Implement unit tests and temporary MathUtil wrappers for transform functionality

These unit tests and wrappers have a short-term home in MathUtil so that we can
safely migrate from WebTransformationMatrix to gfx::Transform in a follow-up
patch. After the migration, we will then proceed to phase out this temporary
code and beef up ui/gfx/transform.h nicely.

BUG=159972

Review URL: https://codereview.chromium.org/11316043

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@168571 0039d316-1c4b-4281-b951-d872f2087c98

1 files changed, 909 insertions, 0 deletions

diff --git a/cc/math_util_unittest.cc b/cc/math_util_unittest.cc
index c29bb12..93a980f 100644
--- a/cc/math_util_unittest.cc
+++ b/cc/math_util_unittest.cc
@@ -180,5 +180,914 @@ TEST(MathUtilTest, vectorProjection)
               projectedVector.y() / targetVector.y());
 }
 
+// TODO(shawnsingh): these macros are redundant with those from
+// web_transformation_matrix_unittests, but for now they
+// are different enough to be appropriate here.
+
+#define EXPECT_ROW1_EQ(a, b, c, d, transform)                 \
+    EXPECT_FLOAT_EQ((a), (transform).matrix().getDouble(0, 0));     \
+    EXPECT_FLOAT_EQ((b), (transform).matrix().getDouble(0, 1));     \
+    EXPECT_FLOAT_EQ((c), (transform).matrix().getDouble(0, 2));     \
+    EXPECT_FLOAT_EQ((d), (transform).matrix().getDouble(0, 3));
+
+#define EXPECT_ROW2_EQ(a, b, c, d, transform)                 \
+    EXPECT_FLOAT_EQ((a), (transform).matrix().getDouble(1, 0));     \
+    EXPECT_FLOAT_EQ((b), (transform).matrix().getDouble(1, 1));     \
+    EXPECT_FLOAT_EQ((c), (transform).matrix().getDouble(1, 2));     \
+    EXPECT_FLOAT_EQ((d), (transform).matrix().getDouble(1, 3));
+
+#define EXPECT_ROW3_EQ(a, b, c, d, transform)              \
+    EXPECT_FLOAT_EQ((a), (transform).matrix().getDouble(2, 0));  \
+    EXPECT_FLOAT_EQ((b), (transform).matrix().getDouble(2, 1));  \
+    EXPECT_FLOAT_EQ((c), (transform).matrix().getDouble(2, 2));  \
+    EXPECT_FLOAT_EQ((d), (transform).matrix().getDouble(2, 3));
+
+#define EXPECT_ROW4_EQ(a, b, c, d, transform)              \
+    EXPECT_FLOAT_EQ((a), (transform).matrix().getDouble(3, 0));  \
+    EXPECT_FLOAT_EQ((b), (transform).matrix().getDouble(3, 1));  \
+    EXPECT_FLOAT_EQ((c), (transform).matrix().getDouble(3, 2));  \
+    EXPECT_FLOAT_EQ((d), (transform).matrix().getDouble(3, 3));
+
+// Checking float values for equality close to zero is not robust using EXPECT_FLOAT_EQ
+// (see gtest documentation). So, to verify rotation matrices, we must use a looser
+// absolute error threshold in some places.
