engine: mesh.hex.project command, MCP, docs and meshing skill (#399)

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-15 16:05:38 -04:00
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| Structured Hex | Quad Faces — All-quad meshes of faces on shared edge nodes | coming soon (M5) | |
| Structured Hex | Hex Mesh — Structured hex mesh of a body: automatic, or extruded, swept, revolved or mapped (the Method drop-down) | ready | `mesh.hex.generate`, (`mesh.hex.sweep`), (`mesh.hex.mapped`) |
| Structured Hex | Partitioned Mesh — One mesh of a partitioned part, a method per cell (hex, tet, or all hex as conforming blocks); cells joined across partitions | ready | `mesh.cells`, (`mesh.hex.blocks`) |
| Structured Hex | Mesh Block — A mapped block of hex, wedge or quad elements between corner points | ready | `mesh.block` |
| Structured Hex | Mesh Block — A mapped block of hex, wedge or quad elements between corner points; projection blocking (a block topology projected onto the part) | ready | `mesh.block`, `mesh.hex.project` |
| Structured Hex | Decompose — Find sweepable and mappable regions of 3D parts (extruded cross-sections are already cut into blocks by Hex Mesh) | coming soon (M5) | |
| Structured Hex | Transition — Conforming tet–hex interfaces with pyramids | coming soon (M5) | |
| Automatic Hex | Octree Hex — Unstructured all-hex mesh of any part: adaptive grid, boundary layers on every sharp edge, untangled and proven valid | ready | `mesh.hex.octree` |
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of a triangle: Van Oosterom and Strackee 1983); closest point on a triangle (C. Ericson, *Real-Time
Collision Detection*, 2005, §5.1.5).
### B9. Projection blocking (implemented in `fieldcraft-mesh::project`)
A block topology is laid over the part and projected onto its B-rep instead of cutting the
geometry into sweepable cells (the block-structured projection method as publicly described:
blocks in index space, carved, outer faces projected onto surfaces, edges onto curves, vertices
onto points, then smoothed). No code, manual or text of any commercial mesher was read.
- **Transfinite interpolation** places face and interior nodes from projected edges and faces:
W. J. Gordon, C. A. Hall, *Construction of curvilinear co-ordinate systems and applications to
mesh generation*, IJNME 7(4):461–477, 1973; W. J. Gordon, L. C. Thiel, *Transfinite mappings and
their application to grid generation*, Appl. Math. Comput. 10–11:171–233, 1982.
- **Elliptic smoothing**: A. M. Winslow, *Numerical solution of the quasilinear Poisson equation
in a nonuniform triangle mesh*, J. Comput. Phys. 2:149–172, 1967; J. F. Thompson, Z. U. A. Warsi,
C. W. Mastin, *Numerical Grid Generation: Foundations and Applications*, North-Holland 1985
(ch. 6, the three-dimensional equations and their point iteration).
- **Control functions**: P. D. Thomas, J. F. Middlecoff, *Direct control of the grid point
distribution in meshes generated by elliptic equations*, AIAA J. 18(6):652–656, 1980 (one-
dimensional form, evaluated on the algebraic grid).
- **Curve and corner projection**: Newton's method on the tangent planes of the two (three)
surfaces, falling back to alternating projections (von Neumann) where they meet tangentially.
- **Worst-element repair**: compass search on the local smallest scaled Jacobian (optimization-
based smoothing, L. A. Freitag, C. Ollivier-Gooch, IJNME 40:3979–4002, 1997; metric: P. M. Knupp,
SIAM J. Sci. Comput. 23(1):193–218, 2001).
## Part C: Datasets and benchmarks
| Dataset | Content | Licence | Usable for FieldCraft? |