/* * Copyright 2011 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "SkMatrix44.h" #include "Test.h" static bool nearly_equal_double(double a, double b) { const double tolerance = 1e-7; double diff = a - b; if (diff < 0) diff = -diff; return diff <= tolerance; } static bool nearly_equal_mscalar(SkMScalar a, SkMScalar b) { const SkMScalar tolerance = SK_MScalar1 / 200000; return SkTAbs<SkMScalar>(a - b) <= tolerance; } static bool nearly_equal_scalar(SkScalar a, SkScalar b) { const SkScalar tolerance = SK_Scalar1 / 200000; return SkScalarAbs(a - b) <= tolerance; } template <typename T> void assert16(skiatest::Reporter* reporter, const T data[], T m0, T m1, T m2, T m3, T m4, T m5, T m6, T m7, T m8, T m9, T m10, T m11, T m12, T m13, T m14, T m15) { REPORTER_ASSERT(reporter, data[0] == m0); REPORTER_ASSERT(reporter, data[1] == m1); REPORTER_ASSERT(reporter, data[2] == m2); REPORTER_ASSERT(reporter, data[3] == m3); REPORTER_ASSERT(reporter, data[4] == m4); REPORTER_ASSERT(reporter, data[5] == m5); REPORTER_ASSERT(reporter, data[6] == m6); REPORTER_ASSERT(reporter, data[7] == m7); REPORTER_ASSERT(reporter, data[8] == m8); REPORTER_ASSERT(reporter, data[9] == m9); REPORTER_ASSERT(reporter, data[10] == m10); REPORTER_ASSERT(reporter, data[11] == m11); REPORTER_ASSERT(reporter, data[12] == m12); REPORTER_ASSERT(reporter, data[13] == m13); REPORTER_ASSERT(reporter, data[14] == m14); REPORTER_ASSERT(reporter, data[15] == m15); } static bool nearly_equal(const SkMatrix44& a, const SkMatrix44& b) { for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { if (!nearly_equal_mscalar(a.get(i, j), b.get(i, j))) { SkDebugf("not equal %g %g\n", a.get(i, j), b.get(i, j)); return false; } } } return true; } static bool is_identity(const SkMatrix44& m) { SkMatrix44 identity(SkMatrix44::kIdentity_Constructor); return nearly_equal(m, identity); } /////////////////////////////////////////////////////////////////////////////// static bool bits_isonly(int value, int mask) { return 0 == (value & ~mask); } static void test_constructor(skiatest::Reporter* reporter) { // Allocate a matrix on the heap SkMatrix44* placeholderMatrix = new SkMatrix44(SkMatrix44::kUninitialized_Constructor); SkAutoTDelete<SkMatrix44> deleteMe(placeholderMatrix); for (int row = 0; row < 4; ++row) { for (int col = 0; col < 4; ++col) { placeholderMatrix->setDouble(row, col, row * col); } } // Use placement-new syntax to trigger the constructor on top of the heap // address we already initialized. This allows us to check that the // constructor did avoid initializing the matrix contents. SkMatrix44* testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kUninitialized_Constructor); REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix); REPORTER_ASSERT(reporter, !testMatrix->isIdentity()); for (int row = 0; row < 4; ++row) { for (int col = 0; col < 4; ++col) { REPORTER_ASSERT(reporter, nearly_equal_double(row * col, testMatrix->getDouble(row, col))); } } // Verify that kIdentity_Constructor really does initialize to an identity matrix. testMatrix = 0; testMatrix = new(placeholderMatrix) SkMatrix44(SkMatrix44::kIdentity_Constructor); REPORTER_ASSERT(reporter, testMatrix == placeholderMatrix); REPORTER_ASSERT(reporter, testMatrix->isIdentity()); REPORTER_ASSERT(reporter, *testMatrix == SkMatrix44::I()); } static void test_translate(skiatest::Reporter* reporter) { SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor); SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor); mat.setTranslate(0, 0, 0); REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask)); mat.setTranslate(1, 2, 3); REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kTranslate_Mask)); REPORTER_ASSERT(reporter, mat.invert(&inverse)); REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kTranslate_Mask)); SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); SkMatrix44 c(SkMatrix44::kUninitialized_Constructor); a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9); b.setTranslate(10, 11, 12); c.setConcat(a, b); mat = a; mat.preTranslate(10, 11, 12); REPORTER_ASSERT(reporter, mat == c); c.setConcat(b, a); mat = a; mat.postTranslate(10, 11, 12); REPORTER_ASSERT(reporter, mat == c); } static void test_scale(skiatest::Reporter* reporter) { SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor); SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor); mat.setScale(1, 1, 1); REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kIdentity_Mask)); mat.setScale(1, 2, 3); REPORTER_ASSERT(reporter, bits_isonly(mat.getType(), SkMatrix44::kScale_Mask)); REPORTER_ASSERT(reporter, mat.invert(&inverse)); REPORTER_ASSERT(reporter, bits_isonly(inverse.getType(), SkMatrix44::kScale_Mask)); SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); SkMatrix44 c(SkMatrix44::kUninitialized_Constructor); a.set3x3(1, 2, 3, 4, 5, 6, 7, 8, 9); b.setScale(10, 11, 12); c.setConcat(a, b); mat = a; mat.preScale(10, 11, 12); REPORTER_ASSERT(reporter, mat == c); c.setConcat(b, a); mat = a; mat.postScale(10, 11, 12); REPORTER_ASSERT(reporter, mat == c); } static void make_i(SkMatrix44* mat) { mat->setIdentity(); } static void make_t(SkMatrix44* mat) { mat->setTranslate(1, 2, 3); } static void make_s(SkMatrix44* mat) { mat->setScale(1, 2, 3); } static void make_st(SkMatrix44* mat) { mat->setScale(1, 2, 3); mat->postTranslate(1, 2, 3); } static void make_a(SkMatrix44* mat) { mat->setRotateDegreesAbout(1, 2, 3, 45); } static void make_p(SkMatrix44* mat) { SkMScalar data[] = { 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, }; mat->setRowMajor(data); } typedef void (*Make44Proc)(SkMatrix44*); static const Make44Proc gMakeProcs[] = { make_i, make_t, make_s, make_st, make_a, make_p }; static void test_map2(skiatest::Reporter* reporter, const SkMatrix44& mat) { SkMScalar src2[] = { 1, 2 }; SkMScalar src4[] = { src2[0], src2[1], 0, 1 }; SkMScalar dstA[4], dstB[4]; for (int i = 0; i < 4; ++i) { dstA[i] = 123456789; dstB[i] = 987654321; } mat.map2(src2, 1, dstA); mat.mapMScalars(src4, dstB); for (int i = 0; i < 4; ++i) { REPORTER_ASSERT(reporter, dstA[i] == dstB[i]); } } static void test_map2(skiatest::Reporter* reporter) { SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor); for (size_t i = 0; i < SK_ARRAY_COUNT(gMakeProcs); ++i) { gMakeProcs[i](&mat); test_map2(reporter, mat); } } static void test_gettype(skiatest::Reporter* reporter) { SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor); REPORTER_ASSERT(reporter, matrix.isIdentity()); REPORTER_ASSERT(reporter, SkMatrix44::kIdentity_Mask == matrix.getType()); int expectedMask; matrix.set(1, 1, 0); expectedMask = SkMatrix44::kScale_Mask; REPORTER_ASSERT(reporter, matrix.getType() == expectedMask); matrix.set(0, 3, 1); // translate-x expectedMask |= SkMatrix44::kTranslate_Mask; REPORTER_ASSERT(reporter, matrix.getType() == expectedMask); matrix.set(2, 0, 1); expectedMask |= SkMatrix44::kAffine_Mask; REPORTER_ASSERT(reporter, matrix.getType() == expectedMask); matrix.set(3, 2, 1); REPORTER_ASSERT(reporter, matrix.getType() & SkMatrix44::kPerspective_Mask); // ensure that negative zero is treated as zero SkMScalar dx = 0; SkMScalar dy = 0; SkMScalar dz = 