentY = 0.0;
+        // The closing edges meet the local origin and contribute zero. The signed
+        // triangle fan also handles concavity without averaging polygon vertices.
+        for (var i = 1; i + 1 < count; i++)
+        {
+            var a = vertices[i] - origin;
+            var b = vertices[i + 1] - origin;
+            var cross = a.X * b.Y - a.Y * b.X;
+            twiceArea += cross;
+            momentX += (a.X + b.X) * cross;
+            momentY += (a.Y + b.Y) * cross;
+        }
+
+        var area = System.Math.Abs(twiceArea) * 0.5;
+        if (!double.IsFinite(area) || area <= 0
+            || !double.IsFinite(momentX) || !double.IsFinite(momentY))
+            return false;
+        // Dividing signed moments by signed area cancels the winding, while Area
+        // stays positive so independently wound fragments always add material.
+        var centroid = origin + new Vector(momentX / twiceArea / 3, momentY / twiceArea / 3);
+        if (!IsFinite(centroid))
+            return false;
+        moments = new PolygonAreaMoments(area, centroid);
+        return true;
+    }
+
+    /// <summary>
+    /// Combines nonoverlapping, already hole-subtracted fragments using positive area
+    /// weights and another local origin. The centroid may lie outside the material.
+    /// Empty input or any invalid fragment fails the entire result.
+    /// </summary>
+    public static bool TryCombine(IEnumerable<PolygonAreaMoments> fragments, out PolygonAreaMoments moments)
+    {
+        moments = default;
+        if (fragments == null)
+            return false;
+        var area = 0.0;
+        var origin = Vector.Zero;
+        var firstMoment = Vector.Zero;
+        foreach (var fragment in fragments)
+        {
+            if (!double.IsFinite(fragment.Area) || fragment.Area <= 0 || !IsFinite(fragment.Centroid))
+                return false;
+            if (area == 0)
+                origin = fragment.Centroid;
+            firstMoment += (fragment.Centroid - origin) * fragment.Area;
+            area += fragment.Area;
+        }
+
+        if (!double.IsFinite(area) || area <= 0 || !IsFinite(firstMoment))
+            return false;
+        var centroid = origin + firstMoment / area;
+        if (!IsFinite(centroid))
+            return false;
+        moments = new PolygonAreaMoments(area, centroid);
+        return true;
+    }
+
+    private static bool IsFinite(Vector point) => double.IsFinite(point.X) && double.IsFinite(point.Y);
+}

OpenNest.Tests/Diagnostics/OverlapHoverPagesTests.cs

@@ -0,0 +1,130 @@
+using System.Globalization;
+using OpenNest.CNC;
+using OpenNest.Diagnostics;
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.Diagnostics;
+
+public class OverlapHoverPagesTests
+{
+    [Fact]
+    public void CrowdedCoincidentPairsRemainAccessibleInOrderWithinEveryPageBudget()
+    {
+        var parts = Enumerable.Range(1, 12).Select(i => Rectangle($"part-{i}")).ToArray();
+        var report = PlateOverlapAnalyzer.Analyze(parts);
+        var pairs = OverlapPairPresentation.HitTest(report.Pairs.Reverse(), p => p, new Vector(2, 2), 96);
+        var text = string.Join("\n\n", pairs.Select(p => OverlapPairPresentation.Details(p, Units.Millimeters, CultureInfo.InvariantCulture)));
+        var pages = OverlapHoverPages.Create(text, pairs.Count, 10, 45, s => s.Length);
+
+        Assert.True(pages.PageCount > 1);
+        Assert.False(pages.NeedsLargerViewport);
+        var displayed = ReadAll(pages, 10, 45);
+        Assert.Equal(text.Replace("\n", ""), displayed);
+        Assert.Contains("Pair 11/12: part-11 / part-12", displayed);
+        Assert.Contains("Shared area ≈ 16 mm²", displayed);
+        Assert.Contains("Centroid: (2, 2) mm", displayed);
+        Assert.Equal(pages.PageCount - 1, pages.PageIndex);
+        Assert.Contains($"Page {pages.PageCount}/{pages.PageCount}", string.Join("", pages.NavigationLines));
+        Assert.Contains("66 pairs", string.Join("", pages.NavigationLines));
+        Assert.Contains("PgUp/PgDn", string.Join("", pages.NavigationLines));
+    }
+
+    [Theory]
+    [InlineData(8, 12)]
+    [InlineData(4, 40)]
+    public void OneDetailWithLongUnbrokenNamesPagesWithoutDroppingText(int rows, int width)
+    {
+        var name = string.Concat(Enumerable.Repeat("veryLongName😀e\u0301", 30));
+        var pair = Assert.Single(PlateOverlapAnalyzer.Analyze(new[] { Rectangle(name), Rectangle("tail") }).Pairs);
+        var text = OverlapPairPresentation.Details(pair, Units.Inches, CultureInfo.InvariantCulture);
+        var pages = OverlapHoverPages.Create(text, 1, rows, width, s => new StringInfo(s).LengthInTextElements);
+
+        Assert.True(pages.PageCount > 1);
+        Assert.False(pages.NeedsLargerViewport);
+        Assert.Equal(text.Replace("\n", ""), ReadAll(pages, rows, width, s => new StringInfo(s).LengthInTextElements));
+        Assert.All(AllLines(text, rows, width), line =>
+        {
+            Assert.False(line.Length > 0 && char.IsLowSurrogate(line[0]));
+            Assert.False(line.StartsWith("\u0301"));
+        });
+    }
+
+    [Fact]
+    public void NavigationClampsAtBothEndsAndNewHoverStartsAtFirstPage()
+    {
+        const string text = "one\ntwo\nthree\nfour\nfive\nsix";
+        var pages = OverlapHoverPages.Create(text, 2, 4, 40, s => s.Length);
+        Assert.True(pages.PageCount > 1);
+        pages.MovePage(int.MaxValue);
+        Assert.Equal(pages.PageCount - 1, pages.PageIndex);
+        pages.MovePage(1);
+        Assert.Equal(pages.PageCount - 1, pages.PageIndex);
+        pages.MovePage(int.MinValue);
+        Assert.Equal(0, pages.PageIndex);
+        pages.MovePage(-1);
+        Assert.Equal(0, pages.PageIndex);
+        pages.MovePage(1);
+        Assert.Equal(0, OverlapHoverPages.Create(text, 2, 4, 40, s => s.Length).PageIndex);
+    }
+
+    [Fact]
+    public void FittingDetailsDoNotSpendSpaceOnNavigation()
+    {
+        var pages = OverlapHoverPages.Create("Pair 1/2\narea\ncentroid", 1, 3, 40, s => s.Length);
+        Assert.Equal(1, pages.PageCount);
+        Assert.Empty(pages.NavigationLines);
+        Assert.Equal(new[] { "Pair 1/2", "area", "centroid" }, pages.Lines);
+        pages.MovePage(1);
+        Assert.Equal(0, pages.PageIndex);
+    }
+
+    [Theory]
+    [InlineData(0, 40)]
+    [InlineData(3, 0)]
+    [InlineData(1, 5)]
+    [InlineData(4, 0.5)]
+    public void ImpossibleViewportExplicitlyRequestsMoreSpaceInsteadOfDroppingDetails(int rows, double width)
+    {
+        var pages = OverlapHoverPages.Create("Pair 1/2\narea\ncentroid", 1, rows, width, s => s.Length);
+        Assert.True(pages.NeedsLargerViewport);
+        Assert.Empty(pages.Lines);
+        Assert.Equal(0, pages.PageCount);
+    }
+
+    private static string ReadAll(OverlapHoverPages pages, int rows, double width, Func<string, double>? measure = null)
+    {
+        measure ??= s => s.Length;
+        var content = new List<string>();
+        for (var index = 0; index < pages.PageCount; index++)
+        {
+            Assert.Equal(index, pages.PageIndex);
+            Assert.InRange(pages.Lines.Count + pages.NavigationLines.Count, 1, rows);
+            Assert.All(pages.Lines.Concat(pages.NavigationLines), line => Assert.InRange(measure(line), 0, width));
+            content.AddRange(pages.Lines);
+            pages.MovePage(1);
+        }
+        return string.Concat(content);
+    }
+
+    private static IEnumerable<string> AllLines(string text, int rows, int width)
+    {
+        var pages = OverlapHoverPages.Create(text, 1, rows, width, s => new StringInfo(s).LengthInTextElements);
+        for (var i = 0; i < pages.PageCount; i++)
+        {
+            foreach (var line in pages.Lines)
+                yield return line;
+            pages.MovePage(1);
+        }
+    }
+
+    private static Part Rectangle(string name)
+    {
+        var program = new Program(Mode.Absolute);
+        program.Codes.Add(new RapidMove(0, 0));
+        program.Codes.Add(new LinearMove(4, 0));
+        program.Codes.Add(new LinearMove(4, 4));
+        program.Codes.Add(new LinearMove(0, 4));
+        program.Codes.Add(new LinearMove(0, 0));
+        return new Part(new Drawing(name, program));
+    }
+}

