diff --git a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_x b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_x
index a7fb40463a5..2f32acec2da 100644
--- a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_x
+++ b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_x
@@ -33,3 +33,14 @@ parameter_space_x 12 MAX_END RIGHT_BOUNDARY
 parameter_space_x 13 MAX_END INTERIOR
 parameter_space_x 14 MAX_END INTERIOR
 parameter_space_x 15 MAX_END INTERIOR
+#
+parameter_space_x 0 INTERIOR
+parameter_space_x 1 INTERIOR
+parameter_space_x 2 INTERIOR
+parameter_space_x 3 INTERIOR
+parameter_space_x 4 INTERIOR
+parameter_space_x 5 INTERIOR
+parameter_space_x 6 INTERIOR
+parameter_space_x 7 INTERIOR
+parameter_space_x 8 INTERIOR
+
diff --git a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_y b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_y
index 50d124873ed..d384f19d33e 100644
--- a/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_y
+++ b/Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/linear/lines/parameter_space_y
@@ -33,3 +33,13 @@ parameter_space_y 12 MAX_END INTERIOR
 parameter_space_y 13 MAX_END TOP_BOUNDARY
 parameter_space_y 14 MAX_END INTERIOR
 parameter_space_y 15 MAX_END INTERIOR
+#
+parameter_space_y 0 INTERIOR
+parameter_space_y 1 INTERIOR
+parameter_space_y 2 INTERIOR
+parameter_space_y 3 INTERIOR
+parameter_space_y 4 INTERIOR
+parameter_space_y 5 INTERIOR
+parameter_space_y 6 INTERIOR
+parameter_space_y 7 INTERIOR
+parameter_space_y 8 INTERIOR