+#define EXPECT_ROW1_NEAR(a, b, c, d, transform, errorThreshold)            \
+    EXPECT_NEAR((a), (transform).matrix().getDouble(0, 0), (errorThreshold));    \
+    EXPECT_NEAR((b), (transform).matrix().getDouble(0, 1), (errorThreshold));    \
+    EXPECT_NEAR((c), (transform).matrix().getDouble(0, 2), (errorThreshold));    \
+    EXPECT_NEAR((d), (transform).matrix().getDouble(0, 3), (errorThreshold));
+
+#define EXPECT_ROW2_NEAR(a, b, c, d, transform, errorThreshold)            \
+    EXPECT_NEAR((a), (transform).matrix().getDouble(1, 0), (errorThreshold));    \
+    EXPECT_NEAR((b), (transform).matrix().getDouble(1, 1), (errorThreshold));    \
+    EXPECT_NEAR((c), (transform).matrix().getDouble(1, 2), (errorThreshold));    \
+    EXPECT_NEAR((d), (transform).matrix().getDouble(1, 3), (errorThreshold));
+
+#define EXPECT_ROW3_NEAR(a, b, c, d, transform, errorThreshold)            \
+    EXPECT_NEAR((a), (transform).matrix().getDouble(2, 0), (errorThreshold));    \
+    EXPECT_NEAR((b), (transform).matrix().getDouble(2, 1), (errorThreshold));    \
+    EXPECT_NEAR((c), (transform).matrix().getDouble(2, 2), (errorThreshold));    \
+    EXPECT_NEAR((d), (transform).matrix().getDouble(2, 3), (errorThreshold));
+
+#define ERROR_THRESHOLD 1e-14
+#define LOOSE_ERROR_THRESHOLD 1e-7
+
+static void initializeTestMatrix(gfx::Transform* transform)
+{
+    SkMatrix44& matrix = transform->matrix();
+    matrix.setDouble(0, 0, 10);
+    matrix.setDouble(1, 0, 11);
+    matrix.setDouble(2, 0, 12);
+    matrix.setDouble(3, 0, 13);
+    matrix.setDouble(0, 1, 14);
+    matrix.setDouble(1, 1, 15);
+    matrix.setDouble(2, 1, 16);
+    matrix.setDouble(3, 1, 17);
+    matrix.setDouble(0, 2, 18);
+    matrix.setDouble(1, 2, 19);
+    matrix.setDouble(2, 2, 20);
+    matrix.setDouble(3, 2, 21);
+    matrix.setDouble(0, 3, 22);
+    matrix.setDouble(1, 3, 23);
+    matrix.setDouble(2, 3, 24);
+    matrix.setDouble(3, 3, 25);
+
+    // Sanity check
+    EXPECT_ROW1_EQ(10, 14, 18, 22, (*transform));
+    EXPECT_ROW2_EQ(11, 15, 19, 23, (*transform));
+    EXPECT_ROW3_EQ(12, 16, 20, 24, (*transform));
+    EXPECT_ROW4_EQ(13, 17, 21, 25, (*transform));
+}
+
+static void initializeTestMatrix2(gfx::Transform* transform)
+{
+    SkMatrix44& matrix = transform->matrix();
+    matrix.setDouble(0, 0, 30);
+    matrix.setDouble(1, 0, 31);
+    matrix.setDouble(2, 0, 32);
+    matrix.setDouble(3, 0, 33);
+    matrix.setDouble(0, 1, 34);
+    matrix.setDouble(1, 1, 35);
+    matrix.setDouble(2, 1, 36);
+    matrix.setDouble(3, 1, 37);
+    matrix.setDouble(0, 2, 38);
+    matrix.setDouble(1, 2, 39);
+    matrix.setDouble(2, 2, 40);
+    matrix.setDouble(3, 2, 41);
+    matrix.setDouble(0, 3, 42);
+    matrix.setDouble(1, 3, 43);
+    matrix.setDouble(2, 3, 44);
+    matrix.setDouble(3, 3, 45);
+
+    // Sanity check
+    EXPECT_ROW1_EQ(30, 34, 38, 42, (*transform));
+    EXPECT_ROW2_EQ(31, 35, 39, 43, (*transform));
+    EXPECT_ROW3_EQ(32, 36, 40, 44, (*transform));
+    EXPECT_ROW4_EQ(33, 37, 41, 45, (*transform));
+}
+
+TEST(MathUtilGfxTransformTest, verifyDefaultConstructorCreatesIdentityMatrix)
+{
+    gfx::Transform A;
+    EXPECT_ROW1_EQ(1, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 1, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+    EXPECT_TRUE(MathUtil::isIdentity(A));
+}
+
+TEST(MathUtilGfxTransformTest, verifyCreateGfxTransformFor2dElements)
+{
+    gfx::Transform A = MathUtil::createGfxTransform(1, 2, 3, 4, 5, 6);
+    EXPECT_ROW1_EQ(1, 3, 0, 5, A);
+    EXPECT_ROW2_EQ(2, 4, 0, 6, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyCreateGfxTransformForAllElements)
+{
+    gfx::Transform A = MathUtil::createGfxTransform(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16);
+    EXPECT_ROW1_EQ(1, 5,  9, 13, A);
+    EXPECT_ROW2_EQ(2, 6, 10, 14, A);
+    EXPECT_ROW3_EQ(3, 7, 11, 15, A);
+    EXPECT_ROW4_EQ(4, 8, 12, 16, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyCopyConstructor)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+
+    // Copy constructor should produce exact same elements as matrix A.
