Move temporary MathUtil wrappers to permanent home in gfx::Transform

This patch moves some of the temporary wrappers to their permanent home. Unit
tests remain in math_util_unittests for now, but no test coverage is lost.

Added 3 static accessors to Vector3dF help readability when calling RotateAbout().

BUG=159972

Review URL: https://codereview.chromium.org/11418197

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@170099 0039d316-1c4b-4281-b951-d872f2087c98

9 files changed, 378 insertions, 141 deletions

diff --git a/cc/layer_sorter_unittest.cc b/cc/layer_sorter_unittest.cc
index 9b13fce..94aa7b5 100644
--- a/cc/layer_sorter_unittest.cc
+++ b/cc/layer_sorter_unittest.cc
@@ -64,7 +64,7 @@ TEST(LayerSorterTest, RightAngleOverlap)
     // Two layers forming a right angle with a perspective viewing transform.
     gfx::Transform leftFaceMatrix;
     leftFaceMatrix.Translate3d(-1, 0, -5);
-    MathUtil::rotateAxisAngle(&leftFaceMatrix, 0, 1, 0, -90);
+    leftFaceMatrix.RotateAboutYAxis(-90);
     leftFaceMatrix.Translate(-1, -1);
     LayerShape leftFace(2, 2, perspectiveMatrix * leftFaceMatrix);
     gfx::Transform frontFaceMatrix;
@@ -94,7 +94,7 @@ TEST(LayerSorterTest, IntersectingLayerOverlap)
 
     gfx::Transform throughMatrix;
     throughMatrix.Translate3d(0, 0, -4);
-    MathUtil::rotateAxisAngle(&throughMatrix, 0, 1, 0, 45);
+    throughMatrix.RotateAboutYAxis(45);
     throughMatrix.Translate(-1, -1);
     LayerShape rotatedFace(2, 2, perspectiveMatrix * throughMatrix);
     overlapResult = LayerSorter::checkOverlap(&frontFace, &rotatedFace, zThreshold, weight);
@@ -131,7 +131,7 @@ TEST(LayerSorterTest, LayersAtAngleOverlap)
     LayerShape layerB(8, 20, transformB);
 
     gfx::Transform transformC;
-    MathUtil::rotateAxisAngle(&transformC, 0, 1, 0, 40);
+    transformC.RotateAboutYAxis(40);
     transformC.Translate(-4, -10);
     LayerShape layerC(8, 20, transformC);
 
diff --git a/cc/layer_tree_host_common.cc b/cc/layer_tree_host_common.cc
index b6c4c4e..0d6909c 100644
--- a/cc/layer_tree_host_common.cc
+++ b/cc/layer_tree_host_common.cc
@@ -85,21 +85,21 @@ static bool isLayerBackFaceVisible(LayerType* layer)
     // rendering context by checking if the parent preserves 3d.
 
     if (layerIsInExisting3DRenderingContext(layer))
-        return MathUtil::isBackFaceVisible(layer->drawTransform());
+        return layer->drawTransform().IsBackFaceVisible();
 
     // In this case, either the layer establishes a new 3d rendering context, or is not in
     // a 3d rendering context at all.
-    return MathUtil::isBackFaceVisible(layer->transform());
+    return layer->transform().IsBackFaceVisible();
 }
 
 template<typename LayerType>
 static bool isSurfaceBackFaceVisible(LayerType* layer, const gfx::Transform& drawTransform)
 {
     if (layerIsInExisting3DRenderingContext(layer))
-        return MathUtil::isBackFaceVisible(drawTransform);
+        return drawTransform.IsBackFaceVisible();
 
     if (isRootLayerOfNewRenderingContext(layer))
-        return MathUtil::isBackFaceVisible(layer->transform());
+        return layer->transform().IsBackFaceVisible();
 
     // If the renderSurface is not part of a new or existing rendering context, then the
     // layers that contribute to this surface will decide back-face visibility for themselves.
@@ -140,14 +140,6 @@ static gfx::Rect calculateVisibleContentRect(LayerType* layer)
     return LayerTreeHostCommon::calculateVisibleRect(targetSurfaceClipRect, gfx::Rect(gfx::Point(), layer->contentBounds()), layer->drawTransform());
 }
 
-static bool isScaleOrTranslation(const gfx::Transform& m)
-{
-    return !m.matrix().getDouble(1, 0) && !m.matrix().getDouble(2, 0) && !m.matrix().getDouble(3, 0)
-           && !m.matrix().getDouble(0, 1) && !m.matrix().getDouble(2, 1) && !m.matrix().getDouble(3, 1)
-           && !m.matrix().getDouble(0, 2) && !m.matrix().getDouble(1, 2) && !m.matrix().getDouble(2, 3)
-           && m.matrix().getDouble(3, 3);
-}
-
 static inline bool transformToParentIsKnown(LayerImpl*)
 {
     return true;
@@ -562,7 +554,7 @@ static void calculateDrawTransformsInternal(LayerType* layer, const gfx::Transfo
 
     gfx::Vector2dF renderSurfaceSublayerScale = MathUtil::computeTransform2dScaleComponents(combinedTransform);
 
