perf(jobs): flatten validator contours once, at a 0.001 chord tolerance

The candidate validator flattened every arc into 1000 segments and rebuilt
both parts' polygons and edge lists for every pair it compared, so spacing
checks on filleted parts cost millions of edge pairs each. Validation, not
the fill pipeline, was nearly all of a solve's wall time.

Placed contours are now flattened once with ToPolygonWithTolerance(0.001),
the tolerance the benchmark NestValidator and Part.Intersects already use,
and each part's shape is built once per candidate. Arcs stay inscribed, so
a layout placed exactly at the spacing still passes.

12-nest PEP corpus, Default + StockLadder, --parallel 1: 2820 s -> 227 s.
Every run that finished before gives the same validity, count, plates and
cost. Three StockLadder runs that used to hit the 5-minute timeout now
finish.

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

OpenNest.Engine/Jobs/NestJobPlacementValidator.cs

@@ -12,6 +12,10 @@ namespace OpenNest.Engine.Jobs;
 internal static class NestJobPlacementValidator
 {
     private const double Epsilon = 0.0000001;
+    // Flattening for placement overlap/spacing checks: the same 0.001 the benchmark's
+    // NestValidator and Part.Intersects use. Arcs are inscribed, so a layout placed exactly at
+    // the spacing passes; outward arcs may come up to this much closer than the spacing.
+    private const double PlacementChordTolerance = 0.001;
 
     internal static void ValidateCandidate(
         PlateCandidate candidate,
@@ -24,6 +28,7 @@ internal static class NestJobPlacementValidator
             throw new InvalidOperationException("The plate nester returned a null candidate.");
         var counts = new Dictionary<string, int>(StringComparer.Ordinal);
         var placed = new List<ShapeTopology>();
+        var sources = new Dictionary<string, ShapeTopology>(StringComparer.Ordinal);
         foreach (var placement in candidate.Placements)
         {
             if (
@@ -48,7 +53,9 @@ internal static class NestJobPlacementValidator
                     "Candidate rotation is not allowed for the requirement."
                 );
 
-            var shape = Transform(CreateShape(part.Geometry), placement);
+            if (!sources.TryGetValue(placement.PartId, out var source))
+                sources[placement.PartId] = source = CreateShape(part.Geometry);
+            var shape = Transform(source, placement);
             if (!FitsWorkArea(shape, stock))
                 throw new InvalidOperationException(
                     "Candidate placement falls outside the usable stock area."
@@ -296,8 +303,8 @@ internal static class NestJobPlacementValidator
 
     private static bool Overlaps(ShapeTopology left, ShapeTopology right)
     {
-        var leftPoly = ToPolygon(left.Perimeter);
-        var rightPoly = ToPolygon(right.Perimeter);
+        var leftPoly = left.Contours[0].Polygon;
+        var rightPoly = right.Contours[0].Polygon;
         if (!leftPoly.BoundingBox.Intersects(rightPoly.BoundingBox))
             return false;
         // True material overlap requires shared interior area, not boundary touching.
@@ -308,8 +315,8 @@ internal static class NestJobPlacementValidator
         return Collision.HasOverlap(
             leftPoly,
             rightPoly,
-            ToPolygons(left.Cutouts),
-            ToPolygons(right.Cutouts)
+            left.CutoutPolygons,
+            right.CutoutPolygons
         );
     }
 
@@ -365,44 +372,22 @@ internal static class NestJobPlacementValidator
     private static double Distance(ShapeTopology left, ShapeTopology right)
     {
         var result = double.PositiveInfinity;
-        foreach (var leftContour in AllContours(left))
-        foreach (var rightContour in AllContours(right))
-            if (BoundsDistance(leftContour.BoundingBox, rightContour.BoundingBox) < result)
+        foreach (var leftContour in left.Contours)
+        foreach (var rightContour in right.Contours)
+            if (BoundsDistance(leftContour.Bounds, rightContour.Bounds) < result)
                 result = System.Math.Min(
                     result,
-                    BoundaryDistance(ToPolygon(leftContour), ToPolygon(rightContour))
+                    BoundaryDistance(leftContour.Lines, rightContour.Lines)
                 );
         return result;
     }
 
-    private static IEnumerable<Shape> AllContours(ShapeTopology shape)
-    {
-        yield return shape.Perimeter;
-        foreach (var cutout in shape.Cutouts)
-            yield return cutout;
-    }
-
-    private static List<Polygon> ToPolygons(List<Shape> contours)
-    {
-        var polygons = new List<Polygon>(contours.Count);
-        foreach (var contour in contours)
-            polygons.Add(ToPolygon(contour));
-        return polygons;
-    }
-
-    private static Polygon ToPolygon(Shape contour)
-    {
-        var polygon = contour.ToPolygon();
-        polygon.UpdateBounds();
-        return polygon;
-    }
-
-    private static double BoundaryDistance(Polygon left, Polygon right)
+    private static double BoundaryDistance(List<Line> left, List<Line> right)
     {
         var result = double.PositiveInfinity;
-        foreach (var leftLine in left.ToLines())
+        foreach (var leftLine in left)
         {
-            foreach (var rightLine in right.ToLines())
+            foreach (var rightLine in right)
             {
                 if (leftLine.Intersects(rightLine))
                     return 0;
@@ -429,7 +414,56 @@ internal static class NestJobPlacementValidator
 
     private sealed class ShapeTopology(Shape perimeter, List<Shape> cutouts)
     {
+        private Contour[] contours;
+        private List<Polygon> cutoutPolygons;
+
         internal Shape Perimeter { get; } = perimeter;
         internal List<Shape> Cutouts { get; } = cutouts;
+
+        /// <summary>The perimeter first, then the cutouts, each flattened once on first use.</summary>
+        internal Contour[] Contours
+        {
+            get
+            {
+                if (contours != null)
+                    return contours;
+                var result = new Contour[Cutouts.Count + 1];
+                result[0] = new Contour(Perimeter);
+                for (var i = 0; i < Cutouts.Count; i++)
+                    result[i + 1] = new Contour(Cutouts[i]);
+                return contours = result;
+            }
+        }
+
+        internal List<Polygon> CutoutPolygons
+        {
+            get
+            {
+                if (cutoutPolygons != null)
+                    return cutoutPolygons;
+                var result = new List<Polygon>(Cutouts.Count);
+                for (var i = 1; i < Contours.Length; i++)
+                    result.Add(Contours[i].Polygon);
+                return cutoutPolygons = result;
+            }
+        }
+    }
+
+    /// <summary>
+    /// A contour flattened once, at <see cref="PlacementChordTolerance"/>, for the overlap and
+    /// spacing checks against every other placement.
+    /// </summary>
+    private sealed class Contour
+    {
+        internal Contour(Shape shape)
+        {
+            Polygon = shape.ToPolygonWithTolerance(PlacementChordTolerance);
+            Bounds = Polygon.BoundingBox;
+            Lines = Polygon.ToLines();
+        }
+
+        internal Box Bounds { get; }
+        internal Polygon Polygon { get; }
+        internal List<Line> Lines { get; }
     }
 }