+    gfx::Transform B(A);
+    EXPECT_ROW1_EQ(10, 14, 18, 22, B);
+    EXPECT_ROW2_EQ(11, 15, 19, 23, B);
+    EXPECT_ROW3_EQ(12, 16, 20, 24, B);
+    EXPECT_ROW4_EQ(13, 17, 21, 25, B);
+}
+
+TEST(MathUtilGfxTransformTest, verifyMatrixInversion)
+{
+    // Invert a translation
+    gfx::Transform translation;
+    translation.PreconcatTranslate3d(2, 3, 4);
+    EXPECT_TRUE(MathUtil::isInvertible(translation));
+
+    gfx::Transform inverseTranslation = MathUtil::inverse(translation);
+    EXPECT_ROW1_EQ(1, 0, 0, -2, inverseTranslation);
+    EXPECT_ROW2_EQ(0, 1, 0, -3, inverseTranslation);
+    EXPECT_ROW3_EQ(0, 0, 1, -4, inverseTranslation);
+    EXPECT_ROW4_EQ(0, 0, 0,  1, inverseTranslation);
+
+    // Note that inversion should not have changed the original matrix.
+    EXPECT_ROW1_EQ(1, 0, 0, 2, translation);
+    EXPECT_ROW2_EQ(0, 1, 0, 3, translation);
+    EXPECT_ROW3_EQ(0, 0, 1, 4, translation);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, translation);
+
+    // Invert a non-uniform scale
+    gfx::Transform scale;
+    scale.PreconcatScale3d(4, 10, 100);
+    EXPECT_TRUE(MathUtil::isInvertible(scale));
+
+    gfx::Transform inverseScale = MathUtil::inverse(scale);
+    EXPECT_ROW1_EQ(0.25,   0,    0, 0, inverseScale);
+    EXPECT_ROW2_EQ(0,    .1f,    0, 0, inverseScale);
+    EXPECT_ROW3_EQ(0,      0, .01f, 0, inverseScale);
+    EXPECT_ROW4_EQ(0,      0,    0, 1, inverseScale);
+
+    // Try to invert a matrix that is not invertible.
+    // The inverse() function should simply return an identity matrix.
+    gfx::Transform notInvertible;
+    notInvertible.matrix().setDouble(0, 0, 0);
+    notInvertible.matrix().setDouble(1, 1, 0);
+    notInvertible.matrix().setDouble(2, 2, 0);
+    notInvertible.matrix().setDouble(3, 3, 0);
+    EXPECT_FALSE(MathUtil::isInvertible(notInvertible));
+
+    gfx::Transform inverseOfNotInvertible;
+    initializeTestMatrix(&inverseOfNotInvertible); // initialize this to something non-identity, to make sure that assignment below actually took place.