-    if (subtreeShouldRenderToSeparateSurface(layer, isScaleOrTranslation(combinedTransform))) {
+    if (subtreeShouldRenderToSeparateSurface(layer, combinedTransform.IsScaleOrTranslation())) {
         // Check back-face visibility before continuing with this surface and its subtree
         if (!layer->doubleSided() && transformToParentIsKnown(layer) && isSurfaceBackFaceVisible(layer, combinedTransform))
             return;
diff --git a/cc/layer_tree_host_common_unittest.cc b/cc/layer_tree_host_common_unittest.cc
index 0623a36..6933335 100644
--- a/cc/layer_tree_host_common_unittest.cc
+++ b/cc/layer_tree_host_common_unittest.cc
@@ -2457,7 +2457,7 @@ TEST(LayerTreeHostCommonTest, verifyBackFaceCullingWithoutPreserves3d)
 
     gfx::Transform backfaceMatrix;
     backfaceMatrix.Translate(50, 50);
-    MathUtil::rotateAxisAngle(&backfaceMatrix, 0, 1, 0, 180);
+    backfaceMatrix.RotateAboutYAxis(180);
     backfaceMatrix.Translate(-50, -50);
 
     // Having a descendant and opacity will force these to have render surfaces.
@@ -2551,7 +2551,7 @@ TEST(LayerTreeHostCommonTest, verifyBackFaceCullingWithPreserves3d)
 
     gfx::Transform backfaceMatrix;
     backfaceMatrix.Translate(50, 50);
-    MathUtil::rotateAxisAngle(&backfaceMatrix, 0, 1, 0, 180);
+    backfaceMatrix.RotateAboutYAxis(180);
     backfaceMatrix.Translate(-50, -50);
 
     // Opacity will not force creation of renderSurfaces in this case because of the
@@ -2637,7 +2637,7 @@ TEST(LayerTreeHostCommonTest, verifyBackFaceCullingWithAnimatingTransforms)
 
     gfx::Transform backfaceMatrix;
     backfaceMatrix.Translate(50, 50);
-    MathUtil::rotateAxisAngle(&backfaceMatrix, 0, 1, 0, 180);
+    backfaceMatrix.RotateAboutYAxis(180);
     backfaceMatrix.Translate(-50, -50);
 
     // Make our render surface.
@@ -2712,7 +2712,7 @@ TEST(LayerTreeHostCommonTest, verifyBackFaceCullingWithPreserves3dForFlatteningS
 
     gfx::Transform backfaceMatrix;
     backfaceMatrix.Translate(50, 50);
-    MathUtil::rotateAxisAngle(&backfaceMatrix, 0, 1, 0, 180);
+    backfaceMatrix.RotateAboutYAxis(180);
     backfaceMatrix.Translate(-50, -50);
 
     setLayerPropertiesForTesting(parent.get(), identityMatrix, identityMatrix, gfx::PointF(0, 0), gfx::PointF(0, 0), gfx::Size(100, 100), true); // parent transform style is preserve3d.
diff --git a/cc/math_util.cc b/cc/math_util.cc
index 9312d10..2e0349c 100644
--- a/cc/math_util.cc
+++ b/cc/math_util.cc
@@ -107,7 +107,7 @@ gfx::Rect MathUtil::mapClippedRect(const gfx::Transform& transform, const gfx::R
 
 gfx::RectF MathUtil::mapClippedRect(const gfx::Transform& transform, const gfx::RectF& srcRect)
 {
-    if (MathUtil::isIdentityOrTranslation(transform))
+    if (transform.IsIdentityOrTranslation())
         return srcRect + gfx::Vector2dF(static_cast<float>(transform.matrix().getDouble(0, 3)), static_cast<float>(transform.matrix().getDouble(1, 3)));
 
     // Apply the transform, but retain the result in homogeneous coordinates.
@@ -122,7 +122,7 @@ gfx::RectF MathUtil::mapClippedRect(const gfx::Transform& transform, const gfx::
 
 gfx::RectF MathUtil::projectClippedRect(const gfx::Transform& transform, const gfx::RectF& srcRect)
 {
-    if (MathUtil::isIdentityOrTranslation(transform))
+    if (transform.IsIdentityOrTranslation())
         return srcRect + gfx::Vector2dF(static_cast<float>(transform.matrix().getDouble(0, 3)), static_cast<float>(transform.matrix().getDouble(1, 3)));
 
     // Perform the projection, but retain the result in homogeneous coordinates.
@@ -241,7 +241,7 @@ gfx::RectF MathUtil::computeEnclosingClippedRect(const HomogeneousCoordinate& h1
 
 gfx::QuadF MathUtil::mapQuad(const gfx::Transform& transform, const gfx::QuadF& q, bool& clipped)
 {
-    if (MathUtil::isIdentityOrTranslation(transform)) {
+    if (transform.IsIdentityOrTranslation()) {
         gfx::QuadF mappedQuad(q);
         mappedQuad += gfx::Vector2dF(static_cast<float>(transform.matrix().getDouble(0, 3)), static_cast<float>(transform.matrix().getDouble(1, 3)));
         clipped = false;
@@ -373,7 +373,7 @@ static inline float scaleOnAxis(double a, double b, double c)
 
 gfx::Vector2dF MathUtil::computeTransform2dScaleComponents(const gfx::Transform& transform)
 {
-    if (hasPerspective(transform))
+    if (transform.HasPerspective())
         return gfx::Vector2dF(1, 1);
     float xScale = scaleOnAxis(transform.matrix().getDouble(0, 0), transform.matrix().getDouble(1, 0), transform.matrix().getDouble(2, 0));
     float yScale = scaleOnAxis(transform.matrix().getDouble(0, 1), transform.matrix().getDouble(1, 1), transform.matrix().getDouble(2, 1));
@@ -394,69 +394,22 @@ gfx::Vector2dF MathUtil::projectVector(gfx::Vector2dF source, gfx::Vector2dF des
     return gfx::Vector2dF(projectedLength * destination.x(), projectedLength * destination.y());
 }
 
