Let pins on turned fine-pitch pads leave along the pad's axis

A QFN placed at 45 degrees had no exit on the grid: every horizontal or
vertical step from a pin passes its neighbours inside clearance. A pin whose
pad is turned more than ten degrees off the grid axes now leaves along the
pad's own axis, away from the part, until an L from there to a grid cell
clears every other net's pad, then searches as usual. The slanted leg is
checked and stored as an exact slab (segment_slab), not its bounding box,
in the grid stub checks and in the exact engine.

Where pins leave side by side, a cell names only its first owner, so stubs
are also indexed per cell for every connection near them; the exact
stub-vs-stub check, trace entry and rip-up all consult that index. A pin
with an axis exit and no clear cell reports no way out instead of falling
back to a cell on another net's route. diagnose.py replays with the exits.

src/freeroute/geometry/__init__.py

@@ -21,7 +21,7 @@ from .direction import Direction, IntDirection
 from .float_point import FloatPoint
 from .limits import CRIT_DOUBLE, CRIT_INT
 from .line import Line
-from .octagon import ceil_sqrt2, overlaps_2d, segment_octagon
+from .octagon import ceil_sqrt2, overlaps_2d, segment_octagon, segment_slab
 from .point import IntPoint, Point, RationalPoint, point, rational_point
 from .polygon import Polygon
 from .polygon_shape import PolygonShape
@@ -59,5 +59,6 @@ __all__ = [
     "shove_segment",
     "ceil_sqrt2",
     "segment_octagon",
+    "segment_slab",
     "overlaps_2d",
 ]

src/freeroute/geometry/octagon.py

@@ -29,7 +29,7 @@ from .line import Line
 from .point import IntPoint
 from .simplex import Simplex
 
-__all__ = ["ceil_sqrt2", "segment_octagon", "overlaps_2d"]
+__all__ = ["ceil_sqrt2", "segment_octagon", "segment_slab", "overlaps_2d"]
 
 
 def ceil_sqrt2(radius: int) -> int:
@@ -82,6 +82,46 @@ def segment_octagon(a: IntPoint, b: IntPoint, radius: int) -> Simplex:
     return Simplex.get_instance(lines)
 
 
+def segment_slab(a: IntPoint, b: IntPoint, radius: int) -> Simplex:
+    """Convex cover of segment ``a``-``b`` swept by ``radius``, at any angle.
+
+    The rectangle along the segment, ``radius`` either side, with flush ends
+    like :func:`polyline.segment_box`: the ends of a trace leg sit on a pad or
+    on the square corner tile of the next leg, which cover them. Corners are
+    rounded away from the middle and the radius gets one unit more, so the
+    side bounds never under-report, and it stays tight for a slanted segment
+    off the 45-degree lines (a pin leaving along its pad's axis on a part
+    turned 30 degrees).
+    """
+    dx, dy = b.x - a.x, b.y - a.y
+    length = math.hypot(dx, dy)
+    r = max(radius, 0) + 1
+    if length == 0:
+        return Simplex.from_corners([
+            IntPoint(a.x - r, a.y - r), IntPoint(a.x + r, a.y - r),
+            IntPoint(a.x + r, a.y + r), IntPoint(a.x - r, a.y + r),
+        ])
+    ux, uy = dx / length, dy / length
+    nx, ny = -uy, ux
+    mx, my = (a.x + b.x) / 2, (a.y + b.y) / 2
+
+    def out(x: float, y: float) -> IntPoint:
+        return IntPoint(math.ceil(x) if x >= mx else math.floor(x),
+                        math.ceil(y) if y >= my else math.floor(y))
+
+    corners = [
+        out(a.x + nx * r, a.y + ny * r),
+        out(b.x + nx * r, b.y + ny * r),
+        out(b.x - nx * r, b.y - ny * r),
+        out(a.x - nx * r, a.y - ny * r),
+    ]
+    for winding in (corners, corners[::-1]):
+        slab = Simplex.from_corners(winding)
+        if not slab.is_empty():
+            return slab
+    return Simplex(())
+
+
 def overlaps_2d(shape_a, shape_b) -> bool:
     """True if the two convex tiles share 2-D area (a real clearance overlap).