test(e2e): add ECEF→WGS84 and Euler→quaternion helpers

Closed-form Heikkinen method for ECEF conversion (centimetre accuracy,
no iteration). ZYX aerospace-convention Euler → quaternion. Both needed
by upcoming VPAIRAdapter rewrite; reusable for other datasets shipping
ECEF or Euler poses (e.g. some MARS-LVIG releases).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/e2e/test_coord.py

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+"""Coordinate conversion helpers — ECEF↔WGS84 + Euler→quaternion."""
+
+import numpy as np
+import pytest
+
+from gps_denied.testing.coord import ecef_to_wgs84, euler_to_quaternion
+
+
+# --- ECEF → WGS84 ---
+
+def test_ecef_origin_is_on_equator_prime_meridian():
+    # Point on equator at lon=0, alt=0 is at x=6378137, y=0, z=0 (WGS84 semi-major)
+    lat, lon, alt = ecef_to_wgs84(6378137.0, 0.0, 0.0)
+    assert lat == pytest.approx(0.0, abs=1e-6)
+    assert lon == pytest.approx(0.0, abs=1e-6)
+    assert alt == pytest.approx(0.0, abs=1e-3)
+
+
+def test_ecef_north_pole():
+    # Semi-minor axis b ≈ 6356752.314 — north pole, lat=90, lon undefined but typically 0
+    lat, lon, alt = ecef_to_wgs84(0.0, 0.0, 6356752.314245)
+    assert lat == pytest.approx(90.0, abs=1e-4)
+    assert alt == pytest.approx(0.0, abs=1e-2)
+
+
+def test_ecef_known_point_munich():
+    # Munich, Germany: lat≈48.1351, lon≈11.5820, alt≈520 m
+    # ECEF from standard converter:
+    #   X ≈ 4177789.3, Y ≈ 855098.1, Z ≈ 4727807.9
+    lat, lon, alt = ecef_to_wgs84(4177789.3, 855098.1, 4727807.9)
+    assert lat == pytest.approx(48.1351, abs=1e-3)
+    assert lon == pytest.approx(11.5820, abs=1e-3)
+    assert alt == pytest.approx(520.0, abs=2.0)
+
+
+def test_ecef_vpair_sample_point():
+    # From VPAIR sample poses_query.txt first row:
+    #   4023518.0, 510303.75, 4906569.65  — should be in Bonn/Eifel region, Germany
+    # (VPAIR was recorded near Bonn). Expected lat ~50.7°, lon ~7.2°, alt ~(200-400) m.
+    lat, lon, alt = ecef_to_wgs84(4023518.0, 510303.75, 4906569.65)
+    assert 50.0 < lat < 51.5, f"lat={lat}"
+    assert 6.5 < lon < 8.0, f"lon={lon}"
+    # Bonn-Eifel area ground elevation 100-500 m
+    assert 100.0 < alt < 700.0, f"alt={alt}"
+
+
+# --- Euler → quaternion ---
+
+def test_euler_zero_is_identity_quaternion():
+    qx, qy, qz, qw = euler_to_quaternion(0.0, 0.0, 0.0)
+    assert qx == pytest.approx(0.0, abs=1e-12)
+    assert qy == pytest.approx(0.0, abs=1e-12)
+    assert qz == pytest.approx(0.0, abs=1e-12)
+    assert qw == pytest.approx(1.0, abs=1e-12)
+
+
+def test_euler_yaw_90_deg_about_z():
+    # Yaw = π/2 around world z, roll=pitch=0
+    # Expected quaternion: (0, 0, sin(π/4), cos(π/4)) ≈ (0, 0, 0.7071, 0.7071)
+    qx, qy, qz, qw = euler_to_quaternion(0.0, 0.0, np.pi / 2)
+    assert qx == pytest.approx(0.0, abs=1e-10)
+    assert qy == pytest.approx(0.0, abs=1e-10)
+    assert qz == pytest.approx(np.sin(np.pi / 4), abs=1e-10)
+    assert qw == pytest.approx(np.cos(np.pi / 4), abs=1e-10)
+
+
+def test_euler_roll_90_deg_about_x():
+    # Roll = π/2 around body x, pitch=yaw=0
+    qx, qy, qz, qw = euler_to_quaternion(np.pi / 2, 0.0, 0.0)
+    assert qx == pytest.approx(np.sin(np.pi / 4), abs=1e-10)
+    assert qy == pytest.approx(0.0, abs=1e-10)
+    assert qz == pytest.approx(0.0, abs=1e-10)
+    assert qw == pytest.approx(np.cos(np.pi / 4), abs=1e-10)
+
+
+def test_euler_unit_norm():
+    # Arbitrary angles — the returned quaternion must be unit norm
+    qx, qy, qz, qw = euler_to_quaternion(0.3, -0.7, 1.2)
+    norm = (qx * qx + qy * qy + qz * qz + qw * qw) ** 0.5
+    assert norm == pytest.approx(1.0, abs=1e-12)