More robust matrix decomposition

ui/gfx/transform_util.cc

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "ui/gfx/transform_util.h"
 
 #include <algorithm>
 #include <cmath>
 
 #include "base/logging.h"
 #include "base/strings/stringprintf.h"
 #include "ui/gfx/point.h"
 #include "ui/gfx/point3_f.h"
 #include "ui/gfx/rect.h"
 
 namespace gfx {
 
 namespace {
 
 SkMScalar Length3(SkMScalar v[3]) {
   double vd[3] = {SkMScalarToDouble(v[0]), SkMScalarToDouble(v[1]),
                   SkMScalarToDouble(v[2])};
   return SkDoubleToMScalar(
       std::sqrt(vd[0] * vd[0] + vd[1] * vd[1] + vd[2] * vd[2]));
 }
 
-void Scale3(SkMScalar v[3], SkMScalar scale) {
-  for (int i = 0; i < 3; ++i)
-    v[i] *= scale;
-}
-
 template <int n>
 SkMScalar Dot(const SkMScalar* a, const SkMScalar* b) {
   double total = 0.0;
   for (int i = 0; i < n; ++i)
     total += a[i] * b[i];
   return SkDoubleToMScalar(total);
 }
 
 template <int n>
 void Combine(SkMScalar* out,
@@ skipping 323 matching lines @@
   for (int i = 0; i < 3; i++)
     decomp->translate[i] = matrix.get(i, 3);
 
   SkMScalar row[3][3];
   for (int i = 0; i < 3; i++)
     for (int j = 0; j < 3; ++j)
       row[i][j] = matrix.get(j, i);
 
   // Compute X scale factor and normalize first row.
   decomp->scale[0] = Length3(row[0]);
-  if (decomp->scale[0] != 0.0)
-    Scale3(row[0], 1.0 / decomp->scale[0]);
+  if (decomp->scale[0] != 0.0) {
+    row[0][0] /= decomp->scale[0];
+    row[0][1] /= decomp->scale[0];
+    row[0][2] /= decomp->scale[0];
+  }
 
   // Compute XY shear factor and make 2nd row orthogonal to 1st.
   decomp->skew[0] = Dot<3>(row[0], row[1]);
   Combine<3>(row[1], row[1], row[0], 1.0, -decomp->skew[0]);
 
   // Now, compute Y scale and normalize 2nd row.
   decomp->scale[1] = Length3(row[1]);
-  if (decomp->scale[1] != 0.0)
-    Scale3(row[1], 1.0 / decomp->scale[1]);
+  if (decomp->scale[1] != 0.0) {
+    row[1][0] /= decomp->scale[1];
+    row[1][1] /= decomp->scale[1];
+    row[1][2] /= decomp->scale[1];
+  }
 
   decomp->skew[0] /= decomp->scale[1];
 
   // Compute XZ and YZ shears, orthogonalize 3rd row
   decomp->skew[1] = Dot<3>(row[0], row[2]);
   Combine<3>(row[2], row[2], row[0], 1.0, -decomp->skew[1]);
   decomp->skew[2] = Dot<3>(row[1], row[2]);
   Combine<3>(row[2], row[2], row[1], 1.0, -decomp->skew[2]);
 
   // Next, get Z scale and normalize 3rd row.
   decomp->scale[2] = Length3(row[2]);
-  if (decomp->scale[2] != 0.0)
-    Scale3(row[2], 1.0 / decomp->scale[2]);
+  if (decomp->scale[2] != 0.0) {
+    row[2][0] /= decomp->scale[2];
+    row[2][1] /= decomp->scale[2];
+    row[2][2] /= decomp->scale[2];
+  }
 
   decomp->skew[1] /= decomp->scale[2];
   decomp->skew[2] /= decomp->scale[2];
 
   // At this point, the matrix (in rows) is orthonormal.
   // Check for a coordinate system flip.  If the determinant
   // is -1, then negate the matrix and the scaling factors.
   SkMScalar pdum3[3];
   Cross3(pdum3, row[1], row[2]);
   if (Dot<3>(row[0], pdum3) < 0) {
@@ skipping 83 matching lines @@
       perspective[1],
       perspective[2],
       perspective[3],
       quaternion[0],
       quaternion[1],
       quaternion[2],
       quaternion[3]);
 }
 
 }  // namespace ui