// For test_matrix_homogeneous, below.
static bool scalar_array_nearly_equal_relative(const SkScalar a[], const SkScalar b[], int count) {
for (int i = 0; i < count; ++i) {
if (!scalar_nearly_equal_relative(a[i], b[i])) {
return false;
}
}
return true;
}
static bool check_matrix_recomposition(const SkMatrix& mat,
const SkPoint& rotation1,
const SkPoint& scale,
const SkPoint& rotation2) {
SkScalar c1 = rotation1.fX;
SkScalar s1 = rotation1.fY;
SkScalar scaleX = scale.fX;
SkScalar scaleY = scale.fY;
SkScalar c2 = rotation2.fX;
SkScalar s2 = rotation2.fY;
// We do a relative check here because large scale factors cause problems with an absolute check
bool result = scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c1*c2 - scaleY*s1*s2) &&
scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s1*c2 - scaleY*c1*s2) &&
scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c1*s2 + scaleY*s1*c2) &&
scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s1*s2 + scaleY*c1*c2);
return result;
}
static void test_matrix_decomposition(skiatest::Reporter* reporter) {
SkMatrix mat;
SkScalar rotation0, scaleX, scaleY, rotation1;
const float kRotation0 = 15.5f;
const float kRotation1 = -50.f;
const float kScale0 = 5000.f;
const float kScale1 = 0.001f;
// identity
mat.reset();
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// make sure it doesn't crash if we pass in NULLs
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, NULL, NULL, NULL, NULL));
// rotation only
mat.setRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation0)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale only
mat.setScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// anisotropic scale only
mat.setScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then uniform scale
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale then rotation
mat.setScale(kScale0, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then uniform scale+reflection
mat.setRotate(kRotation0);
mat.postScale(kScale1, -kScale1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation0)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, -kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale+reflection, then rotate
mat.setScale(kScale0, -kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(-kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, -kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then anisotropic scale
mat.setRotate(kRotation1);
mat.postScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// anisotropic scale then rotation
mat.setScale(kScale1, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation1, SkDegreesToRadians(kRotation0)));
// rotation, uniform scale, then different rotation
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0,
SkDegreesToRadians(kRotation0 + kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation, anisotropic scale, then different rotation
mat.setRotate(kRotation0);
mat.postScale(kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
// Because of the shear/skew we won't get the same results, so we need to multiply it out.
// Generating the matrices requires doing a radian-to-degree calculation, then degree-to-radian
// calculation (in setRotate()), which adds error, so this just computes the matrix elements
// directly.
SkScalar c0;
SkScalar s0 = SkScalarSinCos(rotation0, &c0);
SkScalar c1;
SkScalar s1 = SkScalarSinCos(rotation1, &c1);
// We do a relative check here because large scale factors cause problems with an absolute check
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// try some random matrices
SkMWCRandom rand;
for (int m = 0; m < 1000; ++m) {
SkScalar rot0 = rand.nextRangeF(-SK_ScalarPI, SK_ScalarPI);
SkScalar sx = rand.nextRangeF(-3000.f, 3000.f);
SkScalar sy = rand.nextRangeF(-3000.f, 3000.f);
SkScalar rot1 = rand.nextRangeF(-SK_ScalarPI, SK_ScalarPI);
mat.setRotate(rot0);
mat.postScale(sx, sy);
mat.postRotate(rot1);
if (SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1)) {
SkScalar c0;
SkScalar s0 = SkScalarSinCos(rotation0, &c0);
SkScalar c1;
SkScalar s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
} else {
// if the matrix is degenerate, the basis vectors should be near-parallel or near-zero
SkScalar perpdot = mat[SkMatrix::kMScaleX]*mat[SkMatrix::kMScaleY] -
mat[SkMatrix::kMSkewX]*mat[SkMatrix::kMSkewY];
REPORTER_ASSERT(reporter, SkScalarNearlyZero(perpdot));
}
}
// translation shouldn't affect this
mat.postTranslate(-1000.f, 1000.f);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// perspective shouldn't affect this
mat[SkMatrix::kMPersp0] = 12.f;
mat[SkMatrix::kMPersp1] = 4.f;
mat[SkMatrix::kMPersp2] = 1872.f;
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// rotation, anisotropic scale + reflection, then different rotation
mat.setRotate(kRotation0);
mat.postScale(-kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// degenerate matrices
// mostly zero entries
mat.reset();
mat[SkMatrix::kMScaleX] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
mat.reset();
mat[SkMatrix::kMScaleY] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
mat.reset();
// linearly dependent entries
mat[SkMatrix::kMScaleX] = 1.f;
mat[SkMatrix::kMSkewX] = 2.f;
mat[SkMatrix::kMSkewY] = 4.f;
mat[SkMatrix::kMScaleY] = 8.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
}