fix(demos): DemoBuildMachineTool puts the spindle's pivot on the tool-mount offset

CreateFromChainCode now seeds S with a DynamicRotation about -Z through S's origin (the spindle
role); the sample moves the tool mount to (-72.40, 72.40, 176.44) right after, so it moves the
spindle's pivot there too -- otherwise turning the spindle would swing the tool around S's origin.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Disp/DemoCylindroid.cs

@@ -0,0 +1,53 @@
+using Hi.Disp;
+using Hi.Geom;
+using System;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates the creation and visualization of <see cref="Cylindroid"/> objects.
+    /// Includes examples of building a <see cref="Cylindroid"/> programmatically with
+    /// <see cref="PairZr"/> points and serializing/deserializing via XML.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoCylindroid.cs)]
+    /// </remarks>
+    public static class DemoCylindroid
+    {
+        internal static void BuildCylindorid()
+        {
+            Cylindroid cylindroid = new Cylindroid(
+                new PairZr(0, 1),
+                new PairZr(1, 1),
+                new PairZr(1, 2),
+                new PairZr(2, 2),
+                new PairZr(8, 3));
+
+            DispEngine.Init();
+            DemoUtil.Present("BuildCylindorid", cylindroid.ToFaceDrawing());
+        }
+
+        internal static void TestCylindoridXml()
+        {
+            Cylindroid cylindroid = new Cylindroid(
+                new PairZr(0, 1),
+                new PairZr(1, 1),
+                new PairZr(1, 2),
+                new PairZr(2, 2),
+                new PairZr(4, 3));
+            var xmlElement = cylindroid.MakeXmlSource(null, null, true);
+            Console.WriteLine("XML:" + xmlElement);
+
+            cylindroid = new Cylindroid(xmlElement);
+            DispEngine.Init();
+            DemoUtil.Present("BuildCylindorid", cylindroid.ToFaceDrawing());
+        }
+
+        static void Main()
+        {
+            BuildCylindorid();
+            //TestCylindoridXml();
+        }
+    }
+}

Disp/DemoDiscreteRgb.cs

@@ -0,0 +1,45 @@
+using Hi.Disp;
+using Hi.Disp.Flag;
+using Hi.Geom;
+using Hi.Coloring;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates the use of discrete RGB colors for rendering multiple objects.
+    /// Shows how to apply different colors to similar geometric shapes using the 
+    /// <see cref="ColorUtil.GetDiscreteRGB_Env"/> method from <see cref="ColorUtil"/> class.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoDiscreteRgb.cs)]
+    /// </remarks>
+    public class DemoDiscreteRgb : IDisplayee
+    {
+        /// <inheritdoc/>
+        public void Display(Bind bind)
+        {
+            bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
+            new box3d_t(0, 0, 0, 1, 1, 1).ToDraw_Face().Display(bind);
+
+            bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
+            new box3d_t(1, 0, 0, 2, 1, 1).ToDraw_Face().Display(bind);
+
+            bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
+            new box3d_t(2, 0, 0, 3, 1, 1).ToDraw_Face().Display(bind);
+        }
+        /// <inheritdoc/>
+        public void ExpandToBox3d(ref box3d_t dst)
+        {
+            dst = dst.Expanded(new vec3d_t(0, 0, 0));
+            dst = dst.Expanded(new vec3d_t(3, 1, 1));
+        }
+
+        static void Main()
+        {
+            DemoUtil.Present("Demo Discrete I",
+                new DispList(new CoordinateDrawing(), new DemoDiscreteRgb()));
+        }
+
+    }
+}

