diff --git a/src/c3nav/mapdata/models/geometry/level.py b/src/c3nav/mapdata/models/geometry/level.py
index c9c62052..0d0784cb 100644
--- a/src/c3nav/mapdata/models/geometry/level.py
+++ b/src/c3nav/mapdata/models/geometry/level.py
@@ -19,7 +19,8 @@ from c3nav.mapdata.models import Level
 from c3nav.mapdata.models.access import AccessRestrictionMixin
 from c3nav.mapdata.models.geometry.base import GeometryMixin
 from c3nav.mapdata.models.locations import SpecificLocation
-from c3nav.mapdata.utils.geometry import assert_multilinestring, assert_multipolygon, clean_geometry
+from c3nav.mapdata.utils.geometry import (assert_multilinestring, assert_multipolygon, clean_geometry,
+                                          cut_polygon_with_line)
 
 
 class LevelGeometryMixin(GeometryMixin):
@@ -193,7 +194,7 @@ class AltitudeArea(LevelGeometryMixin, models.Model):
                     if not area.geometry_prep.intersects(stair):
                         continue
 
-                    divided = assert_multipolygon(area.geometry.difference(stair.buffer(0.0001)))
+                    divided = assert_multipolygon(cut_polygon_with_line(area.geometry, stair))
                     if len(divided) > 2:
                         raise ValueError
                     area.geometry = divided[0]
diff --git a/src/c3nav/mapdata/utils/geometry.py b/src/c3nav/mapdata/utils/geometry.py
index c8ed0902..a494cd81 100644
--- a/src/c3nav/mapdata/utils/geometry.py
+++ b/src/c3nav/mapdata/utils/geometry.py
@@ -1,11 +1,14 @@
+from collections import deque, namedtuple
 from itertools import chain
+from typing import List
 
 import matplotlib.pyplot as plt
 from django.core import checks
 from matplotlib.patches import PathPatch
 from matplotlib.path import Path
 from shapely import speedups
-from shapely.geometry import LinearRing, LineString, Polygon
+from shapely.geometry import LinearRing, LineString, Point, Polygon
+from shapely.ops import unary_union
 
 if speedups.available:
     speedups.enable()
@@ -107,3 +110,86 @@ def get_rings(geometry):
         return (geometry, )
 
     return ()
+
+
+cutpoint = namedtuple('cutpoint', ('point', 'polygon', 'ring'))
+
+
+def cut_line_with_point(line, point):
+    distance = line.project(point)
+    pointlist = [(point.x, point.y)]
+    for i, p in enumerate(line.coords):
+        subdistance = line.project(Point(p))
+        if subdistance >= distance:
+            return (LineString(line.coords[:i] + pointlist),
+                    LineString(pointlist + line.coords[i+(1 if subdistance == distance else 0):]))
+
+
+def cut_polygon_with_line(polygon, line):
+    polygons: List[List[LinearRing]] = [[polygon.exterior, *polygon.interiors]
+                                        for polygon in assert_multipolygon(polygon)]
+
+    points = deque()
+    for i, polygon in polygons:
+        for j, ring in polygon:
+            intersection = ring.intersection(line)
+            for item in getattr(intersection, 'geoms', (intersection, )):
+                if isinstance(item, Point):
+                    points.append(cutpoint(item, i, j))
+                elif isinstance(item, LineString):
+                    points.append(cutpoint(item.coords[0], i, j))
+                    points.append(cutpoint(item.coords[-1], i, j))
+                else:
+                    raise ValueError
+
+    points = deque(sorted(points, key=lambda p: line.project(p.point)))
+
+    last = points.popleft()
+    while points:
+        current = points.popleft()
+        if current.polygon == last.polygon:
+            polygon = polygons[current.polygon]
+            if current.ring != last.ring:
+                ring1 = cut_line_with_point(polygon[last.ring], last.point)
+                ring2 = cut_line_with_point(polygon[current.ring], current.point)
+                new_ring = LinearRing(ring1[:-1] + ring1[0:] + ring2[:-1] + ring2[0:] + ring1[:1])
+                if current.ring == 0 or last.ring == 0:
+                    polygon[0] = new_ring
+                    interior = current.ring if last.ring == 0 else last.ring
+                    polygon[interior] = None
+                    mapping = {interior: 0}
+                else:
+                    new_i = len(polygon)
+                    mapping = {last.ring: new_i, current.ring: new_i}
+                    polygon.append(new_ring)
+                    polygon[last.ring] = None
+                    polygon[current.ring] = None
+
+                points = deque((cutpoint(item.point, item.polygon, mapping[item.ring])
+                                if (item.polygon == current.polygon and item.ring in mapping) else item)
+                               for item in points)
+            elif current.ring == 0:
+                new_i = len(polygons)
+                exterior = cut_line_with_point(polygon[0], current.point)
+                exterior = cut_line_with_point(LinearRing(exterior[:-1] + exterior[0:]), last.point)
+                exterior1 = LinearRing(exterior[0][0:] + exterior[0][:1])
+                exterior2 = LinearRing(exterior[1][0:] + exterior[1][:1])
+                geom = Polygon(exterior1)
+                polygon[0] = exterior1
+                new_polygon = [exterior2]
+                polygons.append(new_polygon)
+                mapping = {}
+                for i, interior in enumerate(polygon[1:]):
+                    if not geom.contains(interior):
+                        mapping[i] = len(new_polygon)
+                        new_polygon.append(interior)
+
+                points = deque((cutpoint(item.point, new_i, mapping[item.ring])
+                                if (item.polygon == current.polygon and item.ring in mapping) else item)
+                               for item in points)
+                points = deque((cutpoint(item.point, new_i, 0)
+                                if (item.polygon == current.polygon and item.ring == 0 and
+                                    not exterior1.contains(item.point)) else item)
+                               for item in points)
+
+    return unary_union(tuple(Polygon(polygon[0], polygon[1:]) for polygon in polygons))