Kernel rig: construction cases, where three planes meet, and parallel planes or planes through one line refused

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

tests/kernel-cases/construction/cov-point-three-planes-box-corner/expected.json

@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "the corner where three box faces meet",
+ "source": "analytic",
+ "method": "box 40 x 30 x 20 with a corner at the origin (x 0..40, y 0..30, z 0..20): x = 40, y = 30, z = 20 meet at (40,30,20)",
+ "construction": {
+  "P": {
+   "point": [
+    40,
+    30,
+    20
+   ]
+  }
+ }
+}

tests/kernel-cases/construction/cov-point-three-planes-box-corner/recipe.json

@@ -0,0 +1,40 @@
+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 40,
+    "width": 30,
+    "height": 20,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "construct.point.three_planes",
+   "params": {
+    "a": {
+     "face": [
+      40,
+      15,
+      10
+     ]
+    },
+    "b": {
+     "face": [
+      20,
+      30,
+      10
+     ]
+    },
+    "c": {
+     "face": [
+      20,
+      15,
+      20
+     ]
+    },
+    "name": "P"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-point-three-planes-refuses-planes-through-one-line/expected.json

@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "three planes sharing one line",
+ "source": "analytic",
+ "method": "XZ, YZ and x = y all hold the Z axis: they meet in a line, not a point: refused",
+ "outcome": "refused",
+ "refusal": "the planes don't meet in a point"
+}

tests/kernel-cases/construction/cov-point-three-planes-refuses-planes-through-one-line/recipe.json

@@ -0,0 +1,26 @@
+{
+ "commands": [
+  {
+   "command": "construct.point.three_planes",
+   "params": {
+    "a": "XZ",
+    "b": "YZ",
+    "c": {
+     "plane": {
+      "origin": [
+       0,
+       0,
+       0
+      ],
+      "normal": [
+       1,
+       -1,
+       0
+      ]
+     }
+    },
+    "name": "P"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-point-three-planes-refuses-two-parallel/expected.json

@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "three planes, two of them parallel",
+ "source": "analytic",
+ "method": "XY and z = 5 are parallel: refused",
+ "outcome": "refused",
+ "refusal": "two of the planes are parallel"
+}

tests/kernel-cases/construction/cov-point-three-planes-refuses-two-parallel/recipe.json

@@ -0,0 +1,26 @@
+{
+ "commands": [
+  {
+   "command": "construct.point.three_planes",
+   "params": {
+    "a": "XY",
+    "b": {
+     "plane": {
+      "origin": [
+       0,
+       0,
+       5
+      ],
+      "normal": [
+       0,
+       0,
+       1
+      ]
+     }
+    },
+    "c": "YZ",
+    "name": "P"
+   }
+  }
+ ]
+}

tests/kernel-cases/construction/cov-point-three-planes-slanted/expected.json

@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "the point where three slanted planes meet",
+ "source": "analytic",
+ "method": "x + y = 10, y + z = 6, x + z = 8: adding, x + y + z = 12, so (6,4,2)",
+ "construction": {
+  "P": {
+   "point": [
+    6,
+    4,
+    2
+   ]
+  }
+ }
+}

tests/kernel-cases/construction/cov-point-three-planes-slanted/recipe.json

@@ -0,0 +1,52 @@
+{
+ "commands": [
+  {
+   "command": "construct.point.three_planes",
+   "params": {
+    "a": {
+     "plane": {
+      "origin": [
+       10,
+       0,
+       0
+      ],
+      "normal": [
+       1,
+       1,
+       0
+      ]
+     }
+    },
+    "b": {
+     "plane": {
+      "origin": [
+       0,
+       0,
+       6
+      ],
+      "normal": [
+       0,
+       1,
+       1
+      ]
+     }
+    },
+    "c": {
+     "plane": {
+      "origin": [
+       0,
+       0,
+       8
+      ],
+      "normal": [
+       1,
+       0,
+       1
+      ]
+     }
+    },
+    "name": "P"
+   }
+  }
+ ]
+}