Disp/DemoDrawing.cs

@@ -0,0 +1,201 @@
+using Hi.Geom;
+using Hi.Disp;
+using System.Collections.Generic;
+using Hi.Disp.Treat;
+using Hi.Coloring;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates various drawing techniques using the HiAPI graphics system.
+    /// Provides examples of primitive drawing, attribute specification, and rendering options.
+    /// Includes methods for drawing lines, points, triangles, and other geometric primitives.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoDrawing.cs)]
+    /// </remarks>
+    public static class DemoDrawing
+	{
+		/// <summary>
+		/// Demonstrates simple line drawing using raw vertex coordinates.
+		/// Creates a basic line strip from three vertices and displays it using DemoUtil.
+		/// </summary>
+		public static void FreeDrawing()
+		{
+			#region DocSite.FreeDrawing
+			double[] vs =
+				{0,0,0
+				,1,0,0
+				,0,0,1};
+            DemoUtil.Present("EasyDraw"
+				, new Drawing(vs, Stamp.V, GL.GL_LINE_STRIP));
+			#endregion
+		}
+
+		/// <summary>
+		/// Demonstrates various types of line drawing techniques.
+		/// Shows how to create points, line strips, line strips with normals, and colored line strips.
+		/// Illustrates different ways to specify vertex attributes like position, color, and normal.
+		/// </summary>
+		public static void DrawLines()
+		{
+			List<vec3d_t> ps;
+			double[] vs;
+			int n = 10; //vertex num
+
+			////create drawPoints
+			ps = new List<vec3d_t>(n);
+			for (int i = 0; i < n; i++)
+				ps.Add(new vec3d_t(i, 0, 0));
+			vs = new double[ps.Count * 3];
+			for (int i = 0; i < ps.Count; i++)
+			{
+				vs[3 * i] = ps[i].x;
+				vs[3 * i + 1] = ps[i].y;
+				vs[3 * i + 2] = ps[i].z;
+			}
+
+			//V means Vertex
+			Drawing drawPoints = new Drawing(vs, Stamp.V, GL.GL_POINTS);
+
+			////create drawLineStrip
+			vs = new double[ps.Count * 3];
+			for (int i = 0; i < ps.Count; i++)
+			{
+				vs[3 * i] = i;
+				vs[3 * i + 1] = 0;
+				vs[3 * i + 2] = 1;
+			}
+			Drawing drawLineStrip = new Drawing(vs, Stamp.V, GL.GL_LINE_STRIP);
+
+			////create drawLineStripWithNormal
+			//the content of vs is Nx,Ny,Nz,Vx,Vy,Vz, Nx,Ny,Nz,Vx,Vy,Vz, ...
+			vs = new double[n * 6];
+			for (int i = 0; i < n; i++)
+			{
+				//nx,ny,nz
+				vs[6 * i] = 1;
+				vs[6 * i + 1] = 0;
+				vs[6 * i + 2] = 0;
+				//x,y,z
+				vs[6 * i + 3] = i;
+				vs[6 * i + 4] = 0;
+				vs[6 * i + 5] = 2;
+			}
+			//V means Vertex; N means Normal
+			Drawing drawLineStripWithNormal =
+				new Drawing(vs, Stamp.NV, GL.GL_LINE_STRIP);
+
+			////create drawColorLines
+			vs = new double[n * 6];
+			for (int i = 0; i < n; i++)
+			{
+				//the rgb values set casually.
+				//r,g,b
+				vs[6 * i] = i % 3 / 2D;
+				vs[6 * i + 1] = i % 5 / 4D;
+				vs[6 * i + 2] = i % 7 / 6D;
+				//x,y,z
+				vs[6 * i + 3] = i;
+				vs[6 * i + 4] = 0;
+				vs[6 * i + 5] = 3;
+			}
+			//V means Vertex; C means Color
+			Drawing drawLineStripWithColor = new Drawing(vs, Stamp.CV, GL.GL_LINE_STRIP);
+
+            DemoUtil.Present("DrawLines",
+				new DispList(drawPoints, drawLineStrip
+				, drawLineStripWithNormal, drawLineStripWithColor));
+		}
+
+		/// <summary>
+		/// Demonstrates drawing triangles using OpenGL primitives.
+		/// Shows how to create colored triangles (CV) and colored triangles with normals (CNV).
+		/// Illustrates packing of vertex attributes (color, normal, position) into arrays for rendering.
+		/// </summary>
+		public static void DrawTrianglesByPrimitives()
+		{
+			int n = 10;// triangle num
+			double[] vs;
+
+			////create drawTrisCV
+			//each triangle has 3 point; each point has r,g,b,x,y,z, totally 6 doubles.
+			vs = new double[n * 3 * 6];
+			for (int i = 0, k = 0; i < n; i++)
+			{
+				//the rgb values set as casual.
+				vec3d_t rgb = ColorUtil.GetDiscreteRgb(i);
+				tri3d_t tri = new tri3d_t(new vec3d_t(i, 0, 0), new vec3d_t(i + 1, 0, 0), new vec3d_t(i + 0.5, 0, 1));
+				for (int j = 0; j < 3; j++)
+				{
+					vs[k++] = rgb.x;
+					vs[k++] = rgb.y;
+					vs[k++] = rgb.z;
+					vs[k++] = tri[j].x;
+					vs[k++] = tri[j].y;
+					vs[k++] = tri[j].z;
+				}
+			}
+			//V means Vertex; C means Color
+			Drawing drawTrisCV = new Drawing(vs, Stamp.CV, GL.GL_TRIANGLES);
+
+			////create drawTrisCNV
+			/////each triangle has 3 point; each point has r,g,b,nx,ny,nz,x,y,z, totally 6 doubles.
+			vs = new double[n * 3 * 9];
+			for (int i = 0, k = 0; i < n; i++)
+			{
+				//the rgb values set as casual.
+				vec3d_t rgb = ColorUtil.GetDiscreteRgb(i);
+				tri3d_t tri = new tri3d_t(new vec3d_t(i, 0, 3), new vec3d_t(i + 1, 0, 3), new vec3d_t(i + 0.5, 0, 4));
+				vec3d_t nn = tri.GetNormal();
+				for (int j = 0; j < 3; j++)
+				{
+					vs[k++] = rgb.x;
+					vs[k++] = rgb.y;
+					vs[k++] = rgb.z;
+					vs[k++] = nn.x;
+					vs[k++] = nn.y;
+					vs[k++] = nn.z;
+					vs[k++] = tri[j].x;
+					vs[k++] = tri[j].y;
+					vs[k++] = tri[j].z;
+				}
+			}
+			//V means Vertex; C means Color; N means Normal
+			Drawing drawTrisCNV = new Drawing(vs, Stamp.CNV, GL.GL_TRIANGLES);
+
+            //the color of colorTrisDraw is not influence by outer color setting.
+            DemoUtil.Present("DrawTrianglesByPrimitives",
+				new DispList(new RgbTreat(1, 0, 0), drawTrisCV, drawTrisCNV));
+		}
+
+		/// <summary>
+		/// Demonstrates drawing 3D triangles using the tri3d_t helper class.
+		/// Creates a series of triangles and renders them as both face (filled) and line (wireframe) drawings.
+		/// Shows how to apply different colors to faces and lines of the same geometry.
+		/// </summary>
+		public static void DrawTri3d()
+		{
+			int n = 10;
+			List<tri3d_t> tris = new List<tri3d_t>(n);
+			for (int i = 0; i < n; i++)
+				tris.Add(new tri3d_t(new vec3d_t(i, 0, 0), new vec3d_t(i + 1, 0, 0), new vec3d_t(i + 0.5, 0, 1)));
+
+			Drawing faceDraw = tris.GetFaceDrawing();
+			Drawing linesDraw = tris.ToLineDrawing();
+
+            DemoUtil.Present("DrawTri3d",
+				new DispList(new RgbTreat(0, 0, 1), linesDraw
+				, new RgbTreat(1, 0, 0), faceDraw));
+		}
+
+		static void Main()
+		{
+			//FreeDrawing();
+			//DrawLines();
+			//DrawTrianglesByPrimitives();
+			DrawTri3d();
+		}
+	}
+}

Disp/DemoPick1.cs

@@ -0,0 +1,52 @@
+using Hi.Geom;
+using Hi.Disp;
+using Hi.Native;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates basic object picking with mouse interaction in the HiAPI system.
+    /// Shows how to create a pickable 3D object that responds to mouse events by changing its appearance.
+    /// Implements the Pickable base class to enable mouse event handling.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoPick1.cs)]
+    /// </remarks>
+    public class DemoPick1 : Pickable, IDisplayee
+	{
+		bool isMouseOver = false;
+        /// <inheritdoc/>
+        public void Display(Bind bind)
+		{
+			bind.PickID = PickingID;
+			bind.Rgb = new vec3d_t(isMouseOver ? 0 : 1, 1, 1);
+			new box3d_t(0, 0, 0, 1, 1, 1).DisplayFace(bind);
+			bind.PickID = 0;
+		}
+        /// <inheritdoc/>
+        public void ExpandToBox3d(ref box3d_t dst)
+		{
+			dst = dst.Expanded(new vec3d_t(0, 0, 0));
+			dst = dst.Expanded(new vec3d_t(1, 1, 1));
+		}
+        /// <inheritdoc/>
+        public override void OnMouseEnter(ui_event_type e, DispEngine dispEngine)
+		{
+			isMouseOver = true;
+		}
+        /// <inheritdoc/>
+        public override void OnMouseLeave(ui_event_type e, DispEngine dispEngine)
+		{
+			isMouseOver = false;
+		}		
+		/// <summary>
+		/// Entry point for the DemoPick1 example.
+		/// Creates and displays a simple pickable object that changes color on mouse hover.
+		/// </summary>
+		static void Main()
+		{
+            DemoUtil.Present("DemoPick1", new DemoPick1());
+		}
+	}
+}

Disp/DemoPick2.cs

@@ -0,0 +1,78 @@
+using Hi.Geom;
+using Hi.Disp;
+using System;
+using Hi.Coloring;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates advanced object picking with multiple pickable objects.
+    /// Shows how to create and manage multiple pickable objects with different visual appearances.
+    /// Implements proper resource cleanup through the IDisposable interface.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoPick2.cs)]
+    /// </remarks>
+    public class DemoPick2 : IDisplayee, IDisposable
+	{
+		readonly Pickable pickableA = new ShowEventPickable { Tag = "A" };
+		readonly Pickable pickableB = new ShowEventPickable { Tag = "B" };
+		readonly Pickable pickableC = new ShowEventPickable { Tag = "C" };
+		/// <inheritdoc/>
+		public void Display(Bind bind)
+		{
+			bind.PickID = pickableA.PickingID;
+			bind.Rgb = ColorUtil.GetDiscreteRgb(1);
+			new box3d_t(0, 0, 0, 1, 1, 1).DisplayFace(bind);
+
+			bind.PickID = pickableB.PickingID;
+			bind.Rgb = ColorUtil.GetDiscreteRgb(2);
+			new box3d_t(0, 0, 1, 1, 1, 2).DisplayFace(bind);
+
+			bind.PickID = pickableC.PickingID;
+			bind.Rgb = ColorUtil.GetDiscreteRgb(3);
+			new box3d_t(0, 0, 2, 1, 1, 3).DisplayFace(bind);
+
+			bind.PickID = 0;
+		}
+		/// <inheritdoc/>
+		public void ExpandToBox3d(ref box3d_t dst)
+		{
+			dst = dst.Expanded(new vec3d_t(0, 0, 0));
+			dst = dst.Expanded(new vec3d_t(1, 1, 3));
+		}
+		#region IDisposable Support
+		private bool disposedValue = false; // To detect redundant calls
+		/// <inheritdoc/>
+		protected virtual void Dispose(bool disposing)
+		{
+			if (!disposedValue)
+			{
+				if (disposing)
+				{
+					pickableA.Dispose();
+					pickableB.Dispose();
+					pickableC.Dispose();
+				}
+				disposedValue = true;
+			}
+		}
+		/// <inheritdoc/>
+		public void Dispose()
+		{
+			Dispose(true);
+		}
+		#endregion
+		
+		/// <summary>
+		/// Entry point for the DemoPick2 example.
+		/// Creates and displays multiple pickable objects with distinct colors and positions.
+		/// Demonstrates separation of picking behavior from visual representation.
+		/// </summary>
+		static void Main()
+		{
+            DemoUtil.Present("DemoPick2", new DemoPick2());
+		}
+	}
+}

