Use QR decomposition or it all goes wrong!

Author: photonstorm

src/gameobjects/components/TransformMatrix.js

@@ -727,7 +727,11 @@ var TransformMatrix = new Class({
     },
 
     /**
-     * Decompose this Matrix into its translation, scale and rotation values.
+     * Decompose this Matrix into its translation, scale and rotation values using QR decomposition.
+     * 
+     * The result must be applied in the following order to reproduce the current matrix:
+     * 
+     * translate -> rotate -> scale
      *
      * @method Phaser.GameObjects.Components.TransformMatrix#decomposeMatrix
      * @since 3.0.0
@@ -750,21 +754,33 @@ var TransformMatrix = new Class({
         var c = matrix[2];
         var d = matrix[3];
 
-        var a2 = a * a;
-        var b2 = b * b;
-        var c2 = c * c;
-        var d2 = d * d;
-
-        var sx = Math.sqrt(a2 + c2);
-        var sy = Math.sqrt(b2 + d2);
+        var determ = a * d - b * c;
 
         decomposedMatrix.translateX = matrix[4];
         decomposedMatrix.translateY = matrix[5];
 
-        decomposedMatrix.scaleX = sx;
-        decomposedMatrix.scaleY = sy;
+        if (a || b)
+        {
+            var r = Math.sqrt(a * a + b * b);
 
-        decomposedMatrix.rotation = Math.acos(a / sx) * (Math.atan(-c / a) < 0 ? -1 : 1);
+            decomposedMatrix.rotation = (b > 0) ? Math.acos(a / r) : -Math.acos(a / r);
+            decomposedMatrix.scaleX = r;
+            decomposedMatrix.scaleY = determ / r;
+        }
+        else if (c || d)
+        {
+            var s = Math.sqrt(c * c + d * d);
+
+            decomposedMatrix.rotation = Math.PI * 0.5 - (d > 0 ? Math.acos(-c / s) : -Math.acos(c / s));
+            decomposedMatrix.scaleX = determ / s;
+            decomposedMatrix.scaleY = s;
+        }
+        else
+        {
+            decomposedMatrix.rotation = 0;
+            decomposedMatrix.scaleX = 0;
+            decomposedMatrix.scaleY = 0;
+        }
 
         return decomposedMatrix;
     },