Fix polyslab tests and add interior_angle property to PolySlab

Author: weiliangjin2021

CHANGELOG.md

@@ -10,6 +10,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Added
 - `fill` and `fill_structures` argument in `td.Simulation.plot_structures()` and `td.Simulation.plot()` respectively to disable fill and plot outlines of structures only.
 - New subpixel averaging option `ContourPathAveraging` applied to dielectric material boundaries.
+- A property `interior_angle` in `PolySlab` that stores angles formed inside polygon by two adjacent edges.
 
 ### Fixed
 - Compatibility with `xarray>=2025.03`.

tests/test_components/test_sidewall.py

@@ -259,6 +259,18 @@ def test_edge_events():
     )
 
 
+@pytest.mark.parametrize("execution_number", range(50))
+def test_interior_angle(execution_number):
+    """
+    Validate that the sum of interior angels are (n-2) * np.pi.
+    """
+    N = 10  # number of vertices
+    vertices = convert_valid_polygon(np.random.random((N, 2)) * 10)
+    s = setup_polyslab(vertices, dilation=0, angle=0, bounds=(0, 0.5))
+    n_vertices = s.reference_polygon.shape[0]
+    assert np.isclose((n_vertices - 2) * np.pi, np.sum(s.interior_angle))
+
+
 @pytest.mark.parametrize("execution_number", range(50))
 def test_max_erosion_polygon(execution_number):
     """
@@ -275,18 +287,22 @@ def test_max_erosion_polygon(execution_number):
     # compute maximal allowed erosion distance
     max_dist = s._neighbor_vertices_crossing_detection(s.reference_polygon, -100)
     # verify it is indeed maximal allowed
-    dilation = -max_dist + 1e-10
+    dilation = -max_dist + 1e-8
     # avoid polygon splitting etc. case
-    if not s._edge_events_detection(s.reference_polygon, dilation, ignore_at_dist=False):
-        s = setup_polyslab(vertices, dilation, angle, bounds)
-        assert np.isclose(minimal_edge_length(s.reference_polygon), 0, atol=1e-4)
+    if s._edge_events_detection(s.reference_polygon, dilation, ignore_at_dist=False):
+        pytest.skip("Self-intersecting polygon.")
+    # avoid checking if interior angle too small
+    if any(s.interior_angle < 1e-2):
+        pytest.skip("Interior angle < 1e-2.")
+    s = setup_polyslab(vertices, dilation, angle, bounds)
+    assert np.isclose(minimal_edge_length(s.reference_polygon), 0, atol=1e-4)
 
-        # verify it is indeed maximal allowed
-        dilation = 0.0
-        bounds = (0, max_dist - 1e-10)
-        angle = np.pi / 4
-        s = setup_polyslab(vertices, dilation, angle, bounds)
-        assert np.isclose(minimal_edge_length(s.top_polygon), 0, atol=1e-4)
+    # verify it is indeed maximal allowed
+    dilation = 0.0
+    bounds = (0, max_dist - 1e-10)
+    angle = np.pi / 4
+    s = setup_polyslab(vertices, dilation, angle, bounds)
+    assert np.isclose(minimal_edge_length(s.top_polygon), 0, atol=1e-4)
 
 
 @pytest.mark.parametrize("execution_number", range(50))

tidy3d/components/geometry/polyslab.py

@@ -21,6 +21,7 @@
 from ..base import cached_property, skip_if_fields_missing
 from ..transformation import RotationAroundAxis
 from ..types import (
+    ArrayFloat1D,
     ArrayFloat2D,
     ArrayLike,
     Axis,
@@ -1216,6 +1217,28 @@ def vertices_to_array(vertices_tuple: ArrayFloat2D) -> np.ndarray:
         """Converts a list of tuples (vertices) to a numpy array."""
         return np.array(vertices_tuple)
 
+    @cached_property
+    def interior_angle(self) -> ArrayFloat1D:
+        """Angle formed inside polygon by two adjacent edges."""
+
+        def normalize(v):
+            return v / np.linalg.norm(v, axis=0)
+
+        vs_orig = self.reference_polygon.T
+        vs_next = np.roll(vs_orig, axis=-1, shift=-1)
+        vs_previous = np.roll(vs_orig, axis=-1, shift=+1)
+
+        asp = normalize(vs_next - vs_orig)
+        asm = normalize(vs_previous - vs_orig)
+
+        cos_angle = asp[0] * asm[0] + asp[1] * asm[1]
+        sin_angle = asp[0] * asm[1] - asp[1] * asm[0]
+
+        angle = np.arccos(cos_angle)
+        # concave angles
+        angle[sin_angle < 0] = 2 * np.pi - angle[sin_angle < 0]
+        return angle
+
     @staticmethod
     def _shift_vertices(
         vertices: np.ndarray, dist