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/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
@@ -30,12 +30,12 @@ namespace Sample.Disp
 		{
 			sun.Display(bind);
 			bind.ModelMatStack.Push();
-			bind.ModelMatStack.Mul(new Mat4d(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_earth += 0.03)));
-			bind.ModelMatStack.Mul(new Mat4d(new vec3d_t(12, 0, 0)));
+			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(new AxisAngle4d(new vec3d_t(0, 0, 1), angle_moon += 0.02)));
-			bind.ModelMatStack.Mul(new Mat4d(new vec3d_t(4, 0, 0)));
+			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();

Geom/DemoBuildGeom.cs

@@ -22,7 +22,7 @@ public static class DemoBuildGeom
 	/// <returns>A list of geometries implementing the IGetStl interface</returns>
 	public static List<IGetStl> GenGeoms()
 	{
-		box3d_t box = new box3d_t(0, 0, -50, 70, 50, 0);
+		Box3d box = new Box3d(0, 0, -50, 70, 50, 0);
 		Cylindroid cylindroid = new Cylindroid([ new PairZr(0,12),new PairZr(20,12),
 								new PairZr(20,16),new PairZr(30,16)]);
 		Stl stl = new Stl("geom.stl");

MachineTool/DemoBuildMachineTool.cs

@@ -43,6 +43,9 @@ namespace Sample.MachineTool
                 "[O][Y][X][C][w];[O][Z][B][S][t]");
             if (dst.ToolMountTransformer is StaticTranslation st)
                 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>()
             {

Machining/DemoBuildGeomOnlyMachiningProject.cs

@@ -74,7 +74,7 @@ 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_t(new vec3d_t(-40, -40, 0), new vec3d_t(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_t(0, 0, 10));
 		localProjectService.Fixture = fixture;
@@ -83,7 +83,7 @@ public static class DemoBuildGeomOnlyMachiningProject
 		//mount and to program zero by zero translations.
 		Workpiece workpiece = Workpiece.CreateDefault();
 		workpiece.InitResolution = 0.25;
-		workpiece.InitGeom = new box3d_t(0, 0, -50, 70, 50, 0);
+		workpiece.InitGeom = new Box3d(0, 0, -50, 70, 50, 0);
 		workpiece.IdealGeom = null;
 		localProjectService.Workpiece = workpiece;
 

Machining/DemoBuildMachiningProject.cs

@@ -187,7 +187,7 @@ 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_t(new vec3d_t(-40, -40, 0), new vec3d_t(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_t(0, 0, 10));
 		localProjectService.Fixture = fixture;
@@ -198,7 +198,7 @@ public static class DemoBuildMachiningProject
 		//mount and to program zero by zero translations.
 		Workpiece workpiece = Workpiece.CreateDefault();
 		workpiece.InitResolution = 0.25;
-		workpiece.InitGeom = new box3d_t(0, 0, -50, 70, 50, 0);
+		workpiece.InitGeom = new Box3d(0, 0, -50, 70, 50, 0);
 		workpiece.IdealGeom = null;
 		workpiece.CuttingPara = XFactory.GenByFile<ICuttingPara>(
 			"Resource/CuttingParameter", "Al6061T6.default.mp", progress);

Mech/DemoTopo1.cs

@@ -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