OpenNest.Tests/Diagnostics/OverlapPairPresentationTests.cs

@@ -0,0 +1,78 @@
+using System.Globalization;
+using OpenNest.CNC;
+using OpenNest.Diagnostics;
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.Diagnostics;
+
+public class OverlapPairPresentationTests
+{
+    [Theory]
+    [InlineData(Units.Inches, "in")]
+    [InlineData(Units.Millimeters, "mm")]
+    public void DetailsUseCapturedNamesSequenceIdsAndSuppliedUnits(Units units, string symbol)
+    {
+        var parts = new[] { Rectangle("cutoff"), Rectangle("left"), Rectangle("right") };
+        parts[0].BaseDrawing.IsCutOff = true;
+        var snapshot = PlateOverlapAnalyzer.Capture(parts);
+        parts[1].BaseDrawing.Name = "changed";
+        var pair = Assert.Single(PlateOverlapAnalyzer.Analyze(snapshot).Pairs);
+        Assert.Equal("2/3", OverlapPairPresentation.Label(pair));
+        var text = OverlapPairPresentation.Details(pair, units, CultureInfo.InvariantCulture);
+        Assert.Equal($"Pair 2/3: left / right\nShared area ≈ 16 {symbol}²\nCentroid: (2, 2) {symbol}", text);
+    }
+
+    [Theory]
+    [InlineData(1e-15)]
+    [InlineData(1e-100)]
+    [InlineData(double.Epsilon)]
+    [InlineData(0.000000123456)]
+    public void PositiveTinyValuesNeverFormatAsZero(double value)
+    {
+        var text = OverlapPairPresentation.Number(value, CultureInfo.InvariantCulture);
+        Assert.True(double.Parse(text, CultureInfo.InvariantCulture) > 0, text);
+    }
+
+    [Theory]
+    [InlineData(96, 1)]
+    [InlineData(144, 1.5)]
+    [InlineData(192, 2)]
+    public void HitRadiusIsScreenSizedDpiScaledAndInclusive(int dpi, double factor)
+    {
+        Assert.Equal(6 * factor, OverlapPairPresentation.MarkerHalfSize(dpi));
+        Assert.Equal(10 * factor, OverlapPairPresentation.HitRadius(dpi));
+        var pairs = PlateOverlapAnalyzer.Analyze(new[] { Rectangle("a"), Rectangle("b") }).Pairs;
+        foreach (var zoom in new[] { 0.5, 20.0, 500.0 })
+        {
+            Vector ToScreen(Vector world) => new(100 + world.X * zoom, 200 - world.Y * zoom);
+            var center = ToScreen(pairs[0].Centroid);
+            var radius = OverlapPairPresentation.HitRadius(dpi);
+            Assert.Single(OverlapPairPresentation.HitTest(pairs, ToScreen,
+                center + new Vector(radius, 0), dpi));
+            Assert.Empty(OverlapPairPresentation.HitTest(pairs, ToScreen,
+                center + new Vector(radius + 0.01, 0), dpi));
+            Assert.Empty(OverlapPairPresentation.HitTest(pairs, ToScreen,
+                center + new Vector(radius, radius), dpi));
+        }
+    }
+
+    [Fact]
+    public void CoincidentMarkersReturnEveryPairInIdOrderNotFragmentOrder()
+    {
+        var pairs = PlateOverlapAnalyzer.Analyze(new[] { Rectangle("a"), Rectangle("b"), Rectangle("c") }).Pairs;
+        var hits = OverlapPairPresentation.HitTest(pairs.Reverse(), p => p, new Vector(2, 2), 96);
+        Assert.Equal(new[] { "1/2", "1/3", "2/3" }, hits.Select(OverlapPairPresentation.Label));
+        Assert.All(hits, p => Assert.True(p.Regions.Count > 1));
+    }
+
+    private static Part Rectangle(string name)
+    {
+        var program = new Program(Mode.Absolute);
+        program.Codes.Add(new RapidMove(0, 0));
+        program.Codes.Add(new LinearMove(4, 0));
+        program.Codes.Add(new LinearMove(4, 4));
+        program.Codes.Add(new LinearMove(0, 4));
+        program.Codes.Add(new LinearMove(0, 0));
+        return new Part(new Drawing(name, program));
+    }
+}

OpenNest.Tests/Diagnostics/OverlapReportStateTests.cs

@@ -134,6 +134,22 @@ public class OverlapReportStateTests
         Assert.Null(state.Report);
     }
 
+    [Theory]
+    [InlineData(OverlapDisplayMode.Off, OverlapDisplayMode.Areas)]
+    [InlineData(OverlapDisplayMode.Areas, OverlapDisplayMode.Areas)]
+    [InlineData(OverlapDisplayMode.Centroids, OverlapDisplayMode.Centroids)]
+    [InlineData(OverlapDisplayMode.Both, OverlapDisplayMode.Both)]
+    public void CheckAndRecheckPreserveVisibleMode(OverlapDisplayMode chosen, OverlapDisplayMode expected)
+    {
+        var plate = PlateWithParts();
+        var state = new OverlapReportState { DisplayMode = chosen };
+        var request = state.Begin(plate);
+        Assert.Equal(expected, state.DisplayMode);
+        Assert.True(state.TryPublish(request, plate, Analyze(plate)));
+        state.Begin(plate);
+        Assert.Equal(expected, state.DisplayMode);
+    }
+
     [Fact]
     public void NewPlateResetsStateButRetainsDocumentDisplayPreference()
     {

OpenNest.Tests/Diagnostics/PlateOverlapAnalyzerTests.cs

@@ -19,6 +19,7 @@ public class PlateOverlapAnalyzerTests
         var pair = Assert.Single(report.Pairs);
         Assert.Equal((0, 1), (pair.PartAId, pair.PartBId));
         Assert.Equal(0.5, pair.Area, 9);
+        AssertCentroid(pair, 0.75, 0.5);
         Assert.NotEmpty(pair.Regions);
         Assert.All(pair.Regions, region =>
         {
@@ -43,6 +44,7 @@ public class PlateOverlapAnalyzerTests
             Rectangle(0, 0, 4, 4), Rectangle(1, 1, 1, 1)
         }).Pairs);
         Assert.Equal(1, pair.Area, 9);
+        AssertCentroid(pair, 1.5, 1.5);
     }
 
     [Theory]
@@ -84,7 +86,9 @@ public class PlateOverlapAnalyzerTests
         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);
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(0.5, pair.Area, 9);
+        AssertCentroid(pair, 0.75, 2);
     }
 
     [Fact]
@@ -94,7 +98,9 @@ public class PlateOverlapAnalyzerTests
         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);
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(14, pair.Area, 8);
+        AssertCentroid(pair, 28.5 / 14, 28.5 / 14);
     }
 
     [Fact]
@@ -109,6 +115,7 @@ public class PlateOverlapAnalyzerTests
         Assert.True(report.IsComplete, string.Join("; ", report.Issues));
         var pair = Assert.Single(report.Pairs);
         Assert.Equal(2, pair.Area, 8);
+        AssertCentroid(pair, 1.5, 2.5);
         Assert.All(pair.Regions, region => Assert.True(
             region.Vertices.All(p => p.X <= 1) || region.Vertices.All(p => p.X >= 2)));
     }
@@ -127,6 +134,7 @@ public class PlateOverlapAnalyzerTests
         Assert.True(report.IsComplete, string.Join("; ", report.Issues));
         var pair = Assert.Single(report.Pairs);
         Assert.Equal(0.5, pair.Area, 7);
+        AssertCentroid(pair, x + 0.75, y + 0.5);
         Assert.Equal(x + 0.5, pair.Bounds.Left, 7);
         Assert.Equal(y + 1, pair.Bounds.Top, 7);
     }
@@ -141,7 +149,9 @@ public class PlateOverlapAnalyzerTests
         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);
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(2, pair.Area, 8);
+        AssertCentroid(pair, 9, 9.5);
     }
 
     [Fact]
@@ -297,6 +307,10 @@ public class PlateOverlapAnalyzerTests
         Assert.Throws<NotSupportedException>(() => ((IList<Vector>)region.Vertices)[0] = new Vector(99, 99));
         pair.Bounds.X = 99;
         Assert.Equal(0, pair.Bounds.X);
+        var centroid = pair.Centroid;
+        centroid.X = 99;
+        centroid.Y = 99;
+        AssertCentroid(pair, 0.5, 0.5);
     }
 
     [Fact]
@@ -368,7 +382,9 @@ public class PlateOverlapAnalyzerTests
         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);
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(1, pair.Area, 8);
+        AssertCentroid(pair, 999999998.5, 999999998.5);
     }
 
     [Fact]
@@ -423,6 +439,68 @@ public class PlateOverlapAnalyzerTests
         Assert.Throws<OperationCanceledException>(() => PlateOverlapAnalyzer.Analyze(snapshot, cancellation.Token));
     }
 
+    [Theory]
+    [InlineData(0)]
+    [InlineData(1000000000)]
+    [InlineData(-1000000000)]
+    public void Analyze_UnequalDisconnectedOverlapWeightsAllFragments(double offset)
+    {
+        var u = WithContours(new[]
+        {
+            new Vector(0, 0), new Vector(6, 0), new Vector(6, 3), new Vector(3, 3),
+            new Vector(3, 1), new Vector(1, 1), new Vector(1, 3), new Vector(0, 3)
+        });
+        u.Location = new Vector(offset, offset);
+
+        var report = PlateOverlapAnalyzer.Analyze(new[] { u, Rectangle(offset, offset + 2, 6, 1) });
+
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(4, pair.Area, 8);
+        AssertCentroid(pair, offset + 3.5, offset + 2.5);
+    }
+
+    [Fact]
+    public void Analyze_RotatedTriangleHasTrueMaterialCentroid()
+    {
+        var triangle = WithContours(new[] { new Vector(0, 0), new Vector(6, 0), new Vector(0, 3) });
+        triangle.Rotate(System.Math.PI / 2);
+        triangle.Location = new Vector(10, 20);
+
+        var report = PlateOverlapAnalyzer.Analyze(new[] { Rectangle(0, 0, 30, 30), triangle });
+
+        Assert.True(report.IsComplete, string.Join("; ", report.Issues));
+        var pair = Assert.Single(report.Pairs);
+        Assert.Equal(9, pair.Area, 8);
+        AssertCentroid(pair, 9, 22);
+    }
+
+    [Fact]
+    public void Analyze_OverflowingPairMomentsAreIncompleteAndRetainOtherPairs()
+    {
+        var huge = Rectangle(0, 0, 1e103, 1e103);
+        var report = PlateOverlapAnalyzer.Analyze(new[]
+        {
+            huge, new Part(huge.BaseDrawing), Rectangle(-2, -2, 1, 1), Rectangle(-2, -2, 1, 1)
+        });
+
+        Assert.False(report.IsComplete);
+        var issue = Assert.Single(report.Issues);
+        Assert.Equal((0, (int?)1), (issue.PartAId, issue.PartBId));
+        Assert.Contains("moment", issue.Message, StringComparison.OrdinalIgnoreCase);
+        var valid = Assert.Single(report.Pairs);
+        Assert.Equal((2, 3), (valid.PartAId, valid.PartBId));
+        AssertCentroid(valid, -1.5, -1.5);
+    }
+
+    private static void AssertCentroid(PlateOverlapPair pair, double x, double y)
+    {
+        Assert.True(double.IsFinite(pair.Centroid.X));
+        Assert.True(double.IsFinite(pair.Centroid.Y));
+        Assert.Equal(x, pair.Centroid.X, 7);
+        Assert.Equal(y, pair.Centroid.Y, 7);
+    }
+
     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));

