Add basic SVD support to SkMatrix. Allows you to pull out the x- and y-scale factors, sandwiched by…

src/core/SkMatrix.cpp

Index: src/core/SkMatrix.cpp
diff --git a/src/core/SkMatrix.cpp b/src/core/SkMatrix.cpp
index 13ec7ae322d0a3ff177a372557ace12382479ab1..7334b5bc552ac48a71557f981c6af5909515e93a 100644
--- a/src/core/SkMatrix.cpp
+++ b/src/core/SkMatrix.cpp
@@ -240,6 +240,71 @@ bool SkMatrix::preservesRightAngles(SkScalar tol) const {
                                SkScalarSquare(tol));
 }
 
+bool SkMatrix::decomposeUpper2x2(SkScalar* rotation0, 
+                        SkScalar* xScale, SkScalar* yScale, 
+                        SkScalar* rotation1) const {
+
+    // borrowed from Jim Blinn's article "Consider the Lowly 2x2 Matrix"
+    // Note: he uses row vectors, so we have to do some swapping of terms
+    SkScalar A = fMat[kMScaleX];
+    SkScalar B = fMat[kMSkewX];
+    SkScalar C = fMat[kMSkewY];
+    SkScalar D = fMat[kMScaleY];                            
+
+    SkScalar E = SK_ScalarHalf*(A + D);
+    SkScalar F = SK_ScalarHalf*(A - D);
+    SkScalar G = SK_ScalarHalf*(C + B);
+    SkScalar H = SK_ScalarHalf*(C - B);
+
+    SkScalar sqrt0 = SkScalarSqrt(E*E + H*H);
+    SkScalar sqrt1 = SkScalarSqrt(F*F + G*G);
+
+    // can't have zero yScale, must be degenerate
+    if (SkScalarNearlyEqual(sqrt0, sqrt1)) {
+        return false;
+    }
+    if (NULL != xScale) {
+        *xScale = sqrt0 + sqrt1;
+    }
+    if (NULL != yScale) {
+        *yScale = sqrt0 - sqrt1;
+    }
+
+    // uniformly scaled rotation
+    if (SkScalarNearlyZero(F) && SkScalarNearlyZero(G)) {
+        SkASSERT(!SkScalarNearlyZero(E));
+        if (NULL != rotation0) {
+            *rotation0 = SkScalarATan2(H, E);
+        }
+        if (NULL != rotation1) {
+            *rotation1 = 0;
+        }
+    // uniformly scaled reflection 
+    } else if (SkScalarNearlyZero(E) && SkScalarNearlyZero(H)) {
+        SkASSERT(!SkScalarNearlyZero(F));
+        if (NULL != rotation0) {
+            *rotation0 = -SkScalarATan2(G, F);
+        }
+        if (NULL != rotation1) {
+            *rotation1 = 0;
+        }
+    } else {
+        SkASSERT(!SkScalarNearlyZero(E));
+        SkASSERT(!SkScalarNearlyZero(F));
+
+        SkScalar arctan0 = SkScalarATan2(H, E);  
+        SkScalar arctan1 = SkScalarATan2(G, F);
+        if (NULL != rotation0) {
+            *rotation0 = SK_ScalarHalf*(arctan0 - arctan1);
+        }
+        if (NULL != rotation1) {
+            *rotation1 = SK_ScalarHalf*(arctan0 + arctan1);
+        }
+    }
+
+    return true;
+}
+
 ///////////////////////////////////////////////////////////////////////////////
 
 void SkMatrix::setTranslate(SkScalar dx, SkScalar dy) {