Disp/DemoPickable.cs

@@ -0,0 +1,58 @@
+using Hi.Disp;
+using Hi.Geom;
+using System;
+
+namespace Sample.Disp;
+
+/// <summary>
+/// Demonstrates creation of pickable 3D geometry at the primitive level.
+/// Shows how to assign picking IDs directly to geometry vertices and create interactive triangles.
+/// Uses a lower-level approach than the Pickable base class for more precise control.
+/// </summary>
+/// <remarks>
+/// ### Source Code
+/// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoPickable.cs)]
+/// </remarks>
+public class DemoPickable : IDisplayee
+{
+	private readonly Drawing draw;
+	private readonly ShowEventPickable pickable;
+
+	/// <summary>
+	/// Initializes a new instance of DemoPickable.
+	/// Creates a pickable triangle with a specific picking ID for user interaction.
+	/// </summary>
+	public DemoPickable()
+	{
+		pickable = new ShowEventPickable();
+		double pid = pickable.PickingID;
+		double[] vs = new double[] {
+			//pickID, x,y,z
+			pid, 0,0.1,0.1,
+			pid, 0.1,0,0,
+			pid, 0.1,0,0.1
+		};
+		draw = new Drawing(vs, Stamp.PV, GL.GL_TRIANGLES);
+	}
+	/// <inheritdoc/>
+	public void Display(Bind bind)
+	{
+		draw.Display(bind);
+	}
+	/// <inheritdoc/>
+	public void ExpandToBox3d(ref box3d_t dst)
+	{
+		draw.ExpandToBox3d(ref dst);
+	}
+
+	/// <summary>
+	/// Entry point for the DemoPickable example.
+	/// Creates and displays a pickable triangle that can respond to mouse events.
+	/// Demonstrates integration of picking functionality with geometric primitives.
+	/// </summary>
+	[STAThread]
+	public static void Main()
+	{
+		DemoUtil.Present("DemoPickable", new DemoPickable());
+	}
+}

Disp/DemoSatellite.cs

@@ -0,0 +1,55 @@
+using Hi.Geom;
+using Hi.Disp;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Demonstrates a simple solar system animation using <see cref="IDisplayee"/> interface.
+    /// Shows how to create a hierarchical transform structure with sun, earth and moon using
+    /// <see cref="mat4d_t"/> matrices and model matrix stack transformations.
+    /// </summary>
+    /// <remarks>
+    /// ### Source Code
+    /// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoSatellite.cs)]
+    /// </remarks>
+    public class DemoSatellite : IDisplayee
+	{
+		Drawing sun;
+		Drawing earth;
+		Drawing moon;
+		double angle_earth;
+		double angle_moon;
+		DemoSatellite()
+		{
+			sun = box3d_t.CenterUnitBox.ScaledFromCenter(4).ToDraw_Face();
+			earth = box3d_t.CenterUnitBox.ScaledFromCenter(2).ToDraw_Face();
+			moon = box3d_t.CenterUnitBox.ToDraw_Face();
+		}
+        /// <inheritdoc/>
+        public void Display(Bind bind)
+		{
+			sun.Display(bind);
+			bind.ModelMatStack.Push();
+			bind.ModelMatStack.Mul(new mat4d_t(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_earth += 0.03)));
+			bind.ModelMatStack.Mul(new mat4d_t(new vec3d_t(12, 0, 0)));
+			earth.Display(bind);
+			bind.ModelMatStack.Push();
+			bind.ModelMatStack.Mul(new mat4d_t(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_moon += 0.02)));
+			bind.ModelMatStack.Mul(new mat4d_t(new vec3d_t(4, 0, 0)));
+			moon.Display(bind);
+			bind.ModelMatStack.Pop();
+			bind.ModelMatStack.Pop();
+		}
+		/// <inheritdoc/>
+		public void ExpandToBox3d(ref box3d_t dst)
+		{
+			dst = dst.Expanded(new vec3d_t(-14, -14, -2));
+			dst = dst.Expanded(new vec3d_t(14, 14, 2));
+		}
+
+		static void Main()
+		{
+            DemoUtil.Present("DemoSatellite", new DemoSatellite());
+		}
+	}
+}

Disp/DemoUtil.cs

@@ -0,0 +1,45 @@
+using Hi.Disp;
+using Hi.Geom;
+using Hi.HiNcKits;
+using Microsoft.Extensions.Logging;
+using System;
+
+namespace Sample.Disp;
+
+/// <summary>
+/// Runs a display sample to the point where its <see cref="IDisplayee"/> is ready to be rendered.
+/// HiAPI ships no rendering canvas, so the samples in this project stop at the handover: they
+/// compose the displayee and report it, and the application hands that same object to a canvas of
+/// its own. See the Building Your Own Rendering Canvas guide for the canvas side.
+/// </summary>
+/// <remarks>
+/// ### Source Code
+/// [!code-csharp[SampleCode](~/../Hi.Sample/Disp/DemoUtil.cs)]
+/// </remarks>
+public static class DemoUtil
+{
+	/// <summary>
+	/// Initializes the application, reports the displayee's extent, and shuts down again —
+	/// the headless equivalent of opening a window on it.
+	/// </summary>
+	/// <param name="title">A name for the sample, used in the console output.</param>
+	/// <param name="displayee">The object a rendering canvas would display.</param>
+	public static void Present(string title, IDisplayee displayee)
+	{
+		if (displayee is null) throw new ArgumentNullException(nameof(displayee));
+
+		using var loggerFactory = LoggerFactory.Create(b => b.AddConsole());
+		LocalApp.AppBegin(loggerFactory.CreateLogger("Hi.Sample"));
+		try
+		{
+			box3d_t box = new box3d_t();
+			displayee.ExpandToBox3d(ref box);
+			Console.WriteLine($"{title}: {displayee.GetType().Name} bounding {box}");
+			Console.WriteLine("Assign it to your canvas' DispEngine.Displayee to see it.");
+		}
+		finally
+		{
+			LocalApp.AppEnd();
+		}
+	}
+}