OpenNest.Tests/Geometry/PolygonAreaMomentsTests.cs

@@ -0,0 +1,141 @@
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.Geometry;
+
+public class PolygonAreaMomentsTests
+{
+    [Theory]
+    [InlineData(0, false, false)]
+    [InlineData(0, true, false)]
+    [InlineData(0, false, true)]
+    [InlineData(0, true, true)]
+    [InlineData(1000000000, false, false)]
+    [InlineData(1000000000, true, true)]
+    [InlineData(-1000000000, false, true)]
+    [InlineData(-1000000000, true, false)]
+    public void TryCompute_RectangleUsesSignedMomentsWithLocalOrigin(double offset, bool reverse, bool closed)
+    {
+        var vertices = Rectangle(offset + 0.5, offset, 0.5, 1);
+        if (reverse)
+            Array.Reverse(vertices);
+        if (closed)
+            vertices = vertices.Append(vertices[0]).ToArray();
+
+        Assert.True(PolygonAreaMoments.TryCompute(vertices, out var moments));
+
+        Assert.Equal(0.5, moments.Area);
+        Assert.Equal(offset + 0.75, moments.Centroid.X);
+        Assert.Equal(offset + 0.5, moments.Centroid.Y);
+    }
+
+    [Theory]
+    [InlineData(false)]
+    [InlineData(true)]
+    public void TryCompute_ConcavePolygonUsesAreaNotVertexAverage(bool reverse)
+    {
+        var vertices = new[]
+        {
+            new Vector(0, 0), new Vector(3, 0), new Vector(3, 1),
+            new Vector(1, 1), new Vector(1, 3), new Vector(0, 3)
+        };
+        if (reverse)
+            Array.Reverse(vertices);
+
+        Assert.True(PolygonAreaMoments.TryCompute(vertices, out var moments));
+
+        Assert.Equal(5, moments.Area);
+        Assert.Equal(1.1, moments.Centroid.X, 12);
+        Assert.Equal(1.1, moments.Centroid.Y, 12);
+    }
+
+    [Fact]
+    public void TryCompute_CollinearVerticesDoNotBiasCentroid()
+    {
+        var vertices = new[]
+        {
+            new Vector(0, 0), new Vector(1, 0), new Vector(2, 0), new Vector(3, 0),
+            new Vector(3, 2), new Vector(0, 2), new Vector(0, 0)
+        };
+
+        Assert.True(PolygonAreaMoments.TryCompute(vertices, out var moments));
+
+        Assert.Equal(6, moments.Area);
+        Assert.Equal(1.5, moments.Centroid.X);
+        Assert.Equal(1, moments.Centroid.Y);
+    }
+
+    [Fact]
+    public void TryCompute_NearButNotExactClosingVertexIsNotDiscarded()
+    {
+        var vertices = new[]
+        {
+            new Vector(0, 0), new Vector(1, 0), new Vector(1, 1),
+            new Vector(0, 1), new Vector(0.000001, 0.000001)
+        };
+        // The final triangle removes area d/2 and has center (d/3, (1+d)/3).
+        const double d = 0.000001;
+        var expectedArea = 1 - d / 2;
+
+        Assert.True(PolygonAreaMoments.TryCompute(vertices, out var moments));
+
+        Assert.Equal(expectedArea, moments.Area, 14);
+        Assert.Equal((0.5 - d * d / 6) / expectedArea, moments.Centroid.X, 14);
+        Assert.Equal((0.5 - d * (1 + d) / 6) / expectedArea, moments.Centroid.Y, 14);
+    }
+
+    [Theory]
+    [InlineData(0, false)]
+    [InlineData(0, true)]
+    [InlineData(1000000000, false)]
+    [InlineData(1000000000, true)]
+    [InlineData(-1000000000, false)]
+    public void TryCombine_UnequalDisconnectedFragmentsUsePositiveAreaWeights(double offset, bool swap)
+    {
+        Assert.True(PolygonAreaMoments.TryCompute(Rectangle(offset, offset, 1, 1), out var small));
+        Assert.True(PolygonAreaMoments.TryCompute(
+            Rectangle(offset + 4, offset, 1, 3).Reverse().ToArray(), out var large));
+
+        Assert.True(PolygonAreaMoments.TryCombine(swap ? new[] { large, small } : new[] { small, large },
+            out var combined));
+
+        Assert.Equal(4, combined.Area);
+        Assert.Equal(offset + 3.5, combined.Centroid.X);
+        Assert.Equal(offset + 1.25, combined.Centroid.Y);
+        // The centroid is in the gap, not on either material fragment.
+        Assert.InRange(combined.Centroid.X - offset, 1.01, 3.99);
+    }
+
+    public static IEnumerable<object[]> InvalidPolygons()
+    {
+        yield return new object[] { Array.Empty<Vector>() };
+        yield return new object[] { new[] { new Vector(1, 1), new Vector(2, 2) } };
+        yield return new object[] { new[] { new Vector(1, 1), new Vector(2, 2), new Vector(3, 3) } };
+        yield return new object[] { new[] { new Vector(1, 1), new Vector(1, 1), new Vector(1, 1) } };
+        yield return new object[] { new[] { new Vector(0, 0), new Vector(double.NaN, 0), new Vector(0, 1) } };
+        yield return new object[] { new[] { new Vector(0, 0), new Vector(1, double.PositiveInfinity), new Vector(0, 1) } };
+        yield return new object[] { new[] { new Vector(double.NegativeInfinity, 0), new Vector(1, 0), new Vector(0, 1) } };
+        yield return new object[] { Rectangle(0, 0, 1e200, 1e200) };
+        yield return new object[] { Rectangle(0, 0, 1e103, 1e103) };
+    }
+
+    [Theory]
+    [MemberData(nameof(InvalidPolygons))]
+    public void TryCompute_DegenerateNonfiniteOrOverflowingMomentsAreRejected(Vector[] vertices)
+    {
+        Assert.False(PolygonAreaMoments.TryCompute(vertices, out _));
+    }
+
+    [Fact]
+    public void TryCombine_EmptyOrInvalidFragmentRejectsWholeResult()
+    {
+        Assert.True(PolygonAreaMoments.TryCompute(Rectangle(1, 1, 1, 1), out var valid));
+
+        Assert.False(PolygonAreaMoments.TryCombine(Array.Empty<PolygonAreaMoments>(), out _));
+        Assert.False(PolygonAreaMoments.TryCombine(new[] { valid, default(PolygonAreaMoments) }, out _));
+        Assert.False(PolygonAreaMoments.TryCombine(new[] { default(PolygonAreaMoments), valid }, out _));
+    }
+
+    private static Vector[] Rectangle(double x, double y, double width, double height) =>
+        new[] { new Vector(x, y), new Vector(x + width, y),
+            new Vector(x + width, y + height), new Vector(x, y + height) };
+}

OpenNest.WinForms.Tests/PlateOverlapOverlayTests.cs

@@ -266,11 +266,15 @@ public class PlateOverlapOverlayTests
         var cancel = Menu(host, "mnuOverlapCancel");
         var off = Menu(host, "mnuOverlapOff");
         var areas = Menu(host, "mnuOverlapAreas");
+        var centroids = Menu(host, "mnuOverlapCentroids");
+        var both = Menu(host, "mnuOverlapBoth");
         Assert.False(check.Enabled);
         Assert.False(cancel.Enabled);
         Assert.False(off.Enabled);
         Assert.False(areas.Enabled);
-        Assert.All(new[] { check, cancel, off, areas }, item => Assert.Equal(Keys.None, item.ShortcutKeys));
+        Assert.False(centroids.Enabled);
+        Assert.False(both.Enabled);
+        Assert.All(new[] { check, cancel, off, areas, centroids, both }, item => Assert.Equal(Keys.None, item.ShortcutKeys));
 
         using var first = new EditNestForm(new Nest("first")) { MdiParent = host };
         first.Show();
@@ -286,6 +290,19 @@ public class PlateOverlapOverlayTests
         Assert.True(off.Checked);
         Assert.False(areas.Checked);
         Assert.Equal(OverlapDisplayMode.Areas, second.OverlapDisplay);
+        centroids.PerformClick();
+        Assert.True(centroids.Checked);
+        Assert.False(off.Checked);
+        Assert.Equal(OverlapDisplayMode.Centroids, first.OverlapDisplay);
+        second.Activate();
+        both.PerformClick();
+        Assert.True(both.Checked);
+        Assert.False(centroids.Checked);
+        Assert.Equal(OverlapDisplayMode.Both, second.OverlapDisplay);
+        first.Activate();
+        Assert.True(centroids.Checked);
+        Assert.False(both.Checked);
+        off.PerformClick();
 
         var previous = SynchronizationContext.Current;
         var context = new PumpContext();
@@ -320,6 +337,458 @@ public class PlateOverlapOverlayTests
         Assert.False(cancel.Enabled);
     });
 
