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Kernel rig: 1494 graded on its volume (box and cylinder less the 1 mm-offset cavity, sharp to rounded concave edges) and box
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
@@ -3,7 +3,23 @@
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"tangency-labs/solidcraft#1494"
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],
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"what": "a 47.5x45x30 box with a cylinder r7.5 joined on its side whose axis lies in the plane of the box's front face (y=0), shelled 1 mm open at the bottom",
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"source": "invariants",
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"method": "the cylinder wall's seam lies on the front plane, giving a five-face saddle corner at (47.5,0,2.5). No closed-form volume (the cavity corners follow the offset surfaces); the shell must succeed and give one valid closed body",
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"body_count": 1
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"source": "analytic",
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"method": "the cylinder wall's seam lies on the front plane, giving a five-face saddle corner at (47.5,0,2.5). Body = box 64125 + cylinder pi 7.5^2 30 = 69426.4376 (they share only the half disc on x = 47.5). Cavity with every kept face moved 1 in and extended to meet (sharp): box [1,46.5] x [1,44] x [0,29] (45.5 x 43 x 29) and the cylinder r6.5 from x = 46.5 to 76.5, less, over x 46.5..48.5, its part with y < 1 (the front face's and the uncovered half disc's offsets): 2 (pi 6.5^2/2 + int_0^1 2 sqrt(6.5^2 - y^2) dy) = 158.6294; cavity 60561.8393, material 8864.5983. A cavity that rounds its two concave edges instead (the true 1 mm offset) is larger by at most (1 - pi/4) per mm of each: the front face / half disc line (its offset at most 13 long inside r6.5) and the half circle r7.5 where the cylinder meets the box (at most 7.5 pi): 7.8463, so material 8856.7520 .. 8864.5983. A shell that fails to open leaves 2 shells; the full solid is 69426",
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"body_count": 1,
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"volume_mm3": [
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8856.7,
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8864.7
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],
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"bbox": {
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"min": [
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0,
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-7.5,
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0
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],
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"max": [
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77.5,
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45,
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30
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]
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}
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}
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