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demo video: a horizontal cantilever, checked against beam theory

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The demo used the corpus I-beam, which is extruded along z and so stood
upright. A new corpus part, cantilever-i-beam, is the same section on the
YZ plane extruded along x, web upright: a sweep along a horizontal axis
for the meshers, and a cantilever that bends downward on screen. The
i-beam part is unchanged (its corpus row and the meshing tests keep it).

The demo clamps it at x = 0 and loads the free end with 1000 N in -z
through a kinematic coupling, and now checks the solution against beam
theory and stops when it is off: tip deflection (bending plus shear)
within 3 %, root bending stress (stress_xx along the top flange,
extrapolated to the root, nodes from the Abaqus deck) within 2 %.

docs/meshing/corpus.md regenerated with the new part.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 00:15:50 -04:00
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docs/meshing/corpus.md
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@@ -10,40 +10,41 @@ clock on the machine that ran it; every other column is deterministic.
| part | categories | bodies | faces | triangles | tol. mm | build ms | enclosed mm³ | SolidCraft mm³ | rel. diff | exact mm³ | boundary | genus | feature edges | check ms | CDT tets | Steiner | cavities | tet gate | CDT ms | hex | hex elements | hex8 min SJ | hex20 min SJ | hex ms |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| bent-tube | sweepable, thin-wall, genus | 1 | 18 | 4296 | 0.121 | 454 | 4213.1 | 4159.4 | 1.3e-2 | 4159.8 | ok, 2148 vertices | 1 | 268 | 11.5 | 15550 | 2338 | 0 | pass | 606 | sweep | 192 | 0.859 | 0.997 | 63 |
| bolted-assembly | assembly, blocky | 3 | 22 | 284 | 0.117 | 206 | 33004.7 | 32999.0 | 1.7e-4 | 32998.9 | ok, 144 vertices | 0, 1, 1 | 104 | 0.7 | 690 | 181 | 0 | pass | 34 | extrude | 357 | 0.398 | 0.222 | 40 |
| cross-cylinders | boolean, sharp | 1 | 10 | 1395 | 0.087 | 7920 | 32197.4 | 32357.8 | -5.0e-3 | 32365.8 | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | |
| filleted-bracket | fillet, genus, sweepable | 1 | 13 | 540 | 0.088 | 388 | 32162.3 | 32145.0 | 5.4e-4 | 32144.8 | ok, 268 vertices | 2 | 135 | 1.4 | 5582 | 1613 | 0 | pass | 208 | no: Bracket: not supported yet: no structured hex method fits this body (extrude: cylindrical face 8 is not parallel to the direction; sweep: from face 1: linking face 6 has 2 boundary loops (periodic or holed linking faces are not swept); from face 6: | | | | 5 |
| i-beam | sweepable, thin-wall | 1 | 14 | 44 | 0.208 | 3 | 61600.0 | 61600.0 | 0.0e0 | 61600.0 | ok, 24 vertices | 0 | 36 | 0.1 | 94 | 24 | 0 | pass | 4 | extrude | 336 | 0.707 | 0.707 | 34 |