+    inverseOfNotInvertible = MathUtil::inverse(notInvertible);
+    EXPECT_TRUE(MathUtil::isIdentity(inverseOfNotInvertible));
+}
+
+TEST(MathUtilGfxTransformTest, verifyTo2DTransform)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+
+    gfx::Transform B = MathUtil::to2dTransform(A);
+
+    EXPECT_ROW1_EQ(10, 14, 0, 22, B);
+    EXPECT_ROW2_EQ(11, 15, 0, 23, B);
+    EXPECT_ROW3_EQ(0,  0,  1, 0,  B);
+    EXPECT_ROW4_EQ(13, 17, 0, 25, B);
+
+    // Note that to2DTransform should not have changed the original matrix.
+    EXPECT_ROW1_EQ(10, 14, 18, 22, A);
+    EXPECT_ROW2_EQ(11, 15, 19, 23, A);
+    EXPECT_ROW3_EQ(12, 16, 20, 24, A);
+    EXPECT_ROW4_EQ(13, 17, 21, 25, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyAssignmentOperator)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+    gfx::Transform B;
+    initializeTestMatrix2(&B);
+    gfx::Transform C;
+    initializeTestMatrix2(&C);
+    C = B = A;
+
+    // Both B and C should now have been re-assigned to the value of A.
+    EXPECT_ROW1_EQ(10, 14, 18, 22, B);
+    EXPECT_ROW2_EQ(11, 15, 19, 23, B);
+    EXPECT_ROW3_EQ(12, 16, 20, 24, B);
+    EXPECT_ROW4_EQ(13, 17, 21, 25, B);
+
+    EXPECT_ROW1_EQ(10, 14, 18, 22, C);
+    EXPECT_ROW2_EQ(11, 15, 19, 23, C);
+    EXPECT_ROW3_EQ(12, 16, 20, 24, C);
+    EXPECT_ROW4_EQ(13, 17, 21, 25, C);
+}
+
+TEST(MathUtilGfxTransformTest, verifyEqualsBooleanOperator)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+
+    gfx::Transform B;
+    initializeTestMatrix(&B);
+    EXPECT_TRUE(A == B);
+
+    // Modifying multiple elements should cause equals operator to return false.
+    gfx::Transform C;
+    initializeTestMatrix2(&C);
+    EXPECT_FALSE(A == C);
+
+    // Modifying any one individual element should cause equals operator to return false.
+    gfx::Transform D;
+    D = A;
+    D.matrix().setDouble(0, 0, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(1, 0, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(2, 0, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(3, 0, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(0, 1, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(1, 1, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(2, 1, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(3, 1, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(0, 2, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(1, 2, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(2, 2, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(3, 2, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(0, 3, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(1, 3, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(2, 3, 0);
+    EXPECT_FALSE(A == D);
+
+    D = A;
+    D.matrix().setDouble(3, 3, 0);
+    EXPECT_FALSE(A == D);
+}
+
+TEST(MathUtilGfxTransformTest, verifyMultiplyOperator)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+
+    gfx::Transform B;
+    initializeTestMatrix2(&B);
+
+    gfx::Transform C = A * B;
+    EXPECT_ROW1_EQ(2036, 2292, 2548, 2804, C);
+    EXPECT_ROW2_EQ(2162, 2434, 2706, 2978, C);
+    EXPECT_ROW3_EQ(2288, 2576, 2864, 3152, C);
+    EXPECT_ROW4_EQ(2414, 2718, 3022, 3326, C);
+
+    // Just an additional sanity check; matrix multiplication is not commutative.
