feat: add mitc4 geometry directors

PLAN.md

@@ -13,7 +13,7 @@ Every new agent session must read this file together with `PROGRESS.md` before p
 - If an item becomes obsolete, move it to `PROGRESS.md` with a short reason instead of silently deleting it.
 
 ## Current Objective
-Continue the new Phase 1 rebaseline plan in `phases/1-linear-static-mitc4-rebaseline`, starting with P1R-07 MITC4 geometry, node order, tying points, directors, and local bases. The old `phases/1-linear-static-mitc4` path is historical and superseded by the paper-based MITC4 formulation reset.
+Continue the new Phase 1 rebaseline plan in `phases/1-linear-static-mitc4-rebaseline`, starting with P1R-08 degenerated-continuum displacement, covariant strain rows, and MITC shear tying. The old `phases/1-linear-static-mitc4` path is historical and superseded by the paper-based MITC4 formulation reset.
 
 ## Required Reading For New Agents
 1. `AGENTS.md`
@@ -36,7 +36,7 @@ Continue the new Phase 1 rebaseline plan in `phases/1-linear-static-mitc4-rebase
 ## Active Phase Files
 - Active phase directory: `phases/1-linear-static-mitc4-rebaseline`
 - Execute with: `python scripts/execute.py 1-linear-static-mitc4-rebaseline`
-- Step numbering is zero-based. `step0.md` is complete and recorded in `phases/1-linear-static-mitc4-rebaseline/step0-audit.md`; `step1.md` is complete and created the `quad_02_phase1.inp` normalized reference path; `step2.md` is complete and revalidated core harness guardrails; `step3.md` is complete and revalidated the Phase 1 parser/domain subset; `step4.md` is complete and strengthened validation/singular diagnostics; `step5.md` is complete and revalidated the DofManager/reaction foundation; `step6.md` is complete and revalidated the minimum result model plus displacement CSV comparator; `step15.md` is the independent evaluator closeout.
+- Step numbering is zero-based. `step0.md` is complete and recorded in `phases/1-linear-static-mitc4-rebaseline/step0-audit.md`; `step1.md` is complete and created the `quad_02_phase1.inp` normalized reference path; `step2.md` is complete and revalidated core harness guardrails; `step3.md` is complete and revalidated the Phase 1 parser/domain subset; `step4.md` is complete and strengthened validation/singular diagnostics; `step5.md` is complete and revalidated the DofManager/reaction foundation; `step6.md` is complete and revalidated the minimum result model plus displacement CSV comparator; `step7.md` is complete and revalidated MITC4 natural coordinates, tying points, center directors, and integration bases; `step15.md` is the independent evaluator closeout.
 - Every step file contains a sprint contract with objective, required reading, scope, allowed files, explicit non-goals, tests to write first, reference artifacts, acceptance command, evaluator checklist, and handoff requirements.
 - Historical phase directory: `phases/1-linear-static-mitc4`
 - Historical phase status: blocked/superseded. Do not resume the old P1-15/P1-16 path unless the user explicitly requests recovery of that exact phase.
@@ -76,7 +76,7 @@ Each gate should be satisfied before moving to the next implementation band unle
 | G1 - Build and validation | satisfied | Build system, test framework, and `scripts/validate_workspace.py` run real checks. | Validation command output |
 | G2 - Parser and domain | satisfied | Parser subset revalidated in step 3; validation and singular diagnostics revalidated in step 4. | Parser acceptance/rejection tests, validation negative tests, and validation output |
 | G3 - DOF/math/results infrastructure | partial | Core aliases, DOF mapping, validation harness, model diagnostic context, DofManager, sparse-connectivity inputs, full-vector reaction formula, result model metadata, and displacement CSV comparator were revalidated in steps 2, 5, and 6; assembly remains for step 12. | P1R-02, P1R-05, and P1R-06 validation output |
-| G4 - MITC4 element readiness | reopened | MITC4 formulation was rewritten from local papers; element implementation must be rebuilt or revalidated through steps 7 through 11. | Revised `docs/MITC4_FORMULATION.md`, future element tests |
+| G4 - MITC4 element readiness | partial | MITC4 formulation was rewritten from local papers; Step 7 rebuilt geometry/director/local-basis scaffolding, while strain tying, material/integration, stiffness/drilling, and patch benchmarks remain for steps 8 through 11. | P1R-07 validation output; future element tests |
 | G5 - End-to-end solver | reopened | Linear static path must be revalidated through steps 13 and 14 after the MITC4 rebuild and `quad_02` compatibility path. | Future integration/reference regression output |
 