-bool MathUtil::isBackFaceVisible(const gfx::Transform& transform)
-{
-    // Compute whether a layer with a forward-facing normal of (0, 0, 1) would
-    // have its back face visible after applying the transform.
-    //
-    // This is done by transforming the normal and seeing if the resulting z
-    // value is positive or negative. However, note that transforming a normal
-    // actually requires using the inverse-transpose of the original transform.
-
-    // TODO (shawnsingh) make this perform more efficiently - we do not
-    // actually need to instantiate/invert/transpose any matrices, exploiting the
-    // fact that we only need to transform (0, 0, 1, 0).
-    gfx::Transform inverseTransform = MathUtil::inverse(transform);
-    const SkMatrix44& mInv = inverseTransform.matrix();
-
-    return mInv.getDouble(2, 2) < 0;
-}
-
-bool MathUtil::isIdentityOrTranslation(const gfx::Transform& transform)
-{
-    const SkMatrix44& matrix = transform.matrix();
-
-    bool hasNoPerspective = !matrix.getDouble(3, 0) && !matrix.getDouble(3, 1) && !matrix.getDouble(3, 2) && (matrix.getDouble(3, 3) == 1);
-    bool hasNoRotationOrSkew = !matrix.getDouble(0, 1) && !matrix.getDouble(0, 2) && !matrix.getDouble(1, 0) &&
-        !matrix.getDouble(1, 2) && !matrix.getDouble(2, 0) && !matrix.getDouble(2, 1);
-    bool hasNoScale = matrix.getDouble(0, 0) == 1 && matrix.getDouble(1, 1) == 1 && matrix.getDouble(2, 2) == 1;
-
-    return hasNoPerspective && hasNoRotationOrSkew && hasNoScale;
-}
-
-bool MathUtil::hasPerspective(const gfx::Transform& transform)
-{
-    // Mathematically it is a bit too strict to expect the 4th element to be
-    // equal to 1. However, the only non-perspective case where this element
-    // becomes non-1 is when it was explicitly initialized. In that case it
-    // still causes us to have a nontrivial divide-by-w, so we count it as
-    // being perspective here.
-    const SkMatrix44& matrix = transform.matrix();
-    return matrix.getDouble(3, 0) || matrix.getDouble(3, 1) || matrix.getDouble(3, 2) || (matrix.getDouble(3, 3) != 1);
-}
-
 void MathUtil::rotateEulerAngles(gfx::Transform* transform, double eulerX, double eulerY, double eulerZ)
 {
     // TODO (shawnsingh): make this implementation faster and more accurate by
-    // hard-coding each matrix instead of calling rotateAxisAngle().
+    // hard-coding each matrix instead of calling RotateAbout().
     gfx::Transform rotationAboutX;
     gfx::Transform rotationAboutY;
     gfx::Transform rotationAboutZ;
 
-    MathUtil::rotateAxisAngle(&rotationAboutX, 1, 0, 0, eulerX);
-    MathUtil::rotateAxisAngle(&rotationAboutY, 0, 1, 0, eulerY);
-    MathUtil::rotateAxisAngle(&rotationAboutZ, 0, 0, 1, eulerZ);
+    rotationAboutX.RotateAboutXAxis(eulerX);
+    rotationAboutY.RotateAboutYAxis(eulerY);
+    rotationAboutZ.RotateAboutZAxis(eulerZ);
 
     gfx::Transform composite = rotationAboutZ * rotationAboutY * rotationAboutX;
     transform->PreconcatTransform(composite);
 }
 
-void MathUtil::rotateAxisAngle(gfx::Transform* transform, double i, double j, double k, double degrees)
-{
-    gfx::Vector3dF axis(i, j, k);
-    transform->RotateAbout(axis, degrees);
-}
-
 gfx::Transform MathUtil::inverse(const gfx::Transform& transform)
 {
     gfx::Transform result;
diff --git a/cc/math_util.h b/cc/math_util.h
index 99ee46c..e3ed2d3 100644
--- a/cc/math_util.h
+++ b/cc/math_util.h
@@ -120,11 +120,7 @@ public:
     //
     // TODO(shawnsingh, vollick) we should phase out as much as possible of
     // these temporary functions, putting functionality into gfx::Transform.
-    static bool isBackFaceVisible(const gfx::Transform&);
-    static bool isIdentityOrTranslation(const gfx::Transform&);
-    static bool hasPerspective(const gfx::Transform&);
     static void rotateEulerAngles(gfx::Transform*, double eulerX, double eulerY, double eulerZ);
-    static void rotateAxisAngle(gfx::Transform*, double i, double j, double k, double degrees);
     static gfx::Transform inverse(const gfx::Transform&);
     static gfx::Transform to2dTransform(const gfx::Transform&);
     // Note carefully: the args here are labeled as per Webcore indexing conventions.
diff --git a/cc/math_util_unittest.cc b/cc/math_util_unittest.cc
index c9daf9c..0aa0523 100644
--- a/cc/math_util_unittest.cc
+++ b/cc/math_util_unittest.cc
@@ -21,27 +21,27 @@ TEST(MathUtilTest, verifyBackfaceVisibilityBasicCases)
     gfx::Transform transform;
 
