fix: improve circle nesting with curve-to-curve distance and min copy spacing

Add Phase 3 curve-to-curve direct distance in CpuDistanceComputer to
catch contacts that vertex sampling misses between curved entities.
Enforce minimum copy distance in FillLinear to prevent bounding box
overlap when circumscribed polygon boundaries overshoot true arcs.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

OpenNest.Core/Geometry/SpatialQuery.cs

@@ -104,6 +104,39 @@ namespace OpenNest.Geometry
             return double.MaxValue;
         }
 
+        /// <summary>
+        /// Solves ray-circle intersection, returning the two parametric t values.
+        /// Returns false if no real intersection exists.
+        /// </summary>
+        [System.Runtime.CompilerServices.MethodImpl(
+            System.Runtime.CompilerServices.MethodImplOptions.AggressiveInlining)]
+        private static bool SolveRayCircle(
+            double vx, double vy,
+            double cx, double cy, double r,
+            double dirX, double dirY,
+            out double t1, out double t2)
+        {
+            var ox = vx - cx;
+            var oy = vy - cy;
+
+            var a = dirX * dirX + dirY * dirY;
+            var b = 2.0 * (ox * dirX + oy * dirY);
+            var c = ox * ox + oy * oy - r * r;
+
+            var discriminant = b * b - 4.0 * a * c;
+            if (discriminant < 0)
+            {
+                t1 = t2 = double.MaxValue;
+                return false;
+            }
+
+            var sqrtD = System.Math.Sqrt(discriminant);
+            var inv2a = 1.0 / (2.0 * a);
+            t1 = (-b - sqrtD) * inv2a;
+            t2 = (-b + sqrtD) * inv2a;
+            return true;
+        }
+
         /// <summary>
         /// Computes the distance from a point along a direction to an arc.
         /// Solves ray-circle intersection, then constrains hits to the arc's
@@ -117,25 +150,9 @@ namespace OpenNest.Geometry
             double startAngle, double endAngle, bool reversed,
             double dirX, double dirY)
         {
-            // Ray: P = (vx,vy) + t*(dirX,dirY)
-            // Circle: (x-cx)^2 + (y-cy)^2 = r^2
-            var ox = vx - cx;
-            var oy = vy - cy;
-
-            // a = dirX^2 + dirY^2 = 1 for unit direction, but handle general case
-            var a = dirX * dirX + dirY * dirY;
-            var b = 2.0 * (ox * dirX + oy * dirY);
-            var c = ox * ox + oy * oy - r * r;
-
-            var discriminant = b * b - 4.0 * a * c;
-            if (discriminant < 0)
+            if (!SolveRayCircle(vx, vy, cx, cy, r, dirX, dirY, out var t1, out var t2))
                 return double.MaxValue;
 
-            var sqrtD = System.Math.Sqrt(discriminant);
-            var inv2a = 1.0 / (2.0 * a);
-            var t1 = (-b - sqrtD) * inv2a;
-            var t2 = (-b + sqrtD) * inv2a;
-
             var best = double.MaxValue;
 
             if (t1 > -Tolerance.Epsilon)
@@ -168,27 +185,13 @@ namespace OpenNest.Geometry
             double cx, double cy, double r,
             double dirX, double dirY)
         {
-            var ox = vx - cx;
-            var oy = vy - cy;
-
-            var a = dirX * dirX + dirY * dirY;
-            var b = 2.0 * (ox * dirX + oy * dirY);
-            var c = ox * ox + oy * oy - r * r;
-
-            var discriminant = b * b - 4.0 * a * c;
-            if (discriminant < 0)
+            if (!SolveRayCircle(vx, vy, cx, cy, r, dirX, dirY, out var t1, out var t2))
                 return double.MaxValue;
 
