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kernel-ladder: tier 09 shells grade their geometry

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010, 011 and 014 passed on one valid body alone. 010 (top rounds in
mitres, shelled open below) and 014 (drafted box with tilted rounds:
every level section loses the same elliptic corner) now check closed-form
volumes, exact counts and bbox (014 also its centre of mass). 011, the
running part shelled 1.5, checks the part less its cavity built feature
by feature, the offset faces meeting sharp at concave edges as in the
rest of the tier (a distance-based offset would differ by 0.3%). All hold
on SMLib (worst 1e-6 relative).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
jyviko
2026-10-26 11:17:50 -04:00
parent 0d7acb0ce9
commit c9dcc42a13
4 changed files with 141 additions and 17 deletions
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tests/kernel-cases/ladder/09-shells-and-offsets/010-shell-under-rounded-top/expected.json
+22 -3
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@@ -1,7 +1,26 @@
{
"sources": [],
"what": "the stock with r3 rounds on its four top edges, shelled 2 mm open at the bottom",
"source": "invariants",
"method": "walls meeting rounds and their corner patches; one valid body",
"body_count": 1
"source": "analytic",
"method": "the vertical edges stay sharp, so each pair of top rounds meets in a mitre at a corner (08/011's identity): outside, (1-pi/4) 3^2 (2 60 + 2 40) removed, less 4 x 3^3 (5/3 - pi/2) counted twice; the cavity is the 56 x 36 x 18 box (open at z = 0) with its top edges rounded 3 - 2 = 1, mitred alike. V = outside - cavity. Faces: 9 outside (bottom ring aside: top, 4 sides, 4 rounds), 9 inside, the bottom ring; vertices: 8 at the mitres' ends outside, 8 inside, 8 round the ring; edges 40 (Euler-Poincare with the ring's two loops)",
"body_count": 1,
"volume_mm3": 11375.173947397,
"faces": 19,
"edges": 40,
"vertices": 24,
"bbox": {
"min": [
0,
0,
0
],
"max": [
60,
40,
20
]
},
"tolerance": {
"rel": 1e-05
}
}
tests/kernel-cases/ladder/09-shells-and-offsets/011-part-shell/expected.json
+19 -3
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@@ -1,7 +1,23 @@
{
"sources": [],
"what": "the running part shelled 1.5 mm open at the bottom",
"source": "invariants",
"method": "a shell around holes, a slot, a window, rounds and chamfers; one valid body",
"body_count": 1
"source": "analytic",
"method": "V = the tier-08 part - its cavity, the part's inside at 1.5 from every face but the open bottom, the offset faces extended to meet at the part's concave edges (as every shell in this tier: sharp inner corners). Cavity: the L section (x 1.5..58.5; y 1.5..38.5 under z 18.5, y 31.5..38.5 under z 33.5) less the r5 -> r3.5 front rounds, the wall's r3 -> r1.5 round and its 2 mm chamfer -> a (1.5 sqrt2 - 1) chamfer; the boss column r6.5 z 18.5..28.5 with its 1 mm chamfer -> 0.121, the concave r1 -> r2.5 at its root (Pappus), less the M5 hole grown 1.5 (r3.6, its floor's edge kept sharp); less the slot grown to width 11, the M6 tap drill to r4, the d3.3 hole to r3.15 (its overlaps with the wall's inner round and chamfer, 0.6808 and 0.4392, added back), the window grown 1.5 through the wall's 7 mm inside (Steiner, A + L t + pi t^2, its two corners sharp: + 2 t^2 (tan(th/2) - th/2)), and its overlap with the inner round (0.0416) added back = 37609.223572. A distance-based offset (concave edges rounded r1.5) would leave a cavity 49.17 larger. Bbox: the part's",
"body_count": 1,
"volume_mm3": 15397.712974981,
"bbox": {
"min": [
0,
0,
0
],
"max": [
60,
40,
35
]
},
"tolerance": {
"rel": 0.0001
}
}
tests/kernel-cases/ladder/09-shells-and-offsets/014-drafted-box-with-rounds-shelled/expected.json