 ## Phase 1 Implementation Milestones
@@ -88,7 +88,7 @@ All milestones are intended to become one or more self-contained sprint contract
 | P1R-04 | completed | validation generator | Rebuild validation and singular diagnostic coverage. | P1R-03 | Missing-reference and singular-prone negative tests |
 | P1R-05 | completed | DOF generator | Rebuild six-DOF DofManager, constrained/free mapping, equation numbering, and full-vector reconstruction. | none | DOF mapping and reaction foundation tests |
 | P1R-06 | completed | results generator | Rebuild minimum results model and displacement CSV comparator. | none | U/RF schema tests and CSV comparator tests |
-| P1R-07 | pending | MITC4 generator | Implement MITC4 geometry, node order, tying points, directors, and local bases. | none | Shape/basis/diagnostic tests |
+| P1R-07 | completed | MITC4 generator | Implement MITC4 geometry, node order, tying points, directors, and local bases. | none | Shape/basis/diagnostic tests |
 | P1R-08 | pending | MITC4 generator | Implement degenerated-continuum displacement, covariant strain rows, and MITC shear tying. | P1R-07 | Finite-difference and tying interpolation tests |
 | P1R-09 | pending | MITC4 generator | Implement material matrix, transform, and `2 x 2 x 2` integration scaffolding. | P1R-08 | Material/integration tests |
 | P1R-10 | pending | MITC4 generator | Assemble MITC4 stiffness/internal force with six-DOF transform and drilling stabilization. | P1R-09, P1R-05 | Symmetry, rigid body, drilling sensitivity tests |

PROGRESS.md

@@ -13,10 +13,36 @@ Every new agent session must read this file together with `PLAN.md` before plann
 - Do not remove history unless the user explicitly asks for archival cleanup.
 
 ## Current Status
-Phase 1 has a new rebaseline phase definition in `phases/1-linear-static-mitc4-rebaseline`. Steps 0 through 6 are complete. `quad_02_phase1.inp` is now the normalized Phase 1-compatible input path for the stored `quad_02` S4 reference pair, while the original `quad_02.inp` remains preserved unsupported provenance. Core numeric aliases, DOF mapping, validation harness, model diagnostic context, the Phase 1 parser/domain subset, validation/singular diagnostics, DofManager/reaction foundation, minimum result model metadata, and displacement CSV comparator foundation have been revalidated. The old `phases/1-linear-static-mitc4` path is historical and superseded after the MITC4 formulation reset.
+Phase 1 has a new rebaseline phase definition in `phases/1-linear-static-mitc4-rebaseline`. Steps 0 through 7 are complete. `quad_02_phase1.inp` is now the normalized Phase 1-compatible input path for the stored `quad_02` S4 reference pair, while the original `quad_02.inp` remains preserved unsupported provenance. Core numeric aliases, DOF mapping, validation harness, model diagnostic context, the Phase 1 parser/domain subset, validation/singular diagnostics, DofManager/reaction foundation, minimum result model metadata, displacement CSV comparator foundation, and MITC4 geometry/director scaffolding have been revalidated. The old `phases/1-linear-static-mitc4` path is historical and superseded after the MITC4 formulation reset.
 
