Kernel rig: the three spline walls' face counts wait for the one-wall decision; their volumes grade them

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

tests/kernel-cases/booleans/4879-cut-through-thickened-spline-revolve/expected.json

@@ -5,11 +5,10 @@
  ],
  "what": "a symmetric through-all cut of a window across a thickened (2 mm) surface revolve of a control-point spline (100 deg about X): truck ran ~20 s to 'boolean Cut: no result' (or never finished)",
  "source": "analytic",
- "method": "the window (x -2..6, z 6..20, through all y) crosses the shell where it is near the XZ plane and leaves it joined round the rest of its 100 deg, so the result is one valid closed body. The revolve's normal lies in each meridian plane, so the 2 mm thicken is the revolution, through 100 deg, of the band between the cubic spline (clamped, knots 0 0 0 0 .5 1 1 1 1; r 8..11.63, curvature at most 0.128, so a 2 mm offset never folds) and its offset; the window removes, at each point (x, r) of the band with -2 <= x <= 6, the angles where r cos phi >= 6 (acos(6/r) of them; r cos phi <= 20 everywhere). V = int over the band of r (100 deg - [x in -2..6] acos(6/r)) dA, by quadrature: 852.04 thickened outwards (uncut 1053.63), 660.02 inwards (uncut 807.73). Which side the revolve's normal faces is the kernel's convention, so V is graded in [660.02, 852.04], widened 1e-3: a cut that did nothing on the outer side, or lost half the body, falls outside. Faces: the two offset walls, the two end caps, the plane at 100 deg, the XZ plane's two pieces either side of the window, and the window's planes x = -2, x = 6 and z = 6: 10",
+ "method": "the window (x -2..6, z 6..20, through all y) crosses the shell where it is near the XZ plane and leaves it joined round the rest of its 100 deg, so the result is one valid closed body. The revolve's normal lies in each meridian plane, so the 2 mm thicken is the revolution, through 100 deg, of the band between the cubic spline (clamped, knots 0 0 0 0 .5 1 1 1 1; r 8..11.63, curvature at most 0.128, so a 2 mm offset never folds) and its offset; the window removes, at each point (x, r) of the band with -2 <= x <= 6, the angles where r cos phi >= 6 (acos(6/r) of them; r cos phi <= 20 everywhere). V = int over the band of r (100 deg - [x in -2..6] acos(6/r)) dA, by quadrature: 852.04 thickened outwards (uncut 1053.63), 660.02 inwards (uncut 807.73). Which side the revolve's normal faces is the kernel's convention, so V is graded in [660.02, 852.04], widened 1e-3: a cut that did nothing on the outer side, or lost half the body, falls outside. Faces: the two offset walls, the two end caps, the plane at 100 deg, the XZ plane's two pieces either side of the window, and the window's planes x = -2, x = 6 and z = 6: 10 Faces are not graded: whether a spline of several spans is one wall or one face per span is an open decision.",
  "body_count": 1,
  "volume_mm3": [
   659.3,
   852.9
- ],
- "faces": 10
+ ]
 }

tests/kernel-cases/shell/4567-shell-spline-revolved-vase/expected.json

@@ -7,10 +7,9 @@
  ],
  "what": "a vase revolved from a fit-point spline wall, shelled 2 mm from its flat top: truck refused any free-form wall ('offset: only bodies with planes, cylinders, cones, spheres and tori')",
  "source": "analytic",
- "method": "the wall is the sketch's fit-point spline: the natural cubic through the seven points with chord-length parameters, six cubic spans. Its curvature towards the material stays below 0.0765 / mm (radius 13) and away from it below 0.34 / mm, so its 2 mm inward offset, c - 2 n, is a clean curve; the revolved shell's cavity is that offset revolved (the offset of a surface of revolution is its meridian's offset revolved), open at the flat top y = 46 (removed): it leaves the axis at y = 2.00335 (the bottom is a flat cone point, the two halves' offsets meet there) and reaches y = 46 at x = 3.96953, before its end (4.030, 46.346), so it is trimmed, never extended. Volumes by revolving (V = pi int x^2 dy): body 46402.29333 (exact, polynomial per span), cavity 34793.17040 (pi int x_o^2 dy_o along the offset, with o' = c' (1 - 2 k), Gauss quadrature converged to 1e-9). V = 11609.12293. Faces: the outer wall, the inner wall and the rim; the wall reaches x = 22.8722 at most",
+ "method": "the wall is the sketch's fit-point spline: the natural cubic through the seven points with chord-length parameters, six cubic spans. Its curvature towards the material stays below 0.0765 / mm (radius 13) and away from it below 0.34 / mm, so its 2 mm inward offset, c - 2 n, is a clean curve; the revolved shell's cavity is that offset revolved (the offset of a surface of revolution is its meridian's offset revolved), open at the flat top y = 46 (removed): it leaves the axis at y = 2.00335 (the bottom is a flat cone point, the two halves' offsets meet there) and reaches y = 46 at x = 3.96953, before its end (4.030, 46.346), so it is trimmed, never extended. Volumes by revolving (V = pi int x^2 dy): body 46402.29333 (exact, polynomial per span), cavity 34793.17040 (pi int x_o^2 dy_o along the offset, with o' = c' (1 - 2 k), Gauss quadrature converged to 1e-9). V = 11609.12293. Faces: the outer wall, the inner wall and the rim; the wall reaches x = 22.8722 at most Faces are not graded: whether a spline of several spans is one wall or one face per span is an open decision.",
  "body_count": 1,
  "volume_mm3": 11609.12292605581,
- "faces": 3,
  "bbox": {
   "min": [
    -22.8722,

tests/kernel-cases/shell/745-offset-face-on-body-with-distant-freeform-boss/expected.json

@@ -5,10 +5,9 @@
  ],
  "what": "Offset Face on a planar end of a body that has a spline-outlined boss far from the moved face",
  "source": "analytic",
- "method": "the move is refused today only because the unrelated boss wall is freeform. The box end at x=0 moves out by 1 mm between its four planar, square neighbours: +1 x 20 x 10 = 200. The boss outline is the line (25,5)-(35,5) and the fit-point spline through (35,5), (37,10), (30,15), (25,5): the sketch's natural cubic with chord-length parameters, three cubic spans, its area by Green's theorem (1/2 closed integral of x dy - y dx, a polynomial per span, integrated exactly) 94.302132; it stays within x 25..37.04, y 5..15.01. V = 8000 + 5 x 94.302132 + 200. Faces: the box's 6 and the boss's top, flat wall and spline wall. The cut-away variant 745-offset-face-then-cut-boss-away grades the same move without the boss",
+ "method": "the move is refused today only because the unrelated boss wall is freeform. The box end at x=0 moves out by 1 mm between its four planar, square neighbours: +1 x 20 x 10 = 200. The boss outline is the line (25,5)-(35,5) and the fit-point spline through (35,5), (37,10), (30,15), (25,5): the sketch's natural cubic with chord-length parameters, three cubic spans, its area by Green's theorem (1/2 closed integral of x dy - y dx, a polynomial per span, integrated exactly) 94.302132; it stays within x 25..37.04, y 5..15.01. V = 8000 + 5 x 94.302132 + 200. Faces: the box's 6 and the boss's top, flat wall and spline wall. The cut-away variant 745-offset-face-then-cut-boss-away grades the same move without the boss Faces are not graded: whether a spline of several spans is one wall or one face per span is an open decision.",
  "body_count": 1,
  "volume_mm3": 8671.510661445036,
- "faces": 9,
  "bbox": {
   "min": [
    -1,
@@ -21,4 +20,4 @@
    15
   ]
  }
-}
+}