| loft-transition | organic | 1 | 6 | 292 | 0.075 | 57 | 56390.2 | 56450.6 | -1.1e-3 | – | ok, 148 vertices | 0 | 40 | 0.7 | 1329 | 256 | 1 | pass | 38 | sweep | 2873 | 0.189 | 0.189 | 328 |
| perforated-plate | genus, thin-wall, sweepable | 1 | 54 | 1644 | 0.144 | 273 | 26822.2 | 26764.6 | 2.2e-3 | 26764.2 | ok, 776 vertices | 24 | 828 | 4.8 | 33611 | 9798 | 0 | pass | 1345 | extrude | 467 | 0.304 | 0.033 | 98 |
| pinhole-block | small-feature, genus | 1 | 38 | 4044 | 0.073 | 201 | 49919.4 | 49909.6 | 2.0e-4 | 49909.5 | ok, 1992 vertices | 16 | 1548 | 12.9 | 96411 | 30221 | 0 | pass | 8142 | extrude | 5236 | 0.408 | 0.392 | 735 |
| rounded-box | fillet | 1 | 26 | 2540 | 0.054 | 235 | 23325.7 | 23340.5 | -6.3e-4 | 23340.8 | ok, 1272 vertices | 0 | 216 | 8.4 | 11663 | 1916 | 0 | pass | 469 | no: Box: not supported yet: no structured hex method fits this body (extrude: cylindrical face 8 is not parallel to the direction; sweep: from face 0: 12 faces are not on the sweep path; from face 5: 12 faces are not on the sweep path; revolve: plan | | | | 15 |
| shallow-groove | near-tangent, boolean | 1 | 8 | 62 | 0.075 | 11 | 47795.2 | 47782.3 | 2.7e-4 | 47781.5 | ok, 33 vertices | 0 | 24 | 0.2 | 267 | 87 | 0 | pass | 13 | extrude | 1960 | 0.991 | 0.986 | 201 |
| sharp-wedge | sharp, thin-wall, sweepable | 1 | 5 | 8 | 0.083 | 2 | 3200.0 | 3200.0 | 0.0e0 | 3200.0 | ok, 6 vertices | 0 | 9 | 0.0 | 11 | 3 | 0 | pass | 0 | extrude | 294 | 0.050 | 0.050 | 30 |
| sphere-on-plate | near-tangent, boolean | 1 | 12 | 2826 | 0.098 | 974 | 69353.3 | 69509.0 | -2.2e-3 | 69509.7 | ok, 1415 vertices | 0 | 124 | 7.2 | 4898 | 309 | 9 | pass | 260 | no: Plate: not supported yet: no structured hex method fits this body (extrude: face 6 is curved across the direction; sweep: from face 0: 6 faces are not on the sweep path; from face 5: linking face 11 has 2 boundary loops (periodic or holed linking | | | | 11 |
| spline-vase | organic | 1 | 11 | 3890 | 0.106 | 226 | 94891.2 | 94948.5 | -6.0e-4 | – | ok, 1947 vertices | 0 | 243 | 9.0 | 12461 | 1512 | 0 | pass | 456 | sweep | 4554 | 0.649 | 0.649 | 547 |
| stepped-block | blocky, sharp | 1 | 14 | 96 | 0.078 | 264 | 47000.0 | 47000.0 | 0.0e0 | 47000.0 | ok, 48 vertices | 1 | 60 | 0.4 | 223 | 41 | 0 | pass | 7 | extrude | 1416 | 0.999 | 0.999 | 142 |
| thin-ribs | thin-wall, blocky | 1 | 26 | 92 | 0.119 | 1004 | 32000.0 | 32000.0 | -4.5e-16 | 32000.0 | ok, 48 vertices | 0 | 72 | 0.6 | 171 | 33 | 0 | pass | 8 | extrude | 777 | 0.844 | 0.844 | 100 |
| thin-wall-enclosure | thin-wall, blocky | 1 | 11 | 36 | 0.108 | 340 | 15564.0 | 15564.0 | 0.0e0 | 15564.0 | ok, 20 vertices | 0 | 28 | 0.2 | 191 | 47 | 2 | pass | 11 | extrude | 894 | 0.297 | 0.297 | 112 |
| analytic-sphere | analytic | 1 | 6 | 2784 | 0.069 | 719 | 33353.4 | 33507.9 | -4.6e-3 | 33510.3 | ok, 1394 vertices | 0 | 96 | 12.6 | 4211 | 58 | 0 | pass | 440 | no: Sphere: not supported yet: no structured hex method fits this body (extrude: no direction to try; sweep: no planar face to sweep from; revolve: no axis to try; mapped: meshing failed: meshing failed: mesh validity gate: 8 inverted or degenerate ele | | | | 31 |
