refactor(shapes): generalize OctagonShape to NgonShape

Parameterize side count so users can generate any regular n-gon
(n>=3). Width remains the inscribed-circle diameter, preserving n=8
behavior; circumradius derives as Width / (2*cos(pi/n)).

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

OpenNest.Core/Shapes/NgonShape.cs

@@ -3,33 +3,38 @@ using System.Collections.Generic;
 
 namespace OpenNest.Shapes
 {
-    public class OctagonShape : ShapeDefinition
+    public class NgonShape : ShapeDefinition
     {
+        public int Sides { get; set; }
         public double Width { get; set; }
 
         public override void SetPreviewDefaults()
         {
+            Sides = 8;
             Width = 8;
         }
 
         public override Drawing GetDrawing()
         {
+            var n = Sides < 3 ? 3 : Sides;
             var center = Width / 2.0;
-            var circumRadius = Width / (2.0 * System.Math.Cos(System.Math.PI / 8.0));
+            var circumRadius = Width / (2.0 * System.Math.Cos(System.Math.PI / n));
+            var step = 2.0 * System.Math.PI / n;
+            var start = System.Math.PI / n;
 
-            var vertices = new Vector[8];
-            for (var i = 0; i < 8; i++)
+            var vertices = new Vector[n];
+            for (var i = 0; i < n; i++)
             {
-                var angle = System.Math.PI / 8.0 + i * System.Math.PI / 4.0;
+                var angle = start + i * step;
                 vertices[i] = new Vector(
                     center + circumRadius * System.Math.Cos(angle),
                     center + circumRadius * System.Math.Sin(angle));
             }
 
             var entities = new List<Entity>();
-            for (var i = 0; i < 8; i++)
+            for (var i = 0; i < n; i++)
             {
-                var next = (i + 1) % 8;
+                var next = (i + 1) % n;
                 entities.Add(new Line(vertices[i], vertices[next]));
             }
 

OpenNest.Tests/Shapes/NgonShapeTests.cs

@@ -0,0 +1,51 @@
+using OpenNest.Shapes;
+
+namespace OpenNest.Tests.Shapes;
+
+public class NgonShapeTests
+{
+    [Fact]
+    public void GetDrawing_Octagon_BoundingBoxFitsWithinExpectedSize()
+    {
+        var shape = new NgonShape { Sides = 8, Width = 20 };
+        var drawing = shape.GetDrawing();
+
+        var bbox = drawing.Program.BoundingBox();
+        // Corner-to-corner is larger than flat-to-flat
+        Assert.True(bbox.Width >= 20 - 0.01);
+        Assert.True(bbox.Length >= 20 - 0.01);
+        // But should not be wildly larger (corner-to-corner ~ width / cos(22.5deg) ~ width * 1.0824)
+        Assert.True(bbox.Width < 22);
+        Assert.True(bbox.Length < 22);
+    }
+
+    [Theory]
+    [InlineData(3)]
+    [InlineData(4)]
+    [InlineData(5)]
+    [InlineData(6)]
+    [InlineData(8)]
+    [InlineData(12)]
+    public void GetDrawing_HasOneLinearMovePerSide(int sides)
+    {
+        var shape = new NgonShape { Sides = sides, Width = 20 };
+        var drawing = shape.GetDrawing();
+
+        var moves = drawing.Program.Codes
+            .OfType<OpenNest.CNC.LinearMove>()
+            .Count();
+        Assert.Equal(sides, moves);
+    }
+
+    [Fact]
+    public void GetDrawing_ClampsSidesBelowThreeToTriangle()
+    {
+        var shape = new NgonShape { Sides = 2, Width = 20 };
+        var drawing = shape.GetDrawing();
+
+        var moves = drawing.Program.Codes
+            .OfType<OpenNest.CNC.LinearMove>()
+            .Count();
+        Assert.Equal(3, moves);
+    }
+}

OpenNest.Tests/Shapes/OctagonShapeTests.cs

@@ -1,34 +0,0 @@
-using OpenNest.Shapes;
-
-namespace OpenNest.Tests.Shapes;
-
-public class OctagonShapeTests
-{
-    [Fact]
-    public void GetDrawing_BoundingBoxFitsWithinExpectedSize()
-    {
-        var shape = new OctagonShape { Width = 20 };
-        var drawing = shape.GetDrawing();
-
-        var bbox = drawing.Program.BoundingBox();
-        // Corner-to-corner is larger than flat-to-flat
-        Assert.True(bbox.Width >= 20 - 0.01);
-        Assert.True(bbox.Length >= 20 - 0.01);
-        // But should not be wildly larger (corner-to-corner ~ width / cos(22.5deg) ~ width * 1.0824)
-        Assert.True(bbox.Width < 22);
-        Assert.True(bbox.Length < 22);
-    }
-
-    [Fact]
-    public void GetDrawing_HasEightEdges()
-    {
-        var shape = new OctagonShape { Width = 20 };
-        var drawing = shape.GetDrawing();
-
-        // An octagon program should have 8 linear moves (one per edge)
-        var moves = drawing.Program.Codes
-            .OfType<OpenNest.CNC.LinearMove>()
-            .Count();
-        Assert.Equal(8, moves);
-    }
-}