 ## Completed Work
 
+### 2026-05-04 - P1R-07 MITC4 geometry and directors completed
+Author: Codex
+
+Changed files:
+- `include/fesa/fesa.hpp`
+- `tests/test_main.cpp`
+- `phases/1-linear-static-mitc4-rebaseline/index.json`
+- `PLAN.md`
+- `PROGRESS.md`
+
+Summary:
+- Added MITC4 tests for shape-function derivatives, FESA/Abaqus S4 natural-coordinate node order, tying point labels `A`, `B`, `C`, and `D`, and edge-node mapping.
+- Added Phase 1 MITC4 geometry structures for natural points, tying points, center midsurface derivatives, center-normal director policy, nodal director frames, and integration-point local Cartesian bases.
+- Implemented the documented center director policy `Vn = normalize(G1_c x G2_c)`, nodal `V1 = normalize(EY x Vn)` with deterministic fallback axes, and right-handed `V2 = Vn x V1`.
+- Added integration-basis construction from degenerated-continuum covariant basis vectors and diagnostics for invalid thickness, singular center normal, singular basis, and near-zero Jacobian.
+- Replaced the legacy `computeLocalBasis()` internals with the new center-director geometry policy while leaving stiffness/strain/drilling reimplementation to later steps.
+
+Verification:
+- First ran `python scripts/validate_workspace.py` after adding Step 7 tests; it failed as expected because the MITC4 geometry/director API did not exist yet.
+- After implementation, `python scripts/validate_workspace.py` configured CMake, built `fesa_core` and `fesa_tests`, and ran CTest successfully.
+- CTest result: 1 test executable passed.
+
+Follow-up:
+- Continue with P1R-08 degenerated-continuum displacement, covariant strain rows, and MITC shear tying.
+- The existing stiffness kernel still needs to be rebuilt against the new formulation in steps 8 through 10; Step 7 intentionally did not add stiffness, stress, strain, or S4R behavior.
+
 ### 2026-05-04 - P1R-06 results model and displacement CSV comparator completed
 Author: Codex
 

include/fesa/fesa.hpp

@@ -198,6 +198,22 @@ inline Real norm(const Vec3& value) {
   return std::sqrt(dot(value, value));
 }
 
+inline bool isFinite(Real value) {
+  return std::isfinite(value);
+}
+
+inline bool isFinite(const Vec3& value) {
+  return isFinite(value.x) && isFinite(value.y) && isFinite(value.z);
+}
+
+inline std::optional<Vec3> normalizedIfValid(const Vec3& value, Real tolerance = 1.0e-12) {
+  const Real length = norm(value);
+  if (!isFinite(length) || length <= tolerance) {
+    return std::nullopt;
+  }
+  return (1.0 / length) * value;
+}
+
 inline Vec3 normalized(const Vec3& value) {
   const Real length = norm(value);
   if (length <= std::numeric_limits<Real>::epsilon()) {
@@ -1222,15 +1238,211 @@ struct LocalBasis {
   Vec3 e3;
 };
 
