Add basic SVD support to SkMatrix. Allows you to pull out the x- and y-scale factors, sandwiched by two rotations.
R=reed@google.com
Author: jvanverth@google.com
Review URL: https://chromiumcodereview.appspot.com/19569007
git-svn-id: http://skia.googlecode.com/svn/trunk@10322 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/src/core/SkMatrix.cpp b/src/core/SkMatrix.cpp
index 13ec7ae..488bff7 100644
--- a/src/core/SkMatrix.cpp
+++ b/src/core/SkMatrix.cpp
@@ -1966,3 +1966,86 @@
dst.round(&idst);
return isrc == idst;
}
+
+bool SkDecomposeUpper2x2(const SkMatrix& matrix,
+ SkScalar* rotation0,
+ SkScalar* xScale, SkScalar* yScale,
+ SkScalar* rotation1) {
+
+ // borrowed from Jim Blinn's article "Consider the Lowly 2x2 Matrix"
+ // Note: he uses row vectors, so we have to do some swapping of terms
+ SkScalar A = matrix[SkMatrix::kMScaleX];
+ SkScalar B = matrix[SkMatrix::kMSkewX];
+ SkScalar C = matrix[SkMatrix::kMSkewY];
+ SkScalar D = matrix[SkMatrix::kMScaleY];
+
+ SkScalar E = SK_ScalarHalf*(A + D);
+ SkScalar F = SK_ScalarHalf*(A - D);
+ SkScalar G = SK_ScalarHalf*(C + B);
+ SkScalar H = SK_ScalarHalf*(C - B);
+
+ SkScalar sqrt0 = SkScalarSqrt(E*E + H*H);
+ SkScalar sqrt1 = SkScalarSqrt(F*F + G*G);
+
+ SkScalar xs, ys, r0, r1;
+
+ // can't have zero yScale, must be degenerate
+ if (SkScalarNearlyEqual(sqrt0, sqrt1)) {
+ return false;
+ }
+ xs = sqrt0 + sqrt1;
+ ys = sqrt0 - sqrt1;
+
+ // uniformly scaled rotation
+ if (SkScalarNearlyZero(F) && SkScalarNearlyZero(G)) {
+ SkASSERT(!SkScalarNearlyZero(E));
+ r0 = SkScalarATan2(H, E);
+ r1 = 0;
+ // uniformly scaled reflection
+ } else if (SkScalarNearlyZero(E) && SkScalarNearlyZero(H)) {
+ SkASSERT(!SkScalarNearlyZero(F));
+ r0 = -SkScalarATan2(G, F);
+ r1 = 0;
+ } else {
+ SkASSERT(!SkScalarNearlyZero(E));
+ SkASSERT(!SkScalarNearlyZero(F));
+
+ SkScalar arctan0 = SkScalarATan2(H, E);
+ SkScalar arctan1 = SkScalarATan2(G, F);
+ r0 = SK_ScalarHalf*(arctan0 - arctan1);
+ r1 = SK_ScalarHalf*(arctan0 + arctan1);
+
+ // simplify the results
+ const SkScalar kHalfPI = SK_ScalarHalf*SK_ScalarPI;
+ if (SkScalarNearlyEqual(SkScalarAbs(r0), kHalfPI)) {
+ SkScalar tmp = xs;
+ xs = ys;
+ ys = tmp;
+
+ r1 += r0;
+ r0 = 0;
+ } else if (SkScalarNearlyEqual(SkScalarAbs(r1), kHalfPI)) {
+ SkScalar tmp = xs;
+ xs = ys;
+ ys = tmp;
+
+ r0 += r1;
+ r1 = 0;
+ }
+ }
+
+ if (NULL != xScale) {
+ *xScale = xs;
+ }
+ if (NULL != yScale) {
+ *yScale = ys;
+ }
+ if (NULL != rotation0) {
+ *rotation0 = r0;
+ }
+ if (NULL != rotation1) {
+ *rotation1 = r1;
+ }
+
+ return true;
+}
diff --git a/src/core/SkMatrixUtils.h b/src/core/SkMatrixUtils.h
index 2074267..ee952b6 100644
--- a/src/core/SkMatrixUtils.h
+++ b/src/core/SkMatrixUtils.h
@@ -40,4 +40,15 @@
return SkTreatAsSprite(matrix, width, height, kSkSubPixelBitsForBilerp);
}
+/** Decomposes the upper-left 2x2 of the matrix into a rotation, followed by a non-uniform scale,
+ followed by another rotation. Returns true if successful.
+ If the scale factors are uniform, then rotation1 will be 0.
+ If there is a reflection, yScale will be negative.
+ Returns false if the matrix is degenerate.
+ */
+bool SkDecomposeUpper2x2(const SkMatrix& matrix,
+ SkScalar* rotation0,
+ SkScalar* xScale, SkScalar* yScale,
+ SkScalar* rotation1);
+
#endif
diff --git a/tests/MatrixTest.cpp b/tests/MatrixTest.cpp
index 5dface7..f57a964 100644
--- a/tests/MatrixTest.cpp
+++ b/tests/MatrixTest.cpp
@@ -8,6 +8,7 @@
#include "Test.h"
#include "SkMath.h"
#include "SkMatrix.h"
+#include "SkMatrixUtils.h"
#include "SkRandom.h"
static bool nearly_equal_scalar(SkScalar a, SkScalar b) {
@@ -345,6 +346,252 @@
REPORTER_ASSERT(reporter, mat.isSimilarity());
}
+// For test_matrix_decomposition, below.
+static bool scalar_nearly_equal_relative(SkScalar a, SkScalar b,
+ SkScalar tolerance = SK_ScalarNearlyZero) {
+ // from Bruce Dawson
+ SkScalar diff = SkScalarAbs(a - b);
+ if (diff < tolerance) {
+ return true;
+ }
+
+ a = SkScalarAbs(a);
+ b = SkScalarAbs(b);
+ SkScalar largest = (b > a) ? b : a;
+
+ if (diff <= largest*tolerance) {
+ return true;
+ }
+
+ return false;
+}
+
+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] = 12.0;
+ mat[SkMatrix::kMPersp1] = 4.0;
+ mat[SkMatrix::kMPersp2] = 1872.0;
+ 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));
+}
+
static void TestMatrix(skiatest::Reporter* reporter) {
SkMatrix mat, inverse, iden1, iden2;
@@ -465,6 +712,7 @@
test_matrix_max_stretch(reporter);
test_matrix_is_similarity(reporter);
test_matrix_recttorect(reporter);
+ test_matrix_decomposition(reporter);
}
#include "TestClassDef.h"