+27 -3
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@@ -4,7 +4,31 @@
"tangency-labs/solidcraft#3573"
],
"what": "a 120x80x40 box drafted 5 degrees with 4 mm rounds on the sloping corners, shelled 2 mm open at the top: the inner rounds' edges must lie on their faces (#3573 reports the same design)",
"source": "invariants",
"method": "no closed-form volume (tilted rounds). Invariants: the shell succeeds, one closed body, and the record's geometry check holds (every edge of the four inner rounds lies on its faces; the old offset left them up to 0.02 mm off, which other STEP readers reject)",
"body_count": 1
"source": "analytic",
"method": "the record's geometry check must hold too (every edge of the four inner rounds lies on its faces; the old offset left them up to 0.02 mm off, which other STEP readers reject). A round of radius r between two faces drafted 5 deg is a cylinder along their slanted common edge; a level plane cuts it in an ellipse of semi-axes r and r sqrt(1 + 2 tan^2 5) (the axis leans that much from vertical), tangent to the section's two side lines, and every level section is the same corner moved along: the corner's loss c(r) = p^2 - a b atan(a/b), p = sqrt((a^2 + b^2)/2), is constant (r^2 (1 - pi/4) undrafted). Outside: int_0^40 (120 - 2 z tan5)(80 - 2 z tan5) dz - 4 c(4) 40; the cavity (sides moved in 2 sqrt(1 + tan^2 5) level, floor z = 2, rounds 4 - 2 = 2): int_2^40 ... - 4 c(2) 38; V = outside - cavity, the centre of mass on the axis at the moments' z. Faces 9 outside, 9 inside, the rim; vertices 8 per loop of four; edges 48 (the rim has two loops)",
"body_count": 1,
"volume_mm3": 47497.554428404,
"faces": 19,
"edges": 48,
"vertices": 32,
"center_of_mass": [
0,
0,
12.820492322003297
],
"bbox": {
"min": [
-60,
-40,
0
],
"max": [
60,
40,
40
]
},
"tolerance": {
"rel": 1e-05
}
}
tools/kernel-ladder/cases.py
+73 -8
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@@ -923,12 +923,62 @@ case(T9, "008-offset-cylinder-wall-2", "a cylinder r10 h20 with its side face of
{"body_count": 1, "volume_mm3": PI * 144 * 20, "faces": 3}, "a cylinder r12 h20")
case(T9, "009-shell-outside-t2", "the stock shelled 2 mm outward, open at the top", [S([[30, 20, 20]], 2, direction="outside")],
{"body_count": 1, "volume_mm3": 64 * 44 * 22 - VB, "faces": 11}, "walls grown out of the closed faces: 64 x 44 x 22 less the original box", base=B1)
MITRE = 5 / 3 - PI / 2 # two equal rounds' common part at a mitred corner, per r^3 (07/011)
case(T9, "010-shell-under-rounded-top", "the stock with r3 rounds on its four top edges, shelled 2 mm open at the bottom",
[F([[30, 0, 20], [60, 20, 20], [30, 40, 20], [0, 20, 20]], 3), S([[30, 20, 0]], 2)], {"body_count": 1},
"walls meeting rounds and their corner patches; one valid body", base=B1, source="invariants")
[F([[30, 0, 20], [60, 20, 20], [30, 40, 20], [0, 20, 20]], 3), S([[30, 20, 0]], 2)],
{"body_count": 1, "volume_mm3": (VB - SPANDREL * 9 * 200 + 4 * 27 * MITRE) - (56 * 36 * 18 - SPANDREL * 1 * 184 + 4 * 1 * MITRE),
"faces": 19, "edges": 40, "vertices": 24, "bbox": BBOX, "tolerance": {"rel": 1e-5}},
"the vertical edges stay sharp, so each pair of top rounds meets in a mitre at a corner (08/011's identity): outside, (1-pi/4) 3^2 (2 60 + 2 40) removed, "
"less 4 x 3^3 (5/3 - pi/2) counted twice; the cavity is the 56 x 36 x 18 box (open at z = 0) with its top edges rounded 3 - 2 = 1, mitred alike. V = outside - cavity. "
"Faces: 9 outside (bottom ring aside: top, 4 sides, 4 rounds), 9 inside, the bottom ring; vertices: 8 at the mitres' ends outside, 8 inside, 8 round the ring; "
"edges 40 (Euler-Poincare with the ring's two loops)", base=B1)