| analytic-torus | analytic, genus | 1 | 6 | 7230 | 0.109 | 944 | 37644.1 | 37893.7 | -6.6e-3 | 37899.3 | ok, 3615 vertices | 1 | 180 | 25.6 | 19790 | 466 | 0 | pass | 1412 | revolve | 1134 | 0.706 | 0.706 | 280 |
| analytic-cylinder | analytic, sweepable | 1 | 4 | 1004 | 0.049 | 190 | 12533.1 | 12564.7 | -2.5e-3 | 12566.4 | ok, 504 vertices | 0 | 106 | 3.4 | 7437 | 1568 | 0 | pass | 452 | extrude | 3200 | 0.707 | 0.707 | 585 |
| analytic-pipe | analytic, genus, sweepable | 1 | 6 | 1448 | 0.104 | 336 | 94150.9 | 94238.0 | -9.3e-4 | 94247.8 | ok, 724 vertices | 1 | 220 | 9.0 | 6238 | 1340 | 0 | pass | 479 | extrude | 1288 | 0.998 | 0.998 | 290 |
| analytic-plate-hole | analytic, genus, sweepable | 1 | 8 | 112 | 0.224 | 231 | 98449.1 | 98429.5 | 2.0e-4 | 98429.2 | ok, 56 vertices | 1 | 62 | 0.9 | 1868 | 543 | 0 | pass | 72 | extrude | 321 | 0.320 | 0.142 | 55 |
| bent-tube | sweepable, thin-wall, genus | 1 | 18 | 4296 | 0.121 | 2726 | 4213.1 | 4159.4 | 1.3e-2 | 4159.8 | ok, 2148 vertices | 1 | 268 | 19.8 | 15550 | 2338 | 0 | pass | 4070 | sweep | 192 | 0.859 | 0.997 | 535 |
| bolted-assembly | assembly, blocky | 3 | 22 | 284 | 0.117 | 1141 | 33004.7 | 32999.0 | 1.7e-4 | 32998.9 | ok, 144 vertices | 0, 1, 1 | 104 | 1.6 | 690 | 181 | 0 | pass | 211 | extrude | 357 | 0.398 | 0.222 | 139 |
| cantilever-i-beam | sweepable, thin-wall | 1 | 14 | 44 | 0.208 | 483 | 61600.0 | 61600.0 | 0.0e0 | 61600.0 | ok, 24 vertices | 0 | 36 | 0.2 | 90 | 24 | 0 | pass | 5 | extrude | 336 | 0.707 | 0.707 | 47 |
| cross-cylinders | boolean, sharp | 1 | 10 | 1395 | 0.087 | 59348 | 32197.4 | 32357.8 | -5.0e-3 | 32365.8 | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | | error: Cross: invalid boundary surface: 28 defects; triangles 142 and 184 are oriented inconsistently across edge 0–396 at (-15.488656021315903, 4.577998041166734, 7.853092194999726); triangles 184 and 239 are oriented inconsistently across edge 0–554 at (-18.75000000000002, 5.634596901641276, 7.632255089815496); edge 103–108 at (-0.16007784063084018, 0.03984236936862052, 9.998639270596865) is shared by 3 triangles; … | | | | |
| filleted-bracket | fillet, genus, sweepable | 1 | 13 | 540 | 0.088 | 3706 | 32162.3 | 32145.0 | 5.4e-4 | 32144.8 | ok, 268 vertices | 2 | 135 | 2.1 | 5582 | 1613 | 0 | pass | 1769 | no: Bracket: not supported yet: no structured hex method fits this body (extrude: cylindrical face 8 is not parallel to the direction; sweep: from face 1: linking face 6 has 2 boundary loops (periodic or holed linking faces are not swept); from face 6: | | | | 10 |
| i-beam | sweepable, thin-wall | 1 | 14 | 44 | 0.208 | 280 | 61600.0 | 61600.0 | 0.0e0 | 61600.0 | ok, 24 vertices | 0 | 36 | 0.3 | 94 | 24 | 0 | pass | 7 | extrude | 336 | 0.707 | 0.707 | 52 |
