# Step 2: Shell Director Geometry

## 담당 역할과 필수 스킬

- 담당 역할: `implementation-agent`
- 필수 스킬: `harness`, `fesa-cpp-msvc-tdd`

## 읽어야 할 파일

- `/.agents/skills/harness/SKILL.md`, `/.codex/skills/fesa-cpp-msvc-tdd/SKILL.md`
- `/AGENTS.md`, `/docs/PRD.md`, `/docs/ARCHITECTURE.md`, `/docs/ADR.md`
- `/docs/HARNESS.md`, `/docs/HARNESS_WORKFLOW.md`, `/.codex/hooks.json`
- `/docs/implementation-plans/linear-static-mitc4-shell-implementation-plan.md`
- `/docs/requirements/linear-static-mitc4-shell.md` Requirements 011-016/050/051/054
- `/docs/research/linear-static-mitc4-shell-research.md`
- `/docs/formulations/mitc4-shell-formulation.md` Sections 4, 9, 17
- `/docs/numerical-reviews/linear-static-mitc4-shell-review.md` Sections 5.2, 5.5, 6.1
- `/docs/io-definitions/linear-static-mitc4-shell-io.md` Sections 3.3, 8-9
- `/docs/reference-models/linear-static-mitc4-shell-reference-models.md`
- phase indexes, `step2.md`, Step 0-1 modified paths/summaries
- Candidate new `/include/fesa/model/shell_geometry.hpp`
- Candidate new `/src/fesa/model/shell_geometry.cpp`
- Candidate new `/tests/unit/model/shell_geometry_test.cpp`
- `/src/fesa/CMakeLists.txt`, `/tests/CMakeLists.txt`

## 작업

1. `MITC4-GEO-001..004`를 먼저 작성하고 CMake에 test source를 등록한다.
2. Backend-neutral model geometry module에 element normal candidate, deterministic
   area-weighted nodal director, pairwise positive orientation, right-handed nodal
   tangent frame with documented axis tie-break, structured validation seam을 만든다.
3. Center, eight stiffness points, four tying points, four committed recovery points에서
   finite bases, nonzero surface measure, positive finite Jacobian을 검사한다.
4. Valid planar/rotated/warped cases와 duplicate, bow-tie, zero-area, reversed,
   nonfinite, nonpositive-J, opposed-normal cases를 검증한다.

## Acceptance Criteria

```powershell
$requiredBuildPaths=@("C:/git/googletest","C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl","C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb","C:/Program Files/HDF_Group/HDF5/2.1.1/cmake")
foreach($p in $requiredBuildPaths){if(-not(Test-Path -LiteralPath $p)){throw "Missing $p"}}
cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
  "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
  "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
  "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
  "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4Geometry" --output-on-failure
```

Expected missing geometry API/behavior RED를 확인한 뒤 minimal GREEN. 이후:

```powershell
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4Geometry|DomainModel|InpDomainMapping" --output-on-failure
cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug --show-only=json-v1
ctest --test-dir .harness/build -C Debug --output-on-failure
```

## 검증 및 상태 갱신

RED/VERIFY evidence를 summary에 남기고 현재 Step 상태만 갱신한다. Executor-owned
timestamp/retry/commit/advancement를 쓰지 않는다.

## 금지사항

- Calibrated smooth angle, warp/distortion threshold, NR-O03/NR-O04를 추가하지 마라.
- Parser keyword policy나 element stiffness를 구현하지 마라.
- Invalid geometry를 clamp/repair하지 마라.
- Reference/upstream 문서를 수정하거나 직접 commit/hook 실행을 하지 마라.