diff --git a/pdfminer/layout.py b/pdfminer/layout.py
index 640c87e..af79a85 100644
--- a/pdfminer/layout.py
+++ b/pdfminer/layout.py
@@ -534,7 +534,8 @@ class LTLayoutContainer(LTContainer):
         return
 
     def get_textboxes(self, laparams, lines):
-        plane = Plane(lines)
+        plane = Plane(self.bbox)
+        plane.extend(lines)
         boxes = {}
         for line in lines:
             neighbors = line.find_neighbors(plane, laparams.line_margin)
@@ -596,7 +597,8 @@ class LTLayoutContainer(LTContainer):
                 obj2 = boxes[j]
                 dists.append((0, dist(obj1, obj2), obj1, obj2))
         dists.sort()
-        plane = Plane(boxes)
+        plane = Plane(self.bbox)
+        plane.extend(boxes)
         while dists:
             (c,d,obj1,obj2) = dists.pop(0)
             if c == 0 and isany(obj1, obj2):
diff --git a/pdfminer/utils.py b/pdfminer/utils.py
index 2769e20..670bca4 100644
--- a/pdfminer/utils.py
+++ b/pdfminer/utils.py
@@ -221,13 +221,11 @@ def matrix2str((a,b,c,d,e,f)):
 ##
 class Plane(object):
 
-    def __init__(self, objs=None, gridsize=50):
+    def __init__(self, bbox, gridsize=50):
         self._objs = set()
         self._grid = {}
         self.gridsize = gridsize
-        if objs is not None:
-            for obj in objs:
-                self.add(obj)
+        (self.x0, self.y0, self.x1, self.y1) = bbox
         return
 
     def __repr__(self):
@@ -243,10 +241,20 @@ class Plane(object):
         return obj in self._objs
 
     def _getrange(self, (x0,y0,x1,y1)):
+        x0 = max(self.x0, x0)
+        y0 = max(self.y0, y0)
+        x1 = min(self.x1, x1)
+        y1 = min(self.y1, y1)
         for y in drange(y0, y1, self.gridsize):
             for x in drange(x0, x1, self.gridsize):
                 yield (x,y)
         return
+
+    # extend(objs)
+    def extend(self, objs):
+        for obj in objs:
+            self.add(obj)
+        return
     
     # add(obj): place an object.
     def add(self, obj):