+struct MITC4NaturalPoint {
+  Real xi = 0.0;
+  Real eta = 0.0;
+};
+
+struct MITC4TyingPoint {
+  std::string label;
+  MITC4NaturalPoint natural;
+  std::array<LocalIndex, 2> edge_node_indices{};
+};
+
+inline std::array<MITC4NaturalPoint, 4> mitc4NodeNaturalCoordinates() {
+  return {{{-1.0, -1.0}, {1.0, -1.0}, {1.0, 1.0}, {-1.0, 1.0}}};
+}
+
+inline std::array<MITC4TyingPoint, 4> mitc4TyingPoints() {
+  return {{{"A", {0.0, -1.0}, {0, 1}},
+           {"B", {-1.0, 0.0}, {0, 3}},
+           {"C", {0.0, 1.0}, {3, 2}},
+           {"D", {1.0, 0.0}, {1, 2}}}};
+}
+
+struct MITC4DirectorFrame {
+  Vec3 v1;
+  Vec3 v2;
+  Vec3 vn;
+};
+
+struct MITC4MidsurfaceDerivatives {
+  ShapeData shape;
+  Vec3 g1;
+  Vec3 g2;
+};
+
+struct MITC4Geometry {
+  std::array<Vec3, 4> coordinates{};
+  Real thickness = 0.0;
+  ShapeData center_shape;
+  Vec3 g1_center;
+  Vec3 g2_center;
+  Vec3 center_normal;
+  std::array<MITC4DirectorFrame, 4> nodal_frames{};
+  std::vector<Diagnostic> diagnostics;
+
+  bool ok() const {
+    return !hasError(diagnostics);
+  }
+};
+
+struct MITC4IntegrationBasis {
+  ShapeData shape;
+  Vec3 g1;
+  Vec3 g2;
+  Vec3 g3;
+  Real jacobian = 0.0;
+  LocalBasis local;
+  std::vector<Diagnostic> diagnostics;
+
+  bool ok() const {
+    return !hasError(diagnostics);
+  }
+};
+
+inline Vec3 globalEX() {
+  return {1.0, 0.0, 0.0};
+}
+
+inline Vec3 globalEY() {
+  return {0.0, 1.0, 0.0};
+}
+
+inline Vec3 globalEZ() {
+  return {0.0, 0.0, 1.0};
+}
+
+inline Diagnostic mitc4Diagnostic(std::string code, std::string message) {
+  return makeDiagnostic(Severity::Error, std::move(code), std::move(message), "mitc4", "<element>", 0);
+}
+
+inline MITC4MidsurfaceDerivatives mitc4MidsurfaceDerivatives(const std::array<Vec3, 4>& coordinates, Real xi, Real eta) {
+  MITC4MidsurfaceDerivatives result;
+  result.shape = shapeFunctions(xi, eta);
+  for (std::size_t i = 0; i < 4; ++i) {
+    result.g1 = result.g1 + result.shape.dr[i] * coordinates[i];
+    result.g2 = result.g2 + result.shape.ds[i] * coordinates[i];
+  }
+  return result;
+}
+
+inline std::optional<Vec3> firstNormalizedCross(const std::array<Vec3, 3>& axes, const Vec3& vector, Real tolerance) {
+  for (const Vec3& axis : axes) {
+    auto candidate = normalizedIfValid(cross(axis, vector), tolerance);
+    if (candidate) {
+      return candidate;
+    }
+  }
+  return std::nullopt;
+}
+
+inline std::optional<MITC4DirectorFrame> buildMITC4DirectorFrame(const Vec3& normal, Real tolerance) {
+  auto v1 = normalizedIfValid(cross(globalEY(), normal), tolerance);
+  if (!v1) {
+    v1 = firstNormalizedCross({globalEZ(), globalEX(), globalEY()}, normal, tolerance);
+  }
+  if (!v1) {
+    return std::nullopt;
+  }
+  auto v2 = normalizedIfValid(cross(normal, *v1), tolerance);
+  if (!v2) {
+    return std::nullopt;
+  }
+  return MITC4DirectorFrame{*v1, *v2, normal};
+}
+
+inline MITC4Geometry buildMITC4Geometry(const std::array<Vec3, 4>& coordinates, Real thickness, Real tolerance = 1.0e-12) {
+  MITC4Geometry geometry;
+  geometry.coordinates = coordinates;
+  geometry.thickness = thickness;
+  if (!isFinite(thickness) || thickness <= tolerance) {
+    geometry.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-THICKNESS", "MITC4 shell thickness must be positive and finite"));
+  }
+  for (const Vec3& coordinate : coordinates) {
+    if (!isFinite(coordinate)) {
+      geometry.diagnostics.push_back(
+          mitc4Diagnostic("FESA-MITC4-COORDINATE", "MITC4 element coordinates must be finite"));