+    [Fact]
+    public void CheckCommandCapturesUnitsAndNamesUntilTheNextCheck() => RunSta(() =>
+    {
+        using var form = new EditNestForm(new Nest("units") { Units = Units.Millimeters });
+        form.Show();
+        form.PlateView.Plate.Parts.Add(Rectangle());
+        form.PlateView.Plate.Parts.Add(Rectangle(1));
+        form.OverlapDisplay = OverlapDisplayMode.Both;
+        var previous = SynchronizationContext.Current;
+        var context = new PumpContext();
+        var started = new TaskCompletionSource<PlateOverlapSnapshot>(TaskCreationOptions.RunContinuationsAsynchronously);
+        var result = new TaskCompletionSource<PlateOverlapReport>(TaskCreationOptions.RunContinuationsAsynchronously);
+        Task? task = null;
+        SynchronizationContext.SetSynchronizationContext(context);
+        try
+        {
+            form.PlateView.OverlapOverlay.Analyze = (snapshot, _) =>
+            {
+                started.TrySetResult(snapshot);
+                return WaitForWorkerResult(result.Task);
+            };
+            task = form.CheckOverlapsAsync();
+            var snapshot = WaitForSnapshot(started.Task);
+            form.Nest.Units = Units.Inches;
+            form.PlateView.Plate.Parts[0].BaseDrawing.Name = "changed";
+            result.SetResult(PlateOverlapAnalyzer.Analyze(snapshot));
+            context.Pump(task);
+            var center = form.PlateView.PointWorldToControl(form.PlateView.OverlapReport.Pairs[0].Centroid);
+            form.PlateView.OverlapOverlay.UpdateHover(center);
+            Assert.Contains(" mm²", form.PlateView.OverlapOverlay.HoverText);
+            Assert.Contains("same name / same name", form.PlateView.OverlapOverlay.HoverText);
+            Assert.DoesNotContain("changed", form.PlateView.OverlapOverlay.HoverText);
+            form.PlateView.OverlapOverlay.Analyze = PlateOverlapAnalyzer.Analyze;
+            task = form.CheckOverlapsAsync();
+            Assert.Null(form.PlateView.OverlapOverlay.HoverText);
+            context.Pump(task);
+            form.PlateView.OverlapOverlay.UpdateHover(center);
+            Assert.Contains(" in²", form.PlateView.OverlapOverlay.HoverText);
+            Assert.Contains("changed / same name", form.PlateView.OverlapOverlay.HoverText);
+            Assert.Equal(OverlapDisplayMode.Both, form.OverlapDisplay);
+        }
+        finally
+        {
+            form.CancelOverlapCheck();
+            result.TrySetCanceled();
+            try { if (task != null) context.Pump(task); }
+            finally { SynchronizationContext.SetSynchronizationContext(previous); }
+        }
+    });
+
+    [Fact]
+    public void CleanupReleasesDequeuedWorkersEvenWithoutCompleteOrFail() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        var first = run.Start();
+        var old = run.Next();
+        var second = run.Start();
+        var current = run.Next();
+        run.Dispose();
+        Assert.True(old.Result.Task.IsCompleted);
+        Assert.True(current.Result.Task.IsCompleted);
+        Assert.True(first.IsCompletedSuccessfully);
+        Assert.True(second.IsCompletedSuccessfully);
+    });
+
+    [Theory]
+    [InlineData(OverlapDisplayMode.Areas)]
+    [InlineData(OverlapDisplayMode.Centroids)]
+    [InlineData(OverlapDisplayMode.Both)]
+    public void RecheckPreservesEachVisibleModeAndDisplayOnlyRepaints(OverlapDisplayMode mode) => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.OverlapDisplay = mode;
+        run.Finish();
+        Assert.Equal(mode, run.View.OverlapDisplay);
+        run.Finish();
+        Assert.Equal(mode, run.View.OverlapDisplay);
+        var report = run.View.OverlapReport;
+        using var image = new Bitmap(300, 300);
+        using var graphics = Graphics.FromImage(image);
+        foreach (var display in Enum.GetValues<OverlapDisplayMode>())
+        {
+            run.View.OverlapDisplay = display;
+            run.View.OverlapOverlay.Draw(graphics);
+            Assert.Same(report, run.View.OverlapReport);
+        }
+        Assert.Equal(2, run.Calls);
+    });
+
+    [Fact]
+    public void CentroidMarkerUsesGraphCoordinatesAndFixedScreenSizeAcrossZoom() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.OverlapDisplay = OverlapDisplayMode.Centroids;
+        run.Finish();
+        var pair = Assert.Single(run.View.OverlapReport.Pairs);
+        using var image = new Bitmap(500, 500);
+        using var graphics = Graphics.FromImage(image);
+        foreach (var zoom in new[] { 20f, 2f })
+        {
+            run.View.ZoomToPoint(new Vector(), zoom);
+            run.View.SetOrigin(60, 320);
+            graphics.ResetTransform();
+            graphics.Clear(Color.White);
+            graphics.TranslateTransform(60, 320);
+            run.View.OverlapOverlay.Draw(graphics);
+            Assert.Null(run.View.OverlapOverlay.CachedPath);
+            var center = run.View.PointWorldToControl(pair.Centroid);
+            var radius = (int)OverlapPairPresentation.MarkerHalfSize(run.View.DeviceDpi);
+            Assert.NotEqual(Color.White.ToArgb(), image.GetPixel(center.X - radius + 1, center.Y).ToArgb());
+            Assert.Equal(Color.White.ToArgb(), image.GetPixel(center.X - radius - 4, center.Y).ToArgb());
+            Assert.Equal(Color.White.ToArgb(), image.GetPixel(center.X - 60, center.Y).ToArgb());
+            run.View.MoveTo(new Point(center.X + (int)OverlapPairPresentation.HitRadius(run.View.DeviceDpi), center.Y));
+            Assert.Contains("Pair 1/2", run.View.OverlapOverlay.HoverText);
+            run.View.MoveTo(new Point(center.X + (int)OverlapPairPresentation.HitRadius(run.View.DeviceDpi) + 2, center.Y));
+            Assert.Null(run.View.OverlapOverlay.HoverText);
+        }
+        Assert.Equal(1, run.Calls);
+    });
+
+    [Fact]
+    public void MarkerAndHoverUsePairMaterialCentroidRatherThanBoundsCenter() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.Plate.Parts.Clear();
+        var program = new Program(Mode.Absolute);
+        program.Codes.Add(new RapidMove(0, 0));
+        program.Codes.Add(new LinearMove(6, 0));
+        program.Codes.Add(new LinearMove(0, 3));
+        program.Codes.Add(new LinearMove(0, 0));
+        var drawing = new Drawing("triangle", program);
+        run.View.Plate.Parts.Add(new Part(drawing));
+        run.View.Plate.Parts.Add(new Part(drawing));
+        run.View.OverlapDisplay = OverlapDisplayMode.Centroids;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 30);
+        run.View.SetOrigin(60, 220);
+        using var image = new Bitmap(300, 300);
+        using var graphics = Graphics.FromImage(image);
+        graphics.Clear(Color.White);
+        graphics.TranslateTransform(60, 220);
+        run.View.OverlapOverlay.Draw(graphics);
+        var materialCenter = run.View.PointWorldToControl(new Vector(6.0 / 3, 3.0 / 3));
+        var boundsCenter = run.View.PointWorldToControl(new Vector(6.0 / 2, 3.0 / 2));
+        Assert.NotEqual(Color.White.ToArgb(), image.GetPixel(materialCenter.X, materialCenter.Y).ToArgb());
+        Assert.Equal(Color.White.ToArgb(), image.GetPixel(boundsCenter.X, boundsCenter.Y).ToArgb());
+        run.View.MoveTo(materialCenter);
+        Assert.Contains("Pair 1/2", run.View.OverlapOverlay.HoverText);
+        run.View.MoveTo(boundsCenter);
+        Assert.Null(run.View.OverlapOverlay.HoverText);
+    });
+
+    [Fact]
+    public void BothRetainsAreaPathAndCoincidentHoverListsEveryPairWithoutChangingSelection() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.Plate.Parts.Clear();
+        run.View.Plate.Parts.Add(Rectangle());
+        run.View.Plate.Parts.Add(Rectangle());
+        run.View.Plate.Parts.Add(Rectangle());
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 20);
+        run.View.SetOrigin(60, 220);
+        using var image = new Bitmap(300, 300);
+        using var graphics = Graphics.FromImage(image);
+        graphics.TranslateTransform(60, 220);
+        run.View.OverlapOverlay.Draw(graphics);
+        var path = run.View.OverlapOverlay.CachedPath;
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.View.OverlapOverlay.Draw(graphics);
+        Assert.Same(path, run.View.OverlapOverlay.CachedPath);
+        var center = run.View.PointWorldToControl(new Vector(2, 2));
+        run.View.MoveTo(center);
+        var text = run.View.OverlapOverlay.HoverText!;
+        Assert.True(text.IndexOf("Pair 1/2", StringComparison.Ordinal) < text.IndexOf("Pair 1/3", StringComparison.Ordinal));
+        Assert.True(text.IndexOf("Pair 1/3", StringComparison.Ordinal) < text.IndexOf("Pair 2/3", StringComparison.Ordinal));
+        Assert.Empty(run.View.SelectedParts);
+        run.View.ClickAt(center);
+        Assert.NotEmpty(run.View.SelectedParts); // Informational hover does not consume the selection click.
+        Assert.Null(run.View.OverlapOverlay.HoverText);
+        Assert.Equal(1, run.Calls);
+    });
+
+    [Fact]
+    public void PairDetailsOnlySuppressNormalTooltipWhileVisible() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 20);
+        run.View.SetOrigin(60, 220);
+        run.View.MoveTo(run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid));
+        var flags = System.Reflection.BindingFlags.Instance | System.Reflection.BindingFlags.NonPublic;
+        var hoverCheck = typeof(PlateView).GetMethod("HoverCheck", flags)!;
+        var normalVisible = typeof(PlateView).GetField("showTooltip", flags)!;
+        hoverCheck.Invoke(run.View, null); // Fire the existing normal-tooltip timer deterministically.
+        Assert.True((bool)normalVisible.GetValue(run.View)!);
+        using var image = new Bitmap(300, 300);
+        using var graphics = Graphics.FromImage(image);
+        Assert.True(run.View.OverlapOverlay.DrawHover(graphics));
+        Assert.True((bool)normalVisible.GetValue(run.View)!);
+        run.View.OverlapDisplay = OverlapDisplayMode.Areas;
+        Assert.False(run.View.OverlapOverlay.DrawHover(graphics));
+        Assert.True((bool)normalVisible.GetValue(run.View)!); // PlateView now draws the original tooltip.
+        run.View.LeaveView();
+        hoverCheck.Invoke(run.View, null); // A queued timer cannot resurrect it after leave.
+        Assert.False((bool)normalVisible.GetValue(run.View)!);
+    });
+
+    [Theory]
+    [InlineData("leave")]
+    [InlineData("stale-move")]
+    [InlineData("stale-paint")]
+    [InlineData("invalidate")]
+    [InlineData("mode")]
+    [InlineData("zoom")]
+    [InlineData("pan")]
+    [InlineData("resize")]
+    [InlineData("plate")]
+    [InlineData("restart-cancel")]
+    [InlineData("recreate")]
+    public void HoverClearsBeforeStaleDetailsCanBeShown(string change) => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 20);
+        run.View.SetOrigin(60, 220);
+        var center = run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid);
+        run.View.MoveTo(center);
+        Assert.NotNull(run.View.OverlapOverlay.HoverText);
+        switch (change)
+        {
+            case "leave": run.View.LeaveView(); break;
+            case "stale-move":
+                run.View.Plate.Parts[0].Offset(1e-10, 0);
+                run.View.MoveTo(center);
+                break;
+            case "stale-paint":
+                run.View.Plate.Parts[0].Offset(1e-10, 0);
+                using (var image = new Bitmap(300, 300))
+                using (var graphics = Graphics.FromImage(image))
+                    Assert.False(run.View.OverlapOverlay.DrawHover(graphics));
+                break;
+            case "invalidate": run.View.InvalidateOverlapCheck(); break;
+            case "mode": run.View.OverlapDisplay = OverlapDisplayMode.Centroids; break;
+            case "zoom": run.View.ZoomToPoint(new Vector(), 2); break;
+            case "pan": run.View.Pan(20, 10); break;
+            case "resize": run.View.Size = new System.Drawing.Size(300, 200); break;
+            case "plate": run.View.Plate = new Plate(); break;
+            case "restart-cancel":
+                var task = run.Start();
+                var work = run.Next();
+                Assert.Null(run.View.OverlapOverlay.HoverText);
+                run.View.CancelOverlapCheck();
+                work.Complete();
+                run.Pump(task);
+                break;
+            case "recreate": run.View.Recreate(); break;
+        }
+        Assert.Null(run.View.OverlapOverlay.HoverText);
+    });
+
+    [Fact]
+    public void CrowdedHoverPagesStayInViewportAndReachLastPairWithoutSelectionOrWheelCapture() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        PrepareCrowdedHover(run);
+        var report = run.View.OverlapReport;
+        var positions = run.View.Plate.Parts.Select(p => p.Location).ToArray();
+        run.View.SelectAll();
+        var selection = run.View.SelectedParts.ToArray();
+        using var image = new Bitmap(run.View.Width, run.View.Height);
+        using var graphics = Graphics.FromImage(image);
+        var overlay = run.View.OverlapOverlay;
+        Assert.True(overlay.DrawHover(graphics));
+        var pages = overlay.HoverPages;
+        Assert.True(pages.PageCount > 1);
+        var content = new List<string>();
+        for (var page = 0; page < pages.PageCount; page++)
+        {
+            Assert.True(overlay.DrawHover(graphics));
+            Assert.True(new RectangleF(PointF.Empty, run.View.ClientSize).Contains(overlay.HoverBounds));
+            Assert.Equal(page, pages.PageIndex);
+            content.AddRange(pages.Lines);
+            Assert.Contains("PgUp/PgDn", string.Join("", pages.NavigationLines));
+            Assert.True(run.View.Command(Keys.PageDown));
+        }
+        Assert.Contains("Pair 11/12", string.Concat(content));
+        Assert.Contains(" in²", string.Concat(content));
+        Assert.Equal(overlay.HoverText.Replace("\n", ""), string.Concat(content));
+        Assert.Equal(pages.PageCount - 1, pages.PageIndex);
+        Assert.True(run.View.Command(Keys.PageUp));
+        Assert.Equal(pages.PageCount - 2, pages.PageIndex);
+        var lastIndex = pages.PageIndex;
+        Assert.False(run.View.Command(Keys.Control | Keys.PageDown));
+        Assert.Equal(lastIndex, pages.PageIndex);
+        run.View.MoveTo(run.View.PointWorldToControl(report.Pairs[0].Centroid));
+        Assert.Equal(lastIndex, pages.PageIndex); // Moving within the same hit group retains the page.
+        Assert.Equal(selection, run.View.SelectedParts);
+        Assert.Equal(positions, run.View.Plate.Parts.Select(p => p.Location));
+        Assert.Same(report, run.View.OverlapReport);
+        Assert.Equal(1, run.Calls);
+
+        var scale = run.View.ViewScale;
+        run.View.WheelAt(run.View.PointWorldToControl(report.Pairs[0].Centroid));
+        Assert.True(run.View.ViewScale > scale); // Wheel remains zoom, never paging.
+        Assert.Null(overlay.HoverText);
+        Assert.Null(overlay.HoverPages);
+        Assert.False(run.View.Command(Keys.PageDown));
+        Assert.Equal(selection, run.View.SelectedParts);
+        Assert.Equal(1, run.Calls);
+    });
+
+    [Fact]
+    public void MovingDirectlyToAnotherCoincidentGroupStartsItsFirstPage() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.Size = new System.Drawing.Size(300, 160);
+        run.View.Plate.Parts.Clear();
+        for (var i = 0; i < 12; i++)
+            run.View.Plate.Parts.Add(Rectangle(i < 6 ? 0 : 8));
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 15);
+        run.View.SetOrigin(60, 120);
+        run.View.MoveTo(run.View.PointWorldToControl(new Vector(2, 2)));
+        using var image = new Bitmap(300, 160);
+        using var graphics = Graphics.FromImage(image);
+        var overlay = run.View.OverlapOverlay;
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.True(run.View.Command(Keys.PageDown));
+        Assert.Equal(1, overlay.HoverPages.PageIndex);
+        run.View.MoveTo(run.View.PointWorldToControl(new Vector(10, 2)));
+        Assert.Null(overlay.HoverPages);
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.NotNull(overlay.HoverPages);
+        Assert.Equal(0, overlay.HoverPages.PageIndex);
+        Assert.Contains("Pair 7/8", string.Concat(overlay.HoverPages.Lines));
+        Assert.Equal(1, run.Calls);
+    });
+
+    [Theory]
+    [InlineData("hover")]
+    [InlineData("leave")]
+    [InlineData("mode")]
+    [InlineData("stale-key")]
+    [InlineData("report")]
+    [InlineData("resize")]
+    [InlineData("font")]
+    [InlineData("click")]
+    [InlineData("drag")]
+    public void PagingResetsWithHoverLifetimeAndInactiveKeysAreNotConsumed(string change) => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        Assert.False(run.View.Command(Keys.PageDown));
+        PrepareCrowdedHover(run);
+        using var image = new Bitmap(run.View.Width, run.View.Height);
+        using var graphics = Graphics.FromImage(image);
+        var overlay = run.View.OverlapOverlay;
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.True(run.View.Command(Keys.PageDown));
+        Assert.Equal(1, overlay.HoverPages.PageIndex);
+        var center = run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid);
+        using var largerFont = new Font(run.View.Font.FontFamily, run.View.Font.Size + 1);
+        switch (change)
+        {
+            case "hover": run.View.MoveTo(new Point(5, 5)); break;
+            case "leave": run.View.LeaveView(); break;
+            case "mode": run.View.OverlapDisplay = OverlapDisplayMode.Areas; break;
+            case "stale-key":
+                run.View.Plate.Parts[0].Offset(1e-10, 0);
+                Assert.False(run.View.Command(Keys.PageDown));
+                break;
+            case "report": run.Finish(); break;
+            case "resize": run.View.Width += 10; break;
+            case "font": run.View.Font = largerFont; break;
+            case "click":
+                run.View.ClickAt(center);
+                Assert.NotEmpty(run.View.SelectedParts);
+                break;
+            case "drag": run.View.DragAt(center); break;
+        }
+        Assert.Null(overlay.HoverText);
+        Assert.Null(overlay.HoverPages);
+        Assert.False(run.View.Command(Keys.PageDown));
+        if (change == "stale-key")
+            run.Finish();
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.View.MoveTo(center);
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.NotNull(overlay.HoverPages);
+        Assert.Equal(0, overlay.HoverPages.PageIndex);
+    });
+
+    [Fact]
+    public void LongNameAndTinyViewNeverSilentlyElideTheOnlyPair() => RunSta(() =>
+    {
+        using var run = new OverlayRun();
+        run.View.Size = new System.Drawing.Size(150, 120);
+        run.View.Plate.Parts[0].BaseDrawing.Name = new string('W', 250);
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 10);
+        run.View.SetOrigin(30, 90);
+        var center = run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid);
+        run.View.MoveTo(center);
+        using var image = new Bitmap(150, 120);
+        using var graphics = Graphics.FromImage(image);
+        var overlay = run.View.OverlapOverlay;
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.False(overlay.HoverPages.NeedsLargerViewport);
+        Assert.True(overlay.HoverPages.PageCount > 1);
+        var content = new List<string>();
+        for (var i = 0; i < overlay.HoverPages.PageCount; i++)
+        {
+            Assert.True(overlay.DrawHover(graphics));
+            Assert.True(new RectangleF(PointF.Empty, run.View.ClientSize).Contains(overlay.HoverBounds));
+            content.AddRange(overlay.HoverPages.Lines);
+            run.View.Command(Keys.PageDown);
+        }
+        Assert.Equal(overlay.HoverText.Replace("\n", ""), string.Concat(content));
+        run.View.Size = new System.Drawing.Size(40, 20);
+        overlay.UpdateHover(run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid));
+        Assert.True(overlay.DrawHover(graphics));
+        Assert.True(overlay.HoverPages.NeedsLargerViewport);
+        Assert.False(run.View.Command(Keys.PageDown));
+    });
+
+    private static void PrepareCrowdedHover(OverlayRun run)
+    {
+        run.View.Size = new System.Drawing.Size(260, 160);
+        run.View.Plate.Parts.Clear();
+        for (var i = 0; i < 12; i++)
+            run.View.Plate.Parts.Add(Rectangle());
+        run.View.OverlapDisplay = OverlapDisplayMode.Both;
+        run.Finish();
+        run.View.ZoomToPoint(new Vector(), 15);
+        run.View.SetOrigin(60, 120);
+        run.View.MoveTo(run.View.PointWorldToControl(run.View.OverlapReport.Pairs[0].Centroid));
+    }
+
+    // These waits are deliberate: only Task.Run workers use the result gate; the test's
+    // STA waits for capture delivery, then pumps every UI continuation explicitly.
+    private static PlateOverlapReport WaitForWorkerResult(Task<PlateOverlapReport> task) => task.GetAwaiter().GetResult();
+
+    private static PlateOverlapSnapshot WaitForSnapshot(Task<PlateOverlapSnapshot> task)
+    {
+        Assert.True(task.Wait(TimeSpan.FromSeconds(15)));
+        return task.GetAwaiter().GetResult();
+    }
+
     private static ToolStripMenuItem Menu(MainForm host, string name) =>
         (ToolStripMenuItem)host.MainMenuStrip!.Items.Find(name, true).Single();
 
