feat(geometry): add arc segment support to PolySlab geometry

[weiliangjin2021]

Note

Medium Risk
Changes core geometry computations (inside, intersections, bounds, area/perimeter) and adds new validation constraints, which could subtly affect existing workflows; functionality is gated behind bulges but touches commonly used code paths.

Overview
Adds first-class arc-edge support to PolySlab via an optional bulges array (bulge = tan(θ/4)), including canonicalization of vertices/bulges, arc discretization for Shapely operations, and arc-aware bounds, inside/intersection geometry, and area/perimeter calculations (affecting volume/surface area).

Introduces new validation rules for bulges (length match, finite values, no self-intersecting arc polygons, and rejecting zero-length edges with nonzero bulge) and temporarily restricts arc polyslabs to vertical sidewalls with no dilation; adjoint derivative computation now explicitly raises NotImplementedError when arcs are present. Schemas and tests are updated to serialize/validate bulges across simulation types and cover the new behaviors.

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Side intersections not updated for arc segments

Medium Severity

_intersections_side uses self.reference_polygon (straight-edged vertices) for the vertical sidewall case, while inside and _intersections_normal were both updated to use self._discretized_reference_polygon. This means side-view cross-sections of a PolySlab with arc segments will show straight edges instead of curves, producing incorrect geometry in visualizations and any downstream computations relying on intersections_2d with a non-normal axis.

Additional Locations (2)

• tidy3d/components/geometry/polyslab.py#L661-L663
• tidy3d/components/geometry/polyslab.py#L778-L780

 

[github-actions]

Diff Coverage

Diff: origin/develop...HEAD, staged and unstaged changes

• tidy3d/components/geometry/polyslab.py (94.2%): Missing lines 1283,1291,1302,1367,1453,1512,1541,1950-1951,1969-1972

Summary

• Total: 226 lines
• Missing: 13 lines
• Coverage: 94%

tidy3d/components/geometry/polyslab.py

Lines 1279-1287

  1279             chord_vec = p1 - p0
  1280             chord_length = np.linalg.norm(chord_vec)
  1281 
  1282             if math.isclose(chord_length, 0):
! 1283                 continue
  1284 
  1285             # θ = 4 * atan(|bulge|)
  1286             theta = 4.0 * np.arctan(abs(b))

---

Lines 1287-1295

  1287 
  1288             # Radius: r = chord / (2 * sin(θ/2))
  1289             half_theta = theta / 2.0
  1290             if math.isclose(half_theta, 0) or math.isclose(np.sin(half_theta), 0):
! 1291                 continue
  1292             radius = chord_length / (2.0 * np.sin(half_theta))
  1293 
  1294             # Circular segment area: A = r² * (θ - sin(θ)) / 2
  1295             segment_area = (radius**2) * (theta - np.sin(theta)) / 2.0

---

Lines 1298-1306

  1298             # negative bulge subtracts area
  1299             if b > 0:
  1300                 base_area += segment_area
  1301             else:
! 1302                 base_area -= segment_area
  1303 
  1304         return base_area
  1305 
  1306     @staticmethod

---

Lines 1363-1371

  1363         chord_vec = p1 - p0
  1364         chord_length = np.linalg.norm(chord_vec)
  1365 
  1366         if math.isclose(chord_length, 0):
! 1367             raise SetupError("Arc endpoints are coincident; cannot define arc.")
  1368 
  1369         if math.isclose(bulge, 0):
  1370             # Degenerate case: straight line, no arc
  1371             return {

---

Lines 1449-1457

  1449             Shape (num_points, 2).
  1450         """
  1451         if math.isclose(bulge, 0):
  1452             # Straight line: just return endpoint
! 1453             return np.array([p1])
  1454 
  1455         arc = PolySlab._arc_from_bulge(p0, p1, bulge)
  1456         center = arc["center"]
  1457         radius = arc["radius"]

---

Lines 1508-1516

  1508 
  1509         # r = chord / (2 * sin(θ/2))
  1510         half_theta = theta / 2.0
  1511         if math.isclose(half_theta, 0):
! 1512             return chord_length
  1513         radius = chord_length / (2.0 * np.sin(half_theta))
  1514 
  1515         # arc_length = r * |θ|
  1516         return radius * theta

---

Lines 1537-1545

  1537         p1 = np.asarray(p1, dtype=float)
  1538 
  1539         if math.isclose(bulge, 0):
  1540             # Straight line
! 1541             return np.minimum(p0, p1), np.maximum(p0, p1)
  1542 
  1543         # Use discretized arc points to compute bounds (robust approach)
  1544         arc_points = PolySlab._discretize_arc(p0, p1, bulge)
  1545         all_points = np.vstack([p0, arc_points])

---

Lines 1946-1955

  1946         length = z_max - z_min
  1947 
  1948         # Use arc-aware area calculation when arc segments present
  1949         if self._has_arc_segments:
! 1950             top_area = abs(self._area_with_arcs(self.top_polygon, self._bulges))
! 1951             base_area = abs(self._area_with_arcs(self.base_polygon, self._bulges))
  1952         else:
  1953             top_area = abs(self._area(self.top_polygon))
  1954             base_area = abs(self._area(self.base_polygon))

---

Lines 1965-1976

  1965         base_polygon = self.base_polygon
  1966 
  1967         # Use arc-aware calculations when arc segments present
  1968         if self._has_arc_segments:
! 1969             top_area = abs(self._area_with_arcs(top_polygon, self._bulges))
! 1970             base_area = abs(self._area_with_arcs(base_polygon, self._bulges))
! 1971             top_perim = self._perimeter_with_arcs(top_polygon, self._bulges)
! 1972             base_perim = self._perimeter_with_arcs(base_polygon, self._bulges)
  1973         else:
  1974             top_area = abs(self._area(top_polygon))
  1975             base_area = abs(self._area(base_polygon))
  1976             top_perim = self._perimeter(top_polygon)

---