     transform.MakeIdentity();
-    EXPECT_FALSE(MathUtil::isBackFaceVisible(transform));
+    EXPECT_FALSE(transform.IsBackFaceVisible());
 
     transform.MakeIdentity();
     MathUtil::rotateEulerAngles(&transform, 0, 80, 0);
-    EXPECT_FALSE(MathUtil::isBackFaceVisible(transform));
+    EXPECT_FALSE(transform.IsBackFaceVisible());
 
     transform.MakeIdentity();
     MathUtil::rotateEulerAngles(&transform, 0, 100, 0);
-    EXPECT_TRUE(MathUtil::isBackFaceVisible(transform));
+    EXPECT_TRUE(transform.IsBackFaceVisible());
 
     // Edge case, 90 degree rotation should return false.
     transform.MakeIdentity();
     MathUtil::rotateEulerAngles(&transform, 0, 90, 0);
-    EXPECT_FALSE(MathUtil::isBackFaceVisible(transform));
+    EXPECT_FALSE(transform.IsBackFaceVisible());
 }
 
 TEST(MathUtilTest, verifyBackfaceVisibilityForPerspective)
 {
     gfx::Transform layerSpaceToProjectionPlane;
 
-    // This tests if isBackFaceVisible works properly under perspective transforms.
+    // This tests if IsBackFaceVisible works properly under perspective transforms.
     // Specifically, layers that may have their back face visible in orthographic
     // projection, may not actually have back face visible under perspective projection.
 
@@ -52,7 +52,7 @@ TEST(MathUtilTest, verifyBackfaceVisibilityForPerspective)
     layerSpaceToProjectionPlane.ApplyPerspectiveDepth(1);
     layerSpaceToProjectionPlane.Translate3d(0, 0, 0);
     MathUtil::rotateEulerAngles(&layerSpaceToProjectionPlane, 0, 100, 0);
-    EXPECT_TRUE(MathUtil::isBackFaceVisible(layerSpaceToProjectionPlane));
+    EXPECT_TRUE(layerSpaceToProjectionPlane.IsBackFaceVisible());
 
     // Case 2: Layer is rotated by slightly more than 90 degrees, but shifted off to the
     //         side of the camera. Because of the wide field-of-view, the layer's front
@@ -72,12 +72,12 @@ TEST(MathUtilTest, verifyBackfaceVisibilityForPerspective)
     layerSpaceToProjectionPlane.ApplyPerspectiveDepth(1);
     layerSpaceToProjectionPlane.Translate3d(-10, 0, 0);
     MathUtil::rotateEulerAngles(&layerSpaceToProjectionPlane, 0, 100, 0);
-    EXPECT_FALSE(MathUtil::isBackFaceVisible(layerSpaceToProjectionPlane));
+    EXPECT_FALSE(layerSpaceToProjectionPlane.IsBackFaceVisible());
 
     // Case 3: Additionally rotating the layer by 180 degrees should of course show the
     //         opposite result of case 2.
     MathUtil::rotateEulerAngles(&layerSpaceToProjectionPlane, 0, 180, 0);
-    EXPECT_TRUE(MathUtil::isBackFaceVisible(layerSpaceToProjectionPlane));
+    EXPECT_TRUE(layerSpaceToProjectionPlane.IsBackFaceVisible());
 }
 
 TEST(MathUtilTest, verifyProjectionOfPerpendicularPlane)
@@ -727,13 +727,104 @@ TEST(MathUtilGfxTransformTest, verifyRotateEulerAnglesOrderOfCompositeRotations)
     EXPECT_ROW4_EQ(0, 0, 0, 1, A);
 }
 
-TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForAlignedAxes)
+TEST(MathUtilGfxTransformTest, verifyRotateAboutXAxis)
+{
+    gfx::Transform A;
+    double sin45 = 0.5 * sqrt(2.0);
+    double cos45 = sin45;
+
+    A.MakeIdentity();
+    A.RotateAboutXAxis(90);
+    EXPECT_ROW1_EQ(1, 0, 0, 0, A);
+    EXPECT_ROW2_NEAR(0, 0, -1, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(0, 1, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    A.MakeIdentity();
+    A.RotateAboutXAxis(45);
+    EXPECT_ROW1_EQ(1, 0, 0, 0, A);
+    EXPECT_ROW2_NEAR(0, cos45, -sin45, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(0, sin45, cos45, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that rotateAboutXAxis(angle) post-multiplies the existing matrix.
+    A.MakeIdentity();
+    A.Scale3d(6, 7, 8);
+    A.RotateAboutXAxis(90);
+    EXPECT_ROW1_NEAR(6, 0, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(0, 0, -7, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(0, 8, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotateAboutYAxis)
+{
+    gfx::Transform A;
+    double sin45 = 0.5 * sqrt(2.0);
+    double cos45 = sin45;
+
+    // Note carefully, the expected pattern is inverted compared to rotating about x axis or z axis.
+    A.MakeIdentity();
+    A.RotateAboutYAxis(90);
+    EXPECT_ROW1_NEAR(0, 0, 1, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_EQ(0, 1, 0, 0, A);
+    EXPECT_ROW3_NEAR(-1, 0, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    A.MakeIdentity();
+    A.RotateAboutYAxis(45);
+    EXPECT_ROW1_NEAR(cos45, 0, sin45, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_EQ(0, 1, 0, 0, A);
+    EXPECT_ROW3_NEAR(-sin45, 0, cos45, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that rotateAboutYAxis(angle) post-multiplies the existing matrix.
+    A.MakeIdentity();
+    A.Scale3d(6, 7, 8);
+    A.RotateAboutYAxis(90);
+    EXPECT_ROW1_NEAR(0, 0, 6, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(0, 7, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(-8, 0, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotateAboutZAxis)
+{
+    gfx::Transform A;
+    double sin45 = 0.5 * sqrt(2.0);
+    double cos45 = sin45;
+
+    A.MakeIdentity();
+    A.RotateAboutZAxis(90);
+    EXPECT_ROW1_NEAR(0, -1, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(1, 0, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    A.MakeIdentity();
+    A.RotateAboutZAxis(45);
+    EXPECT_ROW1_NEAR(cos45, -sin45, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(sin45, cos45, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that rotateAboutZAxis(angle) post-multiplies the existing matrix.
+    A.MakeIdentity();
+    A.Scale3d(6, 7, 8);
+    A.RotateAboutZAxis(90);
+    EXPECT_ROW1_NEAR(0, -6, 0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(7, 0,  0, 0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_EQ(0, 0, 8, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotateAboutForAlignedAxes)
 {
     gfx::Transform A;
 
     // Check rotation about z-axis
     A.MakeIdentity();
-    MathUtil::rotateAxisAngle(&A, 0, 0, 1, 90);
+    A.RotateAbout(gfx::Vector3dF(0, 0, 1), 90);
     EXPECT_ROW1_NEAR(0, -1, 0, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW2_NEAR(1, 0, 0, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW3_EQ(0, 0, 1, 0, A);
@@ -741,7 +832,7 @@ TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForAlignedAxes)
 
     // Check rotation about x-axis
     A.MakeIdentity();
-    MathUtil::rotateAxisAngle(&A, 1, 0, 0, 90);
+    A.RotateAbout(gfx::Vector3dF(1, 0, 0), 90);
     EXPECT_ROW1_EQ(1, 0, 0, 0, A);
     EXPECT_ROW2_NEAR(0, 0, -1, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW3_NEAR(0, 1, 0, 0, A, ERROR_THRESHOLD);
@@ -750,7 +841,7 @@ TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForAlignedAxes)
     // Check rotation about y-axis.
     // Note carefully, the expected pattern is inverted compared to rotating about x axis or z axis.
     A.MakeIdentity();
-    MathUtil::rotateAxisAngle(&A, 0, 1, 0, 90);
+    A.RotateAbout(gfx::Vector3dF(0, 1, 0), 90);
     EXPECT_ROW1_NEAR(0, 0, 1, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW2_EQ(0, 1, 0, 0, A);
     EXPECT_ROW3_NEAR(-1, 0, 0, 0, A, ERROR_THRESHOLD);
@@ -759,18 +850,18 @@ TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForAlignedAxes)
     // Verify that rotate3d(axis, angle) post-multiplies the existing matrix.
     A.MakeIdentity();
     A.Scale3d(6, 7, 8);
-    MathUtil::rotateAxisAngle(&A, 0, 0, 1, 90);
+    A.RotateAboutZAxis(90);
     EXPECT_ROW1_NEAR(0, -6, 0, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW2_NEAR(7, 0,  0, 0, A, ERROR_THRESHOLD);
     EXPECT_ROW3_EQ(0, 0, 8, 0, A);
     EXPECT_ROW4_EQ(0, 0, 0, 1, A);
 }
 
-TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForArbitraryAxis)
+TEST(MathUtilGfxTransformTest, verifyRotateAboutForArbitraryAxis)
 {
     // Check rotation about an arbitrary non-axis-aligned vector.
     gfx::Transform A;
-    MathUtil::rotateAxisAngle(&A, 1, 1, 1, 90);
+    A.RotateAbout(gfx::Vector3dF(1, 1, 1), 90);
     EXPECT_ROW1_NEAR(0.3333333333333334258519187,
                      -0.2440169358562924717404030,
                      0.9106836025229592124219380,
@@ -786,18 +877,18 @@ TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForArbitraryAxis)
     EXPECT_ROW4_EQ(0, 0, 0, 1, A);
 }
 
-TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForDegenerateAxis)
+TEST(MathUtilGfxTransformTest, verifyRotateAboutForDegenerateAxis)
 {
     // Check rotation about a degenerate zero vector.
     // It is expected to skip applying the rotation.
     gfx::Transform A;
 
-    MathUtil::rotateAxisAngle(&A, 0, 0, 0, 45);
+    A.RotateAbout(gfx::Vector3dF(0, 0, 0), 45);
     // Verify that A remains unchanged.
     EXPECT_TRUE(A.IsIdentity());
 
     initializeTestMatrix(&A);
-    MathUtil::rotateAxisAngle(&A, 0, 0, 0, 35);
+    A.RotateAbout(gfx::Vector3dF(0, 0, 0), 35);
 
     // Verify that A remains unchanged.
     EXPECT_ROW1_EQ(10, 14, 18, 22, A);
@@ -869,31 +960,31 @@ TEST(MathUtilGfxTransformTest, verifyHasPerspective)
 {
     gfx::Transform A;
     A.ApplyPerspectiveDepth(1);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 
     A.MakeIdentity();
     A.ApplyPerspectiveDepth(0);
-    EXPECT_FALSE(MathUtil::hasPerspective(A));
+    EXPECT_FALSE(A.HasPerspective());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 0, -1);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 1, -1);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 2, -0.3);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 3, 0.5);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 3, 0);
-    EXPECT_TRUE(MathUtil::hasPerspective(A));
+    EXPECT_TRUE(A.HasPerspective());
 }
 
 TEST(MathUtilGfxTransformTest, verifyIsInvertible)
@@ -1033,80 +1124,166 @@ TEST(MathUtilGfxTransformTest, verifyIsIdentityOrTranslation)
     gfx::Transform A;
 
     initializeTestMatrix(&A);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
 
     A.MakeIdentity();
-    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsIdentityOrTranslation());
 
-    // Modifying any non-translation components should cause isIdentityOrTranslation() to
+    // Modifying any non-translation components should cause IsIdentityOrTranslation() to
     // return false. NOTE: (0, 3), (1, 3), and (2, 3) are the translation components, so
-    // modifying them should still return true for isIdentityOrTranslation().
+    // modifying them should still return true.
     A.MakeIdentity();
     A.matrix().setDouble(0, 0, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(1, 0, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(2, 0, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 0, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(0, 1, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
 
     A.MakeIdentity();
+    A.matrix().setDouble(1, 1, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(2, 1, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(3, 1, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(0, 2, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(1, 2, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(2, 2, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(3, 2, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+
+    // Note carefully - expecting true here.
+    A.MakeIdentity();
+    A.matrix().setDouble(0, 3, 2);
+    EXPECT_TRUE(A.IsIdentityOrTranslation());
+
+    // Note carefully - expecting true here.
+    A.MakeIdentity();
+    A.matrix().setDouble(1, 3, 2);
+    EXPECT_TRUE(A.IsIdentityOrTranslation());
+
+    // Note carefully - expecting true here.
+    A.MakeIdentity();
+    A.matrix().setDouble(2, 3, 2);
+    EXPECT_TRUE(A.IsIdentityOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(3, 3, 2);
+    EXPECT_FALSE(A.IsIdentityOrTranslation());
+}
+
+TEST(MathUtilGfxTransformTest, verifyIsScaleOrTranslation)
+{
+    gfx::Transform A;
+
+    initializeTestMatrix(&A);
+    EXPECT_FALSE(A.IsScaleOrTranslation());
+
+    A.MakeIdentity();
+    EXPECT_TRUE(A.IsScaleOrTranslation());
+
+    // Modifying any non-scale or non-translation components should cause
+    // IsScaleOrTranslation() to return false. (0, 0), (1, 1), (2, 2), (0, 3),
+    // (1, 3), and (2, 3) are the scale and translation components, so
+    // modifying them should still return true.
+
+    // Note carefully - expecting true here.
+    A.MakeIdentity();
     A.matrix().setDouble(0, 0, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(1, 0, 2);
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
+    A.matrix().setDouble(2, 0, 2);
+    EXPECT_FALSE(A.IsScaleOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(3, 0, 2);
+    EXPECT_FALSE(A.IsScaleOrTranslation());
+
+    A.MakeIdentity();
+    A.matrix().setDouble(0, 1, 2);
+    EXPECT_FALSE(A.IsScaleOrTranslation());
+
+    // Note carefully - expecting true here.
+    A.MakeIdentity();
     A.matrix().setDouble(1, 1, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(2, 1, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 1, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(0, 2, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(1, 2, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
+    // Note carefully - expecting true here.
     A.MakeIdentity();
     A.matrix().setDouble(2, 2, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 2, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 
     // Note carefully - expecting true here.
     A.MakeIdentity();
     A.matrix().setDouble(0, 3, 2);
-    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
 
     // Note carefully - expecting true here.
     A.MakeIdentity();
     A.matrix().setDouble(1, 3, 2);
-    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
 
     // Note carefully - expecting true here.
     A.MakeIdentity();
     A.matrix().setDouble(2, 3, 2);
-    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_TRUE(A.IsScaleOrTranslation());
 