-            var sqrtD = System.Math.Sqrt(discriminant);
-            var t = (-b - sqrtD) / (2.0 * a);
-
-            if (t > Tolerance.Epsilon) return t;
-            if (t >= -Tolerance.Epsilon) return 0;
-
-            // First root is behind us, try the second
-            t = (-b + sqrtD) / (2.0 * a);
-            if (t > Tolerance.Epsilon) return t;
-            if (t >= -Tolerance.Epsilon) return 0;
+            if (t1 > Tolerance.Epsilon) return t1;
+            if (t1 >= -Tolerance.Epsilon) return 0;
+            if (t2 > Tolerance.Epsilon) return t2;
+            if (t2 >= -Tolerance.Epsilon) return 0;
 
             return double.MaxValue;
         }
@@ -200,57 +203,7 @@ namespace OpenNest.Geometry
         /// </summary>
         public static double DirectionalDistance(List<Line> movingLines, List<Line> stationaryLines, PushDirection direction)
         {
-            var minDist = double.MaxValue;
-
-            // Case 1: Each moving vertex -> each stationary edge
-            var movingVertices = new HashSet<Vector>();
-            for (int i = 0; i < movingLines.Count; i++)
-            {
-                movingVertices.Add(movingLines[i].pt1);
-                movingVertices.Add(movingLines[i].pt2);
-            }
-
-            var stationaryEdges = new (Vector start, Vector end)[stationaryLines.Count];
-            for (int i = 0; i < stationaryLines.Count; i++)
-                stationaryEdges[i] = (stationaryLines[i].pt1, stationaryLines[i].pt2);
-
-            // Sort edges for pruning if not already sorted (usually they aren't here)
-            if (direction == PushDirection.Left || direction == PushDirection.Right)
-                stationaryEdges = stationaryEdges.OrderBy(e => System.Math.Min(e.start.Y, e.end.Y)).ToArray();
-            else
-                stationaryEdges = stationaryEdges.OrderBy(e => System.Math.Min(e.start.X, e.end.X)).ToArray();
-
-            foreach (var mv in movingVertices)
-            {
-                var d = OneWayDistance(mv, stationaryEdges, Vector.Zero, direction);
-                if (d < minDist) minDist = d;
-            }
-
-            // Case 2: Each stationary vertex -> each moving edge (opposite direction)
-            var opposite = OppositeDirection(direction);
-            var stationaryVertices = new HashSet<Vector>();
-            for (int i = 0; i < stationaryLines.Count; i++)
-            {
-                stationaryVertices.Add(stationaryLines[i].pt1);
-                stationaryVertices.Add(stationaryLines[i].pt2);
-            }
-
-            var movingEdges = new (Vector start, Vector end)[movingLines.Count];
-            for (int i = 0; i < movingLines.Count; i++)
-                movingEdges[i] = (movingLines[i].pt1, movingLines[i].pt2);
-
-            if (opposite == PushDirection.Left || opposite == PushDirection.Right)
-                movingEdges = movingEdges.OrderBy(e => System.Math.Min(e.start.Y, e.end.Y)).ToArray();
-            else
-                movingEdges = movingEdges.OrderBy(e => System.Math.Min(e.start.X, e.end.X)).ToArray();
-
-            foreach (var sv in stationaryVertices)
-            {
-                var d = OneWayDistance(sv, movingEdges, Vector.Zero, opposite);
-                if (d < minDist) minDist = d;
-            }
-
-            return minDist;
+            return DirectionalDistance(movingLines, 0, 0, stationaryLines, direction);
         }
 
         /// <summary>
@@ -265,21 +218,10 @@ namespace OpenNest.Geometry
             var movingOffset = new Vector(movingDx, movingDy);
 
             // Case 1: Each moving vertex -> each stationary edge
-            var movingVertices = new HashSet<Vector>();
-            for (int i = 0; i < movingLines.Count; i++)
-            {
-                movingVertices.Add(movingLines[i].pt1 + movingOffset);
-                movingVertices.Add(movingLines[i].pt2 + movingOffset);
-            }
+            var movingVertices = CollectVertices(movingLines, movingOffset);
 
