Model pads and vias as KiCad places them

Measured against KiCad's own pads on the TerraHawk rc4 power stage:

- Back-side parts kept their pads on F.Cu (32 pads). Mirror the copper
  layer for a back-side part.
- Pad outlines were copied unrotated (29 pads on rotated parts). Place the
  outline through the same chain as the pin: pin rotation, back-side
  mirror, part rotation. Oval pads, a path with a width, came out as a
  zero-height sliver; pad them out by the aperture.
- Multi-shape padstacks used the first shape; use the largest.
- Footprint-level keepouts were parsed but never placed. KiCad exports a
  mounting hole's plated ring that way, so the router could not see it.
- Vias were sized like a trace (0.25 mm square for a 0.6 mm via), and every
  remaining short and clearance error was a via. Read the size from the
  DSN's via padstack and use it in all three engines; the grid engine now
  reserves the cells a via's copper reaches.

With these the exact and room engines route that board with no shorts,
clearance or other DRC errors. Pins now carry their component reference.

src/freeroute/route/exact_router.py

@@ -90,6 +90,7 @@ def route_board_exact(
     diagonal: bool = False,
     max_shove_depth: int = 5,
     shove_cap: int = 3,
+    via_half: int | None = None,
 ) -> ExactRouteResult:
     """Route ``board`` orthogonally and verify the result with exact geometry.
 
@@ -102,6 +103,7 @@ def route_board_exact(
         i for i, layer in enumerate(board.layer_structure.arr) if layer.is_signal
     ]
     half_width = max(trace_width // 2, 1)
+    via_half = via_half or half_width
     step = trace_width + clearance
 
     result = route_board(
@@ -113,6 +115,7 @@ def route_board_exact(
         max_passes=max_passes,
         rip_up=rip_up,
         orthogonal=True,
+        via_half=via_half,
     )
 
     tree = ShapeSearchTree()
@@ -141,7 +144,7 @@ def route_board_exact(
     accepted: dict[int, _Accepted] = {}
 
     for net_no in sorted(set(result.wires) | set(result.vias)):
-        boxes = _net_boxes(result, net_no, half_width, via_layers)
+        boxes = _net_boxes(result, net_no, half_width, via_layers, via_half)
         if any(
             tree.clearance_conflict(box, net_no, layer, clearance)
             for box, box_layers in boxes
@@ -543,15 +546,14 @@ def _rollback(shoved, accepted, tree, owner) -> int:  # noqa: ARG001
 # --- helpers -----------------------------------------------------------------
 
 
-def _net_boxes(result, net_no, half_width, via_layers):
+def _net_boxes(result, net_no, half_width, via_layers, via_half=None):
+    via_half = via_half or half_width
     boxes: list[tuple[IntBox, frozenset[int]]] = []
     for layer, points in result.wires.get(net_no, []):
         for box in PolylineShape(Polyline(points), half_width).tiles():
             boxes.append((box, frozenset({layer})))
     for loc in result.vias.get(net_no, []):
-        vbox = IntBox(
-            loc.x - half_width, loc.y - half_width, loc.x + half_width, loc.y + half_width
-        )
+        vbox = IntBox(loc.x - via_half, loc.y - via_half, loc.x + via_half, loc.y + via_half)
         boxes.append((vbox, via_layers))
     return boxes