+      break;
+    }
+  }
+
+  const auto center = mitc4MidsurfaceDerivatives(coordinates, 0.0, 0.0);
+  geometry.center_shape = center.shape;
+  geometry.g1_center = center.g1;
+  geometry.g2_center = center.g2;
+  const auto normal = normalizedIfValid(cross(center.g1, center.g2), tolerance);
+  if (!normal) {
+    geometry.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-NORMAL", "MITC4 element center normal is near zero"));
+    return geometry;
+  }
+  geometry.center_normal = *normal;
+
+  const auto frame = buildMITC4DirectorFrame(*normal, tolerance);
+  if (!frame) {
+    geometry.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 nodal director basis could not be constructed"));
+    return geometry;
+  }
+  geometry.nodal_frames.fill(*frame);
+  return geometry;
+}
+
+inline MITC4IntegrationBasis computeMITC4IntegrationBasis(const MITC4Geometry& geometry, Real xi, Real eta, Real zeta,
+                                                          Real tolerance = 1.0e-12) {
+  MITC4IntegrationBasis result;
+  result.diagnostics = geometry.diagnostics;
+  result.shape = shapeFunctions(xi, eta);
+  for (std::size_t i = 0; i < 4; ++i) {
+    const Vec3& coordinate = geometry.coordinates[i];
+    const Vec3& normal = geometry.nodal_frames[i].vn;
+    result.g1 = result.g1 + result.shape.dr[i] * coordinate +
+                (0.5 * zeta * geometry.thickness * result.shape.dr[i]) * normal;
+    result.g2 = result.g2 + result.shape.ds[i] * coordinate +
+                (0.5 * zeta * geometry.thickness * result.shape.ds[i]) * normal;
+    result.g3 = result.g3 + (0.5 * geometry.thickness * result.shape.n[i]) * normal;
+  }
+
+  result.jacobian = dot(cross(result.g1, result.g2), result.g3);
+  if (!isFinite(result.jacobian) || std::fabs(result.jacobian) <= tolerance) {
+    result.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-JACOBIAN", "MITC4 element Jacobian is near zero"));
+  }
+
+  const auto e3 = normalizedIfValid(result.g3, tolerance);
+  if (!e3) {
+    result.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis normal is near zero"));
+    return result;
+  }
+  auto e1 = normalizedIfValid(cross(result.g2, *e3), tolerance);
+  if (!e1) {
+    e1 = firstNormalizedCross({globalEY(), globalEZ(), globalEX()}, *e3, tolerance);
+  }
+  if (!e1) {
+    result.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis tangent could not be constructed"));
+    return result;
+  }
+  const auto e2 = normalizedIfValid(cross(*e3, *e1), tolerance);
+  if (!e2) {
+    result.diagnostics.push_back(
+        mitc4Diagnostic("FESA-MITC4-SINGULAR-BASIS", "MITC4 integration basis is not right-handed"));
+    return result;
+  }
+  result.local = {*e1, *e2, *e3};
+  return result;
+}
+
 inline LocalBasis computeLocalBasis(const std::array<Vec3, 4>& coordinates) {
-  Vec3 v1 = 0.5 * ((coordinates[1] - coordinates[0]) + (coordinates[2] - coordinates[3]));
+  const MITC4Geometry geometry = buildMITC4Geometry(coordinates, 1.0);
-  Vec3 v2 = 0.5 * ((coordinates[3] - coordinates[0]) + (coordinates[2] - coordinates[1]));
+  if (!geometry.ok()) {
-  Vec3 e1 = normalized(v1);
+    throw std::runtime_error("invalid MITC4 geometry");
-  v2 = v2 - dot(v2, e1) * e1;
+  }
-  Vec3 e2 = normalized(v2);
+  const MITC4DirectorFrame& frame = geometry.nodal_frames[0];
-  Vec3 e3 = normalized(cross(e1, e2));
+  return {frame.v1, frame.v2, frame.vn};
-  e2 = normalized(cross(e3, e1));
-  return {e1, e2, e3};
 }
 
