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..5154097988402f0550eee4e0291158d02a993d08 100644
--- a/ui/gfx/transform.h
+++ b/ui/gfx/transform.h
@@ -39,6 +39,19 @@ class UI_EXPORT Transform {
       : matrix_(lhs.matrix_, rhs.matrix_) {}
   ~Transform() {}
 
+  // Constructs a transform from explicit 16 matrix elements. Elements should be
+  // given in column-major order.
+  Transform(double col1row1, double col1row2, double col1row3, double col1row4,
+            double col2row1, double col2row2, double col2row3, double col2row4,
+            double col3row1, double col3row2, double col3row3, double col3row4,
+            double col4row1, double col4row2, double col4row3, double col4row4);

[Ian Vollick, 2013/01/08 23:52:54]

I'm sorry to start on this again, but can we please do row major instead? This
new constructor has horizontal columns and vertical rows, which is a little
weird, and it doesn't match how matrices are displayed in the spec.

[danakj, 2013/01/09 14:33:46]

+1

OOO for a bit today, will review this later.

+
+  // 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 col1row2, double col2row1,
+            double col2row2, double x_translation, double y_translation);
+
   bool operator==(const Transform& rhs) const { return matrix_ == rhs.matrix_; }
   bool operator!=(const Transform& rhs) const { return matrix_ != rhs.matrix_; }
 
@@ -120,6 +133,22 @@ 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;