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/DemoDiscreteRgb.cs

@@ -20,19 +20,19 @@ namespace Sample.Disp
         public void Display(Bind bind)
         {
             bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
-            new Box3d(0, 0, 0, 1, 1, 1).ToDraw_Face().Display(bind);
+            new box3d_t(0, 0, 0, 1, 1, 1).ToDraw_Face().Display(bind);
 
             bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
-            new Box3d(1, 0, 0, 2, 1, 1).ToDraw_Face().Display(bind);
+            new box3d_t(1, 0, 0, 2, 1, 1).ToDraw_Face().Display(bind);
 
             bind.Rgb = ColorUtil.GetDiscreteRGB_Env();
-            new Box3d(2, 0, 0, 3, 1, 1).ToDraw_Face().Display(bind);
+            new box3d_t(2, 0, 0, 3, 1, 1).ToDraw_Face().Display(bind);
         }
         /// <inheritdoc/>
-        public void ExpandToBox3d(Box3d dst)
+        public void ExpandToBox3d(ref box3d_t dst)
         {
-            dst.Expand(new Vec3d(0, 0, 0));
+            dst = dst.Expanded(new vec3d_t(0, 0, 0));
-            dst.Expand(new Vec3d(3, 1, 1));
+            dst = dst.Expanded(new vec3d_t(3, 1, 1));
         }
 
         static void Main()

Disp/DemoDrawing.cs

@@ -40,14 +40,14 @@ namespace Sample.Disp
 		/// </summary>
 		public static void DrawLines()
 		{
-			List<Vec3d> ps;
+			List<vec3d_t> ps;
 			double[] vs;
 			int n = 10; //vertex num
 
 			////create drawPoints
-			ps = new List<Vec3d>(n);
+			ps = new List<vec3d_t>(n);
 			for (int i = 0; i < n; i++)
-				ps.Add(new Vec3d(i, 0, 0));
+				ps.Add(new vec3d_t(i, 0, 0));
 			vs = new double[ps.Count * 3];
 			for (int i = 0; i < ps.Count; i++)
 			{
@@ -125,16 +125,16 @@ namespace Sample.Disp
 			for (int i = 0, k = 0; i < n; i++)
 			{
 				//the rgb values set as casual.
-				Vec3d rgb = ColorUtil.GetDiscreteRgb(i);
+				vec3d_t rgb = ColorUtil.GetDiscreteRgb(i);
-				Tri3d tri = new Tri3d(new Vec3d(i, 0, 0), new Vec3d(i + 1, 0, 0), new Vec3d(i + 0.5, 0, 1));
+				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.ps[j].x;
+					vs[k++] = tri[j].x;
-					vs[k++] = tri.ps[j].y;
+					vs[k++] = tri[j].y;
-					vs[k++] = tri.ps[j].z;
+					vs[k++] = tri[j].z;
 				}
 			}
 			//V means Vertex; C means Color
@@ -146,9 +146,9 @@ namespace Sample.Disp
 			for (int i = 0, k = 0; i < n; i++)
 			{
 				//the rgb values set as casual.
-				Vec3d rgb = ColorUtil.GetDiscreteRgb(i);
+				vec3d_t rgb = ColorUtil.GetDiscreteRgb(i);
-				Tri3d tri = new Tri3d(new Vec3d(i, 0, 3), new Vec3d(i + 1, 0, 3), new Vec3d(i + 0.5, 0, 4));
+				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 nn = tri.GetNormal();
+				vec3d_t nn = tri.GetNormal();
 				for (int j = 0; j < 3; j++)
 				{
 					vs[k++] = rgb.x;
@@ -157,9 +157,9 @@ namespace Sample.Disp
 					vs[k++] = nn.x;
 					vs[k++] = nn.y;
 					vs[k++] = nn.z;
-					vs[k++] = tri.ps[j].x;
+					vs[k++] = tri[j].x;
-					vs[k++] = tri.ps[j].y;
+					vs[k++] = tri[j].y;
-					vs[k++] = tri.ps[j].z;
+					vs[k++] = tri[j].z;
 				}
 			}
 			//V means Vertex; C means Color; N means Normal
@@ -171,16 +171,16 @@ namespace Sample.Disp
 		}
 
 		/// <summary>
-		/// Demonstrates drawing 3D triangles using the Tri3d helper class.
+		/// 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> tris = new List<Tri3d>(n);
+			List<tri3d_t> tris = new List<tri3d_t>(n);
 			for (int i = 0; i < n; i++)
-				tris.Add(new Tri3d(new Vec3d(i, 0, 0), new Vec3d(i + 1, 0, 0), new Vec3d(i + 0.5, 0, 1)));
+				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();