Disp/HeidenhainCoordinateEntryDisplayee.cs

@@ -0,0 +1,119 @@
+using Hi.Disp.Flag;
+using Hi.Disp;
+using Hi.Machining.MachiningEquipmentUtils;
+using Hi.Mech.Topo;
+using Hi.Numerical;
+using Hi.Numerical.NcArgs;
+using System.Collections;
+using System;
+using Hi.Geom;
+using System.Linq;
+
+namespace Sample.Disp
+{
+    /// <summary>
+    /// Displayee for Heidenhain coordinate entry visualization.
+    /// </summary>
+    public class HeidenhainCoordinateEntryDisplayee : IAnchoredDisplayee
+    {
+        /// <summary>
+        /// Gets or sets whether to show Heidenhain datum preset information.
+        /// </summary>
+        public bool ShowHeidenhainDatumPreset { get; set; } = true;
+        /// <summary>
+        /// Gets or sets whether to show Heidenhain datum shift information.
+        /// </summary>
+        public bool ShowHeidenhainDatumShift { get; set; } = true;
+        /// <summary>
+        /// Gets or sets the function that provides the NcEnv instance.
+        /// </summary>
+        public Func<HardNcEnv> NcEnvFunc { get; set; }
+        /// <summary>
+        /// Gets or sets the function that provides the machining equipment.
+        /// </summary>
+        public Func<IMachiningEquipment> MillingEquipmentFunc { get; set; }
+        HardNcEnv NcEnv => NcEnvFunc?.Invoke();
+        /// <summary>
+        /// Gets or sets the Heidenhain Cycle Def 247 Q339 value.
+        /// </summary>
+        public int HeidenhainCycleDef247Q339 { get; set; }
+        /// <summary>
+        /// Gets or sets the Heidenhain Cycle Def 7 arguments.
+        /// </summary>
+        public HeidenhainCycleDef7Arg HeidenhainCycleDef7Arg { get; set; }
+
+        /// <summary>
+        /// Initializes a new instance.
+        /// </summary>
+        /// <param name="ncEnvFunc">The function that provides the NcEnv instance.</param>
+        /// <param name="millingEquipmentSource">The function that provides the machining equipment.</param>
+        public HeidenhainCoordinateEntryDisplayee(Func<HardNcEnv> ncEnvFunc, Func<IMachiningEquipment> millingEquipmentSource)
+        {
+            NcEnvFunc = ncEnvFunc;
+            MillingEquipmentFunc = millingEquipmentSource;
+        }
+        /// <inheritdoc/>
+        public void Display(Bind bind)
+        {
+            HardNcEnv ncEnv = NcEnv;
+            if (ncEnv == null || NcEnv.CncBrand != CncBrand.Heidenhain)
+                return;
+
+            ////Console.WriteLine($"B: {CoordinateIndex}; {coordinateMove}");
+            IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
+            if (equipment == null
+                || !equipment.TryGetMachinePositionAtTableMountZero(out vec3d_t mcXyz_AttacherAtTableMountZero))
+                return;
+
+            vec3d_t coordinateMove;
+            string text;
+            if (HeidenhainCycleDef247Q339 == 0 && HeidenhainCycleDef7Arg == null)
+                return;
+            coordinateMove = NcFlagUtil.GetHeidenhainCoordinateOffset(
+                HeidenhainCycleDef247Q339, HeidenhainCycleDef7Arg, ncEnv);
+            //Console.WriteLine($"HeidenhainCycleDef7Arg: {HeidenhainCycleDef7Arg==null}");
+            string datumPresetText = null;
+            if (HeidenhainCycleDef247Q339 != 0 && ShowHeidenhainDatumPreset)
+                datumPresetText = $"Datum Preset Q339={HeidenhainCycleDef247Q339}";
+            string datumShiftText = null;
+            if (HeidenhainCycleDef7Arg != null && ShowHeidenhainDatumShift)
+                datumShiftText = $"Datum Shift: {HeidenhainCycleDef7Arg?.ToString() ?? "None"}";
+            text = string.Join(", ",
+                (new string[] { datumPresetText, datumShiftText }).
+                Where(v => v != null));
+            //text = $"Datum Preset Q339={HeidenhainCycleDef247Q339}, Datum Shift: #1";
+            //Console.WriteLine($"text: [{text}]");
+
+            bind.ModelMatStack.Push();
+            bind.ModelMatStack.Trans(coordinateMove - mcXyz_AttacherAtTableMountZero);
+            CoordinateDrawing.Display(bind, text);
+            bind.ModelMatStack.Pop();
+        }
+        /// <inheritdoc/>
+        public void ExpandToBox3d(ref box3d_t dst)
+        {
+            HardNcEnv ncEnv = NcEnv;
+            if (ncEnv == null || NcEnv.CncBrand != CncBrand.Heidenhain)
+                return;
+
+            IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
+            if (equipment == null
+                || !equipment.TryGetMachinePositionAtTableMountZero(out vec3d_t mcXyz_AttacherAtTableMountZero))
+                return;
+            vec3d_t coordinateMove;
+            if (HeidenhainCycleDef247Q339 == 0 && HeidenhainCycleDef7Arg == null)
+                return;
+            coordinateMove = NcFlagUtil.GetHeidenhainCoordinateOffset(
+                HeidenhainCycleDef247Q339, HeidenhainCycleDef7Arg, ncEnv);
+
+
+            dst = dst.Expanded(-mcXyz_AttacherAtTableMountZero + coordinateMove);
+        }
+        /// <inheritdoc/>
+        public Anchor GetAnchor()
+        {
+            return MillingEquipmentFunc?.Invoke()?.GetMachiningChain()
+                ?.GetTableMount()?.GetAnchor();
+        }
+    }
+}

Disp/IsoCoordinateEntryDisplayee.cs

@@ -0,0 +1,81 @@
+using Hi.Disp;
+using Hi.Disp.Flag;
+using Hi.Geom;
+using Hi.Machining.MachiningEquipmentUtils;
+using Hi.Mech.Topo;
+using Hi.Numerical;
+using System;
+
+namespace Sample.Disp;
+
+/// <summary>
+/// Displayee for ISO coordinate entry visualization.
+/// </summary>
+public class IsoCoordinateEntryDisplayee : IAnchoredDisplayee
+{
+	/// <summary>
+	/// Gets or sets the ISO coordinate key (e.g. "G54", "G59.2").
+	/// </summary>
+	public string IsoCoordinateId { get; set; } = "G54";
+	/// <summary>
+	/// Gets or sets the function that provides the NcEnv instance.
+	/// </summary>
+	public Func<HardNcEnv> NcEnvFunc { get; set; }
+
+	/// <summary>
+	/// Gets or sets the function that provides the machining equipment.
+	/// </summary>
+	public Func<IMachiningEquipment> MillingEquipmentFunc { get; set; }
+	HardNcEnv NcEnv => NcEnvFunc?.Invoke();
+	/// <summary>
+	/// Initializes a new instance of the <see cref="IsoCoordinateEntryDisplayee"/> class.
+	/// </summary>
+	/// <param name="ncEnvFunc">The function that provides the NcEnv instance.</param>
+	/// <param name="millingEquipmentSource">The function that provides the machining equipment.</param>
+	public IsoCoordinateEntryDisplayee(Func<HardNcEnv> ncEnvFunc,
+		Func<IMachiningEquipment> millingEquipmentSource)
+	{
+		NcEnvFunc = ncEnvFunc;
+		MillingEquipmentFunc = millingEquipmentSource;
+	}
+	/// <inheritdoc/>
+	public void Display(Bind bind)
+	{
+		HardNcEnv ncEnv = NcEnv;
+		if (ncEnv == null)
+			return;
+
+		if (ncEnv.IsoCoordinateTable?.TryGetValue(IsoCoordinateId, out vec3d_t coordinateMove) != true)
+			return;
+		string text = IsoCoordinateId ?? "";
+
+		IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
+		if (equipment == null || !equipment.TryGetIsoCoordinatePosition(coordinateMove, out vec3d_t attacherPos))
+			return;
+
+		bind.ModelMatStack.Push();
+		bind.ModelMatStack.Trans(attacherPos);
+		CoordinateDrawing.Display(bind, text);
+		bind.ModelMatStack.Pop();
+	}
+	/// <inheritdoc/>
+	public void ExpandToBox3d(ref box3d_t dst)
+	{
+		HardNcEnv ncEnv = NcEnv;
+		if (ncEnv == null)
+			return;
+		if (ncEnv.IsoCoordinateTable?.TryGetValue(IsoCoordinateId, out vec3d_t coordinateMove) != true)
+			return;
+
+		IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
+		if (equipment == null || !equipment.TryGetIsoCoordinatePosition(coordinateMove, out vec3d_t attacherPos))
+			return;
+		dst = dst.Expanded(attacherPos);
+	}
+	/// <inheritdoc/>
+	/// <returns>Table Mount if existed; otherwise, return null.</returns>
+	public Anchor GetAnchor()
+	{
+		return MillingEquipmentFunc?.Invoke()?.GetMachiningChain()?.GetAnchor();
+	}
+}

