diff --git a/test/geometry/test_0d1d_intersection.cc b/test/geometry/test_0d1d_intersection.cc
index 15bd5730e9053368d640c43abc8e0e41b9a3a69b..68286011de8e303e9f9171d311c3389a9355a15b 100644
--- a/test/geometry/test_0d1d_intersection.cc
+++ b/test/geometry/test_0d1d_intersection.cc
@@ -49,12 +49,25 @@ void testIntersections(std::vector<bool>& returns)
         GlobalPosition p5 = a - (b - a);
         GlobalPosition p6(0.5*scaling);
 
+        GlobalPosition delta = b - a;
+        delta *= 1.5e-7;
+        GlobalPosition p7 = a - delta;
+        GlobalPosition p8 = b + delta;
+        GlobalPosition p9 = a + delta;
+        GlobalPosition p10 = b - delta;
+
         returns.push_back(testIntersection(a, b, p1, true));
         returns.push_back(testIntersection(a, b, p2, true));
         returns.push_back(testIntersection(a, b, p3, true));
         returns.push_back(testIntersection(a, b, p4));
         returns.push_back(testIntersection(a, b, p5));
         returns.push_back(testIntersection(a, b, p6));
+
+        // test cases where the point is just on or just outside the segment
+        returns.push_back(testIntersection(a, b, p7));
+        returns.push_back(testIntersection(a, b, p8));
+        returns.push_back(testIntersection(a, b, p9, true));
+        returns.push_back(testIntersection(a, b, p10, true));
     }
 }
 
diff --git a/test/geometry/test_0d2d_intersection.cc b/test/geometry/test_0d2d_intersection.cc
index 077def4387df5b5a88601b7531671ca994b6cf96..a9209b13da2065a62c111b27c0500a548519c7b1 100644
--- a/test/geometry/test_0d2d_intersection.cc
+++ b/test/geometry/test_0d2d_intersection.cc
@@ -45,6 +45,10 @@ void runIntersectionTest(std::vector<bool>& returns, const Transformation& trans
     returns.push_back(testIntersection(triangle, transform({0.5, 0.51}), false, verbose));
     returns.push_back(testIntersection(triangle, transform({0.0, -0.01}), false, verbose));
 
+    // test cases where the point is just inside or just outside the triangle
+    returns.push_back(testIntersection(triangle, transform({0.0, -1.5e-7}), false, verbose));
+    returns.push_back(testIntersection(triangle, transform({1.0+1.5e-7, 1.5e-7}), false, verbose));
+
     // test quadrilateral-point intersections
     if (verbose) std::cout << "\n  -- Test quadrilateral-point intersections" << std::endl;
 
@@ -64,6 +68,9 @@ void runIntersectionTest(std::vector<bool>& returns, const Transformation& trans
     returns.push_back(testIntersection(quadrilateral, transform({0.5, 1.01}), false, verbose));
     returns.push_back(testIntersection(quadrilateral, transform({0.0, -0.01}), false, verbose));
 
+    // test cases where the point is just inside or just outside the triangle
+    returns.push_back(testIntersection(quadrilateral, transform({0.0, -1.5e-7}), false, verbose));
+    returns.push_back(testIntersection(quadrilateral, transform({1.0+1.5e-7, 1.5e-7}), false, verbose));
 }
 
 template<class Transformation>