fix(ui): scale part label search precision to material width

The plate view searched for each part's label point with PolyLabel's fixed
0.5" precision, a third of a 1.5" part, so the search stopped on the first
interior cell and put labels near edges instead of in the thickest spot.
Precision is now 5% of the part's mean material width (2 x net area over
total outline length), so small, slender or heavily cut-out parts refine
further while large solid ones stay cheap.

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

OpenNest.Core/Geometry/PolyLabel.cs

@@ -24,6 +24,43 @@ namespace OpenNest.Geometry
         public static Vector Find(Polygon outer, IList<Polygon> holes, double precision, int maxCells) =>
             Find(outer, holes, precision, maxCells, out _);
 
+        /// <summary>
+        /// A precision proportional to the shape's mean material width (twice the net area over
+        /// the total outline length, holes included), so small or slender shapes refine further
+        /// than large solid ones. A fixed precision near the shape's size stops at the first
+        /// interior cell.
+        /// </summary>
+        public static double ThicknessPrecision(Polygon outer, IList<Polygon> holes = null, double fraction = 0.05)
+        {
+            var area = outer.Area();
+            var length = ClosedLength(outer);
+
+            if (holes != null)
+            {
+                for (var i = 0; i < holes.Count; i++)
+                {
+                    area -= holes[i].Area();
+                    length += ClosedLength(holes[i]);
+                }
+            }
+
+            if (!(area > 0) || !(length > 0))
+                return 1e-9;
+
+            return System.Math.Max(fraction * 2 * area / length, 1e-9);
+        }
+
+        private static double ClosedLength(Polygon polygon)
+        {
+            var verts = polygon.Vertices;
+            var sum = 0.0;
+
+            for (int i = 0, j = verts.Count - 1; i < verts.Count; j = i++)
+                sum += verts[j].DistanceTo(verts[i]);
+
+            return sum;
+        }
+
         internal static Vector Find(
             Polygon outer,
             IList<Polygon> holes,

OpenNest.Tests/Geometry/PolyLabelTests.cs

@@ -115,6 +115,44 @@ public class PolyLabelTests
         Assert.True(result.X < 20, $"Expected label in left bar, got X={result.X}");
     }
 
+    [Fact]
+    public void ThicknessPrecision_FindsThickBarOfSmallPart()
+    {
+        // 1.5-unit C-shape: left bar 0.6 wide, arms 0.15 tall. A fixed 0.5 precision is a
+        // third of the part and stops on the first interior cell.
+        var p = new Polygon();
+        p.Vertices.Add(new Vector(0, 0));
+        p.Vertices.Add(new Vector(1.5, 0));
+        p.Vertices.Add(new Vector(1.5, 0.15));
+        p.Vertices.Add(new Vector(0.6, 0.15));
+        p.Vertices.Add(new Vector(0.6, 1.35));
+        p.Vertices.Add(new Vector(1.5, 1.35));
+        p.Vertices.Add(new Vector(1.5, 1.5));
+        p.Vertices.Add(new Vector(0, 1.5));
+
+        var result = PolyLabel.Find(p, null, PolyLabel.ThicknessPrecision(p));
+
+        // Any height along the bar is equally clear; its centreline is not.
+        Assert.Equal(0.3, result.X, 0.02);
+        Assert.InRange(result.Y, 0.3, 1.2);
+    }
+
+    [Fact]
+    public void ThicknessPrecision_ScalesWithMaterialWidth()
+    {
+        var hole = new Polygon();
+        hole.Vertices.Add(new Vector(20, 20));
+        hole.Vertices.Add(new Vector(80, 20));
+        hole.Vertices.Add(new Vector(80, 80));
+        hole.Vertices.Add(new Vector(20, 80));
+
+        // Square side s: 2 * s^2 / 4s = s / 2.
+        Assert.Equal(0.05 * 50, PolyLabel.ThicknessPrecision(Square(100)), 9);
+        Assert.Equal(0.05 * 0.5, PolyLabel.ThicknessPrecision(Square(1)), 9);
+        // A 20-wide frame is thinner than the solid square, so it refines further.
+        Assert.True(PolyLabel.ThicknessPrecision(Square(100), new[] { hole }) < PolyLabel.ThicknessPrecision(Square(100)));
+    }
+
     [Fact]
     public void DegeneratePolygon_ReturnsFallback()
     {

OpenNest/LayoutPart.cs

@@ -237,7 +237,7 @@ namespace OpenNest
                     holes.Add(cutout.ToPolygonWithTolerance(0.1));
             }
 
-            return PolyLabel.Find(outer, holes);
+            return PolyLabel.Find(outer, holes, PolyLabel.ThicknessPrecision(outer, holes));
         }
 
         public void Update(DrawControl plateView)