| loft-transition | organic | 1 | 6 | 292 | 0.075 | 397 | 56390.2 | 56450.6 | -1.1e-3 | – | ok, 148 vertices | 0 | 40 | 1.0 | 1329 | 256 | 1 | pass | 172 | sweep | 2873 | 0.189 | 0.189 | 2056 |
| perforated-plate | genus, thin-wall, sweepable | 1 | 54 | 1644 | 0.144 | 2864 | 26822.2 | 26764.6 | 2.2e-3 | 26764.2 | ok, 776 vertices | 24 | 828 | 10.6 | 33611 | 9798 | 0 | pass | 6513 | extrude | 467 | 0.304 | 0.033 | 480 |
| pinhole-block | small-feature, genus | 1 | 38 | 4044 | 0.073 | 2053 | 49919.4 | 49909.6 | 2.0e-4 | 49909.5 | ok, 1992 vertices | 16 | 1548 | 41.8 | 96411 | 30221 | 0 | pass | 28180 | extrude | 5236 | 0.408 | 0.392 | 3838 |
| rounded-box | fillet | 1 | 26 | 2540 | 0.054 | 1069 | 23325.7 | 23340.5 | -6.3e-4 | 23340.8 | ok, 1272 vertices | 0 | 216 | 11.5 | 11653 | 1914 | 0 | pass | 2265 | no: Box: not supported yet: no structured hex method fits this body (extrude: cylindrical face 8 is not parallel to the direction; sweep: from face 0: 12 faces are not on the sweep path; from face 5: 12 faces are not on the sweep path; revolve: plan | | | | 67 |
| shallow-groove | near-tangent, boolean | 1 | 8 | 62 | 0.075 | 218 | 47795.2 | 47782.3 | 2.7e-4 | 47781.5 | ok, 33 vertices | 0 | 24 | 0.2 | 267 | 87 | 0 | pass | 24 | extrude | 1960 | 0.991 | 0.986 | 1078 |
| sharp-wedge | sharp, thin-wall, sweepable | 1 | 5 | 8 | 0.083 | 72 | 3200.0 | 3200.0 | 0.0e0 | 3200.0 | ok, 6 vertices | 0 | 9 | 0.0 | 11 | 3 | 0 | pass | 1 | extrude | 294 | 0.050 | 0.050 | 87 |
| sphere-on-plate | near-tangent, boolean | 1 | 12 | 2826 | 0.098 | 3775 | 69353.3 | 69509.0 | -2.2e-3 | 69509.7 | ok, 1415 vertices | 0 | 124 | 8.3 | 4898 | 309 | 9 | pass | 1265 | no: Plate: not supported yet: no structured hex method fits this body (extrude: face 6 is curved across the direction; sweep: from face 0: 6 faces are not on the sweep path; from face 5: linking face 11 has 2 boundary loops (periodic or holed linking | | | | 75 |
| spline-vase | organic | 1 | 11 | 3890 | 0.106 | 1097 | 94891.2 | 94948.5 | -6.0e-4 | – | ok, 1947 vertices | 0 | 243 | 23.5 | 12461 | 1512 | 0 | pass | 2487 | sweep | 4554 | 0.649 | 0.649 | 3030 |
| stepped-block | blocky, sharp | 1 | 14 | 96 | 0.078 | 438 | 47000.0 | 47000.0 | 0.0e0 | 47000.0 | ok, 48 vertices | 1 | 60 | 0.6 | 223 | 41 | 0 | pass | 11 | extrude | 1416 | 0.999 | 0.999 | 906 |
| thin-ribs | thin-wall, blocky | 1 | 26 | 92 | 0.119 | 1085 | 32000.0 | 32000.0 | -4.5e-16 | 32000.0 | ok, 48 vertices | 0 | 72 | 0.7 | 171 | 33 | 0 | pass | 10 | extrude | 777 | 0.844 | 0.844 | 236 |
| thin-wall-enclosure | thin-wall, blocky | 1 | 11 | 36 | 0.108 | 189 | 15564.0 | 15564.0 | 0.0e0 | 15564.0 | ok, 20 vertices | 0 | 28 | 0.2 | 191 | 47 | 2 | pass | 8 | extrude | 894 | 0.297 | 0.297 | 349 |