0; matrix.setTranslate(-dx, -dy, -dz); REPORTER_ASSERT(reporter, matrix.isIdentity()); matrix.preTranslate(-dx, -dy, -dz); REPORTER_ASSERT(reporter, matrix.isIdentity()); matrix.postTranslate(-dx, -dy, -dz); REPORTER_ASSERT(reporter, matrix.isIdentity()); } static void test_common_angles(skiatest::Reporter* reporter) { SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor); // Test precision of rotation in common cases int common_angles[] = { 0, 90, -90, 180, -180, 270, -270, 360, -360 }; for (int i = 0; i < 9; ++i) { rot.setRotateDegreesAbout(0, 0, -1, SkIntToScalar(common_angles[i])); SkMatrix rot3x3 = rot; REPORTER_ASSERT(reporter, rot3x3.rectStaysRect()); } } static void test_concat(skiatest::Reporter* reporter) { int i; SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); SkMatrix44 c(SkMatrix44::kUninitialized_Constructor); SkMatrix44 d(SkMatrix44::kUninitialized_Constructor); a.setTranslate(10, 10, 10); b.setScale(2, 2, 2); SkScalar src[8] = { 0, 0, 0, 1, 1, 1, 1, 1 }; SkScalar dst[8]; c.setConcat(a, b); d = a; d.preConcat(b); REPORTER_ASSERT(reporter, d == c); c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4); for (i = 0; i < 3; ++i) { REPORTER_ASSERT(reporter, 10 == dst[i]); REPORTER_ASSERT(reporter, 12 == dst[i + 4]); } c.setConcat(b, a); d = a; d.postConcat(b); REPORTER_ASSERT(reporter, d == c); c.mapScalars(src, dst); c.mapScalars(src + 4, dst + 4); for (i = 0; i < 3; ++i) { REPORTER_ASSERT(reporter, 20 == dst[i]); REPORTER_ASSERT(reporter, 22 == dst[i + 4]); } } static void test_determinant(skiatest::Reporter* reporter) { SkMatrix44 a(SkMatrix44::kIdentity_Constructor); REPORTER_ASSERT(reporter, nearly_equal_double(1, a.determinant())); a.set(1, 1, 2); REPORTER_ASSERT(reporter, nearly_equal_double(2, a.determinant())); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); REPORTER_ASSERT(reporter, a.invert(&b)); REPORTER_ASSERT(reporter, nearly_equal_double(0.5, b.determinant())); SkMatrix44 c = b = a; c.set(0, 1, 4); b.set(1, 0, 4); REPORTER_ASSERT(reporter, nearly_equal_double(a.determinant(), b.determinant())); SkMatrix44 d = a; d.set(0, 0, 8); REPORTER_ASSERT(reporter, nearly_equal_double(16, d.determinant())); SkMatrix44 e = a; e.postConcat(d); REPORTER_ASSERT(reporter, nearly_equal_double(32, e.determinant())); e.set(0, 0, 0); REPORTER_ASSERT(reporter, nearly_equal_double(0, e.determinant())); } static void test_invert(skiatest::Reporter* reporter) { SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor); double inverseData[16]; SkMatrix44 identity(SkMatrix44::kIdentity_Constructor); identity.invert(&inverse); inverse.asRowMajord(inverseData); assert16<double>(reporter, inverseData, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1); SkMatrix44 translation(SkMatrix44::kUninitialized_Constructor); translation.setTranslate(2, 3, 4); translation.invert(&inverse); inverse.asRowMajord(inverseData); assert16<double>(reporter, inverseData, 1, 0, 0, -2, 0, 1, 0, -3, 0, 0, 1, -4, 0, 0, 0, 1); SkMatrix44 scale(SkMatrix44::kUninitialized_Constructor); scale.setScale(2, 4, 8); scale.invert(&inverse); inverse.asRowMajord(inverseData); assert16<double>(reporter, inverseData, 0.5, 0, 0, 0, 0, 0.25, 0, 0, 0, 0, 0.125, 0, 0, 0, 0, 1); SkMatrix44 scaleTranslation(SkMatrix44::kUninitialized_Constructor); scaleTranslation.setScale(10, 100, 1000); scaleTranslation.preTranslate(2, 3, 4); scaleTranslation.invert(&inverse); inverse.asRowMajord(inverseData); assert16<double>(reporter, inverseData, 0.1, 0, 0, -2, 0, 0.01, 0, -3, 0, 0, 0.001, -4, 0, 0, 0, 1); SkMatrix44 rotation(SkMatrix44::kUninitialized_Constructor); rotation.setRotateDegreesAbout(0, 0, 1, 90); rotation.invert(&inverse); SkMatrix44 