 struct NaturalDerivatives {

phases/1-linear-static-mitc4-rebaseline/index.json

@@ -9,7 +9,7 @@
     { "step": 4, "name": "validation-singular-diagnostics", "status": "completed" },
     { "step": 5, "name": "dof-manager-reaction-foundation", "status": "completed" },
     { "step": 6, "name": "results-comparator-foundation", "status": "completed" },
-    { "step": 7, "name": "mitc4-geometry-directors", "status": "pending" },
+    { "step": 7, "name": "mitc4-geometry-directors", "status": "completed" },
     { "step": 8, "name": "mitc4-covariant-strain-tying", "status": "pending" },
     { "step": 9, "name": "mitc4-material-integration", "status": "pending" },
     { "step": 10, "name": "mitc4-stiffness-drilling", "status": "pending" },

tests/test_main.cpp

@@ -124,6 +124,22 @@ std::size_t diagnosticCount(const std::vector<fesa::Diagnostic>& diagnostics, co
   return count;
 }
 
+void checkVecNear(const fesa::Vec3& actual, const fesa::Vec3& expected, fesa::Real tolerance) {
+  FESA_CHECK_NEAR(actual.x, expected.x, tolerance);
+  FESA_CHECK_NEAR(actual.y, expected.y, tolerance);
+  FESA_CHECK_NEAR(actual.z, expected.z, tolerance);
+}
+
+void checkRightHandedOrthonormal(const fesa::Vec3& e1, const fesa::Vec3& e2, const fesa::Vec3& e3) {
+  FESA_CHECK_NEAR(fesa::norm(e1), 1.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::norm(e2), 1.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::norm(e3), 1.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::dot(e1, e2), 0.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::dot(e1, e3), 0.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::dot(e2, e3), 0.0, 1.0e-14);
+  FESA_CHECK_NEAR(fesa::dot(fesa::cross(e1, e2), e3), 1.0, 1.0e-14);
+}
+
 fesa::Domain singleElementValidationDomain() {
   fesa::Domain domain;
   domain.nodes[1] = {1, {0, 0, 0}};
@@ -800,6 +816,111 @@ FESA_TEST(displacement_comparator_reports_duplicate_actual_nodes) {
   FESA_CHECK(fesa::containsDiagnostic(compared.diagnostics, "FESA-COMPARE-DUPLICATE-ACTUAL"));
 }
 
