Kernel rig: construction cases, a plane turned about an axis in it, off it and along its own normal

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/kernel-cases/construction/cov-plane-at-angle-about-its-own-normal/expected.json

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+{
+ "sources": [],
+ "what": "XY turned about Z, its own normal",
+ "source": "analytic",
+ "method": "a turn about the plane's normal maps the plane onto itself: XY, normal Z through the origin",
+ "construction": {
+  "P": {
+   "plane": {
+    "through": [
+     3,
+     4,
+     0
+    ],
+    "normal": [
+     0,
+     0,
+     1
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-at-angle-about-its-own-normal/recipe.json

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+{
+ "commands": [
+  {
+   "command": "construct.plane.at_angle",
+   "params": {
+    "base": "XY",
+    "axis": "Z",
+    "angle": "30 deg",
+    "name": "P"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-at-angle-face-off-the-axis/expected.json

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+{
+ "sources": [],
+ "what": "a box's top turned 45 degrees about X, which lies off it",
+ "source": "analytic",
+ "method": "box 40 x 30 x 20 with a corner at the origin (x 0..40, y 0..30, z 0..20): the top z = 20 turned +45 deg about the X axis through the origin: normal (0, -1/sqrt2, 1/sqrt2), and its point (0,0,20) goes to (0, -20/sqrt2, 20/sqrt2): the plane -y + z = 20 sqrt2, 20 from the axis",
+ "construction": {
+  "P": {
+   "plane": {
+    "through": [
+     0,
+     -14.14213562373095,
+     14.14213562373095
+    ],
+    "normal": [
+     0,
+     -1,
+     1
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-at-angle-face-off-the-axis/recipe.json

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+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 40,
+    "width": 30,
+    "height": 20,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "construct.plane.at_angle",
+   "params": {
+    "base": {
+     "face": [
+      5,
+      5,
+      20
+     ]
+    },
+    "axis": "X",
+    "angle": "45 deg",
+    "name": "P"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-at-angle-xy-about-x-30/expected.json

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+{
+ "sources": [],
+ "what": "XY turned 30 degrees about X",
+ "source": "analytic",
+ "method": "turning XY's normal Z by +30 deg about +X (right hand): (0, -sin 30, cos 30) = (0, -1/2, sqrt3/2); the plane keeps the X axis",
+ "construction": {
+  "P": {
+   "plane": {
+    "through": [
+     25,
+     0,
+     0
+    ],
+    "normal": [
+     0,
+     -0.5,
+     0.8660254037844386
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-at-angle-xy-about-x-30/recipe.json

@@ -0,0 +1,13 @@
+{
+ "commands": [
+  {
+   "command": "construct.plane.at_angle",
+   "params": {
+    "base": "XY",
+    "axis": "X",
+    "angle": "30 deg",
+    "name": "P"
+   }
+  }
+ ]
+}