     A.MakeIdentity();
     A.matrix().setDouble(3, 3, 2);
-    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+    EXPECT_FALSE(A.IsScaleOrTranslation());
 }
 
 }  // namespace
diff --git a/cc/occlusion_tracker_unittest.cc b/cc/occlusion_tracker_unittest.cc
index c46e8fd..e03e849 100644
--- a/cc/occlusion_tracker_unittest.cc
+++ b/cc/occlusion_tracker_unittest.cc
@@ -1934,7 +1934,7 @@ protected:
         gfx::Transform transform;
         transform.Translate(150, 150);
         transform.ApplyPerspectiveDepth(400);
-        MathUtil::rotateAxisAngle(&transform, 1, 0, 0, -30);
+        transform.RotateAboutXAxis(-30);
         transform.Translate(-150, -150);
 
         typename Types::ContentLayerType* parent = this->createRoot(this->identityMatrix, gfx::PointF(0, 0), gfx::Size(300, 300));
@@ -1966,7 +1966,7 @@ protected:
         transform.ApplyPerspectiveDepth(10);
         transform.Translate(-250, -50);
         transform.Translate(250, 50);
-        MathUtil::rotateAxisAngle(&transform, 1, 0, 0, -167);
+        transform.RotateAboutXAxis(-167);
         transform.Translate(-250, -50);
 
         typename Types::ContentLayerType* parent = this->createRoot(this->identityMatrix, gfx::PointF(0, 0), gfx::Size(500, 100));
diff --git a/ui/gfx/transform.cc b/ui/gfx/transform.cc
index 19b59da..b75bb7f 100644
--- a/ui/gfx/transform.cc
+++ b/ui/gfx/transform.cc
@@ -49,34 +49,71 @@ void Transform::MakeIdentity() {
   matrix_.setIdentity();
 }
 
-void Transform::Rotate(double degree) {
+void Transform::RotateAboutXAxis(double degrees) {
+  double radians = degrees * M_PI / 180;
+  double cosTheta = std::cos(radians);
+  double sinTheta = std::sin(radians);
+  if (matrix_.isIdentity()) {
+      matrix_.set3x3(1, 0, 0,
+                     0, cosTheta, sinTheta,
+                     0, -sinTheta, cosTheta);
+  } else {
+    SkMatrix44 rot;
+    rot.set3x3(1, 0, 0,
+               0, cosTheta, sinTheta,
+               0, -sinTheta, cosTheta);
+    matrix_.preConcat(rot);
+  }
+}
+
+void Transform::RotateAboutYAxis(double degrees) {
+  double radians = degrees * M_PI / 180;
+  double cosTheta = std::cos(radians);
+  double sinTheta = std::sin(radians);
+  if (matrix_.isIdentity()) {
+      // Note carefully the placement of the -sinTheta for rotation about
+      // y-axis is different than rotation about x-axis or z-axis.
+      matrix_.set3x3(cosTheta, 0, -sinTheta,
+                     0, 1, 0,
+                     sinTheta, 0, cosTheta);
+  } else {
+    SkMatrix44 rot;
+    rot.set3x3(cosTheta, 0, -sinTheta,
+               0, 1, 0,
+               sinTheta, 0, cosTheta);
+    matrix_.preConcat(rot);
+  }
+}
+
+void Transform::RotateAboutZAxis(double degrees) {
+  double radians = degrees * M_PI / 180;
+  double cosTheta = std::cos(radians);
+  double sinTheta = std::sin(radians);
   if (matrix_.isIdentity()) {
-    matrix_.setRotateDegreesAbout(SkDoubleToMScalar(0),
-                                  SkDoubleToMScalar(0),
-                                  SkDoubleToMScalar(1),
-                                  SkDoubleToMScalar(degree));
+      matrix_.set3x3(cosTheta, sinTheta, 0,
+                     -sinTheta, cosTheta, 0,
+                     0, 0, 1);
   } else {
     SkMatrix44 rot;
-    rot.setRotateDegreesAbout(SkDoubleToMScalar(0),
-                              SkDoubleToMScalar(0),
-                              SkDoubleToMScalar(1),
-                              SkDoubleToMScalar(degree));
+    rot.set3x3(cosTheta, sinTheta, 0,
+               -sinTheta, cosTheta, 0,
+               0, 0, 1);
     matrix_.preConcat(rot);
   }
 }
 
-void Transform::RotateAbout(const Vector3dF& axis, double degree) {
+void Transform::RotateAbout(const Vector3dF& axis, double degrees) {
   if (matrix_.isIdentity()) {
     matrix_.setRotateDegreesAbout(SkDoubleToMScalar(axis.x()),
                                   SkDoubleToMScalar(axis.y()),
                                   SkDoubleToMScalar(axis.z()),
-                                  SkDoubleToMScalar(degree));
+                                  SkDoubleToMScalar(degrees));
   } else {
     SkMatrix44 rot;
     rot.setRotateDegreesAbout(SkDoubleToMScalar(axis.x()),
                               SkDoubleToMScalar(axis.y()),
                               SkDoubleToMScalar(axis.z()),
-                              SkDoubleToMScalar(degree));
+                              SkDoubleToMScalar(degrees));
     matrix_.preConcat(rot);
   }
 }
@@ -185,10 +222,75 @@ bool Transform::IsIdentity() const {
   return matrix_.isIdentity();
 }
 
