rename XFactory.Regs to XFactory.Generators.

App/wwwroot/HiAPI-docsite/api/Hi.NcParsers.LogicSyntaxs.IsoG68RotationSyntax.html

@@ -188,6 +188,93 @@ Managed commands: G68, G69 (idempotent with <a class="xref" href="Hi.NcParsers.L
   </dd></dl>
 
 
+  <h2 id="Hi_NcParsers_LogicSyntaxs_IsoG68RotationSyntax_examples">Examples</h2>
+  <p>All cases below avoid the cos/sin rotation math by using either G69
+cancel (identity), the first-block default (no transform composed),
+or modal carry of an identity Mat4d. <code>Mat4d</code> arrays are 16
+plain doubles in column-major order — see
+<a class="xref" href="Hi.NcParsers.LogicSyntaxs.IsoCoordinateOffsetSyntax.html">IsoCoordinateOffsetSyntax</a> for the template. A future
+round can add a non-trivial G68 case by dumping the actual output
+and pasting the 16 doubles back into the marker.</p>
+<p>
+First block of the stream (no <code>#Previous:</code>, no G68/G69 on the
+block) — <code>CarryForwardFromPrevious</code> stamps a default
+<code>TiltTransform.Term = "G69"</code> so downstream lookback always
+sees a concrete state; no transform chain entry is composed:
+</p>
+#BeforeBuild:
+<pre><code class="lang-csharp">{ }</code></pre>
+#AfterBuild:
+<pre><code class="lang-csharp">{ "TiltTransform": { "Term": "G69" } }</code></pre>
+G69 flag on the block — <code>TryHandleG69</code> consumes it, writes the
+G69 section, and composes the identity Mat4d into the chain so any
+previously composed tilt rotation is overridden:
+#BeforeBuild:
+<pre><code class="lang-csharp">{ "Parsing": { "Flags": ["G69"] } }</code></pre>
+#AfterBuild:
+<pre><code class="lang-csharp">{
+  "TiltTransform": { "Term": "G69" },
+  "ProgramToMcTransform": [
+    {
+      "Source": "TiltTransform",
+      "Kind": "Static",
+      "Mat4d": [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
+    }
+  ]
+}</code></pre>
+Modal carry: no G68/G69 on the current block, but
+<code>#Previous:</code> carries an active G68 with identity tilt Mat4d in
+its chain. The current block inherits <code>TiltTransform.Term = "G68"</code>
+and re-composes the same Mat4d into its own chain; unrelated M03
+flag survives because this syntax does not touch <code>Parsing</code>
+during the carry path:
+#Previous:
+<pre><code class="lang-csharp">{
+  "TiltTransform": { "Term": "G68" },
+  "ProgramToMcTransform": [
+    {
+      "Source": "TiltTransform",
+      "Kind": "Static",
+      "Mat4d": [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
+    }
+  ]
+}</code></pre>
+#BeforeBuild:
+<pre><code class="lang-csharp">{ "Parsing": { "Flags": ["M03"] } }</code></pre>
+#AfterBuild:
+<pre><code class="lang-csharp">{
+  "Parsing": { "Flags": ["M03"] },
+  "TiltTransform": { "Term": "G68" },
+  "ProgramToMcTransform": [
+    {
+      "Source": "TiltTransform",
+      "Kind": "Static",
+      "Mat4d": [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
+    }
+  ]
+}</code></pre>
+Non-trivial G68 rotation: 90° around the Z axis (no I/J/K → plane
+normal of the default G17 plane) at the origin (no X/Y/Z → all 0).
+The Mat4d column-major layout is rotation 90° about Z (no
+translation since pivot is the origin); <code>cos(π/2)</code> is not
+exactly 0 in IEEE-754 so the diagonal carries the
+<code>6.123233995736766E-17</code> drift produced by
+<code>Math.Cos(Math.PI / 2)</code> — preserved verbatim per the
+no-shorthand marker convention:
+#BeforeBuild:
+<pre><code class="lang-csharp">{ "Parsing": { "G68": { "R": 90 } } }</code></pre>
+#AfterBuild:
+<pre><code class="lang-csharp">{
+  "TiltTransform": { "Term": "G68" },
+  "ProgramToMcTransform": [
+    {
+      "Source": "TiltTransform",
+      "Kind": "Static",
+      "Mat4d": [6.123233995736766E-17, 1, 0, 0, -1, 6.123233995736766E-17, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]
+    }
+  ]
+}</code></pre>
+
 
   <h2 id="Hi_NcParsers_LogicSyntaxs_IsoG68RotationSyntax_remarks">Remarks</h2>
   <div class="markdown level0 remarks"><p>Input: Parsing.G68 → {X,Y,Z,I,J,K,R} from ParameterizedFlagSyntax.