-            var stationaryEdges = new (Vector start, Vector end)[stationaryLines.Count];
-            for (int i = 0; i < stationaryLines.Count; i++)
-                stationaryEdges[i] = (stationaryLines[i].pt1, stationaryLines[i].pt2);
-
-            if (direction == PushDirection.Left || direction == PushDirection.Right)
-                stationaryEdges = stationaryEdges.OrderBy(e => System.Math.Min(e.start.Y, e.end.Y)).ToArray();
-            else
-                stationaryEdges = stationaryEdges.OrderBy(e => System.Math.Min(e.start.X, e.end.X)).ToArray();
+            var stationaryEdges = ToEdgeArray(stationaryLines);
+            SortEdgesForPruning(stationaryEdges, direction);
 
             foreach (var mv in movingVertices)
             {
@@ -289,21 +231,10 @@ namespace OpenNest.Geometry
 
             // Case 2: Each stationary vertex -> each moving edge (opposite direction)
             var opposite = OppositeDirection(direction);
-            var stationaryVertices = new HashSet<Vector>();
-            for (int i = 0; i < stationaryLines.Count; i++)
-            {
-                stationaryVertices.Add(stationaryLines[i].pt1);
-                stationaryVertices.Add(stationaryLines[i].pt2);
-            }
+            var stationaryVertices = CollectVertices(stationaryLines, Vector.Zero);
 
-            var movingEdges = new (Vector start, Vector end)[movingLines.Count];
-            for (int i = 0; i < movingLines.Count; i++)
-                movingEdges[i] = (movingLines[i].pt1, movingLines[i].pt2);
-
-            if (opposite == PushDirection.Left || opposite == PushDirection.Right)
-                movingEdges = movingEdges.OrderBy(e => System.Math.Min(e.start.Y, e.end.Y)).ToArray();
-            else
-                movingEdges = movingEdges.OrderBy(e => System.Math.Min(e.start.X, e.end.X)).ToArray();
+            var movingEdges = ToEdgeArray(movingLines);
+            SortEdgesForPruning(movingEdges, opposite);
 
             foreach (var sv in stationaryVertices)
             {
@@ -342,15 +273,11 @@ namespace OpenNest.Geometry
         {
             var minDist = double.MaxValue;
 
-            // Extract unique vertices from moving edges.
-            var movingVertices = new HashSet<Vector>();
-            for (var i = 0; i < movingEdges.Length; i++)
-            {
-                movingVertices.Add(movingEdges[i].start + movingOffset);
-                movingVertices.Add(movingEdges[i].end + movingOffset);
-            }
+            SortEdgesForPruning(stationaryEdges, direction);
 
             // Case 1: Each moving vertex -> each stationary edge
+            var movingVertices = CollectVertices(movingEdges, movingOffset);
+
             foreach (var mv in movingVertices)
             {
                 var d = OneWayDistance(mv, stationaryEdges, stationaryOffset, direction);
@@ -359,12 +286,9 @@ namespace OpenNest.Geometry
 
             // Case 2: Each stationary vertex -> each moving edge (opposite direction)
             var opposite = OppositeDirection(direction);
-            var stationaryVertices = new HashSet<Vector>();
-            for (var i = 0; i < stationaryEdges.Length; i++)
-            {
-                stationaryVertices.Add(stationaryEdges[i].start + stationaryOffset);
-                stationaryVertices.Add(stationaryEdges[i].end + stationaryOffset);
-            }
+            SortEdgesForPruning(movingEdges, opposite);
+
+            var stationaryVertices = CollectVertices(stationaryEdges, stationaryOffset);
 
             foreach (var sv in stationaryVertices)
             {
@@ -556,12 +480,7 @@ namespace OpenNest.Geometry
             var dirX = direction.X;
             var dirY = direction.Y;
 