+bool Transform::IsIdentityOrTranslation() const {
+  bool has_no_perspective = !matrix_.getDouble(3, 0) &&
+                            !matrix_.getDouble(3, 1) &&
+                            !matrix_.getDouble(3, 2) &&
+                            (matrix_.getDouble(3, 3) == 1);
+
+  bool has_no_rotation_or_skew = !matrix_.getDouble(0, 1) &&
+                                 !matrix_.getDouble(0, 2) &&
+                                 !matrix_.getDouble(1, 0) &&
+                                 !matrix_.getDouble(1, 2) &&
+                                 !matrix_.getDouble(2, 0) &&
+                                 !matrix_.getDouble(2, 1);
+
+  bool has_no_scale = matrix_.getDouble(0, 0) == 1 &&
+                      matrix_.getDouble(1, 1) == 1 &&
+                      matrix_.getDouble(2, 2) == 1;
+
+  return has_no_perspective && has_no_rotation_or_skew && has_no_scale;
+}
+
+bool Transform::IsScaleOrTranslation() const {
+  bool has_no_perspective = !matrix_.getDouble(3, 0) &&
+                            !matrix_.getDouble(3, 1) &&
+                            !matrix_.getDouble(3, 2) &&
+                            (matrix_.getDouble(3, 3) == 1);
+
+  bool has_no_rotation_or_skew = !matrix_.getDouble(0, 1) &&
+                                 !matrix_.getDouble(0, 2) &&
+                                 !matrix_.getDouble(1, 0) &&
+                                 !matrix_.getDouble(1, 2) &&
+                                 !matrix_.getDouble(2, 0) &&
+                                 !matrix_.getDouble(2, 1);
+
+  return has_no_perspective && has_no_rotation_or_skew;
+}
+
+bool Transform::HasPerspective() const {
+  return matrix_.getDouble(3, 0) ||
+         matrix_.getDouble(3, 1) ||
+         matrix_.getDouble(3, 2) ||
+         (matrix_.getDouble(3, 3) != 1);
+}
+
 bool Transform::IsInvertible() const {
   return std::abs(matrix_.determinant()) > kTooSmallForDeterminant;
 }
 
+bool Transform::IsBackFaceVisible() const {
+  // Compute whether a layer with a forward-facing normal of (0, 0, 1) would
+  // have its back face visible after applying the transform.
+  //
+  // This is done by transforming the normal and seeing if the resulting z
+  // value is positive or negative. However, note that transforming a normal
+  // actually requires using the inverse-transpose of the original transform.
+
+  // TODO (shawnsingh) make this perform more efficiently - we do not
+  // actually need to instantiate/invert/transpose any matrices, exploiting the
+  // fact that we only need to transform (0, 0, 1, 0).
+  SkMatrix44 inverse;
+  bool invertible = matrix_.invert(&inverse);
+
+  // Assume the transform does not apply if it's not invertible, so it's
+  // front face remains visible.
+  if (!invertible)
+    return false;
+
+  return inverse.getDouble(2, 2) < 0;
+}
+
 bool Transform::GetInverse(Transform* transform) const {
   return matrix_.invert(&transform->matrix_);
 }
diff --git a/ui/gfx/transform.h b/ui/gfx/transform.h
index 52d15cf..cccbe72 100644
--- a/ui/gfx/transform.h
+++ b/ui/gfx/transform.h
@@ -29,13 +29,16 @@ class UI_EXPORT Transform {
   // Resets this transform to the identity transform.
   void MakeIdentity();
 
-  // Applies the current transformation on a rotation and assigns the result
+  // Applies the current transformation on a 2d rotation and assigns the result
   // to |this|.
-  void Rotate(double degree);
+  void Rotate(double degrees) { RotateAboutZAxis(degrees); }
 
   // Applies the current transformation on an axis-angle rotation and assigns
   // the result to |this|.
-  void RotateAbout(const Vector3dF& point, double degree);
+  void RotateAboutXAxis(double degrees);
+  void RotateAboutYAxis(double degrees);
+  void RotateAboutZAxis(double degrees);
+  void RotateAbout(const Vector3dF& axis, double degrees);
 
   // Applies the current transformation on a scaling and assigns the result
   // to |this|.
@@ -67,9 +70,23 @@ class UI_EXPORT Transform {
   // Returns true if this is the identity matrix.
   bool IsIdentity() const;
 
+  // Returns true if the matrix is either identity or pure translation.
+  bool IsIdentityOrTranslation() const;
+
+  // Returns true if the matrix is has only scaling and translation components.
+  bool IsScaleOrTranslation() const;
+
+  // Returns true if the matrix has any perspective component that would
+  // change the w-component of a homogeneous point.
+  bool HasPerspective() const;
+
   // Returns true if this transform is non-singular.
   bool IsInvertible() const;
 
+  // Returns true if a layer with a forward-facing normal of (0, 0, 1) would
+  // have its back side facing frontwards after applying the transform.
+  bool IsBackFaceVisible() const;
+
   // Inverts the transform which is passed in. Returns true if successful.
   bool GetInverse(Transform* transform) const WARN_UNUSED_RESULT;