# 011: the tier-08 part's cavity at t = 1.5 (offset faces extended to meet at concave edges).
t9 = 1.5
SQ9 = t9 * t9
chord9 = lambda y: 2 * math.sqrt(max(3.15 ** 2 - (y - 35) ** 2, 0))
ov_ch = quad_split(lambda y: chord9(y) * max(0, 33.5 - (73 - t9 * math.sqrt(2) - y)), 73 - t9 * math.sqrt(2) - 33.5, 38.15, 200, 16)
ov_rd = quad_split(lambda y: chord9(y) * max(0, 33.5 - (32 + math.sqrt(max(SQ9 - (y - 33) ** 2, 0)))), 31.85, 33, 200, 16)
def dist_arch(x, z):
lo, hi = (0.0, 0.5) if x >= 30 else (0.5, 1.0)
f = lambda u: math.dist(bez(Pw, u), (x, z))
for _ in range(100):
m1, m2 = lo + (hi - lo) * 0.382, lo + (hi - lo) * 0.618
if f(m1) < f(m2):
hi = m2
else:
lo = m1
return f((lo + hi) / 2)
def half_len(z):
if dist_arch(30, z) > t9:
return 0.0
a, b = 30.0, 40.0
for _ in range(60):
m = (a + b) / 2
if dist_arch(m, z) <= t9:
a = m
else:
b = m
return a - 30
ov_win = quad_split(lambda z: 2 * half_len(z) * max(0.0, 33 - math.sqrt(max(SQ9 - (z - 32) ** 2, 0)) - 31.5), 32, 31 + t9, 50, 16)
th9 = PI - math.acos(3 / math.sqrt(153))
lb9 = 6.5 + 28.5 - (37 - t9 * math.sqrt(2))
Vcav9 = (57 * (37 * 18.5 + 7 * 15) - 2 * SPANDREL * 3.5 ** 2 * 18.5 - 57 * SPANDREL * SQ9 - 57 * (t9 * math.sqrt(2) - 1) ** 2 / 2
+ PI * 6.5 ** 2 * 10 - 2 * PI * (6.5 - lb9 / 3) * lb9 * lb9 / 2 + 2 * PI * (6.5 + XBAR * 2.5) * SPANDREL * 6.25
- PI * 3.6 ** 2 * 6.5 - PI * 2.1 ** 2 * t9 - 2 * PI * (2.1 + t9 / 2) * SQ9
- 18.5 * (15 * 11 + PI * 5.5 ** 2) - PI * 16 * 18.5 - PI * 3.15 ** 2 * 33.5 + ov_ch + ov_rd
- 7 * (Awin + (bez_len(Pw) + 20) * t9 + PI * SQ9 + 2 * SQ9 * (math.tan(th9 / 2) - th9 / 2)) + ov_win)
cav_round_extra = 57 * SQ9 * SPANDREL + 2 * PI * (2.1 + t9 / 2) * SQ9 - 2 * PI * (2.1 + 4 * t9 / (3 * PI)) * PI * SQ9 / 4 + 7 * 2 * SQ9 * (math.tan(th9 / 2) - th9 / 2)
V9 = V8 - Vcav9
case(T9, "011-part-shell", "the running part shelled 1.5 mm open at the bottom",
[S([[30, 20, 0]], 1.5)], {"body_count": 1},
"a shell around holes, a slot, a window, rounds and chamfers; one valid body", base=C8, source="invariants")
[S([[30, 20, 0]], 1.5)],
{"body_count": 1, "volume_mm3": V9, "bbox": {"min": [0, 0, 0], "max": [60, 40, 35]}, "tolerance": {"rel": 1e-4}},
"V = the tier-08 part - its cavity, the part's inside at 1.5 from every face but the open bottom, the offset faces extended to meet at the part's concave edges "
"(as every shell in this tier: sharp inner corners). Cavity: the L section (x 1.5..58.5; y 1.5..38.5 under z 18.5, y 31.5..38.5 under z 33.5) less the r5 -> r3.5 front "
"rounds, the wall's r3 -> r1.5 round and its 2 mm chamfer -> a (1.5 sqrt2 - 1) chamfer; the boss column r6.5 z 18.5..28.5 with its 1 mm chamfer -> 0.121, the concave r1 "
"-> r2.5 at its root (Pappus), less the M5 hole grown 1.5 (r3.6, its floor's edge kept sharp); less the slot grown to width 11, the M6 tap drill to r4, the d3.3 hole to r3.15 "
"(its overlaps with the wall's inner round and chamfer, %.4f and %.4f, added back), the window grown 1.5 through the wall's 7 mm inside (Steiner, A + L t + pi t^2, its two "
"corners sharp: + 2 t^2 (tan(th/2) - th/2)), and its overlap with the inner round (%.4f) added back = %.6f. A distance-based offset (concave edges rounded r1.5) "
"would leave a cavity %.2f larger. Bbox: the part's" % (ov_ch, ov_rd, ov_win, Vcav9, cav_round_extra), base=C8)
C9 = up(T9, "011-part-shell")
case(T9, "012-closed-shell-sealed-void", "the stock shelled 2 mm with no face open: a closed body with a sealed void", [S([], 2)],