Disp/MachiningProjectDisplayee.cs

@@ -0,0 +1,250 @@
+using Hi.Coloring;
+using Hi.MachiningProcs;
+using Hi.Common;
+using Hi.Disp;
+using Hi.Disp.Flag;
+using Hi.Mech.Topo;
+using System.Collections.Generic;
+using System.Collections;
+using Hi.Geom;
+using System.Linq;
+using Hi.NcMech.Solids;
+using Hi.Numerical;
+using System;
+
+namespace Sample.Disp;
+
+/// <summary>
+/// Represents a displayable wrapper for a machining project.
+/// </summary>
+public class MachiningProjectDisplayee : IDisplayee, IGetAnchor
+{
+	/// <summary>
+	/// Gets the current milling course from the host function.
+	/// </summary>
+	public MachiningProject MachiningProject => LocalProjectService.MachiningProject;
+	/// <summary>
+	/// Gets or sets the function that provides the machining project.
+	/// </summary>
+	public LocalProjectService LocalProjectService { get; set; }
+
+	///// <summary>
+	///// Initializes a new instance of the <see cref="MachiningProjectDisplayee"/> class.
+	///// </summary>
+	///// <param name="machiningProject">The machining project to display.</param>
+	///// <param name="renderingFlagBitArray">The bit array controlling rendering flags.</param>
+	//public MachiningProjectDisplayee(MachiningProject machiningProject,
+	//          BitArray renderingFlagBitArray)
+	//      {
+	//          RenderingFlagBitArray = renderingFlagBitArray;
+	//      }
+
+	/// <summary>
+	/// Initializes a new instance of the <see cref="MachiningProjectDisplayee"/> class with default rendering flags.
+	/// </summary>
+	public MachiningProjectDisplayee(LocalProjectService localProjectService)
+	{ LocalProjectService = localProjectService; }
+
+	/// <summary>
+	/// Gets or sets the bit array that controls which elements are rendered.
+	/// </summary>
+	public BitArray RenderingFlagBitArray { get; set; } = new BitArray(EnumUtil.GetEnumBitArrayCap<RenderingFlag>())
+	{
+		[(int)RenderingFlag.DimensionBar] = true,
+		[(int)RenderingFlag.WorkpieceGeom] = true,
+		[(int)RenderingFlag.Fixture] = true,
+		[(int)RenderingFlag.ClStrip] = true,
+		//[(int)RenderingFlag.Mech] = true,
+	};
+	IsoCoordinateEntryDisplayee isoCoordinateEntryDisplayee;
+	/// <summary>
+	/// Gets the ISO coordinate entry displayee for ISO-based coordinate systems.
+	/// </summary>
+	public IsoCoordinateEntryDisplayee IsoCoordinateEntryDisplayee =>
+		isoCoordinateEntryDisplayee ??= new IsoCoordinateEntryDisplayee(
+		() => MachiningProject.NcEnv,
+		() => LocalProjectService.MachiningEquipment);
+	HeidenhainCoordinateEntryDisplayee heidenhainCoordinateEntryDisplayee;
+	/// <summary>
+	/// Gets the Heidenhain coordinate entry displayee for Heidenhain-based coordinate systems.
+	/// </summary>
+	public HeidenhainCoordinateEntryDisplayee HeidenhainCoordinateEntryDisplayee =>
+		heidenhainCoordinateEntryDisplayee ??= new HeidenhainCoordinateEntryDisplayee(
+		() => MachiningProject.NcEnv,
+		() => LocalProjectService.MachiningEquipment);
+
+	/// <summary>
+	/// Gets a list of anchored displayees based on current rendering flags.
+	/// </summary>
+	/// <returns>A list of anchored displayees for rendering</returns>
+	List<IAnchoredDisplayee> GetAnchoredDisplayeeList()
+	{
+		List<IAnchoredDisplayee> dst = new List<IAnchoredDisplayee>();
+		MachiningProject machiningProject = MachiningProject;
+		if (machiningProject == null)
+			return dst;
+
+		LocalProjectService localProjectService = LocalProjectService;
+		HardNcEnv ncEnv = machiningProject.NcEnv;
+		//the execution scene draws the RUNTIME face throughout (equipment
+		//split: the service facades expose the authored setup face instead)
+		var machiningEquipment = localProjectService.MachiningEquipment;
+		var workpiece = machiningEquipment?.Workpiece;
+
+		if (RenderingFlagBitArray[(int)RenderingFlag.ClStrip])
+		{
+			localProjectService.ClStrip.IsKeepingDispAlive = true;
+			dst.Add(new AnchoredDisplayee(
+				workpiece?.ProgramZeroAnchor,
+				localProjectService.ClStrip));
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.Mech])
+		{
+			if (machiningEquipment != null)
+			{
+				List<IAnchoredDisplayee> machAncDisplayees =
+					machiningEquipment.GetAnchoredDisplayeeList() ?? [];
+				HashSet<Anchor> exclusiveAnchorSet = new([
+					.. workpiece?.Asmb.DescendantAnchors()??[],
+						.. machiningEquipment.MachiningTool?.GetAsmb().DescendantAnchors()??[],
+						.. machiningEquipment.Fixture?.Asmb.DescendantAnchors()??[],
+					]);
+				dst.AddRange(machAncDisplayees.Where(ad =>
+					!exclusiveAnchorSet.Contains(ad.GetAnchor())));
+			}
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.WorkpieceGeom])
+		{
+			if (workpiece != null)
+				dst.AddRange(localProjectService.WorkpieceService
+					.GetAnchoredDisplayeeList());
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.Tool])
+		{
+			if (machiningEquipment?.MachiningTool != null)
+				dst.Add(new AnchoredDisplayee(
+				machiningEquipment.MachiningTool?.GetAnchor(),
+				machiningEquipment.MachiningTool));
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.Fixture])
+		{
+			if (machiningEquipment?.Fixture != null)
+				dst.Add(new AnchoredDisplayee(
+				machiningEquipment.Fixture.GetAnchor(),
+				machiningEquipment.Fixture));
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.ProgramZero])
+		{
+			if (workpiece != null)
+				dst.Add(workpiece.ProgramZeroAnchor);
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.IsoCoordinate])
+		{
+			dst.Add(IsoCoordinateEntryDisplayee);
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.HeidenhainCoordinate]
+			&& ncEnv.CncBrand == CncBrand.Heidenhain)
+		{
+			dst.Add(HeidenhainCoordinateEntryDisplayee);
+		}
+		return dst;
+	}
+	/// <summary>
+	/// Gets the root anchor for the display hierarchy based on current rendering flags.
+	/// </summary>
+	/// <returns>The root anchor to use for rendering</returns>
+	internal static Anchor GetRootAnchor(
+	LocalProjectService localProjectService, BitArray renderingFlagBitArray)
+	{
+		//runtime face throughout: this roots the execution scene
+		var machiningEquipment = localProjectService?.MachiningEquipment;
+		if (renderingFlagBitArray[(int)RenderingFlag.Mech])
+			return machiningEquipment?.GetAnchor();
+		else if (renderingFlagBitArray[(int)RenderingFlag.WorkpieceGeom])
+			return machiningEquipment?.Workpiece?.GetAnchor();
+		else if (renderingFlagBitArray[(int)RenderingFlag.Fixture])
+			return machiningEquipment?.Fixture?.GetAnchor();
+		else if (renderingFlagBitArray[(int)RenderingFlag.Tool])
+			return machiningEquipment?.MachiningTool?.GetAnchor();
+		else
+			return null;
+	}
+	/// <inheritdoc/>
+	public Anchor GetAnchor() => GetRootAnchor(LocalProjectService, RenderingFlagBitArray);
+	/// <inheritdoc/>
+	public void Display(Bind bind)
+	{
+		//Console.WriteLine($"RB: {string.Join(',', Enumerable.Range(0,
+		//    RenderingFlagBitArray.Length).Select(RenderingFlagBitArray.Get))}");
+
+		//ClStrip pos has to be update by ClStrip.
+		if (RenderingFlagBitArray[(int)RenderingFlag.WorkpieceGeom]
+				&& !RenderingFlagBitArray[(int)RenderingFlag.ClStrip]
+				&& LocalProjectService?.ClStrip.CallRefreshDrawing == true)
+			LocalProjectService?.ClStrip.RefreshDrawingInRendering(false);
+
+		bind.PushCoveringPixelMode();
+		double offsetHOnCover = 0;
+		if (RenderingFlagBitArray[(int)RenderingFlag.DimensionBar])
+		{
+			bind.ModelMatStack.Push();
+			bind.ModelMatStack.Trans(0, offsetHOnCover, 0);
+			DimensionBar.Display(bind, "mm");
+			bind.ModelMatStack.Pop();
+			offsetHOnCover += DimensionBar.OffsetH;
+		}
+		if (RenderingFlagBitArray[(int)RenderingFlag.ColorScaleBar]
+			&& MachiningProject?.MillingGuide?.DictionaryColorGuide?.SelectedColorGuide
+			is IGetRangeColorRule getRangeColorRule)
+		{
+			var rangeColorRule = getRangeColorRule.GetRangeColorRule();
+			if (rangeColorRule != null)
+			{
+				bind.ModelMatStack.Push();
+				bind.ModelMatStack.Trans(0, offsetHOnCover, 0);
+
+				ColorScaleBar.Display(bind,
+					rangeColorRule.Floor, rangeColorRule.Ceiling,
+					rangeColorRule.GetRgb, "L.", "");
+				bind.ModelMatStack.Pop();
+				offsetHOnCover += ColorScaleBar.OffsetH;
+			}
+		}
+		if (LocalProjectService?.WorkpieceService?.HasDiffOverlay == true)
+		{
+			bind.ModelMatStack.Push();
+			bind.ModelMatStack.Trans(0, offsetHOnCover, 0);
+
+			var rangeColorRule = LocalProjectService.WorkpieceService.DiffRangeColorRule;
+			ColorScaleBar.Display(bind,
+				rangeColorRule.Floor, rangeColorRule.Ceiling,
+				rangeColorRule.GetRgb, "Df.", "");
+			bind.ModelMatStack.Pop();
+			offsetHOnCover += ColorScaleBar.OffsetH;
+		}
+		bind.ModelMatStack.Pop();
+
+		bind.PushColorByRgb(1, 1, 1);
+		var machiningEquipment = LocalProjectService?.MachiningEquipment;
+		//Collision red is per-scenario state owned by the execution equipment
+		//(never stored on the shared Solid geometry): scope it to this scene
+		//so the setup topology never paints it.
+		using (CollisionRedScope.Enter(
+			machiningEquipment == null ? null : machiningEquipment.IsCollisionRed))
+		{
+			machiningEquipment?.GetAsmb()?.Display(bind,
+					GetAnchor(),
+					GetAnchoredDisplayeeList().ToArray());
+		}
+		bind.PopColor();
+	}
+	/// <inheritdoc/>
+	public void ExpandToBox3d(ref box3d_t dst)
+	{
+		//Console.WriteLine($"dst.A: {dst}");
+		LocalProjectService?.MachiningEquipment?.GetAsmb()?.ExpandToBox3d(ref dst,
+				GetAnchor(),
+				GetAnchoredDisplayeeList().ToArray());
+		//Console.WriteLine($"dst.B: {dst}");
+	}
+}