-            var movingVertices = new HashSet<Vector>();
-            for (var i = 0; i < movingLines.Count; i++)
-            {
-                movingVertices.Add(movingLines[i].pt1);
-                movingVertices.Add(movingLines[i].pt2);
-            }
+            var movingVertices = CollectVertices(movingLines, Vector.Zero);
 
             foreach (var mv in movingVertices)
             {
@@ -576,12 +495,7 @@ namespace OpenNest.Geometry
             var oppX = -dirX;
             var oppY = -dirY;
 
-            var stationaryVertices = new HashSet<Vector>();
-            for (var i = 0; i < stationaryLines.Count; i++)
-            {
-                stationaryVertices.Add(stationaryLines[i].pt1);
-                stationaryVertices.Add(stationaryLines[i].pt2);
-            }
+            var stationaryVertices = CollectVertices(stationaryLines, Vector.Zero);
 
             foreach (var sv in stationaryVertices)
             {
@@ -648,6 +562,57 @@ namespace OpenNest.Geometry
                 }
             }
 
+            // Phase 3: Curve-to-curve direct distance.
+            // The vertex-to-entity approach misses the closest contact between two
+            // curved entities (circles/arcs) because only a few cardinal vertices are
+            // sampled. The true closest contact along the push direction is found by
+            // treating it as a ray from one center to an expanded circle at the other
+            // center (radius = r1 + r2).
+            for (var i = 0; i < movingEntities.Count; i++)
+            {
+                var me = movingEntities[i];
+                if (!TryGetCurveParams(me, out var mcx, out var mcy, out var mr))
+                    continue;
+
+                for (var j = 0; j < stationaryEntities.Count; j++)
+                {
+                    var se = stationaryEntities[j];
+                    if (!TryGetCurveParams(se, out var scx, out var scy, out var sr))
+                        continue;
+
+                    var d = RayCircleDistance(mcx, mcy, scx, scy, mr + sr, dirX, dirY);
+
+                    if (d >= minDist || d == double.MaxValue)
+                        continue;
+
+                    // For arcs, verify the contact point falls within both arcs' angular ranges.
+                    if (me is Arc || se is Arc)
+                    {
+                        var mx = mcx + d * dirX;
+                        var my = mcy + d * dirY;
+                        var toCx = scx - mx;
+                        var toCy = scy - my;
+
+                        if (me is Arc mArc)
+                        {
+                            var angle = Angle.NormalizeRad(System.Math.Atan2(toCy, toCx));
+                            if (!Angle.IsBetweenRad(angle, mArc.StartAngle, mArc.EndAngle, mArc.IsReversed))
+                                continue;
+                        }
+
+                        if (se is Arc sArc)
+                        {
+                            var angle = Angle.NormalizeRad(System.Math.Atan2(-toCy, -toCx));
+                            if (!Angle.IsBetweenRad(angle, sArc.StartAngle, sArc.EndAngle, sArc.IsReversed))
+                                continue;
+                        }
+                    }
+
+                    minDist = d;
+                    if (d <= 0) return 0;
+                }
+            }
+
             return minDist;
         }
 
@@ -728,6 +693,62 @@ namespace OpenNest.Geometry
                 points.Add(new Vector(arc.Center.X, arc.Center.Y - arc.Radius));
         }
 