| analytic-sphere | analytic | 1 | 6 | 2784 | 0.069 | 1340 | 33353.4 | 33507.9 | -4.6e-3 | 33510.3 | ok, 1394 vertices | 0 | 96 | 8.9 | 4211 | 58 | 0 | pass | 1430 | no: Sphere: not supported yet: no structured hex method fits this body (extrude: no direction to try; sweep: no planar face to sweep from; revolve: no axis to try; mapped: meshing failed: meshing failed: mesh validity gate: 8 inverted or degenerate ele | | | | 159 |
| analytic-torus | analytic, genus | 1 | 6 | 7230 | 0.109 | 1725 | 37644.1 | 37893.7 | -6.6e-3 | 37899.3 | ok, 3615 vertices | 1 | 180 | 31.7 | 19790 | 466 | 0 | pass | 4946 | revolve | 1134 | 0.706 | 0.706 | 1155 |
| analytic-cylinder | analytic, sweepable | 1 | 4 | 1004 | 0.049 | 368 | 12533.1 | 12564.7 | -2.5e-3 | 12566.4 | ok, 504 vertices | 0 | 106 | 9.3 | 7437 | 1568 | 0 | pass | 1797 | extrude | 3200 | 0.707 | 0.707 | 2316 |
| analytic-pipe | analytic, genus, sweepable | 1 | 6 | 1448 | 0.104 | 506 | 94150.9 | 94238.0 | -9.3e-4 | 94247.8 | ok, 724 vertices | 1 | 220 | 9.5 | 6238 | 1340 | 0 | pass | 1734 | extrude | 1288 | 0.998 | 0.998 | 1059 |
| analytic-plate-hole | analytic, genus, sweepable | 1 | 8 | 112 | 0.224 | 524 | 98449.1 | 98429.5 | 2.0e-4 | 98429.2 | ok, 56 vertices | 1 | 62 | 0.6 | 1868 | 543 | 0 | pass | 78 | extrude | 321 | 0.320 | 0.142 | 248 |
## Categories
| category | stresses | parts |
|---|---|---|
| thin-wall | walls thin against the part's size | 6 |
| thin-wall | walls thin against the part's size | 7 |
| small-feature | features much smaller than the part | 1 |
| fillet | blends between faces | 2 |
| genus | through holes (genus > 0) | 7 |
| sharp | sharp edges and acute dihedral angles | 3 |
| near-tangent | faces meeting at a shallow angle | 2 |
| boolean | intersection curves from booleans | 3 |
| sweepable | extrusions and sweeps (one-to-one sweep meshing) | 8 |
| sweepable | extrusions and sweeps (one-to-one sweep meshing) | 9 |
| blocky | axis-aligned blocks (polycube-friendly) | 4 |
| organic | free-form, lofted or revolved spline surfaces | 2 |
| assembly | several bodies placed by component transforms | 1 |
@@ -53,6 +54,7 @@ clock on the machine that ran it; every other column is deterministic.
- `bent-tube`: A 10 mm tube with a 1 mm wall, bent through R30: a thin-walled sweep along a line-arc-line path.
- `bolted-assembly`: A base plate with a clamp block component placed twice, once turned 90 degrees: bodies placed by component transforms.
- `cantilever-i-beam`: The 200 mm I-beam of `i-beam` lying along X with its web upright (Z up): a sweep along a horizontal axis, and the cantilever of the README demo.
- `cross-cylinders`: Two orthogonal R10 cylinders joined: equal radii, so the intersection curves cross at two singular points.
- `filleted-bracket`: An 8 mm L-bracket with an R6 inside fillet and a hole through each leg: a blend beside holes.
- `i-beam`: A 200 mm I-beam with 3 mm flanges and a 2 mm web: a long sweepable prism with thin walls.