diff --git a/lib/loadObj.js b/lib/loadObj.js
index 7359ff9..eb5131b 100644
--- a/lib/loadObj.js
+++ b/lib/loadObj.js
@@ -350,15 +350,17 @@ function loadObj(objPath, options) {
     }
 
     var scratch3 = new Cartesian3();
+    var scratch4 = new Cartesian3();
+    var scratch5 = new Cartesian3();
     // Checks if winding order matches the given normal.
     function checkWindingCorrect(positionIndex1, positionIndex2, positionIndex3, normal) {
         var A = get3DPoint(positionIndex1, scratch1);
         var B = get3DPoint(positionIndex2, scratch2);
         var C = get3DPoint(positionIndex3, scratch3);
 
-        Cartesian3.subtract(B, A, B);
-        Cartesian3.subtract(C, A, C);
-        var cross = Cartesian3.cross(A, C, scratch1);
+        var BA = Cartesian3.subtract(B, A, scratch4);
+        var CA = Cartesian3.subtract(C, A, scratch5);
+        var cross = Cartesian3.cross(BA, CA, scratch3);
 
         return (Cartesian3.dot(normal, cross) >= 0);
     }