Add test for path simplification accuracy.

tests/test_path_functionality.py

@@ -0,0 +1,47 @@
+import pathlib
+
+import numpy as np
+import pytest
+
+from pg_rad.dataloader import load_data
+from pg_rad.path import Path, path_from_RT90
+
+@pytest.fixture
+def test_df():
+    csv_path = pathlib.Path(__file__).parent / "data/coordinates.csv"
+    return load_data(csv_path)
+
+def test_piecewise_regression(test_df):
+    """_Verify whether the intermediate points deviate less than 0.1 SD._"""
+        
+    p_full = path_from_RT90(
+        test_df,
+        east_col="East",
+        north_col="North",
+        simplify_path=False
+    )
+ 
+    p_simpl = path_from_RT90(
+        test_df,
+        east_col="East",
+        north_col="North",
+        simplify_path=True
+    )
+
+    x_f = np.array(p_full.x_list)
+    y_f = np.array(p_full.y_list)
+
+    x_s = np.array(p_simpl.x_list)
+    y_s = np.array(p_simpl.y_list)
+
+    sd = np.std(y_f)
+
+    for xb, yb in zip(x_s[1:-1], y_s[1:-1]):
+        # find nearest original x index
+        idx = np.argmin(np.abs(x_f - xb))
+        deviation = abs(yb - y_f[idx])
+
+        assert deviation < 0.1 * sd, (
+            f"Breakpoint deviation too large: {deviation:.4f} "
+            f"(threshold {0.1 * sd:.4f}) at x={xb:.2f}"
+            )