expected(SkMatrix44::kUninitialized_Constructor); double expectedInverseRotation[16] = {0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1}; expected.setRowMajord(expectedInverseRotation); REPORTER_ASSERT(reporter, nearly_equal(expected, inverse)); SkMatrix44 affine(SkMatrix44::kUninitialized_Constructor); affine.setRotateDegreesAbout(0, 0, 1, 90); affine.preScale(10, 20, 100); affine.preTranslate(2, 3, 4); affine.invert(&inverse); double expectedInverseAffine[16] = {0, 0.1, 0, -2, -0.05, 0, 0, -3, 0, 0, 0.01, -4, 0, 0, 0, 1}; expected.setRowMajord(expectedInverseAffine); REPORTER_ASSERT(reporter, nearly_equal(expected, inverse)); SkMatrix44 perspective(SkMatrix44::kIdentity_Constructor); perspective.setDouble(3, 2, 1.0); perspective.invert(&inverse); double expectedInversePerspective[16] = {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 1}; expected.setRowMajord(expectedInversePerspective); REPORTER_ASSERT(reporter, nearly_equal(expected, inverse)); SkMatrix44 affineAndPerspective(SkMatrix44::kIdentity_Constructor); affineAndPerspective.setDouble(3, 2, 1.0); affineAndPerspective.preScale(10, 20, 100); affineAndPerspective.preTranslate(2, 3, 4); affineAndPerspective.invert(&inverse); double expectedInverseAffineAndPerspective[16] = {0.1, 0, 2, -2, 0, 0.05, 3, -3, 0, 0, 4.01, -4, 0, 0, -1, 1}; expected.setRowMajord(expectedInverseAffineAndPerspective); REPORTER_ASSERT(reporter, nearly_equal(expected, inverse)); } static void test_transpose(skiatest::Reporter* reporter) { SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); int i = 0; for (int row = 0; row < 4; ++row) { for (int col = 0; col < 4; ++col) { a.setDouble(row, col, i); b.setDouble(col, row, i++); } } a.transpose(); REPORTER_ASSERT(reporter, nearly_equal(a, b)); } static void test_get_set_double(skiatest::Reporter* reporter) { SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); for (int row = 0; row < 4; ++row) { for (int col = 0; col < 4; ++col) { a.setDouble(row, col, 3.141592653589793); REPORTER_ASSERT(reporter, nearly_equal_double(3.141592653589793, a.getDouble(row, col))); a.setDouble(row, col, 0); REPORTER_ASSERT(reporter, nearly_equal_double(0, a.getDouble(row, col))); } } } static void test_set_row_col_major(skiatest::Reporter* reporter) { SkMatrix44 a(SkMatrix44::kUninitialized_Constructor); SkMatrix44 b(SkMatrix44::kUninitialized_Constructor); for (int row = 0; row < 4; ++row) { for (int col = 0; col < 4; ++col) { a.setDouble(row, col, row * 4 + col); } } double bufferd[16]; float bufferf[16]; a.asColMajord(bufferd); b.setColMajord(bufferd); REPORTER_ASSERT(reporter, nearly_equal(a, b)); b.setRowMajord(bufferd); b.transpose(); REPORTER_ASSERT(reporter, nearly_equal(a, b)); a.asColMajorf(bufferf); b.setColMajorf(bufferf); REPORTER_ASSERT(reporter, nearly_equal(a, b)); b.setRowMajorf(bufferf); b.transpose(); REPORTER_ASSERT(reporter, nearly_equal(a, b)); } static void test_3x3_conversion(skiatest::Reporter* reporter) { SkMScalar values4x4[16] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 }; SkScalar values3x3[9] = { 1, 2, 4, 5, 6, 8, 13, 14, 16 }; SkMScalar values4x4flattened[16] = { 1, 2, 0, 4, 5, 6, 0, 8, 0, 0, 1, 0, 13, 14, 0, 16 }; SkMatrix44 a44(SkMatrix44::kUninitialized_Constructor); a44.setRowMajor(values4x4); SkMatrix a33 = a44; SkMatrix expected33; for (int i = 0; i < 9; i++) expected33[i] = values3x3[i]; REPORTER_ASSERT(reporter, expected33 == a33); SkMatrix44 a44flattened = a33; SkMatrix44 expected44flattened(SkMatrix44::kUninitialized_Constructor); expected44flattened.setRowMajor(values4x4flattened); REPORTER_ASSERT(reporter, nearly_equal(a44flattened, expected44flattened)); // Test