Geom/DemoBuildGeom.cs

@@ -30,8 +30,8 @@ public static class DemoBuildGeom
 		TransformationGeom transformationGeom = new TransformationGeom()
 		{
 			Transformer = new GeneralTransform(1,
-				new StaticRotation(new Vec3d(0, 0, 1), MathUtil.ToRad(15), new Vec3d(0, 0, 0)),
+				new StaticRotation(new vec3d_t(0, 0, 1), MathUtil.ToRad(15), new vec3d_t(0, 0, 0)),
-				new StaticTranslation(new Vec3d(0, 0, 0))),
+				new StaticTranslation(new vec3d_t(0, 0, 0))),
 			Geom = stl
 		};
 		GeomCombination geomCombination = new GeomCombination(stlFile, transformationGeom);

Geom/DemoIExpandToBox3d.cs

@@ -5,7 +5,7 @@ namespace Sample.Geom;
 
 /// <summary>
 /// Demonstrates how to create and calculate bounding boxes for different geometric objects.
-/// Shows the use of Box3d to encompass multiple geometric elements with a single boundary.
+/// Shows the use of box3d_t to encompass multiple geometric elements with a single boundary.
 /// </summary>
 /// <remarks>
 /// ### Source Code
@@ -16,11 +16,11 @@ public static class DemoIExpandToBox3d
 	static void Main()
 	{
 		#region DocSite.CountBoundingBox
-		Box3d objA = new Box3d(0, 0, 0, 1, 1, 1);
+		box3d_t objA = new box3d_t(0, 0, 0, 1, 1, 1);
-		Box3d objB = new Box3d(-1, -2, -3, 3, 2, 1);
+		box3d_t objB = new box3d_t(-1, -2, -3, 3, 2, 1);
-		Vec3d objC = new Vec3d(-2, 3, -5);
+		vec3d_t objC = new vec3d_t(-2, 3, -5);
 
