Migrate more functions from MathUtil to gfx::Transform

ui/gfx/transform.h

Index: ui/gfx/transform.h
diff --git a/ui/gfx/transform.h b/ui/gfx/transform.h
index 95de30fa3f4c0d3275c19cd61c3e4663f232c38f..b8635b60f3adc0511c4ea3e893f77cd1d4597636 100644
--- a/ui/gfx/transform.h
+++ b/ui/gfx/transform.h
@@ -37,6 +37,18 @@ class UI_EXPORT Transform {
   // Initialize with the concatenation of lhs * rhs.
   Transform(const Transform& lhs, const Transform& rhs)
       : matrix_(lhs.matrix_, rhs.matrix_) {}
+  // Constructs a transform from explicit 16 matrix elements. NOTE: Elements

[danakj, 2013/01/11 04:14:12]

nit: drop the NOTE? the variable names kinda say this already.

Or if you feel strongly, just drop the "NOTE: " part..

+  // should be given in row-major order.
+  Transform(double col1row1, double col2row1, double col3row1, double col4row1,
+            double col1row2, double col2row2, double col3row2, double col4row2,
+            double col1row3, double col2row3, double col3row3, double col4row3,
+            double col1row4, double col2row4, double col3row4, double col4row4);
+  // Constructs a transform from explicit 2d elements. All other matrix
+  // elements remain the same as the corresponding elements of an identity
+  // matrix.
+  Transform(double col1row1, double col2row1,
+            double col1row2, double col2row2,
+            double x_translation, double y_translation);
   ~Transform() {}
 
   bool operator==(const Transform& rhs) const { return matrix_ == rhs.matrix_; }
@@ -120,6 +132,22 @@ class UI_EXPORT Transform {
   // Transposes this transform in place.
   void Transpose();
 
+  // Set 3rd row and 3rd colum to (0, 0, 1, 0). Note that this flattening
+  // operation is not quite the same as an orthographic projection and is
+  // technically not a linear operation.
+  //
+  // One useful interpretation of doing this operation:
+  //  - For x and y values, the new transform behaves effectively like an
+  //    orthographic projection was added to the matrix sequence.
+  //  - For z values, the new transform overrides any effect that the transform
+  //    had on z, and instead it preserves the z value for any points that are
+  //    transformed.
+  //  - Because of linearity of transforms, this flattened transform also
+  //    preserves the effect that any subsequent (multiplied from the right)
+  //    transforms would have on z values.
+  //
+  void FlattenTo2d();
+
   // Applies the transformation on the point. Returns true if the point is
   // transformed successfully.
   void TransformPoint(Point3F& point) const;