# Sprint Contract: MITC4 Geometry Directors

## Objective
Implement or rebuild MITC4 shape functions, natural-coordinate node order, element-center director policy, local director axes, and integration-point local bases.

## Required Reading
- /AGENTS.md
- /docs/MITC4_FORMULATION.md
- /docs/NUMERICAL_CONVENTIONS.md
- /docs/ADR.md

## Scope
- Define `N1..N4` and derivatives for FESA natural coordinates.
- Define tying points `A`, `B`, `C`, and `D`.
- Build element-center director `Vn` from midsurface geometry.
- Build nodal `V1`, `V2`, `Vn` and integration local Cartesian basis.
- Add invalid/singular element diagnostics for near-zero normal, basis, Jacobian, and thickness.

## Allowed Files
- `include/`
- `src/`
- `tests/`
- `PLAN.md`
- `PROGRESS.md`

## Explicit Non-Goals
- Do not compute stiffness.
- Do not add Abaqus `*Orientation` or nodal normal parsing.
- Do not add mesh quality diagnostics.

## Tests To Write First
- Shape function partition-of-unity and derivative tests.
- Node order and tying-point coordinate tests.
- Flat element normal and right-handed basis tests.
- Fallback axis tests when `EY x Vn` is near zero.
- Invalid geometry diagnostic tests.

## Reference Artifacts
- None.

## Acceptance Commands
```bash
python scripts/validate_workspace.py
```

## Evaluator Checklist
- Geometry matches `docs/MITC4_FORMULATION.md`.
- The old averaged-edge basis is not used as the binding formulation.
- No stress/strain or stiffness logic is slipped into this step.

## Handoff Requirements
- Record MITC4 geometry readiness in `PROGRESS.md`.

## Do Not
- Do not silently support strongly warped/nodal-director behavior beyond the documented Phase 1 policy.