@@ -335,6 +804,20 @@ public class PlateOverlapOverlayTests
         public void Pan(float x, float y) { origin.X += x; origin.Y += y; }
         public void SetOrigin(float x, float y) => origin = new PointF(x, y);
         public void Recreate() => RecreateHandle();
+        public void MoveTo(Point point) => OnMouseMove(new MouseEventArgs(MouseButtons.None, 0, point.X, point.Y, 0));
+        public void LeaveView() => OnMouseLeave(EventArgs.Empty);
+        public bool Command(Keys keys)
+        {
+            var message = new Message();
+            return ProcessCmdKey(ref message, keys);
+        }
+        public void WheelAt(Point point) => OnMouseWheel(new MouseEventArgs(MouseButtons.None, 0, point.X, point.Y, 120));
+        public void DragAt(Point point) => OnMouseMove(new MouseEventArgs(MouseButtons.Left, 0, point.X, point.Y, 0));
+        public void ClickAt(Point point)
+        {
+            OnMouseDown(new MouseEventArgs(MouseButtons.Left, 1, point.X, point.Y, 0));
+            OnMouseUp(new MouseEventArgs(MouseButtons.Left, 1, point.X, point.Y, 0));
+        }
     }
 
     private sealed class OverlayRun : IDisposable
@@ -342,6 +825,9 @@ public class PlateOverlapOverlayTests
         private readonly PumpContext context = new();
         private readonly SynchronizationContext? previous;
         private readonly BlockingCollection<Work> work = new();
+        private readonly List<Work> outstanding = new();
+        private readonly List<Task> tasks = new();
+        private bool disposed;
         public TestView View { get; } = new();
         public int Calls;
 