+        private static HashSet<Vector> CollectVertices(List<Line> lines, Vector offset)
+        {
+            var vertices = new HashSet<Vector>();
+            for (var i = 0; i < lines.Count; i++)
+            {
+                vertices.Add(lines[i].pt1 + offset);
+                vertices.Add(lines[i].pt2 + offset);
+            }
+            return vertices;
+        }
+
+        private static HashSet<Vector> CollectVertices((Vector start, Vector end)[] edges, Vector offset)
+        {
+            var vertices = new HashSet<Vector>();
+            for (var i = 0; i < edges.Length; i++)
+            {
+                vertices.Add(edges[i].start + offset);
+                vertices.Add(edges[i].end + offset);
+            }
+            return vertices;
+        }
+
+        private static (Vector start, Vector end)[] ToEdgeArray(List<Line> lines)
+        {
+            var edges = new (Vector start, Vector end)[lines.Count];
+            for (var i = 0; i < lines.Count; i++)
+                edges[i] = (lines[i].pt1, lines[i].pt2);
+            return edges;
+        }
+
+        private static void SortEdgesForPruning((Vector start, Vector end)[] edges, PushDirection direction)
+        {
+            if (direction == PushDirection.Left || direction == PushDirection.Right)
+                System.Array.Sort(edges, (a, b) =>
+                    System.Math.Min(a.start.Y, a.end.Y).CompareTo(System.Math.Min(b.start.Y, b.end.Y)));
+            else
+                System.Array.Sort(edges, (a, b) =>
+                    System.Math.Min(a.start.X, a.end.X).CompareTo(System.Math.Min(b.start.X, b.end.X)));
+        }
+
+        private static bool TryGetCurveParams(Entity entity, out double cx, out double cy, out double r)
+        {
+            if (entity is Circle circle)
+            {
+                cx = circle.Center.X; cy = circle.Center.Y; r = circle.Radius;
+                return true;
+            }
+            if (entity is Arc arc)
+            {
+                cx = arc.Center.X; cy = arc.Center.Y; r = arc.Radius;
+                return true;
+            }
+            cx = cy = r = 0;
+            return false;
+        }
+
         private static double BoxProjectionMin(Box box, double dx, double dy)
         {
             var x = dx >= 0 ? box.Left : box.Right;

OpenNest.Engine/BestFit/CpuDistanceComputer.cs

@@ -104,6 +104,9 @@ namespace OpenNest.Engine.BestFit
             var allMovingVerts = ExtractVerticesFromEntities(movingEntities);
             var allStationaryVerts = ExtractVerticesFromEntities(stationaryEntities);
 
+            var movingCurves = ExtractCurveParams(movingEntities);
+            var stationaryCurves = ExtractCurveParams(stationaryEntities);
+
             var vertexCache = new Dictionary<(double, double), (Vector[] leading, Vector[] facing)>();
 
             foreach (var offset in offsets)
@@ -165,12 +168,84 @@ namespace OpenNest.Engine.BestFit
                     }
                 }
 
+                // Phase 3: Curve-to-curve direct distance.
+                // Vertex sampling misses the true contact between two curved entities
+                // when the approach angle doesn't align with a sampled vertex.
+                for (var m = 0; m < movingCurves.Length; m++)
+                {
+                    var mc = movingCurves[m];
+                    var mcx = mc.Cx + offset.Dx;
+                    var mcy = mc.Cy + offset.Dy;
+
+                    for (var s = 0; s < stationaryCurves.Length; s++)
+                    {
+                        var sc = stationaryCurves[s];
+                        var d = SpatialQuery.RayCircleDistance(
+                            mcx, mcy, sc.Cx, sc.Cy, mc.Radius + sc.Radius, dirX, dirY);
+
+                        if (d >= minDist || d == double.MaxValue)
+                            continue;
+
+                        if (mc.Entity is Arc || sc.Entity is Arc)
+                        {
+                            var mx = mcx + d * dirX;
+                            var my = mcy + d * dirY;
+                            var toCx = sc.Cx - mx;
+                            var toCy = sc.Cy - my;
+
+                            if (mc.Entity is Arc mArc)
+                            {
+                                var angle = Angle.NormalizeRad(System.Math.Atan2(toCy, toCx));
+                                if (!Angle.IsBetweenRad(angle, mArc.StartAngle, mArc.EndAngle, mArc.IsReversed))
+                                    continue;
+                            }
+
+                            if (sc.Entity is Arc sArc)
+                            {
+                                var angle = Angle.NormalizeRad(System.Math.Atan2(-toCy, -toCx));
+                                if (!Angle.IsBetweenRad(angle, sArc.StartAngle, sArc.EndAngle, sArc.IsReversed))
+                                    continue;
+                            }
+                        }
+
+                        minDist = d;
+                        if (d <= 0) { results[i] = 0; return; }
+                    }
+                }
+
                 results[i] = minDist;
             });
 