+    EXPECT_FALSE(A * B == B * A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyMatrixMultiplication)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+
+    gfx::Transform B;
+    initializeTestMatrix2(&B);
+
+    A.PreconcatTransform(B);
+    EXPECT_ROW1_EQ(2036, 2292, 2548, 2804, A);
+    EXPECT_ROW2_EQ(2162, 2434, 2706, 2978, A);
+    EXPECT_ROW3_EQ(2288, 2576, 2864, 3152, A);
+    EXPECT_ROW4_EQ(2414, 2718, 3022, 3326, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyMakeIdentiy)
+{
+    gfx::Transform A;
+    initializeTestMatrix(&A);
+    MathUtil::makeIdentity(&A);
+    EXPECT_ROW1_EQ(1, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 1, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+    EXPECT_TRUE(MathUtil::isIdentity(A));
+}
+
+TEST(MathUtilGfxTransformTest, verifyTranslate)
+{
+    gfx::Transform A;
+    A.PreconcatTranslate(2, 3);
+    EXPECT_ROW1_EQ(1, 0, 0, 2, A);
+    EXPECT_ROW2_EQ(0, 1, 0, 3, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that PreconcatTranslate() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale(5, 5);
+    A.PreconcatTranslate(2, 3);
+    EXPECT_ROW1_EQ(5, 0, 0, 10, A);
+    EXPECT_ROW2_EQ(0, 5, 0, 15, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0,  A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1,  A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyTranslate3d)
+{
+    gfx::Transform A;
+    A.PreconcatTranslate3d(2, 3, 4);
+    EXPECT_ROW1_EQ(1, 0, 0, 2, A);
+    EXPECT_ROW2_EQ(0, 1, 0, 3, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 4, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that PreconcatTranslate3d() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    A.PreconcatTranslate3d(2, 3, 4);
+    EXPECT_ROW1_EQ(6, 0, 0, 12, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 21, A);
+    EXPECT_ROW3_EQ(0, 0, 8, 32, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1,  A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyScale)
+{
+    gfx::Transform A;
+    A.PreconcatScale(6, 7);
+    EXPECT_ROW1_EQ(6, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that PreconcatScale() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatTranslate3d(2, 3, 4);
+    A.PreconcatScale(6, 7);
+    EXPECT_ROW1_EQ(6, 0, 0, 2, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 3, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 4, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyScale3d)
+{
+    gfx::Transform A;
+    A.PreconcatScale3d(6, 7, 8);
+    EXPECT_ROW1_EQ(6, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 8, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that scale3d() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatTranslate3d(2, 3, 4);
+    A.PreconcatScale3d(6, 7, 8);
+    EXPECT_ROW1_EQ(6, 0, 0, 2, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 3, A);
+    EXPECT_ROW3_EQ(0, 0, 8, 4, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotate)
+{
+    gfx::Transform A;
+    A.PreconcatRotate(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);
+
+    // Verify that PreconcatRotate() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    A.PreconcatRotate(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, verifyRotateEulerAngles)
+{
+    gfx::Transform A;
+
+    // Check rotation about z-axis
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateEulerAngles(&A, 0, 0, 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);
+
+    // Check rotation about x-axis
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateEulerAngles(&A, 90, 0, 0);
+    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);
+
+    // Check rotation about y-axis.
+    // Note carefully, the expected pattern is inverted compared to rotating about x axis or z axis.
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateEulerAngles(&A, 0, 90, 0);
+    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);
+
+    // Verify that rotate3d(rx, ry, rz) post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    MathUtil::rotateEulerAngles(&A, 0, 0, 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, verifyRotateEulerAnglesOrderOfCompositeRotations)
+{
+    // Rotate3d(degreesX, degreesY, degreesZ) is actually composite transform consiting of
+    // three primitive rotations. This test verifies that the ordering of those three
+    // transforms is the intended ordering.
+    //
+    // The correct ordering for this test case should be:
+    //   1. rotate by 30 degrees about z-axis
+    //   2. rotate by 20 degrees about y-axis
+    //   3. rotate by 10 degrees about x-axis
+    //
+    // Note: there are 6 possible orderings of 3 transforms. For the specific transforms
+    // used in this test, all 6 combinations produce a unique matrix that is different
+    // from the other orderings. That way, this test verifies the exact ordering.
+
+    gfx::Transform A;
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateEulerAngles(&A, 10, 20, 30);
+
+    EXPECT_ROW1_NEAR(0.8137976813493738026394908,
+                     -0.4409696105298823720630708,
+                     0.3785223063697923939763257,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(0.4698463103929541584413698,
+                     0.8825641192593856043657752,
+                     0.0180283112362972230968694,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(-0.3420201433256686573969318,
+                     0.1631759111665348205288950,
+                     0.9254165783983233639631294,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForAlignedAxes)
+{
+    gfx::Transform A;
+
+    // Check rotation about z-axis
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateAxisAngle(&A, 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);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Check rotation about x-axis
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateAxisAngle(&A, 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);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Check rotation about y-axis.