{"body_count": 1, "shells": 2, "volume_mm3": VB - 56 * 36 * 16, "faces": 12},
@@ -939,15 +989,30 @@ case(T9, "013-dome-shelled-from-base", "a dome r20 shelled 2 mm, open at its fla
{"body_count": 1, "volume_mm3": 2 / 3 * PI * (20 ** 3 - 18 ** 3), "faces": 3},
"V = (2/3) pi (20^3 - 18^3); faces: outer sphere, inner sphere, base ring")
dr5 = 20 * math.tan(math.radians(5))
tan5 = math.tan(math.radians(5))
def drafted_corner(r):
a, b = r * math.sqrt(1 + 2 * tan5 * tan5), r
p = math.sqrt((a * a + b * b) / 2)
return p * p - a * b * math.atan(a / b)
o14 = 2 * math.sqrt(1 + tan5 * tan5)
sec_out = lambda z: 4 * (60 - tan5 * z) * (40 - tan5 * z) - 4 * drafted_corner(4)
sec_in = lambda z: 4 * (60 - tan5 * z - o14) * (40 - tan5 * z - o14) - 4 * drafted_corner(2)
V14 = quad(sec_out, 0, 40) - quad(sec_in, 2, 40)
Z14 = (quad(lambda z: z * sec_out(z), 0, 40) - quad(lambda z: z * sec_in(z), 2, 40)) / V14
case(T9, "014-drafted-box-with-rounds-shelled",
"a 120x80x40 box drafted 5 degrees with 4 mm rounds on the sloping corners, shelled 2 mm open at the top: the inner rounds' edges must lie on their faces (#3573 reports the same design)",
sketch("XY", C("sketch.rectangle.center", center=[0, 0], corner=[60, 40]))
+ [C("solid.extrude", distance=40, taper="-5 deg", operation="new"),
F([[sx * (60 - dr5), sy * (40 - dr5), 20] for sx, sy in [(1, 1), (1, -1), (-1, 1), (-1, -1)]], 4), S([[0, 0, 40]], 2)],
{"body_count": 1},
"no closed-form volume (tilted rounds). Invariants: the shell succeeds, one closed body, and the record's geometry check holds "
"(every edge of the four inner rounds lies on its faces; the old offset left them up to 0.02 mm off, which other STEP readers reject)",
source="invariants", sources=["tangency-labs/solidcraft#3576", "tangency-labs/solidcraft#3573"])
{"body_count": 1, "volume_mm3": V14, "faces": 19, "edges": 48, "vertices": 32, "center_of_mass": [0, 0, Z14], "bbox": {"min": [-60, -40, 0], "max": [60, 40, 40]},
"tolerance": {"rel": 1e-5}},
"the record's geometry check must hold too (every edge of the four inner rounds lies on its faces; the old offset left them up to 0.02 mm off, which other STEP readers reject). "
"A round of radius r between two faces drafted 5 deg is a cylinder along their slanted common edge; a level plane cuts it in an ellipse of semi-axes r and r sqrt(1 + 2 tan^2 5) "
"(the axis leans that much from vertical), tangent to the section's two side lines, and every level section is the same corner moved along: the corner's loss "
"c(r) = p^2 - a b atan(a/b), p = sqrt((a^2 + b^2)/2), is constant (r^2 (1 - pi/4) undrafted). Outside: int_0^40 (120 - 2 z tan5)(80 - 2 z tan5) dz - 4 c(4) 40; the cavity "
"(sides moved in 2 sqrt(1 + tan^2 5) level, floor z = 2, rounds 4 - 2 = 2): int_2^40 ... - 4 c(2) 38; V = outside - cavity, the centre of mass on the axis at the moments' "
"z. Faces 9 outside, 9 inside, the rim; vertices 8 per loop of four; edges 48 (the rim has two loops)",
source="analytic", sources=["tangency-labs/solidcraft#3576", "tangency-labs/solidcraft#3573"])
case(T9, "015-shelled-dome-ring-joined-back",
"a dome (a quarter disc r20 revolved) shelled 2 mm from its flat base, then the base ring (r 18..20) face-extruded 10 mm back into the dome as a join: ~120 s, then 'boolean Union: no result'",
sketch(vplane([0, 0, 0]), line([[0, 0], [20, 0]]), C("sketch.arc.three_point", start=[20, 0], through=[14.142136, 14.142136], end=[0, 20]), line([[0, 20], [0, 0]]), name="Quarter")