kernel-cases: ladder 07/019, a concave corner's G2 patch

The inner corner of a 20 x 20 x 10 notch in the 60 x 40 x 20 box, three
concave r5 rounds with corner: g2: one valid body of 13 faces within the box,
the patch's twelve seams jumping at most 1e-3 per mm clear of the hole's six
corners (2.7e-4 measured; the ball corner jumps 0.2). The continuity check
looks within 11 mm of the corner: the vertical round, 2.5 mm long past its
setback, meets its faces 11.2 mm out with every round's G1 jump.

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

tests/kernel-cases/ladder/07-fillets/019-concave-corner-g2-patch/expected.json

@@ -0,0 +1,30 @@
+{
+ "sources": [],
+ "what": "three concave r5 rounds at the inner corner of a 20x20x10 notch, with the g2 corner patch",
+ "source": "invariants",
+ "method": "the notch's inner corner (40,20,10), three concave edges, set back 1.5 r = 7.5 and filled with one patch G2 to the three rounds and the three faces; one valid body with the faces of the ball corner (13); across the patch's seams the curvature jump is at most 1e-3 per mm (the ball's corner jumps 1/r = 0.2) clear of the six points where a round's section ends on a face (within 11 mm of the corner: the hole reaches 7.5 sqrt 2; the vertical round, 2.5 mm long past its setback, meets its faces 11.2 mm out, with the G1 jump every round has)",
+ "body_count": 1,
+ "faces": 13,
+ "bbox": {
+  "min": [
+   0,
+   0,
+   0
+  ],
+  "max": [
+   60,
+   40,
+   20
+  ]
+ },
+ "continuity": {
+  "near": [
+   40,
+   20,
+   10
+  ],
+  "within_mm": 11,
+  "clear_mm": 1.2,
+  "curvature_jump_per_mm": 0.001
+ }
+}

tests/kernel-cases/ladder/07-fillets/019-concave-corner-g2-patch/recipe.json

@@ -0,0 +1,53 @@
+{
+ "base": "../../01-primitives/001-box",
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "corner": [
+     40,
+     20,
+     10
+    ],
+    "length": 30,
+    "width": 30,
+    "height": 20,
+    "body_name": "Notch"
+   }
+  },
+  {
+   "command": "solid.combine",
+   "params": {
+    "target": "Part",
+    "tools": [
+     "Notch"
+    ],
+    "operation": "cut"
+   }
+  },
+  {
+   "command": "solid.fillet",
+   "params": {
+    "edges": [
+     [
+      50,
+      20,
+      10
+     ],
+     [
+      40,
+      30,
+      10
+     ],
+     [
+      40,
+      20,
+      15
+     ]
+    ],
+    "radius": 5,
+    "corner": "g2"
+   }
+  }
+ ]
+}

tests/kernel-cases/ladder/golden.json

@@ -1200,6 +1200,18 @@
       "seconds": 2.184099933,
       "status": "pass"
     },
+    "ladder/07-fillets/019-concave-corner-g2-patch": {
+      "measured": {
+        "area_mm2": 8702.800595617835,
+        "body_count": 1,
+        "edges": 33,
+        "faces": 13,
+        "vertices": 22,
+        "volume_mm3": 44254.3419135911
+      },
+      "seconds": 2.217877403,
+      "status": "pass"
+    },
     "ladder/07-fillets/016-corner-three-sequential-r5-r3-r7": {
       "seconds": 0.045599545,
       "status": "pass"

tests/kernel-cases/ladder/ladder.json

@@ -124,6 +124,7 @@
     {
       "cases": [
         "ladder/07-fillets/015-corner-g2-patch",
+        "ladder/07-fillets/019-concave-corner-g2-patch",
         "ladder/07-fillets/006-variable-r5-to-zero",
         "ladder/07-fillets/001-single-edge-r5",
         "ladder/07-fillets/007-variable-r5-to-1e-3",

tools/kernel-ladder/cases.py

@@ -871,6 +871,17 @@ case(T7, "015-corner-g2-patch", "three r5 rounds at a corner with the g2 corner
      "(the ball's corner, 009, jumps 1/r = 0.2) clear of the six points where a round's section ends on a face, where the round's "
      "own G1 seam with the face ends (the patch passes from one curvature to the other within 15% of each side: 1.2 mm covers it)",
      base=B1, source="invariants")
+notch = [[50, 20, 10], [40, 30, 10], [40, 20, 15]]
+case(T7, "019-concave-corner-g2-patch", "three concave r5 rounds at the inner corner of a 20x20x10 notch, with the g2 corner patch",
+     [box([40, 20, 10], 30, 30, 20, body_name="Notch"), C("solid.combine", target="Part", tools=["Notch"], operation="cut"),
+      F(notch, 5, corner="g2")],
+     {"body_count": 1, "faces": 13, "bbox": {"min": [0, 0, 0], "max": [60, 40, 20]},
+      "continuity": {"near": [40, 20, 10], "within_mm": 11, "clear_mm": 1.2, "curvature_jump_per_mm": 0.001}},
+     "the notch's inner corner (40,20,10), three concave edges, set back 1.5 r = 7.5 and filled with one patch G2 to the three "
+     "rounds and the three faces; one valid body with the faces of the ball corner (13); across the patch's seams the curvature "
+     "jump is at most 1e-3 per mm (the ball's corner jumps 1/r = 0.2) clear of the six points where a round's section ends on a face (within 11 mm of the corner: the hole reaches 7.5 sqrt 2; "
+     "the vertical round, 2.5 mm long past its setback, meets its faces 11.2 mm out, with the G1 jump every round has)",
+     base=B1, source="invariants")
 V7 = V5 - 2 * SPANDREL * 25 * 20 - SPANDREL * 9 * 60 + SPANDREL * 1 * 2 * PI * (8 + XBAR * 1)
 case(T7, "017-part-rounds", "the running part: r5 on the front vertical edges, r3 on the back wall's top front edge, r1 where the boss meets the top",
      [F([[0, 0, 10], [60, 0, 10]], 5), F([[30, 30, 35]], 3), F([[23, 15, 20]], 1)],