Add unit tests for fit_ellipse_to_points center estimation

tests/test_unit/test_fit_ellipse.py

@@ -0,0 +1,82 @@
+import numpy as np
+import pytest
+
+from derotation.analysis.fit_ellipse import fit_ellipse_to_points
+
+
+def generate_ellipse_points(
+    center=(120.0, 100.0),
+    axes=(40.0, 20.0),
+    angle=np.pi / 6,
+    n_points=200,
+    noise_std=0.5,
+):
+    """
+    Generate synthetic points lying on ellipse with optional noise.
+    """
+    cx, cy = center
+    a, b = axes
+
+    t = np.linspace(0, 2 * np.pi, n_points)
+
+    # Parametric ellipse before rotation
+    x = a * np.cos(t)
+    y = b * np.sin(t)
+
+    # Rotation matrix
+    R = np.array(
+        [
+            [np.cos(angle), -np.sin(angle)],
+            [np.sin(angle),  np.cos(angle)],
+        ]
+    )
+
+    points = R @ np.vstack((x, y))
+    points[0] += cx
+    points[1] += cy
+
+    # Add Gaussian noise
+    points += np.random.normal(scale=noise_std, size=points.shape)
+
+    return points.T
+
+
+def test_fit_ellipse_recovers_center():
+    """
+    Validate that fit_ellipse_to_points correctly estimates
+    the center of a well-defined ellipse.
+    """
+    true_center = (120.0, 100.0)
+
+    points = generate_ellipse_points(center=true_center)
+
+    center_x, center_y, a, b, theta = fit_ellipse_to_points(points)
+
+    estimated_center = np.array([center_x, center_y])
+
+    assert np.allclose(
+        estimated_center,
+        true_center,
+        atol=2.0,
+    ), f"Estimated center {estimated_center} deviates from true center {true_center}"
+
+
+def test_fit_ellipse_circle_case_center():
+    """
+    Edge case: circular ellipse (a == b).
+    """
+    true_center = (80.0, 150.0)
+
+    points = generate_ellipse_points(
+        center=true_center,
+        axes=(30.0, 30.0),
+        noise_std=0.0,
+    )
+
+    center_x, center_y, a, b, theta = fit_ellipse_to_points(points)
+
+    assert np.allclose(
+        [center_x, center_y],
+        true_center,
+        atol=1e-1,
+    )