diff --git a/exp/tests/test_geometry.py b/exp/tests/test_geometry.py
--- a/exp/tests/test_geometry.py
+++ b/exp/tests/test_geometry.py
@@ -65,3 +65,27 @@ class TestLine(TestCase):
 		self.assertAlmostEqual(r.distanceTo(a),1)
 		self.assertAlmostEqual(r.distanceTo(b),1)
 		self.assertAlmostEqual(r.distanceTo(c),0)
+
+	def testShiftBasis(self):
+		newBasis=EPoint(-200,150)
+		r=Line(0,-100)
+		r_=r.shiftBasis(newBasis)
+		self.assertAlmostEqual(r_._alpha,0)
+		self.assertAlmostEqual(r_._d,100)
+
+		s=Line(0,100)
+		s_=s.shiftBasis(newBasis)
+		self.assertAlmostEqual(s_._alpha,0)
+		self.assertAlmostEqual(s_._d,300)
+
+		newBasis=EPoint(-100,100)
+		diag=100*math.sqrt(2)
+		p=Line(math.pi*3/4,diag/2)
+		p_=p.shiftBasis(newBasis)
+		self.assertAlmostEqual(p_._alpha,math.pi*7/4)
+		self.assertAlmostEqual(p_._d,diag/2)
+
+		q=Line(math.pi*3/4,-diag/2)
+		q_=q.shiftBasis(newBasis)
+		self.assertAlmostEqual(q_._alpha,math.pi*7/4)
+		self.assertAlmostEqual(q_._d,3/2*diag)