-		Box3d boundingbox = new Box3d(objA, objB, objC);
+		box3d_t boundingbox = new box3d_t(objA, objB, objC);
 		Console.WriteLine("boundingbox: " + boundingbox);
 		#endregion
 	}

Hi.Sample.csproj

@@ -11,7 +11,7 @@
 		</Description>
 		<Configurations>Debug;Release</Configurations>
 		<VersionBuild>0</VersionBuild>
-		<VersionPrefix>3.1.$(VersionBuild)</VersionPrefix>
+		<VersionPrefix>3.2.$(VersionBuild)</VersionPrefix>
 		<Product>$(AssemblyName)</Product>
 		<ApplicationIcon>techcoordinate.ico</ApplicationIcon>
 		<Copyright>Copyright 2025 Tech Coordinate Co., Ltd.</Copyright>
@@ -32,7 +32,7 @@
 		<ProjectReference Include="..\HiNc\HiNc.csproj" />
 	</ItemGroup>
 	<ItemGroup Condition="'$(Configuration)'=='Release'">
-		<PackageReference Include="HiNc" Version="3.1.*" />
+		<PackageReference Include="HiNc" Version="3.2.*" />
 	</ItemGroup>
 	
 </Project>

MachineTool/DemoBuildMachineTool.cs

@@ -21,7 +21,7 @@ namespace Sample.MachineTool
     /// ### Source Code
     /// [!code-csharp[SampleCode](~/../Hi.Sample/MachineTool/DemoBuildMachineTool.cs)]
     /// </remarks>
-    public class DemoBuildMachineTool : IGetCodeXyzabcMachineTool
+    public class DemoBuildMachineTool
     {
         /// <summary>
         /// Registers this type's deserializer with the given <see cref="XFactory"/>
@@ -37,12 +37,16 @@ namespace Sample.MachineTool
         /// Generates an XYZ-ABC machine tool instance from embedded resources.
         /// </summary>
         /// <returns>A configured machine tool model.</returns>
-        public static CodeXyzabcMachineTool GenXyzabcMachineTool()
+        public static GeneralXyzabcMachineTool GenXyzabcMachineTool()
         {
-            CodeXyzabcChain chain = new CodeXyzabcChain("[O][Y][X][C][w];[O][Z][B][S][t]");
+            GeneralXyzabcMachineTool dst = GeneralXyzabcMachineTool.CreateFromChainCode(
-            if (chain.ToolBuckleTransformer is StaticTranslation st)
+                "[O][Y][X][C][w];[O][Z][B][S][t]");
-                st.Trans = new Vec3d(-72.40, 72.40, 176.44);
+            if (dst.ToolMountTransformer is StaticTranslation st)
-            chain.TransformerB.Pivot = new Vec3d(-72.4, -177.4, 225.94);
+                st.Trans = new vec3d_t(-72.40, 72.40, 176.44);
+            //the spindle turns the tool about its own axis: the rotation's pivot
+            //sits on the tool mount's origin, where the offset above moved it.
+            dst.SpindleTransformer.Pivot = new vec3d_t(-72.40, 72.40, 176.44);
+            dst.TransformerB.Pivot = new vec3d_t(-72.4, -177.4, 225.94);
             Dictionary<string, Solid> solidMap = new Dictionary<string, Solid>()
             {
                 ["O"] = new Solid(new Stl("MachineTool/base.stl")),
@@ -53,10 +57,8 @@ namespace Sample.MachineTool
                 ["C"] = new Solid(new Stl("MachineTool/C.stl")),
                 ["S"] = new Solid(new Stl("MachineTool/spindle.stl")),
             };
-            chain.AnchorToSolid.BuildAnchorToSolid(
+            dst.AnchorToSolid.BuildAnchorToSolid(
-                chain.Asmb.GetDescendantAnchors(), solidMap);
+                dst.Asmb.DescendantAnchors(), solidMap);
-
-            CodeXyzabcMachineTool dst = new CodeXyzabcMachineTool(chain);
             dst.GenerateCollisionIndexPairs();
             return dst;
         }
@@ -64,7 +66,7 @@ namespace Sample.MachineTool
         /// <summary>
         /// The cached machine tool instance.
         /// </summary>
-        CodeXyzabcMachineTool MachineTool { get; }
+        GeneralXyzabcMachineTool MachineTool { get; }
 
         /// <summary>
         /// Default constructor that initializes the machine tool model.
@@ -81,9 +83,15 @@ namespace Sample.MachineTool
         /// <inheritdoc/>
         public XElement ToXElement() => new XElement(XName);
         #endregion
-        /// <inheritdoc/>
+        /// <summary>
-        public CodeXyzabcMachineTool GetXyzabcMachineTool() => MachineTool;
+        /// Gets the built machine tool.
-        /// <inheritdoc/>
+        /// </summary>
+        /// <returns>Machine tool.</returns>
+        public GeneralXyzabcMachineTool GetXyzabcMachineTool() => MachineTool;
+        /// <summary>
+        /// Gets the machine tool as a machining chain.
+        /// </summary>
+        /// <returns>Machining chain.</returns>
         public IMachiningChain GetMachiningChain() => MachineTool;
     }
 }

MachineTool/DemoBuildMachineToolWithoutGeometrys.cs

@@ -18,12 +18,12 @@ public static class DemoBuildMachineToolWithoutGeometrys
 	/// Generates an empty machine tool with basic configuration.
 	/// </summary>
 	/// <returns>A configured but empty machine tool without solids.</returns>
-	public static CodeXyzabcMachineTool GenEmptyMachineTool()
+	public static GeneralXyzabcMachineTool GenEmptyMachineTool()
 	{
-		CodeXyzabcChain chain = new CodeXyzabcChain("[O][C][w];[O][X][Y][Z][B][S][t]");
+		GeneralXyzabcMachineTool xyzabcMachineTool = GeneralXyzabcMachineTool.CreateFromChainCode(
-		if (chain.ToolBuckleTransformer is StaticTranslation st)
+			"[O][C][w];[O][X][Y][Z][B][S][t]");
-			st.Trans = new Vec3d(-200, 200, 400);
+		if (xyzabcMachineTool.ToolMountTransformer is StaticTranslation st)
-		CodeXyzabcMachineTool xyzabcMachineTool = new CodeXyzabcMachineTool(chain);
+			st.Trans = new vec3d_t(-200, 200, 400);
 		return xyzabcMachineTool;
 	}
 }

Machining/DemoBuildGeomOnlyMachiningProject.cs

@@ -70,23 +70,26 @@ public static class DemoBuildGeomOnlyMachiningProject
 			},
 		};
 
-		localProjectService.Fixture = new Fixture()
+		//The fixture topology is free; the default shape has one branch from the
-		{
+		//geometry anchor to each mount, so the workpiece mount is placed by the
-			Geom = new Box3d(new Vec3d(-40, -40, 0), new Vec3d(40, 40, 10)),
+		//transformer of the branch to it: on top of the 10 mm thick fixture geom.
-			GeomToWorkpieceTransformer = new StaticTranslation(new Vec3d(0, 0, 10)),
+		Fixture fixture = Fixture.CreateDefault();
-		};
+		fixture.Geom = new Box3d(new vec3d_t(-40, -40, 0), new vec3d_t(40, 40, 10));
+		Branch.Get(fixture.GeomAnchor, fixture.WorkpieceMount).Transformer
+			= new StaticTranslation(new vec3d_t(0, 0, 10));
+		localProjectService.Fixture = fixture;
 
