feat(phase4a+4b): Newton solver + CGAL mesh I/O

Phase 4a — newton_solver.hpp:
  - newton_euclidean(): SimplicialLDLT on H (PSD); solves H·Δx = −G
  - newton_spherical(): SimplicialLDLT on −H (NSD→PSD); solves (−H)·Δx = G
  - Backtracking line search (halving α up to 20×) for global convergence
  - NewtonResult struct: x, iterations, grad_inf_norm, converged
  - 7 tests: 4 spherical (convergence, few iters, large perturbation,
    field consistency) + 3 Euclidean (triangle pinned, quad pinned,
    mixed pinned — all with natural-theta equilibrium at x=0)

Phase 4b — mesh_io.hpp:
  - read_mesh() / write_mesh(): CGAL::IO::read/write_polygon_mesh wrappers
  - load_mesh() / save_mesh(): throwing convenience versions
  - Supports OFF, OBJ, PLY (format detected by file extension)
  - 6 tests: OFF round-trip (tet + quad), OBJ round-trip, missing-file throw,
    vertex-position preservation, save/load convenience wrappers

All 75 cgal tests pass (3 skipped as before).

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

code/tests/cgal/test_mesh_io.cpp

@@ -0,0 +1,170 @@
+// test_mesh_io.cpp
+//
+// Phase 4b — CGAL::IO mesh round-trip tests.
+//
+// Tests:
+//   1. OFF write + read round-trip: vertex count, face count, edge count preserved.
+//   2. OBJ write + read round-trip: same topology checks.
+//   3. load_mesh() throws on non-existent file.
+//   4. Round-trip preserves vertex positions (within floating-point precision).
+
+#include "conformal_mesh.hpp"
+#include "mesh_builder.hpp"
+#include "mesh_io.hpp"
+#include <gtest/gtest.h>
+#include <cmath>
+#include <cstdio>
+#include <filesystem>
+#include <stdexcept>
+
+using namespace conformallab;
+
+// Helper: temp file path with given extension
+static std::string tmp_path(const char* ext)
+{
+    return std::string("/tmp/conformallab_test.") + ext;
+}
+
+// Helper: delete file if it exists
+static void rm(const std::string& path)
+{
+    std::filesystem::remove(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// OFF round-trip: tetrahedron
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, OFF_RoundTrip_Tetrahedron)
+{
+    auto path = tmp_path("off");
+    rm(path);
+
+    auto mesh_out = make_tetrahedron();
+    ASSERT_TRUE(write_mesh(path, mesh_out))
+        << "write_mesh should succeed for tetrahedron";
+
+    ConformalMesh mesh_in;
+    ASSERT_TRUE(read_mesh(path, mesh_in))
+        << "read_mesh should succeed for the written OFF file";
+
+    EXPECT_EQ(mesh_in.number_of_vertices(), mesh_out.number_of_vertices());
+    EXPECT_EQ(mesh_in.number_of_faces(),    mesh_out.number_of_faces());
+    EXPECT_EQ(mesh_in.number_of_edges(),    mesh_out.number_of_edges());
+
+    rm(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// OFF round-trip: quad strip
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, OFF_RoundTrip_QuadStrip)
+{
+    auto path = tmp_path("off");
+    rm(path);
+
+    auto mesh_out = make_quad_strip();
+    ASSERT_TRUE(write_mesh(path, mesh_out));
+
+    ConformalMesh mesh_in;
+    ASSERT_TRUE(read_mesh(path, mesh_in));
+
+    EXPECT_EQ(mesh_in.number_of_vertices(), mesh_out.number_of_vertices());
+    EXPECT_EQ(mesh_in.number_of_faces(),    mesh_out.number_of_faces());
+
+    rm(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// OBJ round-trip: tetrahedron
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, OBJ_RoundTrip_Tetrahedron)
+{
+    auto path = tmp_path("obj");
+    rm(path);
+
+    auto mesh_out = make_tetrahedron();
+    ASSERT_TRUE(write_mesh(path, mesh_out))
+        << "write_mesh (OBJ) should succeed";
+
+    ConformalMesh mesh_in;
+    ASSERT_TRUE(read_mesh(path, mesh_in))
+        << "read_mesh (OBJ) should succeed";
+
+    EXPECT_EQ(mesh_in.number_of_vertices(), mesh_out.number_of_vertices());
+    EXPECT_EQ(mesh_in.number_of_faces(),    mesh_out.number_of_faces());
+
+    rm(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// load_mesh throws on missing file
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, LoadMeshThrowsOnMissingFile)
+{
+    EXPECT_THROW(load_mesh("/tmp/does_not_exist_conflab.off"), std::runtime_error);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// Vertex positions survive a round-trip (OFF)
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, OFF_VertexPositionsPreserved)
+{
+    auto path = tmp_path("off");
+    rm(path);
+
+    auto mesh_out = make_tetrahedron();
+    ASSERT_TRUE(write_mesh(path, mesh_out));
+
+    ConformalMesh mesh_in;
+    ASSERT_TRUE(read_mesh(path, mesh_in));
+
+    // Collect and sort vertex positions from both meshes to compare
+    auto collect_sorted = [](const ConformalMesh& m) {
+        std::vector<std::array<double,3>> pts;
+        for (auto v : m.vertices()) {
+            auto p = m.point(v);
+            pts.push_back({CGAL::to_double(p.x()),
+                           CGAL::to_double(p.y()),
+                           CGAL::to_double(p.z())});
+        }
+        std::sort(pts.begin(), pts.end());
+        return pts;
+    };
+
+    auto pts_out = collect_sorted(mesh_out);
+    auto pts_in  = collect_sorted(mesh_in);
+
+    ASSERT_EQ(pts_out.size(), pts_in.size());
+    for (std::size_t i = 0; i < pts_out.size(); ++i) {
+        EXPECT_NEAR(pts_out[i][0], pts_in[i][0], 1e-10);
+        EXPECT_NEAR(pts_out[i][1], pts_in[i][1], 1e-10);
+        EXPECT_NEAR(pts_out[i][2], pts_in[i][2], 1e-10);
+    }
+
+    rm(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// save_mesh / load_mesh convenience wrappers
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(MeshIO, SaveLoadConvenienceWrappers)
+{
+    auto path = tmp_path("off");
+    rm(path);
+
+    auto mesh_out = make_quad_strip();
+    EXPECT_NO_THROW(save_mesh(path, mesh_out));
+
+    ConformalMesh mesh_in;
+    EXPECT_NO_THROW(mesh_in = load_mesh(path));
+
+    EXPECT_EQ(mesh_in.number_of_vertices(), mesh_out.number_of_vertices());
+
+    rm(path);
+}