             return results;
         }
 
+        private readonly struct CurveParams
+        {
+            public readonly Entity Entity;
+            public readonly double Cx, Cy, Radius;
+
+            public CurveParams(Entity entity, double cx, double cy, double radius)
+            {
+                Entity = entity;
+                Cx = cx;
+                Cy = cy;
+                Radius = radius;
+            }
+        }
+
+        private static CurveParams[] ExtractCurveParams(List<Entity> entities)
+        {
+            var curves = new List<CurveParams>();
+            for (var i = 0; i < entities.Count; i++)
+            {
+                if (entities[i] is Circle circle)
+                    curves.Add(new CurveParams(circle, circle.Center.X, circle.Center.Y, circle.Radius));
+                else if (entities[i] is Arc arc)
+                    curves.Add(new CurveParams(arc, arc.Center.X, arc.Center.Y, arc.Radius));
+            }
+            return curves.ToArray();
+        }
+
         private static double RayEntityDistance(
             double vx, double vy, Entity entity,
             double entityOffsetX, double entityOffsetY,

OpenNest.Engine/Fill/FillLinear.cs

@@ -119,10 +119,11 @@ namespace OpenNest.Engine.Fill
             var maxCopyDistance = FindMaxPairDistance(
                 patternA.Parts, boundaries, offset, pushDir, opposite, startOffset);
 
-            if (maxCopyDistance < Tolerance.Epsilon)
-                return bboxDim + PartSpacing;
-
-            return maxCopyDistance;
+            // The copy distance must be at least bboxDim + PartSpacing to prevent
+            // bounding box overlap. Cross-pair slides can underestimate when the
+            // circumscribed polygon boundary overshoots the true arc, creating
+            // spurious contacts between diagonal parts in adjacent copies.
+            return System.Math.Max(maxCopyDistance, bboxDim + PartSpacing);
         }
 