that a point with a Z value of 0 is transformed the same way. SkScalar vec4[4] = { 2, 4, 0, 8 }; SkScalar vec3[3] = { 2, 4, 8 }; SkScalar vec4transformed[4]; SkScalar vec3transformed[3]; SkScalar vec4transformed2[4]; a44.mapScalars(vec4, vec4transformed); a33.mapHomogeneousPoints(vec3transformed, vec3, 1); a44flattened.mapScalars(vec4, vec4transformed2); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec3transformed[0])); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec3transformed[1])); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec3transformed[2])); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[0], vec4transformed2[0])); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[1], vec4transformed2[1])); REPORTER_ASSERT(reporter, !nearly_equal_scalar(vec4transformed[2], vec4transformed2[2])); REPORTER_ASSERT(reporter, nearly_equal_scalar(vec4transformed[3], vec4transformed2[3])); } DEF_TEST(Matrix44, reporter) { SkMatrix44 mat(SkMatrix44::kUninitialized_Constructor); SkMatrix44 inverse(SkMatrix44::kUninitialized_Constructor); SkMatrix44 iden1(SkMatrix44::kUninitialized_Constructor); SkMatrix44 iden2(SkMatrix44::kUninitialized_Constructor); SkMatrix44 rot(SkMatrix44::kUninitialized_Constructor); mat.setTranslate(1, 1, 1); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); mat.setScale(2, 2, 2); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); mat.setScale(SK_MScalar1/2, SK_MScalar1/2, SK_MScalar1/2); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); mat.setScale(3, 3, 3); rot.setRotateDegreesAbout(0, 0, -1, 90); mat.postConcat(rot); REPORTER_ASSERT(reporter, mat.invert(NULL)); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); iden2.setConcat(inverse, mat); REPORTER_ASSERT(reporter, is_identity(iden2)); // test tiny-valued matrix inverse mat.reset(); mat.setScale(1.0e-12, 1.0e-12, 1.0e-12); rot.setRotateDegreesAbout(0, 0, -1, 90); mat.postConcat(rot); mat.postTranslate(1.0e-12, 1.0e-12, 1.0e-12); REPORTER_ASSERT(reporter, mat.invert(NULL)); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); // test mixed-valued matrix inverse mat.reset(); mat.setScale(1.0e-10, 3.0, 1.0e+10); rot.setRotateDegreesAbout(0, 0, -1, 90); mat.postConcat(rot); mat.postTranslate(1.0e+10, 3.0, 1.0e-10); REPORTER_ASSERT(reporter, mat.invert(NULL)); mat.invert(&inverse); iden1.setConcat(mat, inverse); REPORTER_ASSERT(reporter, is_identity(iden1)); // test degenerate matrix mat.reset(); mat.set3x3(1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0); REPORTER_ASSERT(reporter, !mat.invert(NULL)); // test rol/col Major getters { mat.setTranslate(2, 3, 4); float dataf[16]; double datad[16]; mat.asColMajorf(dataf); assert16<float>(reporter, dataf, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 3, 4, 1); mat.asColMajord(datad); assert16<double>(reporter, datad, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 3, 4, 1); mat.asRowMajorf(dataf); assert16<float>(reporter, dataf, 1, 0, 0, 2, 0, 1, 0, 3, 0, 0, 1, 4, 0, 0, 0, 1); mat.asRowMajord(datad); assert16<double>(reporter, datad, 1, 0, 0, 2, 0, 1, 0, 3, 0, 0, 1, 4, 0, 0, 0, 1); } test_concat(reporter); if (false) { // avoid bit rot, suppress warning (working on making this pass) test_common_angles(reporter); } test_constructor(reporter); test_gettype(reporter); test_determinant(reporter); test_invert(reporter); test_transpose(reporter); test_get_set_double(reporter); test_set_row_col_major(reporter); test_translate(reporter); test_scale(reporter); test_map2(reporter); test_3x3_conversion(reporter); }