diff --git a/tools/python/src/line.cpp b/tools/python/src/line.cpp
index a0393b13f..7f0eef12d 100644
--- a/tools/python/src/line.cpp
+++ b/tools/python/src/line.cpp
@@ -132,15 +132,27 @@ is perpendicular to the line.";
     !*/
         );
 
-    m.def("count_points_on_side_of_line", &count_points_on_side_of_line<long>, py::arg("l"), py::arg("reference_point"), py::arg("pts"), py::arg("dist_thresh"));
-    m.def("count_points_on_side_of_line", &count_points_on_side_of_line<double>, py::arg("l"), py::arg("reference_point"), py::arg("pts"), py::arg("dist_thresh"),
+    m.def("count_points_on_side_of_line", &count_points_on_side_of_line<long>, 
+        py::arg("l"), py::arg("reference_point"), py::arg("pts"), py::arg("dist_thresh_min")=0, py::arg("dist_thresh_max")=std::numeric_limits<double>::infinity());
+    m.def("count_points_on_side_of_line", &count_points_on_side_of_line<double>, 
+        py::arg("l"), py::arg("reference_point"), py::arg("pts"), py::arg("dist_thresh_min")=0, py::arg("dist_thresh_max")=std::numeric_limits<double>::infinity(),
 "ensures \n\
-    - Returns a count of how many points in pts are on the same side of l as \n\
-      reference_point, but also no more than dist_thresh distance from the line." 
+    - Returns a count of how many points in pts have a distance from the line l \n\
+      that is in the range [dist_thresh_min, dist_thresh_max].  This distance is a \n\
+      signed value that indicates how far a point is from the line. Moreover, if \n\
+      the point is on the same side as reference_point then the distance is \n\
+      positive, otherwise it is negative.  So for example, If this range is [0, \n\
+      infinity] then this function counts how many points are on the same side of l \n\
+      as reference_point." 
     /*!
         ensures
-            - Returns a count of how many points in pts are on the same side of l as
-              reference_point, but also no more than dist_thresh distance from the line.
+            - Returns a count of how many points in pts have a distance from the line l
+              that is in the range [dist_thresh_min, dist_thresh_max].  This distance is a
+              signed value that indicates how far a point is from the line. Moreover, if
+              the point is on the same side as reference_point then the distance is
+              positive, otherwise it is negative.  So for example, If this range is [0,
+              infinity] then this function counts how many points are on the same side of l
+              as reference_point.
     !*/
         );