+    // Note carefully, the expected pattern is inverted compared to rotating about x axis or z axis.
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateAxisAngle(&A, 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);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that rotate3d(axis, angle) post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    MathUtil::rotateAxisAngle(&A, 0, 0, 1, 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)
+{
+    // Check rotation about an arbitrary non-axis-aligned vector.
+    gfx::Transform A;
+    MathUtil::rotateAxisAngle(&A, 1, 1, 1, 90);
+    EXPECT_ROW1_NEAR(0.3333333333333334258519187,
+                     -0.2440169358562924717404030,
+                     0.9106836025229592124219380,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW2_NEAR(0.9106836025229592124219380,
+                     0.3333333333333334258519187,
+                     -0.2440169358562924717404030,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW3_NEAR(-0.2440169358562924717404030,
+                     0.9106836025229592124219380,
+                     0.3333333333333334258519187,
+                     0, A, ERROR_THRESHOLD);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyRotateAxisAngleForDegenerateAxis)
+{
+    // 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);
+    // Verify that A remains unchanged.
+    EXPECT_TRUE(MathUtil::isIdentity(A));
+
+    initializeTestMatrix(&A);
+    MathUtil::rotateAxisAngle(&A, 0, 0, 0, 35);
+
+    // Verify that A remains unchanged.
+    EXPECT_ROW1_EQ(10, 14, 18, 22, A);
+    EXPECT_ROW2_EQ(11, 15, 19, 23, A);
+    EXPECT_ROW3_EQ(12, 16, 20, 24, A);
+    EXPECT_ROW4_EQ(13, 17, 21, 25, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifySkewX)
+{
+    gfx::Transform A;
+    A.PreconcatSkewX(45);
+    EXPECT_ROW1_EQ(1, 1, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 1, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that skewX() post-multiplies the existing matrix.
+    // Row 1, column 2, would incorrectly have value "7" if the matrix is pre-multiplied instead of post-multiplied.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    A.PreconcatSkewX(45);
+    EXPECT_ROW1_EQ(6, 6, 0, 0, A);
+    EXPECT_ROW2_EQ(0, 7, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 8, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifySkewY)
+{
+    gfx::Transform A;
+    A.PreconcatSkewY(45);
+    EXPECT_ROW1_EQ(1, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(1, 1, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+
+    // Verify that skewY() post-multiplies the existing matrix.
+    // Row 2, column 1, would incorrectly have value "6" if the matrix is pre-multiplied instead of post-multiplied.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    A.PreconcatSkewY(45);
+    EXPECT_ROW1_EQ(6, 0, 0, 0, A);
+    EXPECT_ROW2_EQ(7, 7, 0, 0, A);
+    EXPECT_ROW3_EQ(0, 0, 8, 0, A);
+    EXPECT_ROW4_EQ(0, 0, 0, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyPerspectiveDepth)
+{
+    gfx::Transform A;
+    A.PreconcatPerspectiveDepth(1);
+    EXPECT_ROW1_EQ(1, 0,  0, 0, A);
+    EXPECT_ROW2_EQ(0, 1,  0, 0, A);
+    EXPECT_ROW3_EQ(0, 0,  1, 0, A);
+    EXPECT_ROW4_EQ(0, 0, -1, 1, A);
+
+    // Verify that PreconcatPerspectiveDepth() post-multiplies the existing matrix.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatTranslate3d(2, 3, 4);
+    A.PreconcatPerspectiveDepth(1);
+    EXPECT_ROW1_EQ(1, 0, -2, 2, A);
+    EXPECT_ROW2_EQ(0, 1, -3, 3, A);
+    EXPECT_ROW3_EQ(0, 0, -3, 4, A);
+    EXPECT_ROW4_EQ(0, 0, -1, 1, A);
+}
+
+TEST(MathUtilGfxTransformTest, verifyHasPerspective)
+{
+    gfx::Transform A;
+    A.PreconcatPerspectiveDepth(1);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.PreconcatPerspectiveDepth(0);
+    EXPECT_FALSE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 0, -1);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 1, -1);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 2, -0.3);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 3, 0.5);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 3, 0);
+    EXPECT_TRUE(MathUtil::hasPerspective(A));
+}
+
+TEST(MathUtilGfxTransformTest, verifyIsInvertible)
+{
+    gfx::Transform A;
+
+    // Translations, rotations, scales, skews and arbitrary combinations of them are invertible.