Disp/DemoPick1.cs

@@ -20,15 +20,15 @@ namespace Sample.Disp
         public void Display(Bind bind)
 		{
 			bind.PickID = PickingID;
-			bind.Rgb = new Vec3d(isMouseOver ? 0 : 1, 1, 1);
+			bind.Rgb = new vec3d_t(isMouseOver ? 0 : 1, 1, 1);
-			new Box3d(0, 0, 0, 1, 1, 1).DisplayFace(bind);
+			new box3d_t(0, 0, 0, 1, 1, 1).DisplayFace(bind);
 			bind.PickID = 0;
 		}
         /// <inheritdoc/>
-        public void ExpandToBox3d(Box3d dst)
+        public void ExpandToBox3d(ref box3d_t dst)
 		{
-			dst.Expand(new Vec3d(0, 0, 0));
+			dst = dst.Expanded(new vec3d_t(0, 0, 0));
-			dst.Expand(new Vec3d(1, 1, 1));
+			dst = dst.Expanded(new vec3d_t(1, 1, 1));
 		}
         /// <inheritdoc/>
         public override void OnMouseEnter(ui_event_type e, DispEngine dispEngine)

Disp/DemoPick2.cs

@@ -24,23 +24,23 @@ namespace Sample.Disp
 		{
 			bind.PickID = pickableA.PickingID;
 			bind.Rgb = ColorUtil.GetDiscreteRgb(1);
-			new Box3d(0, 0, 0, 1, 1, 1).DisplayFace(bind);
+			new box3d_t(0, 0, 0, 1, 1, 1).DisplayFace(bind);
 
 			bind.PickID = pickableB.PickingID;
 			bind.Rgb = ColorUtil.GetDiscreteRgb(2);
-			new Box3d(0, 0, 1, 1, 1, 2).DisplayFace(bind);
+			new box3d_t(0, 0, 1, 1, 1, 2).DisplayFace(bind);
 
 			bind.PickID = pickableC.PickingID;
 			bind.Rgb = ColorUtil.GetDiscreteRgb(3);
-			new Box3d(0, 0, 2, 1, 1, 3).DisplayFace(bind);
+			new box3d_t(0, 0, 2, 1, 1, 3).DisplayFace(bind);
 
 			bind.PickID = 0;
 		}
 		/// <inheritdoc/>
-		public void ExpandToBox3d(Box3d dst)
+		public void ExpandToBox3d(ref box3d_t dst)
 		{
-			dst.Expand(new Vec3d(0, 0, 0));
+			dst = dst.Expanded(new vec3d_t(0, 0, 0));
-			dst.Expand(new Vec3d(1, 1, 3));
+			dst = dst.Expanded(new vec3d_t(1, 1, 3));
 		}
 		#region IDisposable Support
 		private bool disposedValue = false; // To detect redundant calls

Disp/DemoPickable.cs

@@ -40,9 +40,9 @@ public class DemoPickable : IDisplayee
 		draw.Display(bind);
 	}
 	/// <inheritdoc/>
-	public void ExpandToBox3d(Box3d dst)
+	public void ExpandToBox3d(ref box3d_t dst)
 	{
-		draw.ExpandToBox3d(dst);
+		draw.ExpandToBox3d(ref dst);
 	}
 
 	/// <summary>

Disp/DemoSatellite.cs

@@ -6,7 +6,7 @@ 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"/> matrices and model matrix stack transformations.
+    /// <see cref="mat4d_t"/> matrices and model matrix stack transformations.
     /// </summary>
     /// <remarks>
     /// ### Source Code
@@ -21,30 +21,30 @@ namespace Sample.Disp
 		double angle_moon;
 		DemoSatellite()
 		{
-			sun = Box3d.CenterUnitBox.ScaleFromCenter(4).ToDraw_Face();
+			sun = box3d_t.CenterUnitBox.ScaledFromCenter(4).ToDraw_Face();
-			earth = Box3d.CenterUnitBox.ScaleFromCenter(2).ToDraw_Face();
+			earth = box3d_t.CenterUnitBox.ScaledFromCenter(2).ToDraw_Face();
-			moon = Box3d.CenterUnitBox.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(new AxisAngle4d(new Vec3d(0, 0, 1), angle_earth += 0.03)));
+			bind.ModelMatStack.Mul(new mat4d_t(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_earth += 0.03)));
-			bind.ModelMatStack.Mul(new Mat4d(new Vec3d(12, 0, 0)));
+			bind.ModelMatStack.Mul(new mat4d_t(new vec3d_t(12, 0, 0)));
 			earth.Display(bind);
 			bind.ModelMatStack.Push();
-			bind.ModelMatStack.Mul(new Mat4d(new AxisAngle4d(new Vec3d(0, 0, 1), angle_moon += 0.02)));
+			bind.ModelMatStack.Mul(new mat4d_t(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_moon += 0.02)));
-			bind.ModelMatStack.Mul(new Mat4d(new Vec3d(4, 0, 0)));
+			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(Box3d dst)
+		public void ExpandToBox3d(ref box3d_t dst)
 		{
-			dst.Expand(new Vec3d(-14, -14, -2));
+			dst = dst.Expanded(new vec3d_t(-14, -14, -2));
-			dst.Expand(new Vec3d(14, 14, 2));
+			dst = dst.Expanded(new vec3d_t(14, 14, 2));
 		}
 
