Finer routing grid: --grid-resolution K with trace halos

A cell was exactly one trace plus its clearance, so a trace owning its cell
was the whole clearance model, and the 0.4 mm grid could not reach most
pins of a 0.5 mm pitch package: between two 0.3 mm pads a trace's centre
has a legal band only 0.15 mm wide. Resolution K makes cells K times
finer and has every trace claim a halo, the cells whose centre is nearer
than trace + clearance to one of its own, released again on rip-up.

K = 1 has an empty halo and is the old grid exactly (tested). On a 0.5 mm
row, K = 4 gets every pin out where K = 1 gets two. On the rc4 boards, K = 2
cuts the sense board's opens from 66 to 41 (JAR: 32) and the power board's
to 7 (JAR: 12), still with no DRC errors from freeroute's own copper.

src/freeroute/route/pipeline.py

@@ -75,6 +75,7 @@ def _via_half_board(dsn: DsnBoard, scale: int) -> int | None:
 def route_dsn_board(
     dsn: DsnBoard,
     *,
+    resolution: int = 1,
     edge_clearance_mm: float | None = None,
     layers: list[int] | None = None,
     rip_up: bool = True,
@@ -91,6 +92,7 @@ def route_dsn_board(
     clearance_board = round(_rule_clearance_dsn(dsn) * scale)
     result = route_board(
         board,
+        resolution=resolution,
         via_half=_via_half_board(dsn, scale),
         edge_clearance=edge_clearance_board,
         trace_width=width_board,
@@ -130,6 +132,7 @@ def _to_routing_result(route, dsn: DsnBoard, scale: int, layer_names: list[str])
 def build_routing_result(
     dsn: DsnBoard,
     *,
+    resolution: int = 1,
     layers: list[int] | None = None,
     rip_up: bool = True,
     max_passes: int = 10,
@@ -138,7 +141,7 @@ def build_routing_result(
     """Route ``dsn`` (grid track) and convert to a DSN-unit RoutingResult."""
     route, scale, layer_names = route_dsn_board(
         dsn, layers=layers, rip_up=rip_up, max_passes=max_passes,
-        edge_clearance_mm=edge_clearance_mm,
+        edge_clearance_mm=edge_clearance_mm, resolution=resolution,
     )
     return _to_routing_result(route, dsn, scale, layer_names)
 
@@ -146,6 +149,7 @@ def build_routing_result(
 def route_dsn_board_exact(
     dsn: DsnBoard,
     *,
+    resolution: int = 1,
     edge_clearance_mm: float | None = None,
     layers: list[int] | None = None,
     max_passes: int = 10,
@@ -165,6 +169,7 @@ def route_dsn_board_exact(
     clearance_board = round(_rule_clearance_dsn(dsn) * scale)
     exact = route_board_exact(
         board,
+        resolution=resolution,
         via_half=_via_half_board(dsn, scale),
         edge_clearance=edge_clearance_board,
         trace_width=width_board,
@@ -181,6 +186,7 @@ def route_dsn_board_exact(
 def build_exact_routing_result(
     dsn: DsnBoard,
     *,
+    resolution: int = 1,
     layers: list[int] | None = None,
     shove: bool = False,
     diagonal: bool = False,
@@ -197,6 +203,7 @@ def build_exact_routing_result(
         rip_up=rip_up,
         max_passes=max_passes,
         edge_clearance_mm=edge_clearance_mm,
+        resolution=resolution,
     )
     return _to_routing_result(exact.result, dsn, scale, layer_names)
 
@@ -255,6 +262,7 @@ def route(
     pack: bool = False,
     diagonal: bool = False,
     edge_clearance_mm: float | None = None,
+    resolution: int = 1,
 ) -> str:
     """Route a Specctra DSN string and return the routed SES string.
 
@@ -269,12 +277,15 @@ def route(
     dsn = parse_dsn(dsn_text)
     if engine == "exact":
         result = build_exact_routing_result(
-            dsn, layers=layers, shove=shove, diagonal=diagonal, edge_clearance_mm=edge_clearance_mm
+            dsn, layers=layers, shove=shove, diagonal=diagonal,
+            edge_clearance_mm=edge_clearance_mm, resolution=resolution,
         )
     elif engine == "room":
         result = build_rooms_routing_result(
             dsn, layers=layers, shove=shove, pack=pack, edge_clearance_mm=edge_clearance_mm
         )
     else:
-        result = build_routing_result(dsn, layers=layers, edge_clearance_mm=edge_clearance_mm)
+        result = build_routing_result(
+            dsn, layers=layers, edge_clearance_mm=edge_clearance_mm, resolution=resolution
+        )
     return write_ses(dsn, result)