-		localProjectService.Workpiece = new Workpiece()
+		//The default shape already leads from the geometry anchor to the fixture
-		{
+		//mount and to program zero by zero translations.
-			InitResolution = 0.25,
+		Workpiece workpiece = Workpiece.CreateDefault();
-			InitGeom = new Box3d(0, 0, -50, 70, 50, 0),
+		workpiece.InitResolution = 0.25;
-			IdealGeom = null,
+		workpiece.InitGeom = new Box3d(0, 0, -50, 70, 50, 0);
-			WorkpieceGeomToFixtureBuckleTransformer = new StaticTranslation(new Vec3d(0, 0, 0)),
+		workpiece.IdealGeom = null;
-		};
+		localProjectService.Workpiece = workpiece;
 
 		IProgress<object> progress = null;
 		localProjectService.MachiningChain
-				= XFactory.GenByFile<CodeXyzabcMachineTool>(
+				= XFactory.GenByFile<GeneralXyzabcMachineTool>(
 					"Resource", "MachineTool/Table-B1.default/Table-B1.mt", progress);
 		localProjectService.MachiningChainFile = "Table-B1.default/Table-B1.mt";
 

Machining/DemoBuildMachiningProject.cs

@@ -64,11 +64,11 @@ public static class DemoBuildMachiningProject
 			InnerBeamProfile = new FluteDependentRatioProfile(),
 			MillingCutterOptLimit = new MillingCutterOptOption(),
 		};
-		//build FluteContourTray property 
+		//build Fluting property
 		double helixAngle_deg = 50;
 		double radialRakeAngle_deg = 15;
 		double bottomOuterRadius_mm = diameter_mm / 2 - roundRadius_mm;
-		millingCutter.FluteContourTray = new UniformContourTray()
+		millingCutter.Fluting = new UniformFluting()
 		{
 			TrackNum = 3,
 			BaselineOneContour = new FluteContour()
@@ -111,10 +111,10 @@ public static class DemoBuildMachiningProject
 			MillingCutterOptLimit = new MillingCutterOptOption()
 		};
 
-		//build FluteContourTray property 
+		//build Fluting property
 		double helixAngle_deg = 50;
 		double radialRakeAngle_deg = 15;
-		millingCutter.FluteContourTray = new UniformContourTray()
+		millingCutter.Fluting = new UniformFluting()
 		{
 			TrackNum = 3,
 			BaselineOneContour = new FluteContour()
@@ -183,30 +183,33 @@ public static class DemoBuildMachiningProject
 		#endregion
 
 		#region ConfigureFixture
-		localProjectService.Fixture = new Fixture()
+		//The fixture topology is free; the default shape has one branch from the
-		{
+		//geometry anchor to each mount, so the workpiece mount is placed by the
-			Geom = new Box3d(new Vec3d(-40, -40, 0), new Vec3d(40, 40, 10)),
+		//transformer of the branch to it: on top of the 10 mm thick fixture geom.
-			GeomToWorkpieceTransformer = new StaticTranslation(new Vec3d(0, 0, 10)),
+		Fixture fixture = Fixture.CreateDefault();
-		};
+		fixture.Geom = new Box3d(new vec3d_t(-40, -40, 0), new vec3d_t(40, 40, 10));
+		Branch.Get(fixture.GeomAnchor, fixture.WorkpieceMount).Transformer
+			= new StaticTranslation(new vec3d_t(0, 0, 10));
+		localProjectService.Fixture = fixture;
 		#endregion
 
 		#region ConfigureWorkpiece
-		localProjectService.Workpiece = new Workpiece()
+		//The default shape already leads from the geometry anchor to the fixture
-		{
+		//mount and to program zero by zero translations.
-			InitResolution = 0.25,
+		Workpiece workpiece = Workpiece.CreateDefault();
-			InitGeom = new Box3d(0, 0, -50, 70, 50, 0),
+		workpiece.InitResolution = 0.25;
-			IdealGeom = null,
+		workpiece.InitGeom = new Box3d(0, 0, -50, 70, 50, 0);
-			WorkpieceGeomToFixtureBuckleTransformer = new StaticTranslation(new Vec3d(0, 0, 0)),
+		workpiece.IdealGeom = null;
-			CuttingPara = XFactory.GenByFile<ICuttingPara>(
+		workpiece.CuttingPara = XFactory.GenByFile<ICuttingPara>(
-				"Resource/CuttingParameter", "Al6061T6.default.mp", progress),
+			"Resource/CuttingParameter", "Al6061T6.default.mp", progress);
-			WorkpieceMaterial = XFactory.GenByFile<WorkpieceMaterial>(
+		workpiece.WorkpieceMaterial = XFactory.GenByFile<WorkpieceMaterial>(
-				"Resource/WorkpieceMaterial", "Al6061T6.default.WorkpieceMaterial", progress),
+			"Resource/WorkpieceMaterial", "Al6061T6.default.WorkpieceMaterial", progress);
-		};
+		localProjectService.Workpiece = workpiece;
 		#endregion
 
 		#region ConfigureMachineChain
 		localProjectService.MachiningChain
-			= XFactory.GenByFile<CodeXyzabcMachineTool>(
+			= XFactory.GenByFile<GeneralXyzabcMachineTool>(
 				"Resource", "MachineTool/Table-B1.default/Table-B1.mt", progress);
 		#endregion
 

Mech/DemoTopo1.cs

@@ -33,10 +33,10 @@ public static class DemoTopo1
 		Anchor B = new Anchor(asmb, "B");
 
 		//build kinematic link
-		Branch.Attach(O, O1, new StaticTranslation(new Vec3d(0, 0, 80)));
+		Branch.Attach(O, O1, new StaticTranslation(new vec3d_t(0, 0, 80)));
-		Branch brnX = Branch.Attach(O1, X, new DynamicTranslation(new Vec3d(1, 0, 0)));
+		Branch brnX = Branch.Attach(O1, X, new DynamicTranslation(new vec3d_t(1, 0, 0)));
-		Branch brnZ = Branch.Attach(X, Z, new DynamicTranslation(new Vec3d(0, 0, 1)));
+		Branch brnZ = Branch.Attach(X, Z, new DynamicTranslation(new vec3d_t(0, 0, 1)));
-		Branch brnB = Branch.Attach(Z, B, new DynamicRotation(new Vec3d(0, 1, 0), 0, new Vec3d(-100, 0, 0)));
+		Branch brnB = Branch.Attach(Z, B, new DynamicRotation(new vec3d_t(0, 1, 0), 0, new vec3d_t(-100, 0, 0)));
 
 		//drive the dynamic transformation by single value for each branch.
 		brnX.Step = 200;
@@ -44,9 +44,9 @@ public static class DemoTopo1
 		brnB.Step = MathUtil.ToRad(-60);
 
 		//Get and show the transform matrices relative to O.
-		Dictionary<Anchor, Mat4d> matMap = asmb.GetMat4dMap(O);
+		Dictionary<Anchor, mat4d_t> matMap = asmb.GetMat4dMap(O);
 		Console.WriteLine("Transform Matrix relative to O:");
-		foreach (KeyValuePair<Anchor, Mat4d> keyValue in matMap)
+		foreach (KeyValuePair<Anchor, mat4d_t> keyValue in matMap)
 			Console.WriteLine($"{keyValue.Key.Name} : {keyValue.Value}");
 		#endregion