 		static void Main()

Disp/DemoUtil.cs

@@ -32,8 +32,8 @@ public static class DemoUtil
 		LocalApp.AppBegin(loggerFactory.CreateLogger("Hi.Sample"));
 		try
 		{
-			Box3d box = new Box3d();
+			box3d_t box = new box3d_t();
-			displayee.ExpandToBox3d(box);
+			displayee.ExpandToBox3d(ref box);
 			Console.WriteLine($"{title}: {displayee.GetType().Name} bounding {box}");
 			Console.WriteLine("Assign it to your canvas' DispEngine.Displayee to see it.");
 		}

Disp/HeidenhainCoordinateEntryDisplayee.cs

@@ -62,10 +62,10 @@ namespace Sample.Disp
             ////Console.WriteLine($"B: {CoordinateIndex}; {coordinateMove}");
             IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
             if (equipment == null
-                || !equipment.TryGetMachinePositionAtTableMountZero(out Vec3d mcXyz_AttacherAtTableMountZero))
+                || !equipment.TryGetMachinePositionAtTableMountZero(out vec3d_t mcXyz_AttacherAtTableMountZero))
                 return;
 
-            Vec3d coordinateMove;
+            vec3d_t coordinateMove;
             string text;
             if (HeidenhainCycleDef247Q339 == 0 && HeidenhainCycleDef7Arg == null)
                 return;
@@ -90,7 +90,7 @@ namespace Sample.Disp
             bind.ModelMatStack.Pop();
         }
         /// <inheritdoc/>
-        public void ExpandToBox3d(Box3d dst)
+        public void ExpandToBox3d(ref box3d_t dst)
         {
             HardNcEnv ncEnv = NcEnv;
             if (ncEnv == null || NcEnv.CncBrand != CncBrand.Heidenhain)
@@ -98,16 +98,16 @@ namespace Sample.Disp
 
             IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
             if (equipment == null
-                || !equipment.TryGetMachinePositionAtTableMountZero(out Vec3d mcXyz_AttacherAtTableMountZero))
+                || !equipment.TryGetMachinePositionAtTableMountZero(out vec3d_t mcXyz_AttacherAtTableMountZero))
                 return;
-            Vec3d coordinateMove;
+            vec3d_t coordinateMove;
             if (HeidenhainCycleDef247Q339 == 0 && HeidenhainCycleDef7Arg == null)
                 return;
             coordinateMove = NcFlagUtil.GetHeidenhainCoordinateOffset(
                 HeidenhainCycleDef247Q339, HeidenhainCycleDef7Arg, ncEnv);
 
 
-            dst.Expand(-mcXyz_AttacherAtTableMountZero + coordinateMove);
+            dst = dst.Expanded(-mcXyz_AttacherAtTableMountZero + coordinateMove);
         }
         /// <inheritdoc/>
         public Anchor GetAnchor()

Disp/IsoCoordinateEntryDisplayee.cs

@@ -45,12 +45,12 @@ public class IsoCoordinateEntryDisplayee : IAnchoredDisplayee
 		if (ncEnv == null)
 			return;
 
