diff --git a/Bowerbird/DGridPath.cs b/Bowerbird/DGridPath.cs
index 69c95f1..4276a44 100644
--- a/Bowerbird/DGridPath.cs
+++ b/Bowerbird/DGridPath.cs
@@ -110,21 +110,22 @@ bool FindDirections(double u, double v, out Vector3d dir1, out Vector3d dir2, ou
                 return false;
             }
 
+            var normal = Vector3d.CrossProduct(refA1, refA2);
+
             if (Math.Abs(e[2]) < 1e-8)
             {
                 dir1 = refA1 / refA1.Length;
             }
             else
             {
-                var d1 = (e[0] - e[1] + tmp) / (2 * e[2]) * refA1 + refA2;
+                var alpha = Math.Atan2(2 * e[2], e[0] - e[1]) / 2;
 
-                dir1 = d1 / d1.Length;
+                dir1 = refA1 / refA1.Length;
+                dir1.Rotate(alpha, normal);
             }
 
             dir2 = dir1;
 
-            var normal = Vector3d.CrossProduct(refA1, refA2);
-
             var angle = Math.Atan(Math.Sqrt(n2 / n1));
             
             dir1.Rotate(angle, normal);
diff --git a/Bowerbird/PSPath.cs b/Bowerbird/PSPath.cs
index 2ffe255..05ab391 100644
--- a/Bowerbird/PSPath.cs
+++ b/Bowerbird/PSPath.cs
@@ -99,24 +99,23 @@ bool FindDirections(double u, double v, out Vector3d dir1, out Vector3d dir2, ou
             e.Transform(TransformToLocalCartesian(refA1, refA2));
             e.Transform(Material);
 
-            var tmp = Math.Sqrt(Math.Pow(e[0] - e[1], 2) + 4 * Math.Pow(e[2], 2));
-            var n1 = 0.5 * (e[0] + e[1] + tmp);
-            var n2 = 0.5 * (e[0] + e[1] - tmp);
+            var normal = Vector3d.CrossProduct(refA1, refA2);
 
             if (Math.Abs(e[2]) < 1e-8)
             {
                 dir1 = refA1 / refA1.Length;
-                dir2 = refA2 / refA2.Length;
             }
             else
             {
-                var d1 = (e[0] - e[1] + tmp) / (2 * e[2]) * refA1 + refA2;
-                var d2 = (e[0] - e[1] - tmp) / (2 * e[2]) * refA1 + refA2;
+                var alpha = Math.Atan2(2 * e[2], e[0] - e[1]) / 2;
 
-                dir1 = d1 / d1.Length;
-                dir2 = d2 / d2.Length;
+                dir1 = refA1 / refA1.Length;
+                dir1.Rotate(alpha, normal);
             }
 
+            dir2 = dir1;
+            dir2.Rotate(Math.PI / 2, normal);
+
             return true;
         }