@@ -356,12 +842,24 @@ public class PlateOverlapOverlayTests
             {
                 Interlocked.Increment(ref Calls);
                 var request = new Work(snapshot, token);
-                work.Add(request);
+                lock (outstanding)
+                {
+                    outstanding.Add(request);
+                    if (disposed)
+                        request.Release();
+                    else
+                        work.Add(request);
+                }
                 return request.WaitForResult();
             };
         }
 
-        public Task Start() => View.CheckOverlapsAsync();
+        public Task Start()
+        {
+            var task = View.CheckOverlapsAsync(Units.Inches);
+            tasks.Add(task);
+            return task;
+        }
         public Work Next()
         {
             Assert.True(work.TryTake(out var result, TimeSpan.FromSeconds(15)), "Worker did not start.");
@@ -376,9 +874,27 @@ public class PlateOverlapOverlayTests
         }
         public void Dispose()
         {
-            View.Dispose();
-            SynchronizationContext.SetSynchronizationContext(previous);
-            work.Dispose();
+            if (disposed)
+                return;
+            try
+            {
+                View.Dispose();
+            }
+            finally
+            {
+                lock (outstanding)
+                {
+                    disposed = true;
+                    foreach (var request in outstanding)
+                        request.Release();
+                }
+                try { context.Pump(Task.WhenAll(tasks)); }
+                finally
+                {
+                    SynchronizationContext.SetSynchronizationContext(previous);
+                    work.Dispose();
+                }
+            }
         }
     }
 
@@ -390,6 +906,9 @@ public class PlateOverlapOverlayTests
         public PlateOverlapReport WaitForResult() => Result.Task.GetAwaiter().GetResult();
         public void Complete() => Result.SetResult(PlateOverlapAnalyzer.Analyze(snapshot));
         public void Fail() => Result.SetException(new InvalidOperationException("test failure"));
+        // Cancellation is deliberately ignored while testing late completions. Cleanup alone
+        // releases every gate, including requests already taken from the pending queue.
+        public void Release() => Result.TrySetCanceled();
     }
 
     private sealed class PumpContext : SynchronizationContext

OpenNest/Controls/OverlapOverlayController.cs

@@ -1,4 +1,5 @@
 using System;
+using System.Collections.Generic;
 using System.Diagnostics;
 using System.Drawing;
 using System.Drawing.Drawing2D;
@@ -7,6 +8,7 @@ using System.Threading;
 using System.Threading.Tasks;
 using OpenNest.Collections;
 using OpenNest.Diagnostics;
+using OpenNest.Geometry;
 
 namespace OpenNest.Controls;
 
@@ -23,6 +25,12 @@ internal sealed class OverlapOverlayController : IDisposable
     private GraphicsPath path;
     private PlateOverlapReport pathReport;
     private float pathScale;
+    private Units capturedUnits;
+    private IReadOnlyList<PlateOverlapPair> hoveredPairs = Array.Empty<PlateOverlapPair>();
+    private string hoverText;
+    private OverlapHoverPages hoverPages;
+    private Point hoverPoint;
+    private (float Scale, PointF Offset, int Dpi) hoverTransform;
     private bool disposed;
 
     public OverlapOverlayController(PlateView view) => this.view = view;
@@ -36,6 +44,8 @@ internal sealed class OverlapOverlayController : IDisposable
     internal Func<PlateOverlapSnapshot, CancellationToken, PlateOverlapReport> Analyze { get; set; }
         = PlateOverlapAnalyzer.Analyze;
     internal GraphicsPath CachedPath => path;
+    internal OverlapHoverPages HoverPages => hoverPages;
+    internal RectangleF HoverBounds { get; private set; }
 
     public OverlapDisplayMode DisplayMode
     {
@@ -65,7 +75,7 @@ internal sealed class OverlapOverlayController : IDisposable
         NotifyChanged();
     }
 
-    public async Task CheckAsync()
+    public async Task CheckAsync(Units units)
     {
         if (!CanUseView || view.Plate == null)
             return;
@@ -75,6 +85,7 @@ internal sealed class OverlapOverlayController : IDisposable
         CancelWorker();
         var plate = view.Plate;
         var generation = state.Begin(plate);
+        capturedUnits = units; // Same request boundary as the owned geometry/names, never read live units in paint.
         var source = new CancellationTokenSource();
         cancellation = source;
         var token = source.Token;
@@ -162,6 +173,7 @@ internal sealed class OverlapOverlayController : IDisposable
 
     private void NotifyChanged()
     {
+        ClearHover();
         if (disposed || view.IsDisposed || view.Disposing)
             return;
         view.Status = state.Message;
@@ -187,26 +199,194 @@ internal sealed class OverlapOverlayController : IDisposable
     {
         if (disposed)
             return;
+        EnsureFresh();
+        ValidateHoverTransform();
+
+        if (state.Report != null)
+        {
+            if (state.DisplayMode is OverlapDisplayMode.Areas or OverlapDisplayMode.Both)
+            {
+                EnsurePath();
+                if (path.PointCount > 0)
+                {
+                    using var brush = new SolidBrush(Color.FromArgb(100, 255, 0, 80));
+                    // A single winding fill is the union: triple overlap is not painted darker.
+                    graphics.FillPath(brush, path);
+                }
+            }
+            if (ShowsCentroids)
+                DrawCentroids(graphics);
+        }
+        DrawStateLabel(graphics);
+    }
+
+    private bool EnsureFresh()
+    {
+        if (disposed)
+            return false;
         var generation = state.Generation;
-        state.EnsureFresh(view.Plate);
+        var fresh = state.EnsureFresh(view.Plate);
         if (generation != state.Generation)
         {
             CancelWorker();
             ReleasePath();
             NotifyChanged();
         }
+        return fresh;
+    }
 
-        if (state.DisplayMode == OverlapDisplayMode.Areas && state.Report != null)
+    private bool ShowsCentroids => state.DisplayMode is OverlapDisplayMode.Centroids or OverlapDisplayMode.Both;
+    private (float, PointF, int) ViewTransform => (view.ViewScale, view.PointControlToGraph(Point.Empty), view.DeviceDpi);
+
+    internal string HoverText
+    {
+        get
         {
-            EnsurePath();
-            if (path.PointCount > 0)
-            {
-                using var brush = new SolidBrush(Color.FromArgb(100, 255, 0, 80));
-                // A single winding fill is the union: triple overlap is not painted darker.
-                graphics.FillPath(brush, path);
-            }
+            if (!EnsureFresh())
+                ClearHover();
+            ValidateHoverTransform();
+            return hoverText;
         }
-        DrawStateLabel(graphics);
+    }
+
+    public void UpdateHover(Point point)
+    {
+        ValidateHoverTransform();
+        if (!EnsureFresh() || !ShowsCentroids || state.Report == null)
+        {
+            ClearHover();
+            return;
+        }
+
+        // Graph coordinates are already screen-scaled; remove pan from the pointer once.
+        var graphPoint = view.PointControlToGraph(point);
+        var hits = OverlapPairPresentation.HitTest(state.Report.Pairs, world =>
+        {
+            var graph = view.PointWorldToGraph(world);
+            return new Vector(graph.X, graph.Y);
+        }, new Vector(graphPoint.X, graphPoint.Y), view.DeviceDpi);
+        var changed = !hits.SequenceEqual(hoveredPairs);
+        var moved = point != hoverPoint;
+        hoveredPairs = hits;
+        hoverPoint = point;
+        hoverTransform = ViewTransform;
+        if (changed)
+        {
+            hoverPages = null;
+            HoverBounds = RectangleF.Empty;
+            hoverText = hits.Count == 0 ? null : string.Join("\n\n",
+                hits.Select(pair => OverlapPairPresentation.Details(pair, capturedUnits)));
+        }
+        if (changed || (moved && hoverText != null))
+            view.Invalidate();
+    }
+
+    private void ValidateHoverTransform()
+    {
+        if (hoverText != null && hoverTransform != ViewTransform)
+            ClearHover();
+    }
+
+    public void ClearHover()
+    {
+        var visible = hoverText != null;
+        hoverText = null;
+        hoverPages = null;
+        HoverBounds = RectangleF.Empty;
+        hoveredPairs = Array.Empty<PlateOverlapPair>();
+        if (visible && !disposed && !view.IsDisposed && !view.Disposing)
+            view.Invalidate();
+    }
+
+    public bool TryPageHover(int delta)
+    {
+        // Revalidate even when a key arrives before the next paint/mouse event.
+        if (HoverText == null || hoverPages == null || hoverPages.PageCount < 2)
+            return false;
+        hoverPages.MovePage(delta);
+        view.Invalidate();
+        return true;
+    }
+
+    private void DrawCentroids(Graphics graphics)
+    {
+        var dpiScale = view.DeviceDpi / 96f;
+        var radius = (float)OverlapPairPresentation.MarkerHalfSize(view.DeviceDpi);
+        using var halo = new Pen(Color.White, 4 * dpiScale);
+        using var crosshair = new Pen(Color.DarkRed, 2 * dpiScale);
+        // Stack coincident pair labels instead of replacing them with a fragment count.
+        var labelRows = new Dictionary<PointF, int>();
+        foreach (var pair in state.Report.Pairs.OrderBy(pair => pair.PartAId).ThenBy(pair => pair.PartBId))
+        {
+            var center = view.PointWorldToGraph(pair.Centroid);
+            if (!float.IsFinite(center.X) || !float.IsFinite(center.Y))
+                continue;
+            foreach (var pen in new[] { halo, crosshair })
+            {
+                graphics.DrawLine(pen, center.X - radius, center.Y, center.X + radius, center.Y);
+                graphics.DrawLine(pen, center.X, center.Y - radius, center.X, center.Y + radius);
+            }
+            var label = OverlapPairPresentation.Label(pair);
+            var size = graphics.MeasureString(label, view.Font);
+            labelRows.TryGetValue(center, out var row);
+            labelRows[center] = row + 1;
+            var x = center.X + radius + 3 * dpiScale;
+            var y = center.Y - radius + row * size.Height;
+            graphics.FillRectangle(Brushes.White, x, y, size.Width, size.Height);
+            graphics.DrawString(label, view.Font, Brushes.DarkRed, x, y);
+        }
+    }
+
+    // Draw last, over action adorners. The normal part tooltip is suppressed only while
+    // these details are actually visible; its independent timer/state is not stolen.
+    public bool DrawHover(Graphics graphics)
+    {
+        var text = HoverText; // Includes a fresh stamp check even if no mouse move/paint preceded this.
+        if (text == null)
+            return false;
+        var saved = graphics.Save();
+        try
+        {
+            graphics.ResetTransform();
+            graphics.SetClip(view.ClientRectangle, CombineMode.Intersect);
+            var scale = view.DeviceDpi / 96f;
+            var padding = 4 * scale;
+            var maxWidth = System.Math.Min(560 * scale, view.ClientSize.Width - 2) - padding * 2;
+            var lineHeight = (float)System.Math.Ceiling(view.Font.GetHeight(graphics));
+            var maxRows = (int)((view.ClientSize.Height - 2 - padding * 2) / lineHeight);
+            using var format = (StringFormat)StringFormat.GenericTypographic.Clone();
+            format.FormatFlags |= StringFormatFlags.NoWrap | StringFormatFlags.MeasureTrailingSpaces;
+            float Measure(string line) => graphics.MeasureString(line, view.Font, PointF.Empty, format).Width;
+            hoverPages ??= OverlapHoverPages.Create(text, hoveredPairs.Count, maxRows, maxWidth, line => Measure(line));
+            if (hoverPages.NeedsLargerViewport)
+            {
+                // A viewport smaller than a content line plus its paging hint cannot
+                // show details legibly. Say so rather than presenting clipped data.
+                HoverBounds = new RectangleF(0, 0, view.ClientSize.Width, view.ClientSize.Height);
+                graphics.FillRectangle(Brushes.White, HoverBounds);
+                graphics.DrawString("Enlarge view to read overlap details", view.Font, Brushes.DarkRed, HoverBounds);
+                return true;
+            }
+            var lines = hoverPages.Lines.Concat(hoverPages.NavigationLines).ToArray();
+            var width = lines.Max(Measure) + padding * 2;
+            var height = lines.Length * lineHeight + padding * 2;
+            var x = System.Math.Max(0, System.Math.Min(hoverPoint.X + 16 * scale, view.ClientSize.Width - width));
+            var y = hoverPoint.Y - height - 6 * scale;
+            if (y < 0)
+                y = System.Math.Max(0, System.Math.Min(hoverPoint.Y + 20 * scale, view.ClientSize.Height - height));
+            HoverBounds = new RectangleF(x, y, width, height);
+            graphics.FillRectangle(Brushes.White, x, y, width, height);
+            graphics.DrawRectangle(Pens.DimGray, x, y, width, height);
+            for (var row = 0; row < lines.Length; row++)
+                graphics.DrawString(lines[row], view.Font,
+                    row < hoverPages.Lines.Count ? Brushes.Black : Brushes.DarkRed,
+                    new PointF(x + padding, y + padding + row * lineHeight), format);
+        }
+        finally
+        {
+            graphics.Restore(saved);
+        }
+        return true;
     }
 