+FESA_TEST(mitc4_shape_functions_node_order_and_tying_points) {
+  auto center = fesa::shapeFunctions(0.0, 0.0);
+  const fesa::Real sum = center.n[0] + center.n[1] + center.n[2] + center.n[3];
+  FESA_CHECK_NEAR(sum, 1.0, 1.0e-15);
+  FESA_CHECK_NEAR(center.dr[0], -0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.dr[1], 0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.dr[2], 0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.dr[3], -0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.ds[0], -0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.ds[1], -0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.ds[2], 0.25, 1.0e-15);
+  FESA_CHECK_NEAR(center.ds[3], 0.25, 1.0e-15);
+
+  const auto node_points = fesa::mitc4NodeNaturalCoordinates();
+  FESA_CHECK_NEAR(node_points[0].xi, -1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[0].eta, -1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[1].xi, 1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[1].eta, -1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[2].xi, 1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[2].eta, 1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[3].xi, -1.0, 1.0e-15);
+  FESA_CHECK_NEAR(node_points[3].eta, 1.0, 1.0e-15);
+
+  for (std::size_t i = 0; i < 4; ++i) {
+    const auto corner = fesa::shapeFunctions(node_points[i].xi, node_points[i].eta);
+    FESA_CHECK_NEAR(corner.n[i], 1.0, 1.0e-15);
+  }
+
+  const auto tying_points = fesa::mitc4TyingPoints();
+  FESA_CHECK(tying_points[0].label == "A");
+  FESA_CHECK_NEAR(tying_points[0].natural.xi, 0.0, 1.0e-15);
+  FESA_CHECK_NEAR(tying_points[0].natural.eta, -1.0, 1.0e-15);
+  FESA_CHECK((tying_points[0].edge_node_indices == std::array<fesa::LocalIndex, 2>{0, 1}));
+  FESA_CHECK(tying_points[1].label == "B");
+  FESA_CHECK_NEAR(tying_points[1].natural.xi, -1.0, 1.0e-15);
+  FESA_CHECK_NEAR(tying_points[1].natural.eta, 0.0, 1.0e-15);
+  FESA_CHECK((tying_points[1].edge_node_indices == std::array<fesa::LocalIndex, 2>{0, 3}));
+  FESA_CHECK(tying_points[2].label == "C");
+  FESA_CHECK_NEAR(tying_points[2].natural.xi, 0.0, 1.0e-15);
+  FESA_CHECK_NEAR(tying_points[2].natural.eta, 1.0, 1.0e-15);
+  FESA_CHECK((tying_points[2].edge_node_indices == std::array<fesa::LocalIndex, 2>{3, 2}));
+  FESA_CHECK(tying_points[3].label == "D");
+  FESA_CHECK_NEAR(tying_points[3].natural.xi, 1.0, 1.0e-15);
+  FESA_CHECK_NEAR(tying_points[3].natural.eta, 0.0, 1.0e-15);
+  FESA_CHECK((tying_points[3].edge_node_indices == std::array<fesa::LocalIndex, 2>{1, 2}));
+}
+
+FESA_TEST(mitc4_geometry_builds_flat_directors_and_integration_basis) {
+  const std::array<fesa::Vec3, 4> coords = {{{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}}};
+  auto geometry = fesa::buildMITC4Geometry(coords, 0.2);
+  FESA_CHECK(geometry.ok());
+  checkVecNear(geometry.center_normal, {0, 0, 1}, 1.0e-14);
+  checkVecNear(geometry.g1_center, {0.5, 0, 0}, 1.0e-14);
+  checkVecNear(geometry.g2_center, {0, 0.5, 0}, 1.0e-14);
+  for (const auto& frame : geometry.nodal_frames) {
+    checkVecNear(frame.v1, {1, 0, 0}, 1.0e-14);
+    checkVecNear(frame.v2, {0, 1, 0}, 1.0e-14);
+    checkVecNear(frame.vn, {0, 0, 1}, 1.0e-14);
+    checkRightHandedOrthonormal(frame.v1, frame.v2, frame.vn);
+  }
+
+  auto basis = fesa::computeMITC4IntegrationBasis(geometry, 0.0, 0.0, 0.0);
+  FESA_CHECK(basis.ok());
+  checkVecNear(basis.g1, {0.5, 0, 0}, 1.0e-14);
+  checkVecNear(basis.g2, {0, 0.5, 0}, 1.0e-14);
+  checkVecNear(basis.g3, {0, 0, 0.1}, 1.0e-14);
+  checkVecNear(basis.local.e1, {1, 0, 0}, 1.0e-14);
+  checkVecNear(basis.local.e2, {0, 1, 0}, 1.0e-14);
+  checkVecNear(basis.local.e3, {0, 0, 1}, 1.0e-14);
+  checkRightHandedOrthonormal(basis.local.e1, basis.local.e2, basis.local.e3);
+  FESA_CHECK_NEAR(basis.jacobian, 0.025, 1.0e-14);
+}
+
+FESA_TEST(mitc4_geometry_uses_deterministic_director_fallback_axis) {
+  const std::array<fesa::Vec3, 4> coords = {{{0, 0, 0}, {1, 0, 0}, {1, 0, -1}, {0, 0, -1}}};
+  auto geometry = fesa::buildMITC4Geometry(coords, 0.1);
+  FESA_CHECK(geometry.ok());
+  checkVecNear(geometry.center_normal, {0, 1, 0}, 1.0e-14);
+  for (const auto& frame : geometry.nodal_frames) {
+    checkVecNear(frame.v1, {-1, 0, 0}, 1.0e-14);
+    checkVecNear(frame.v2, {0, 0, 1}, 1.0e-14);
+    checkVecNear(frame.vn, {0, 1, 0}, 1.0e-14);
+    checkRightHandedOrthonormal(frame.v1, frame.v2, frame.vn);
+  }
+}
+
+FESA_TEST(mitc4_geometry_reports_singular_geometry_and_thickness) {
+  const std::array<fesa::Vec3, 4> flat = {{{0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}}};
+  auto invalid_thickness = fesa::buildMITC4Geometry(flat, 0.0);
+  FESA_CHECK(!invalid_thickness.ok());
+  FESA_CHECK(fesa::containsDiagnostic(invalid_thickness.diagnostics, "FESA-MITC4-THICKNESS"));
+
+  const std::array<fesa::Vec3, 4> collinear = {{{0, 0, 0}, {1, 0, 0}, {2, 0, 0}, {3, 0, 0}}};
+  auto singular = fesa::buildMITC4Geometry(collinear, 0.1);
+  FESA_CHECK(!singular.ok());
+  FESA_CHECK(fesa::containsDiagnostic(singular.diagnostics, "FESA-MITC4-SINGULAR-NORMAL"));
+
+  const std::array<fesa::Vec3, 4> collapsed_corner = {{{0, 0, 0}, {0, 0, 0}, {1, 1, 0}, {0, 1, 0}}};
+  auto geometry = fesa::buildMITC4Geometry(collapsed_corner, 0.1);
+  FESA_CHECK(geometry.ok());
+  auto corner_basis = fesa::computeMITC4IntegrationBasis(geometry, -1.0, -1.0, 0.0);
+  FESA_CHECK(!corner_basis.ok());
+  FESA_CHECK(fesa::containsDiagnostic(corner_basis.diagnostics, "FESA-MITC4-SINGULAR-JACOBIAN"));
+}
+
 FESA_TEST(mitc4_shape_functions_and_stiffness_baseline) {
   auto shape = fesa::shapeFunctions(0.25, -0.5);
   const fesa::Real sum = shape.n[0] + shape.n[1] + shape.n[2] + shape.n[3];