diff --git a/src/basic/Line.js b/src/basic/Line.js
index b8fae4ec..2aeb7aa3 100644
--- a/src/basic/Line.js
+++ b/src/basic/Line.js
@@ -133,14 +133,25 @@ var Line = Base.extend(/** @lends Line# */{
             if (!Numerical.isZero(cross)) {
                 var dx = p1x - p2x,
                     dy = p1y - p2y,
-                    t1 = (v2x * dy - v2y * dx) / cross,
-                    t2 = (v1x * dy - v1y * dx) / cross;
+                    u1 = (v2x * dy - v2y * dx) / cross,
+                    u2 = (v1x * dy - v1y * dx) / cross,
+                    // Compare the u values with EPSILON tolerance over the
+                    // [0, 1] bounds.
+                    uMin = -/*#=*/Numerical.EPSILON,
+                    uMax = 1 + uMin;
                 // Check the ranges of t parameters if the line is not allowed
                 // to extend beyond the definition points.
-                if (isInfinite || 0 <= t1 && t1 <= 1 && 0 <= t2 && t2 <= 1)
+                if (isInfinite
+                        || uMin < u1 && u1 < uMax && uMin < u2 && u2 < uMax) {
+                    if (!isInfinite) {
+                        // Address the tolerance at the bounds by clipping to
+                        // the actual range.
+                        u1 = u1 < 0 ? 0 : u1 > 1 ? 1 : u1;
+                    }
                     return new Point(
-                            p1x + t1 * v1x,
-                            p1y + t1 * v1y);
+                            p1x + u1 * v1x,
+                            p1y + u1 * v1y);
+                }
             }
         },
 
diff --git a/src/path/Curve.js b/src/path/Curve.js
index f4bc01cb..f33926c0 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -1379,11 +1379,11 @@ new function() { // Scope for intersection using bezier fat-line clipping
         //   which connects back to the beginning, but only if it's not part of
         //   a found overlap. The normal intersection will already be found at
         //   the beginning, and would be added twice otherwise.
-        if (t1 >= (startConnected ? tMin : 0) &&
+        if (t1 !== null && t1 >= (startConnected ? tMin : 0) &&
             t1 <= (endConnected ? tMax : 1)) {
             if (t2 == null)
                 t2 = Curve.getParameterOf(v2, p2.x, p2.y);
-            if (t2 >= (endConnected ? tMin : 0) &&
+            if (t2 !== null && t2 >= (endConnected ? tMin : 0) &&
                 t2 <= (startConnected ? tMax : 1)) {
                 // TODO: Don't we need to check the range of t2 as well? Does it
                 // also need startConnected / endConnected values?
diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index d1853cd5..1afbe575 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -112,7 +112,7 @@ var Numerical = new function() {
         KAPPA: 4 * (sqrt(2) - 1) / 3,
 
         /**
-         * Check if the value is 0, within a tolerance defined by
+         * Checks if the value is 0, within a tolerance defined by
          * Numerical.EPSILON.
          */
         isZero: function(val) {