         /// <summary>

OpenNest.Tests/Fill/FillLinearCircleTests.cs

@@ -0,0 +1,130 @@
+using OpenNest;
+using OpenNest.CNC;
+using OpenNest.Converters;
+using OpenNest.Engine.Fill;
+using OpenNest.Geometry;
+using OpenNest.Math;
+using Xunit;
+using Xunit.Abstractions;
+using System.Collections.Generic;
+using System.Linq;
+
+namespace OpenNest.Tests.Fill
+{
+    public class FillLinearCircleTests
+    {
+        private readonly ITestOutputHelper _output;
+
+        public FillLinearCircleTests(ITestOutputHelper output) => _output = output;
+
+        private static Drawing MakeCircleDrawing(double radius)
+        {
+            var pgm = new Program();
+            var startPt = new Vector(radius * 2, radius); // rightmost point
+            pgm.Codes.Add(new RapidMove(startPt));
+            pgm.Codes.Add(new ArcMove(startPt, new Vector(radius, radius), RotationType.CCW));
+            return new Drawing("circle", pgm);
+        }
+
+        private static Drawing MakeRingDrawing(double outerRadius, double innerRadius)
+        {
+            var pgm = new Program();
+            // Outer circle (CCW)
+            var outerStart = new Vector(outerRadius * 2, outerRadius);
+            pgm.Codes.Add(new RapidMove(outerStart));
+            pgm.Codes.Add(new ArcMove(outerStart, new Vector(outerRadius, outerRadius), RotationType.CCW));
+            // Inner circle (CW = hole)
+            var innerStart = new Vector(outerRadius + innerRadius, outerRadius);
+            pgm.Codes.Add(new RapidMove(innerStart));
+            pgm.Codes.Add(new ArcMove(innerStart, new Vector(outerRadius, outerRadius), RotationType.CW));
+            return new Drawing("ring", pgm);
+        }
+
+        [Theory]
+        [InlineData(2.0, 0.125)]   // 4" diameter circle, 1/8" spacing
+        [InlineData(1.0, 0.125)]   // 2" diameter circle
+        [InlineData(3.0, 0.0625)]  // 6" diameter circle, 1/16" spacing
+        [InlineData(0.5, 0.25)]    // 1" diameter circle, 1/4" spacing
+        public void CircleFill_OffsetBoundaries_DoNotOverlap(double radius, double spacing)
+        {
+            var drawing = MakeCircleDrawing(radius);
+            var workArea = new Box(0, 0, 48, 48);
+            var engine = new FillLinear(workArea, spacing);
+            var parts = engine.Fill(drawing, 0, NestDirection.Horizontal);
+
+            _output.WriteLine($"Circle R={radius}, spacing={spacing}: {parts.Count} parts");
+
+            AssertNoOffsetOverlap(parts, spacing, radius * 2);
+        }
+
+        [Theory]
+        [InlineData(2.0, 1.5, 0.125)]  // Ring: outer R=2, inner R=1.5
+        [InlineData(1.5, 1.0, 0.125)]  // Ring: outer R=1.5, inner R=1.0
+        public void RingFill_OffsetBoundaries_DoNotOverlap(double outerR, double innerR, double spacing)
+        {
+            var drawing = MakeRingDrawing(outerR, innerR);
+            var workArea = new Box(0, 0, 48, 48);
+            var engine = new FillLinear(workArea, spacing);
+            var parts = engine.Fill(drawing, 0, NestDirection.Horizontal);
+
+            _output.WriteLine($"Ring outerR={outerR}, innerR={innerR}, spacing={spacing}: {parts.Count} parts");
+
+            AssertNoOffsetOverlap(parts, spacing, outerR * 2);
+        }
+
+        private void AssertNoOffsetOverlap(List<Part> parts, double spacing, double expectedDiameter)
+        {
+            if (parts.Count < 2)
+            {
+                _output.WriteLine("  Only 1 part placed, skipping overlap check");
+                return;
+            }
+
+            var halfSpacing = spacing / 2;
+            var radius = expectedDiameter / 2;
+            var minGap = double.MaxValue;
+            var violationCount = 0;
+
+            // For circular parts, the center is at Location + (radius, radius).
+            for (var i = 0; i < parts.Count; i++)
+            {
+                var ci = parts[i].Location + new Vector(radius, radius);
+
+                for (var j = i + 1; j < parts.Count; j++)
+                {
+                    var cj = parts[j].Location + new Vector(radius, radius);
+                    var centerDist = ci.DistanceTo(cj);
+
+                    // Gap between raw circle perimeters
+                    var rawGap = centerDist - expectedDiameter;
+
+                    // Gap between offset circle perimeters (halfSpacing each side)
+                    var offsetGap = centerDist - expectedDiameter - spacing;
+
+                    if (rawGap < minGap)
+                        minGap = rawGap;
+
+                    if (rawGap < spacing - Tolerance.Epsilon)
+                    {
+                        violationCount++;
+                        if (violationCount <= 5)
+                        {
+                            _output.WriteLine($"  SPACING VIOLATION parts[{i}] vs parts[{j}]: " +
+                                $"centerDist={centerDist:F6}, rawGap={rawGap:F6}, offsetGap={offsetGap:F6}, " +
+                                $"expected>={spacing:F4}");
+                        }
+                    }
+                }
+            }
+
+            _output.WriteLine($"  Min gap={minGap:F6}, expected>={spacing:F4}, violations={violationCount}");
+
+            if (violationCount > 0)
+            {
+                var maxDeficit = spacing - minGap;
+                _output.WriteLine($"  Max deficit={maxDeficit:F6}");
+                Assert.Fail($"{violationCount} pairs violate spacing: min gap={minGap:F6}, expected>={spacing}, deficit={maxDeficit:F6}");
+            }
+        }
+    }
+}