docs(topology): add module README for reference shapes

Outline topology types, aliases, and downstream consumers (`Mesh`, basis). - Provide quick navigation for contributors touching shape definitions.
2026-08-06 04:21:33 +00:00 · 2026-05-09 18:36:33 +03:00
parent 3788199791
commit 086bc061d0
1 changed files with 99 additions and 0 deletions
@@ -0,0 +1,99 @@
+# src/topology/
+
+Reference shapes for finite elements: parametric coordinates, edge and
+face connectivity, topological entities. Topology owns geometry; basis
+functions and quadrature are separate concerns and live in
+`src/basis/` and `src/quadrature/`.
+
+## Files
+
+- `api.jl`            — `AbstractTopology{N}`, the topological-entity
+  hierarchy (`TopologicalEntity`, `Vertex`, `Edge`, `Face`, `Cell`),
+  the entity-counting helpers (`nvertices`, `nedges`, `nfaces`) and the
+  generic interface (`nnodes`, `dim`, `reference_coordinates`, `edges`,
+  `faces`).
+- `topology.jl`       — small compatibility shim included by
+  `JuliaFEM.jl`.
+- `segments.jl`       — `Segment{N}` plus the `Seg2`, `Seg3` aliases.
+- `triangles.jl`      — `Triangle{N}` plus `Tri3`, `Tri6`, `Tri7`,
+  `Tri10`.
+- `quadrilaterals.jl` — `Quadrilateral{N}` plus `Quad4`, `Quad8`,
+  `Quad9`.
+- `tetrahedra.jl`     — `Tetrahedron{N}` plus `Tet4`, `Tet10`.
+- `hexahedra.jl`      — `Hexahedron{N}` plus `Hex8`, `Hex20`, `Hex27`.
+- `pyramids.jl`       — `Pyramid{N}` plus `Pyr5`.
+- `wedges.jl`         — `Wedge{N}` plus `Wedge6`, `Wedge15`.
+
+## Topologies provided
+
+The full set of currently exported aliases:
+
+| Family         | Type signature        | Aliases                  |
+|----------------|------------------------|---------------------------|
+| Segment (1D)   | `Segment{N}`           | `Seg2`, `Seg3`            |
+| Triangle (2D)  | `Triangle{N}`          | `Tri3`, `Tri6`, `Tri7`, `Tri10` |
+| Quad (2D)      | `Quadrilateral{N}`     | `Quad4`, `Quad8`, `Quad9` |
+| Tetrahedron    | `Tetrahedron{N}`       | `Tet4`, `Tet10`           |
+| Hexahedron     | `Hexahedron{N}`        | `Hex8`, `Hex20`, `Hex27`  |
+| Pyramid        | `Pyramid{N}`           | `Pyr5`                    |
+| Wedge / Prism  | `Wedge{N}`             | `Wedge6`, `Wedge15`       |
+
+## Interface
+
+Every topology implements:
+
+```julia
+nnodes(::Triangle{6})              # 6
+dim(::Triangle{6})                 # 2
+reference_coordinates(::Tri6)      # SVector{6, Vec{2, Float64}}
+edges(::Tri6)                      # NTuple of (i, j) corner pairs
+faces(::Tet4)                      # NTuple of (i, j, k) corner triples
+```
+
+The functions return compile-time constants (`nnodes`, `dim`) or static
+data (`SVector`, `NTuple`) so they are inlined at the call site and add
+no allocations to the assembly hot path.
+
+Reference coordinate conventions:
+
+- Segments        — `xi in [-1, 1]`.
+- Triangles       — `(u, v)` with `u, v >= 0` and `u + v <= 1`.
+- Quadrilaterals  — `(u, v) in [-1, 1]^2`.
+- Tetrahedra      — `(u, v, w) >= 0` with `u + v + w <= 1`.
+- Hexahedra       — `(u, v, w) in [-1, 1]^3`.
+
+## Pairing topology and basis
+
+Topology and basis are independent type parameters of the element
+template. The basis dispatches on its own type parameter only:
+
+```julia
+get_basis_functions(::Type{Triangle{6}}, ::Type{Lagrange{2}}, xi)
+```
+
+so the same `Triangle{6}` can be combined with any compatible basis
+family (`Lagrange{2}`, `Serendipity{2}`, …) without redefining the
+topology.
+
+## Adding a new topology
+
+1. Create the file under `src/topology/` (or extend an existing family
+   with a new `N`).
+2. Define the `struct` and any aliases.
+3. Implement `nnodes`, `dim`, `reference_coordinates`, `edges` and
+   `faces`. Use `SVector` / `NTuple` returns; keep them allocation
+   free.
+4. Add the export to `src/JuliaFEM.jl`.
+5. Add unit tests under `test/topology/`.
+6. If you also want a Lagrange basis on this topology, add the
+   matching `VandermondeBasisDescription` to
+   `src/basis/basis_descriptions.jl` and re-run
+   `julia --project=. src/basis/basis_generator.jl`.
+
+## Related code
+
+- `src/basis/`        — basis functions and the symbolic generator.
+- `src/quadrature/`   — integration points for each topology.
+- `src/mesh/`         — `Mesh{N, T<:AbstractTopology{N}}`.
+- `src/elements/`     — `Element{K, P, S, N}` template.
+- `test/topology/`    — public test suite.