+    MathUtil::makeIdentity(&A);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    MathUtil::makeIdentity(&A);
+    A.PreconcatTranslate3d(2, 3, 4);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    MathUtil::makeIdentity(&A);
+    A.PreconcatScale3d(6, 7, 8);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    MathUtil::makeIdentity(&A);
+    MathUtil::rotateEulerAngles(&A, 10, 20, 30);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    MathUtil::makeIdentity(&A);
+    A.PreconcatSkewX(45);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    // A perspective matrix (projection plane at z=0) is invertible. The intuitive
+    // explanation is that perspective is eqivalent to a skew of the w-axis; skews are
+    // invertible.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatPerspectiveDepth(1);
+    EXPECT_TRUE(MathUtil::isInvertible(A));
+
+    // A "pure" perspective matrix derived by similar triangles, with m44() set to zero
+    // (i.e. camera positioned at the origin), is not invertible.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatPerspectiveDepth(1);
+    A.matrix().setDouble(3, 3, 0);
+    EXPECT_FALSE(MathUtil::isInvertible(A));
+
+    // Adding more to a non-invertible matrix will not make it invertible in the general case.
+    MathUtil::makeIdentity(&A);
+    A.PreconcatPerspectiveDepth(1);
+    A.matrix().setDouble(3, 3, 0);
+    A.PreconcatScale3d(6, 7, 8);
+    MathUtil::rotateEulerAngles(&A, 10, 20, 30);
+    A.PreconcatTranslate3d(6, 7, 8);
+    EXPECT_FALSE(MathUtil::isInvertible(A));
+
+    // A degenerate matrix of all zeros is not invertible.
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 0, 0);
+    A.matrix().setDouble(1, 1, 0);
+    A.matrix().setDouble(2, 2, 0);
+    A.matrix().setDouble(3, 3, 0);
+    EXPECT_FALSE(MathUtil::isInvertible(A));
+}
+
+TEST(MathUtilGfxTransformTest, verifyIsIdentity)
+{
+    gfx::Transform A;
+
+    initializeTestMatrix(&A);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    EXPECT_TRUE(MathUtil::isIdentity(A));
+
+    // Modifying any one individual element should cause the matrix to no longer be identity.
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 3, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 3, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 3, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 3, 2);
+    EXPECT_FALSE(MathUtil::isIdentity(A));
+}
+
+TEST(MathUtilGfxTransformTest, verifyIsIdentityOrTranslation)
+{
+    gfx::Transform A;
+
+    initializeTestMatrix(&A);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+
+    // 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().
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 0, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 1, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 2, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+
+    // Note carefully - expecting true here.
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(0, 3, 2);
+    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+
+    // Note carefully - expecting true here.
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(1, 3, 2);
+    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+
+    // Note carefully - expecting true here.
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(2, 3, 2);
+    EXPECT_TRUE(MathUtil::isIdentityOrTranslation(A));
+
+    MathUtil::makeIdentity(&A);
+    A.matrix().setDouble(3, 3, 2);
+    EXPECT_FALSE(MathUtil::isIdentityOrTranslation(A));
+}
+
 }  // namespace
 }  // namespace cc