diff --git a/src/freeroute/geometry/__init__.py b/src/freeroute/geometry/__init__.py
index 950d640..4756bc7 100644
--- a/src/freeroute/geometry/__init__.py
+++ b/src/freeroute/geometry/__init__.py
@@ -24,7 +24,7 @@ from .line import Line
 from .point import IntPoint, Point, RationalPoint, point, rational_point
 from .polygon import Polygon
 from .polygon_shape import PolygonShape
-from .polyline import Polyline, PolylineShape, segment_box
+from .polyline import Polyline, PolylineShape, segment_box, shove_segment
 from .side import Side, Signum
 from .simplex import Simplex
 from .tile import TileShape
@@ -55,4 +55,5 @@ __all__ = [
     "Polyline",
     "PolylineShape",
     "segment_box",
+    "shove_segment",
 ]
diff --git a/src/freeroute/geometry/polyline.py b/src/freeroute/geometry/polyline.py
index 303679c..b5ccbb4 100644
--- a/src/freeroute/geometry/polyline.py
+++ b/src/freeroute/geometry/polyline.py
@@ -53,6 +53,51 @@ def corner_box(corner: IntPoint, half_width: int) -> IntBox:
     )
 
 
+def shove_segment(corners: list[IntPoint], k: int, dx: int, dy: int) -> list[IntPoint]:
+    """Displace segment ``k`` (``corners[k]``-``corners[k+1]``) by ``(dx, dy)``.
+
+    ``(dx, dy)`` must be perpendicular to the segment (parallel to its adjacent
+    segments), so the trace stays orthogonal. The two endpoints ``corners[0]``
+    and ``corners[-1]`` (pad anchors) are kept fixed: if the moved segment is the
+    first or last, a jog corner is inserted so the trace still starts/ends on its
+    pad; interior neighbours simply resize. Collinear/duplicate corners are
+    dropped. This is the geometric shove primitive.
+    """
+    n = len(corners)
+    if not (0 <= k < n - 1):
+        return list(corners)
+    new_a = IntPoint(corners[k].x + dx, corners[k].y + dy)
+    new_b = IntPoint(corners[k + 1].x + dx, corners[k + 1].y + dy)
+    result: list[IntPoint] = []
+    if k == 0:
+        result.append(corners[0])  # keep the start pad; jog to the moved run
+        result.append(new_a)
+    else:
+        result.extend(corners[:k])  # neighbour segment resizes to reach new_a
+        result.append(new_a)
+    if k + 1 == n - 1:
+        result.append(new_b)
+        result.append(corners[-1])  # jog back to the end pad
+    else:
+        result.append(new_b)
+        result.extend(corners[k + 2 :])
+    return _dedupe_collinear(result)
+
+
+def _dedupe_collinear(corners: list[IntPoint]) -> list[IntPoint]:
+    out: list[IntPoint] = []
+    for p in corners:
+        if out and out[-1].x == p.x and out[-1].y == p.y:
+            continue
+        if len(out) >= 2:
+            a, b = out[-2], out[-1]
+            if (b.x - a.x) * (p.y - a.y) - (b.y - a.y) * (p.x - a.x) == 0:
+                out[-1] = p
+                continue
+        out.append(p)
+    return out
+
+
 class Polyline:
     """A trace centreline: a sequence of integer corners."""
 
diff --git a/tests/geometry/test_polyline.py b/tests/geometry/test_polyline.py
index 6a27351..c6fc5b9 100644
--- a/tests/geometry/test_polyline.py
+++ b/tests/geometry/test_polyline.py
@@ -2,7 +2,14 @@
 
 from __future__ import annotations
 
-from freeroute.geometry import IntBox, IntPoint, Polyline, PolylineShape, segment_box
+from freeroute.geometry import (
+    IntBox,
+    IntPoint,
+    Polyline,
+    PolylineShape,
+    segment_box,
+    shove_segment,
+)
 
 
 def test_polyline_segments():
@@ -42,3 +49,33 @@ def test_polyline_shape_bounding_box():
 def test_diagonal_segment_box_is_conservative_bbox():
     box = segment_box(IntPoint(0, 0), IntPoint(50, 50), 10)
     assert box == IntBox(-10, -10, 60, 60)
+
+
+# --- shove primitive --------------------------------------------------------
+
+
+def test_shove_single_segment_inserts_jogs_and_keeps_pads():
+    # a horizontal pad-to-pad trace shoved up by 30 keeps its endpoints
+    corners = [IntPoint(0, 0), IntPoint(100, 0)]
+    out = shove_segment(corners, 0, 0, 30)
+    assert [(p.x, p.y) for p in out] == [(0, 0), (0, 30), (100, 30), (100, 0)]
+    assert out[0] == corners[0] and out[-1] == corners[1]  # pads fixed
+
+
+def test_shove_interior_segment_resizes_neighbours():
+    # the middle horizontal run of a U shoved up 20; verticals resize, pads fixed
+    corners = [IntPoint(0, 0), IntPoint(0, 50), IntPoint(100, 50), IntPoint(100, 0)]
+    out = shove_segment(corners, 1, 0, 20)
+    assert [(p.x, p.y) for p in out] == [(0, 0), (0, 70), (100, 70), (100, 0)]
+
+
+def test_shove_stays_orthogonal():
+    corners = [IntPoint(0, 0), IntPoint(0, 40), IntPoint(80, 40), IntPoint(80, 0)]
+    out = shove_segment(corners, 1, 0, 15)
+    for a, b in zip(out, out[1:], strict=False):
+        assert a.x == b.x or a.y == b.y  # every segment axis-aligned
+
+
+def test_shove_out_of_range_is_noop():
+    corners = [IntPoint(0, 0), IntPoint(100, 0)]
+    assert shove_segment(corners, 5, 0, 30) == corners