Matrix: Switch to a better implementation of #decompose()

This now also correctly handles skewing in SVG export.

src/basic/Matrix.js

@@ -652,40 +652,39 @@ var Matrix = Base.extend(/** @lends Matrix# */{
      */
     decompose: function() {
         // http://dev.w3.org/csswg/css3-2d-transforms/#matrix-decomposition
-        // http://stackoverflow.com/questions/4361242/
+        // http://www.maths-informatique-jeux.com/blog/frederic/?post/2013/12/01/Decomposition-of-2D-transform-matrices
         // https://github.com/wisec/DOMinator/blob/master/layout/style/nsStyleAnimation.cpp#L946
-        var a = this._a, b = this._c, c = this._b, d = this._d;
-        if (Numerical.isZero(a * d - b * c))
-            return null;
-
-        var scaleX = Math.sqrt(a * a + b * b);
-        a /= scaleX;
-        b /= scaleX;
-
-        var shear = a * c + b * d;
-        c -= a * shear;
-        d -= b * shear;
-
-        var scaleY = Math.sqrt(c * c + d * d);
-        c /= scaleY;
-        d /= scaleY;
-        shear /= scaleY;
-
-        // a * d - b * c should now be 1 or -1
-        if (a * d < b * c) {
-            a = -a;
-            b = -b;
-            // We don't need c & d anymore, but if we did, we'd have to do this:
-            // c = -c;
-            // d = -d;
-            shear = -shear;
-            scaleX = -scaleX;
+        var a = this._a,
+            b = this._b,
+            c = this._c,
+            d = this._d,
+            det = a * d - b * c,
+            sqrt = Math.sqrt,
+            atan2 = Math.atan2,
+            degrees = 180 / Math.PI,
+            rotate,
+            scale,
+            skew;
+        if (a !== 0 || b !== 0) {
+            var r = sqrt(a * a + b * b);
+            rotate = Math.acos(a / r) * (b > 0 ? 1 : -1);
+            scale = [r, det / r];
+            skew = [atan2(a * c + b * d, r * r), 0];
+        } else if (c !== 0 || d !== 0) {
+            var s = sqrt(c * c + d * d);
+            // rotate = Math.PI/2 - (d > 0 ? Math.acos(-c/s) : -Math.acos(c/s));
+            rotate = Math.asin(c / s)  * (d > 0 ? 1 : -1);
+            scale = [det / s, s];
+            skew = [0, atan2(a * c + b * d, s * s)];
+        } else { // a = b = c = d = 0
+            rotate = 0;
+            skew = scale = [0, 0];
         }
-
         return {
-            scaling: new Point(scaleX, scaleY),
-            rotation: -Math.atan2(b, a) * 180 / Math.PI,
-            shearing: shear
+            translation: this.getTranslation(),
+            rotation: rotate * degrees,
+            scaling: new Point(scale),
+            skewing: new Point(skew[0] * degrees, skew[1] * degrees)
         };
     },
 

src/item/Item.js

@@ -1032,7 +1032,7 @@ new function() { // // Scope to inject various item event handlers
     beans: true,
 
     _decompose: function() {
-        return this._decomposed = this._matrix.decompose();
+        return this._decomposed || (this._decomposed = this._matrix.decompose());
     },
 
     /**
@@ -1043,7 +1043,7 @@ new function() { // // Scope to inject various item event handlers
      * @type Number
      */
     getRotation: function() {
-        var decomposed = this._decomposed || this._decompose();
+        var decomposed = this._decompose();
         return decomposed && decomposed.rotation;
     },
 
@@ -1067,7 +1067,7 @@ new function() { // // Scope to inject various item event handlers
      * @type Point
      */
     getScaling: function(_dontLink) {
-        var decomposed = this._decomposed || this._decompose(),
+        var decomposed = this._decompose(),
             scaling = decomposed && decomposed.scaling,
             ctor = _dontLink ? Point : LinkedPoint;
         return scaling && new ctor(scaling.x, scaling.y, this, 'setScaling');

src/svg/SvgExport.js

@@ -39,17 +39,22 @@ new function() {
             // See if we can decompose the matrix and can formulate it as a
             // simple translate/scale/rotate command sequence.
             var decomposed = matrix.decompose();
-            if (decomposed && !decomposed.shearing) {
+            if (decomposed) {
                 var parts = [],
                     angle = decomposed.rotation,
-                    scale = decomposed.scaling;
+                    scale = decomposed.scaling,
+                    skew = decomposed.skewing;
                 if (trans && !trans.isZero())
                     parts.push('translate(' + formatter.point(trans) + ')');
+                if (angle)
+                    parts.push('rotate(' + formatter.number(angle) + ')');
                 if (!Numerical.isZero(scale.x - 1)
                         || !Numerical.isZero(scale.y - 1))
                     parts.push('scale(' + formatter.point(scale) +')');
-                if (angle)
-                    parts.push('rotate(' + formatter.number(angle) + ')');
+                if (skew && skew.x)
+                    parts.push('skewX(' + formatter.number(skew.x) + ')');
+                if (skew && skew.y)
+                    parts.push('skewY(' + formatter.number(skew.y) + ')');
                 attrs.transform = parts.join(' ');
             } else {
                 attrs.transform = 'matrix(' + matrix.getValues().join(',') + ')';

test/tests/Matrix.js

@@ -48,19 +48,19 @@ test('Decomposition: scale()', function() {
     }
 
     testScale(1, 1);
-    testScale(1, -1, -1, 1, -180); // Decomposing results in correct flipping
-    testScale(-1, 1);
-    testScale(-1, -1, 1, 1, 180); // Decomposing results in correct flipping
+    testScale(1, -1);
+    testScale(-1, 1, 1, -1, -180); // Decomposing results in correct flipping
+    testScale(-1, -1, 1, 1, -180); // Decomposing results in correct flipping
     testScale(2, 4);
-    testScale(2, -4, -2, 4, -180); // Decomposing results in correct flipping
+    testScale(2, -4);
     testScale(4, 2);
-    testScale(-4, 2);
-    testScale(-4, -4, 4, 4, 180); // Decomposing results in correct flipping
+    testScale(-4, 2, 4, -2, -180); // Decomposing results in correct flipping
+    testScale(-4, -4, 4, 4, -180); // Decomposing results in correct flipping
 });
 
-test('Decomposition: rotate() & scale()', function() {
+test('Decomposition: scale() & rotate()', function() {
     function testAngleAndScale(sx, sy, a, ex, ey, ea) {
-        var m = new Matrix().scale(sx, sy).rotate(a),
+        var m = new Matrix().rotate(a).scale(sx, sy),
             s = 'new Matrix().scale(' + sx + ', ' + sy + ').rotate(' + a + ')';
         equals(m.getRotation(), ea || a,
                 s + '.getRotation()');
@@ -69,7 +69,7 @@ test('Decomposition: rotate() & scale()', function() {
     }
 
     testAngleAndScale(2, 4, 45);
-    testAngleAndScale(2, -4, 45, -2, 4, -135);
-    testAngleAndScale(-2, 4, 45);
+    testAngleAndScale(2, -4, 45);
+    testAngleAndScale(-2, 4, 45, 2, -4, -135);
     testAngleAndScale(-2, -4, 45, 2, 4, -135);
 });