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.

tests/route/test_real_board_geometry.py

@@ -51,16 +51,25 @@ def test_routes_keep_edge_clearance_at_a_rounded_corner():
                 assert outline.edge_distance(p) >= half + 500 * scale - 1
 
 
-@pytest.mark.xfail(
-    strict=True,
-    reason="known gap: the grid step (trace + clearance, 0.4 mm here) does not line up "
-    "with a 0.5 mm pin row, so only the outer pins get a column; the FreeRouting JAR, "
-    "being gridless, routes all five. This is most of the gap on an LQFP.",
-)
-def test_every_pin_of_a_half_millimetre_pitch_row_escapes():
-    # five pads at 0.5 mm pitch, each wired to its own pad 8 mm away
+@pytest.mark.parametrize(("resolution", "escape"), [(1, 2), (4, 5)])
+def test_every_pin_of_a_half_millimetre_pitch_row_escapes(resolution, escape):
+    # Five 0.3 mm pads at 0.5 mm pitch, each wired to its own pad 8 mm away.
+    # Between two neighbours a trace's centre has a legal band only 0.15 mm
+    # wide. At resolution 1 the 0.4 mm grid misses most bands; at 4 its
+    # 0.1 mm columns cannot, and every pin gets out, as the JAR manages.
     places = " ".join(f"(place R{i} {6000 + 500 * i} -6000 front 0)" for i in range(5))
     places += " " + " ".join(f"(place F{i} {6000 + 500 * i} -14000 front 0)" for i in range(5))
     nets = " ".join(f"(net N{i} (pins R{i}-1 F{i}-1))" for i in range(5))
-    result, _, _ = route_dsn_board_exact(parse_dsn(_dsn(f"(component P {places})", nets)))
-    assert len(result.routed_net_numbers) == 5
+    result, _, _ = route_dsn_board_exact(
+        parse_dsn(_dsn(f"(component P {places})", nets)), resolution=resolution
+    )
+    assert len(result.routed_net_numbers) == escape
+
+
+def test_resolution_one_has_no_halo_so_the_grid_is_unchanged():
+    from freeroute.route.grid_router import GridRouter
+
+    board = build_board(parse_dsn(_dsn("", "")))
+    assert GridRouter(board, trace_width=2500, clearance=1500)._halo_offsets == []
+    fine = GridRouter(board, trace_width=2500, clearance=1500, resolution=2)
+    assert fine.step == 2000 and (1, 0) in fine._halo_offsets and (2, 0) not in fine._halo_offsets