-		if (ncEnv.IsoCoordinateTable?.TryGetValue(IsoCoordinateId, out Vec3d coordinateMove) != true)
+		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 attacherPos))
+		if (equipment == null || !equipment.TryGetIsoCoordinatePosition(coordinateMove, out vec3d_t attacherPos))
 			return;
 
 		bind.ModelMatStack.Push();
@@ -59,18 +59,18 @@ public class IsoCoordinateEntryDisplayee : IAnchoredDisplayee
 		bind.ModelMatStack.Pop();
 	}
 	/// <inheritdoc/>
-	public void ExpandToBox3d(Box3d dst)
+	public void ExpandToBox3d(ref box3d_t dst)
 	{
 		HardNcEnv ncEnv = NcEnv;
 		if (ncEnv == null)
 			return;
-		if (ncEnv.IsoCoordinateTable?.TryGetValue(IsoCoordinateId, out Vec3d coordinateMove) != true)
+		if (ncEnv.IsoCoordinateTable?.TryGetValue(IsoCoordinateId, out vec3d_t coordinateMove) != true)
 			return;
 
 		IMachiningEquipment equipment = MillingEquipmentFunc?.Invoke();
-		if (equipment == null || !equipment.TryGetIsoCoordinatePosition(coordinateMove, out Vec3d attacherPos))
+		if (equipment == null || !equipment.TryGetIsoCoordinatePosition(coordinateMove, out vec3d_t attacherPos))
 			return;
-		dst.Expand(attacherPos);
+		dst = dst.Expanded(attacherPos);
 	}
 	/// <inheritdoc/>
 	/// <returns>Table Mount if existed; otherwise, return null.</returns>

Disp/MachiningProjectDisplayee.cs

@@ -239,10 +239,10 @@ public class MachiningProjectDisplayee : IDisplayee, IGetAnchor
 		bind.PopColor();
 	}
 	/// <inheritdoc/>
-	public void ExpandToBox3d(Box3d dst)
+	public void ExpandToBox3d(ref box3d_t dst)
 	{
 		//Console.WriteLine($"dst.A: {dst}");
-		LocalProjectService?.MachiningEquipment?.GetAsmb()?.ExpandToBox3d(dst,
+		LocalProjectService?.MachiningEquipment?.GetAsmb()?.ExpandToBox3d(ref dst,
 				GetAnchor(),
 				GetAnchoredDisplayeeList().ToArray());
 		//Console.WriteLine($"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
 	}

MachineTool/DemoBuildMachineTool.cs

@@ -42,8 +42,11 @@ namespace Sample.MachineTool
             GeneralXyzabcMachineTool dst = GeneralXyzabcMachineTool.CreateFromChainCode(
                 "[O][Y][X][C][w];[O][Z][B][S][t]");
             if (dst.ToolMountTransformer is StaticTranslation st)
-                st.Trans = new Vec3d(-72.40, 72.40, 176.44);
+                st.Trans = new vec3d_t(-72.40, 72.40, 176.44);
-            dst.TransformerB.Pivot = new Vec3d(-72.4, -177.4, 225.94);
+            //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")),

MachineTool/DemoBuildMachineToolWithoutGeometrys.cs

@@ -23,7 +23,7 @@ public static class DemoBuildMachineToolWithoutGeometrys
 		GeneralXyzabcMachineTool xyzabcMachineTool = GeneralXyzabcMachineTool.CreateFromChainCode(
 			"[O][C][w];[O][X][Y][Z][B][S][t]");
 		if (xyzabcMachineTool.ToolMountTransformer is StaticTranslation st)
-			st.Trans = new Vec3d(-200, 200, 400);
+			st.Trans = new vec3d_t(-200, 200, 400);
 		return xyzabcMachineTool;
 	}
 }

Machining/DemoBuildGeomOnlyMachiningProject.cs

@@ -74,9 +74,9 @@ public static class DemoBuildGeomOnlyMachiningProject
 		//geometry anchor to each mount, so the workpiece mount is placed by the
 		//transformer of the branch to it: on top of the 10 mm thick fixture geom.
 		Fixture fixture = Fixture.CreateDefault();
-		fixture.Geom = new Box3d(new Vec3d(-40, -40, 0), new Vec3d(40, 40, 10));
+		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(0, 0, 10));
+			= new StaticTranslation(new vec3d_t(0, 0, 10));
 		localProjectService.Fixture = fixture;
 
 		//The default shape already leads from the geometry anchor to the fixture

Machining/DemoBuildMachiningProject.cs

@@ -187,9 +187,9 @@ public static class DemoBuildMachiningProject
 		//geometry anchor to each mount, so the workpiece mount is placed by the
 		//transformer of the branch to it: on top of the 10 mm thick fixture geom.
 		Fixture fixture = Fixture.CreateDefault();
-		fixture.Geom = new Box3d(new Vec3d(-40, -40, 0), new Vec3d(40, 40, 10));
+		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(0, 0, 10));
+			= new StaticTranslation(new vec3d_t(0, 0, 10));
 		localProjectService.Fixture = fixture;
 		#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