     private void EnsurePath()
@@ -283,5 +463,6 @@ internal sealed class OverlapOverlayController : IDisposable
         CancelWorker();
         state.Reset();
         ReleasePath();
+        ClearHover();
     }
 }

OpenNest/Controls/PlateView.cs

@@ -41,6 +41,7 @@ namespace OpenNest.Controls
         private LayoutPart hoveredPart;
         private Point hoverPoint;
         private bool showTooltip;
+        private bool hoverPending;
         private Timer hoverTimer;
 
         public Box ActiveWorkArea
@@ -229,7 +230,7 @@ namespace OpenNest.Controls
             add => overlapOverlay.StateChanged += value;
             remove => overlapOverlay.StateChanged -= value;
         }
-        public Task CheckOverlapsAsync() => overlapOverlay.CheckAsync();
+        public Task CheckOverlapsAsync(Units units) => overlapOverlay.CheckAsync(units);
         public void CancelOverlapCheck() => overlapOverlay.Cancel();
         public void InvalidateOverlapCheck() => overlapOverlay.Invalidate();
 
@@ -250,6 +251,40 @@ namespace OpenNest.Controls
             base.OnMouseEnter(e);
         }
 
+        protected override void OnMouseLeave(EventArgs e)
+        {
+            ClearHover();
+            base.OnMouseLeave(e);
+        }
+
+        private void ClearHover()
+        {
+            overlapOverlay?.ClearHover();
+            hoverTimer?.Stop();
+            hoverPending = false;
+            hoveredPart = null;
+            showTooltip = false;
+            Invalidate();
+        }
+
+        protected override void OnResize(EventArgs e)
+        {
+            ClearHover();
+            base.OnResize(e);
+        }
+
+        protected override void OnDpiChangedAfterParent(EventArgs e)
+        {
+            ClearHover();
+            base.OnDpiChangedAfterParent(e);
+        }
+
+        protected override void OnFontChanged(EventArgs e)
+        {
+            ClearHover();
+            base.OnFontChanged(e);
+        }
+
         protected override void OnDragEnter(DragEventArgs drgevent)
         {
             if (drgevent.Data.GetData(typeof(Drawing)) != null)
@@ -271,6 +306,7 @@ namespace OpenNest.Controls
 
         protected override void OnMouseDown(MouseEventArgs e)
         {
+            ClearHover();
             if (!Focused)
                 Focus();
 
@@ -359,6 +395,8 @@ namespace OpenNest.Controls
 
         protected override void OnMouseMove(MouseEventArgs e)
         {
+            if (e.Button != MouseButtons.None)
+                ClearHover();
             if (e.Button == MouseButtons.Middle)
             {
                 if (AllowPan)
@@ -389,19 +427,18 @@ namespace OpenNest.Controls
             if (e.Button == MouseButtons.None && actionManager.CurrentAction is ActionSelect)
             {
                 hoverPoint = e.Location;
+                hoverPending = true;
                 showTooltip = false;
                 hoverTimer.Stop();
                 hoverTimer.Start();
 
                 if (hoveredPart != null)
                     Invalidate();
+                overlapOverlay.UpdateHover(e.Location);
             }
-            else if (hoveredPart != null || showTooltip)
+            else
             {
-                hoveredPart = null;
-                hoverTimer.Stop();
-                showTooltip = false;
-                Invalidate();
+                ClearHover();
             }
 
             base.OnMouseMove(e);
@@ -415,6 +452,18 @@ namespace OpenNest.Controls
                 ZoomToFit();
         }
 
+        protected override bool ProcessCmdKey(ref Message msg, Keys keyData)
+        {
+            // Audited: DrawControl/PlateView, Action key handlers, EditNestForm,
+            // MainForm.ProcessCmdKey and menu shortcuts have no plain PgUp/PgDn
+            // binding. BestFitViewerForm owns these only in its separate dialog.
+            // No modifier keys, clicks, or wheel events are consumed by hover paging.
+            if ((keyData == Keys.PageUp || keyData == Keys.PageDown)
+                && overlapOverlay.TryPageHover(keyData == Keys.PageUp ? -1 : 1))
+                return true;
+            return base.ProcessCmdKey(ref msg, keyData);
+        }
+
         protected override void OnKeyDown(KeyEventArgs e)
         {
             switch (e.KeyCode)
@@ -517,7 +566,7 @@ namespace OpenNest.Controls
 
             base.OnPaint(e);
 
-            if (hoveredPart != null && showTooltip)
+            if (!overlapOverlay.DrawHover(e.Graphics) && hoveredPart != null && showTooltip)
             {
                 e.Graphics.ResetTransform();
                 var text = hoveredPart.BasePart.BaseDrawing.Name;
@@ -542,6 +591,7 @@ namespace OpenNest.Controls
 
         protected override void OnHandleDestroyed(EventArgs e)
         {
+            ClearHover();
             overlapOverlay.ReleaseHandle();
             base.OnHandleDestroyed(e);
             actionManager.Cleanup();
@@ -550,7 +600,12 @@ namespace OpenNest.Controls
         protected override void Dispose(bool disposing)
         {
             if (disposing)
+            {
                 overlapOverlay?.Dispose();
+                hoverTimer?.Dispose();
+                hoverTimer = null;
+                redrawTimer?.Dispose();
+            }
             base.Dispose(disposing);
         }
 
@@ -706,6 +761,9 @@ namespace OpenNest.Controls
 
         private void HoverCheck()
         {
+            if (!hoverPending || IsDisposed || Disposing)
+                return;
+            hoverPending = false;
             var graphPt = PointControlToGraph(hoverPoint);
             LayoutPart hitPart = null;
 
@@ -793,6 +851,7 @@ namespace OpenNest.Controls
 
         protected override void UpdateMatrix()
         {
+            ClearHover();
             base.UpdateMatrix();
             parts.ForEach(p => p.Update(this));
             previewManager.Update();

OpenNest/Forms/EditNestForm.cs

@@ -28,7 +28,7 @@ namespace OpenNest.Forms
         public readonly Document Document;
         public readonly PlateView PlateView;
 
-        public System.Threading.Tasks.Task CheckOverlapsAsync() => PlateView.CheckOverlapsAsync();
+        public System.Threading.Tasks.Task CheckOverlapsAsync() => PlateView.CheckOverlapsAsync(Nest.Units);
         public void CancelOverlapCheck() => PlateView.CancelOverlapCheck();
         public OverlapDisplayMode OverlapDisplay
         {

