Kernel rig: construction cases, the tangent plane to a cylinder and a sphere, and a point on the axis refused

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

tests/kernel-cases/construction/cov-plane-tangent-refuses-a-point-on-the-axis/expected.json

@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "a tangent plane to a cylinder at a point on its axis",
+ "source": "analytic",
+ "method": "cylinder r 5, h 10 on (60,0,0) along +Z: (60,0,5) is on the axis, equally far from every line of the side: refused",
+ "outcome": "refused",
+ "refusal": "the point is on the face's axis"
+}

tests/kernel-cases/construction/cov-plane-tangent-refuses-a-point-on-the-axis/recipe.json

@@ -0,0 +1,36 @@
+{
+ "commands": [
+  {
+   "command": "solid.cylinder",
+   "params": {
+    "base": [
+     60,
+     0,
+     0
+    ],
+    "radius": 5,
+    "height": 10,
+    "body_name": "Cyl",
+    "operation": "new"
+   }
+  },
+  {
+   "command": "construct.plane.tangent",
+   "params": {
+    "face": {
+     "face": [
+      65,
+      0,
+      5
+     ]
+    },
+    "at": [
+     60,
+     0,
+     5
+    ],
+    "name": "T"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-tangent-to-a-cylinder-at-a-point/expected.json

@@ -0,0 +1,22 @@
+{
+ "sources": [],
+ "what": "the tangent plane to a cylinder where a point projects on it",
+ "source": "analytic",
+ "method": "cylinder r 5, h 10 on (60,0,0) along +Z: (66,8,5) lies along (0.6,0.8,0) from the axis: it touches at (63,4,5) with normal (0.6,0.8,0)",
+ "construction": {
+  "T": {
+   "plane": {
+    "through": [
+     63,
+     4,
+     5
+    ],
+    "normal": [
+     3,
+     4,
+     0
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-tangent-to-a-cylinder-at-a-point/recipe.json

@@ -0,0 +1,36 @@
+{
+ "commands": [
+  {
+   "command": "solid.cylinder",
+   "params": {
+    "base": [
+     60,
+     0,
+     0
+    ],
+    "radius": 5,
+    "height": 10,
+    "body_name": "Cyl",
+    "operation": "new"
+   }
+  },
+  {
+   "command": "construct.plane.tangent",
+   "params": {
+    "face": {
+     "face": [
+      65,
+      0,
+      5
+     ]
+    },
+    "at": [
+     66,
+     8,
+     5
+    ],
+    "name": "T"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-plane-tangent-to-a-sphere/expected.json

@@ -0,0 +1,22 @@
+{
+ "sources": [],
+ "what": "the tangent plane to a sphere",
+ "source": "analytic",
+ "method": "sphere r 5 on (0,0,60); towards (0,3,64), (0,0.6,0.8) from the centre: it touches at (0,3,64) with normal (0,3,4)",
+ "construction": {
+  "T": {
+   "plane": {
+    "through": [
+     0,
+     3,
+     64
+    ],
+    "normal": [
+     0,
+     3,
+     4
+    ]
+   }
+  }
+ }
+}

tests/kernel-cases/construction/cov-plane-tangent-to-a-sphere/recipe.json

@@ -0,0 +1,35 @@
+{
+ "commands": [
+  {
+   "command": "solid.sphere",
+   "params": {
+    "center": [
+     0,
+     0,
+     60
+    ],
+    "radius": 5,
+    "body_name": "Ball",
+    "operation": "new"
+   }
+  },
+  {
+   "command": "construct.plane.tangent",
+   "params": {
+    "face": {
+     "face": [
+      0,
+      0,
+      65
+     ]
+    },
+    "at": [
+     0,
+     3,
+     64
+    ],
+    "name": "T"
+   }
+  }
+ ]
+}