OpenNest/Forms/MainForm.Designer.cs

@@ -54,6 +54,8 @@
             mnuOverlapDisplay = new System.Windows.Forms.ToolStripMenuItem();
             mnuOverlapOff = new System.Windows.Forms.ToolStripMenuItem();
             mnuOverlapAreas = new System.Windows.Forms.ToolStripMenuItem();
+            mnuOverlapCentroids = new System.Windows.Forms.ToolStripMenuItem();
+            mnuOverlapBoth = new System.Windows.Forms.ToolStripMenuItem();
             mnuViewDrawRapids = new System.Windows.Forms.ToolStripMenuItem();
             mnuViewDrawPiercePoints = new System.Windows.Forms.ToolStripMenuItem();
             mnuViewDrawBounds = new System.Windows.Forms.ToolStripMenuItem();
@@ -353,7 +355,7 @@
             //
             mnuOverlapDisplay.Name = "mnuOverlapDisplay";
             mnuOverlapDisplay.Text = "Display";
-            mnuOverlapDisplay.DropDownItems.AddRange(new System.Windows.Forms.ToolStripItem[] { mnuOverlapOff, mnuOverlapAreas });
+            mnuOverlapDisplay.DropDownItems.AddRange(new System.Windows.Forms.ToolStripItem[] { mnuOverlapOff, mnuOverlapAreas, mnuOverlapCentroids, mnuOverlapBoth });
             mnuOverlapDisplay.DropDownOpening += OverlapMenu_Opening;
             //
             // mnuOverlapOff
@@ -367,6 +369,18 @@
             mnuOverlapAreas.Name = "mnuOverlapAreas";
             mnuOverlapAreas.Text = "Areas";
             mnuOverlapAreas.Click += OverlapAreas_Click;
+            //
+            // mnuOverlapCentroids
+            //
+            mnuOverlapCentroids.Name = "mnuOverlapCentroids";
+            mnuOverlapCentroids.Text = "Centroids";
+            mnuOverlapCentroids.Click += OverlapCentroids_Click;
+            //
+            // mnuOverlapBoth
+            //
+            mnuOverlapBoth.Name = "mnuOverlapBoth";
+            mnuOverlapBoth.Text = "Both";
+            mnuOverlapBoth.Click += OverlapBoth_Click;
             // 
             // mnuViewDrawRapids
             // 
@@ -1292,6 +1306,8 @@
         private System.Windows.Forms.ToolStripMenuItem mnuOverlapDisplay;
         private System.Windows.Forms.ToolStripMenuItem mnuOverlapOff;
         private System.Windows.Forms.ToolStripMenuItem mnuOverlapAreas;
+        private System.Windows.Forms.ToolStripMenuItem mnuOverlapCentroids;
+        private System.Windows.Forms.ToolStripMenuItem mnuOverlapBoth;
         private System.Windows.Forms.ToolStripMenuItem mnuViewDrawRapids;
         private System.Windows.Forms.ToolStripMenuItem mnuViewDrawPiercePoints;
         private System.Windows.Forms.ToolStripMenuItem mnuViewDrawBounds;

OpenNest/Forms/MainForm.cs

@@ -675,8 +675,12 @@ namespace OpenNest.Forms
             mnuOverlapDisplay.Enabled = hasPlate;
             mnuOverlapOff.Enabled = hasPlate;
             mnuOverlapAreas.Enabled = hasPlate;
+            mnuOverlapCentroids.Enabled = hasPlate;
+            mnuOverlapBoth.Enabled = hasPlate;
             mnuOverlapOff.Checked = hasPlate && activeForm.OverlapDisplay == OverlapDisplayMode.Off;
             mnuOverlapAreas.Checked = hasPlate && activeForm.OverlapDisplay == OverlapDisplayMode.Areas;
+            mnuOverlapCentroids.Checked = hasPlate && activeForm.OverlapDisplay == OverlapDisplayMode.Centroids;
+            mnuOverlapBoth.Checked = hasPlate && activeForm.OverlapDisplay == OverlapDisplayMode.Both;
         }
 
         private async void CheckOverlaps_Click(object sender, EventArgs e)
@@ -700,6 +704,18 @@ namespace OpenNest.Forms
                 activeForm.OverlapDisplay = OverlapDisplayMode.Areas;
         }
 
+        private void OverlapCentroids_Click(object sender, EventArgs e)
+        {
+            if (activeForm != null)
+                activeForm.OverlapDisplay = OverlapDisplayMode.Centroids;
+        }
+
+        private void OverlapBoth_Click(object sender, EventArgs e)
+        {
+            if (activeForm != null)
+                activeForm.OverlapDisplay = OverlapDisplayMode.Both;
+        }
+
         private void ToggleDrawRapids_Click(object sender, EventArgs e)
         {
             if (activeForm == null)

README.md

@@ -12,7 +12,7 @@ A Windows desktop application for CNC nesting — imports DXF drawings, arranges
 - **Import / export** — DXF & DWG parts (ACadSharp), Excel BOMs, bend-line detection, built-in parametric shapes; export DXF or post-processed G-code.
 - **Nesting** — pluggable whole-job engines (Default, Strip, Vertical/Horizontal Remnant, StockLadder, plus DLL plugins), NFP-based interlocking pair evaluation, gravity compaction, rotation sweeps, multi-plate/multi-material jobs.
 - **Plate operations** — manual sheet cut-offs, [automatic scrap cutoffs with unused-tail preservation](docs/automatic-scrap-cutoffs.md), oversized-part splitting (straight, weld-gap tabs, spike-groove), interactive editing, and spacing-aware pushes that can slide along or away from touching parts.
-- **Visual overlap check** — manually highlight shared material on the active plate, including containment and cutouts, through View > Overlap Check. [Usage and limitations](docs/geometry/visual-overlap-check.md).
+- **Visual overlap check** — manually highlight shared material on the active plate, including containment and cutouts, with area shading, pair centroids, and hover details through View > Overlap Check. [Usage and limitations](docs/geometry/visual-overlap-check.md).
 - **CNC output** — configurable lead-ins/outs and tabs, contour editing, user-defined G-code variables (`$name` → `#200+` machine variables), plugin post-processors (Cincinnati CL-707/800/900/940/CLX included).
 
 ## Requirements

docs/geometry/visual-overlap-check.md

@@ -6,8 +6,25 @@ Choose **View > Overlap Check > Check Active Plate** to check committed parts on
 this plate. Shared material is shaded red/magenta without changing the nest,
 selection, cutting paths, or export behavior. Cutoffs and temporary preview parts
 are excluded. **Cancel Check** discards the running request. **Display > Off /
-Areas** changes visibility without rerunning analysis; checking from Off shows
-Areas. Display preferences belong to the current document and are not saved.
+Areas / Centroids / Both** changes visibility without rerunning analysis. Areas
+is the default; rechecking preserves a visible mode, while checking from Off
+shows Areas. Display preferences belong to the current document and are not saved.
+
+Centroids and Both show fixed-screen-size, DPI-scaled pair crosshairs with a
+contrasting halo. Labels such as `1/3` identify the two plate sequence positions
+at capture time, including gaps occupied by cutoffs. Hover near a marker to see
+captured names, approximate shared area in in² or mm², and centroid coordinates
+in the same linear units. Units are captured with the request; hover does not
+relabel an old report from live settings. Nearby/coincident markers show all
+matching pairs in sequence order. If details exceed the view, the tooltip wraps
+and pages them with a `Page x/y` hint: keep the pointer near the marker and use
+plain **PageUp / PageDown** while PlateView has focus. Long individual details
+continue across pages without truncation; an impossibly small viewport asks you
+to enlarge it. These keys act only while a multipage diagnostic tooltip is
+visible; wheel zoom, modified keys, selection clicks, and dragging are unchanged.
+Small positive areas use significant-figure formatting rather than rounding to
+zero. Selection and dragging remain ordinary plate operations, not overlay
+interactions.
 
 A persistent label distinguishes unchecked, checking, current, incomplete, stale,
 canceled, and failed checks. Only a completed, current, fully checked report can
@@ -41,7 +58,7 @@ 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($"{pair.PartAId} / {pair.PartBId}: {pair.Area}");
+    Console.WriteLine($"{pair.PartAId} / {pair.PartBId}: {pair.Area}, centroid {pair.Centroid}");
     foreach (var region in pair.Regions)
     {
         // region.Vertices: closed, read-only world-coordinate polygon
@@ -129,6 +146,20 @@ 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.
 
+`pair.Centroid` is the true area-weighted center of every shared-material fragment
+for that pair, after hole subtraction. It is not an average of crossings or
+vertices. For a disconnected or concave overlap, the mathematical centroid can
+lie outside the red material (for example, between two separate patches). This
+is intentional: shaded Areas are authoritative for actual overlap locations;
+use Both for detailed inspection rather than interpreting a centroid as an
+interior collision point. There is one centroid per pair, not per connected island.
+
+`PolygonAreaMoments` evaluates signed moments about local origins and combines
+fragments with positive area weights independent of winding. The analyzer does
+this on rebased clipping fragments before adding the world origin back. Invalid,
+degenerate, or nonfinite moments produce an incomplete pair issue, not a marker
+at zero. Curved-outline centroids inherit the polygonization approximation.
+
 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
@@ -165,6 +196,10 @@ is filled once, avoiding fragment outlines, internal triangulation seams, and
 darker triple coverage. World-to-graph conversion excludes pan, because PlateView
 already applies origin translation. Paths are rebuilt for report/scale changes,
 not ordinary repaints or panning. The state label saves/restores graphics state.
+Centroid hit tests use only cached report coordinates and DPI-scaled screen
+radii. Hover clears on edits, mode/request/view changes, leave, and teardown.
+Diagnostic details draw above action adorners and take precedence over the normal
+part-name tooltip only while visible.
 
 Next hardening: measure real-plate capture/analysis cost and cancellation latency
 before adding cached triangulations or background capture. Cancellation cannot
@@ -180,11 +215,17 @@ inputs, snapshot isolation, read-only output, cutting-program independence, and
 cancellation. Run:
 
 ```sh
-dotnet test OpenNest.Tests/OpenNest.Tests.csproj --filter 'FullyQualifiedName~PlateOverlapAnalyzerTests|FullyQualifiedName~OverlapReportStateTests'
+dotnet test OpenNest.Tests/OpenNest.Tests.csproj --filter 'FullyQualifiedName~PlateOverlapAnalyzerTests|FullyQualifiedName~OverlapReportStateTests|FullyQualifiedName~PolygonAreaMomentsTests|FullyQualifiedName~OverlapPairPresentationTests|FullyQualifiedName~OverlapHoverPagesTests'
 ```
 
 `OverlapReportStateTests` verifies request supersession, exact pose/reference
 freshness, stale clearing, cancellation, and incomplete-versus-clear messaging.
+`PolygonAreaMomentsTests` covers analytic
+centers, unequal/disconnected fragments, winding, closure, large translations,
+and invalid/overflow cases. `OverlapPairPresentationTests` checks adaptive unit
+formatting, sequence labels, coincident ordering, and zoom-independent DPI hit
+radii. `OverlapHoverPagesTests` proves bounded continuation pages retain every
+pair and long/Unicode name, with navigation bounds and explicit tiny-view failure.
 `OpenNest.WinForms.Tests/PlateOverlapOverlayTests.cs` adds STA worker/publication,
 menu/MDI, path-cache, uniform-fill pixel, and control-lifetime checks. Run those
 on Windows:
@@ -197,4 +238,5 @@ Linux can cross-build with `-p:EnableWindowsTargeting=true`, but that does not
 execute Windows tests or verify appearance, DPI, or interaction. On Windows,
 check partial overlap, containment, inside-hole placement, pan/zoom and quadrant
 alignment, stale clearing during edits/plate switches, converter cancellation,
-and repeated check/toggle/close cycles without GDI/disposed-control errors.
+crowded-marker PageUp/PageDown access to the last pair, and repeated
+check/toggle/close cycles without GDI/disposed-control errors.