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-/*
- * Copyright (C) 2012 Google Inc. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS'' AND ANY
- * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
- * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
- * DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS BE LIABLE FOR ANY
- * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
- * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
- * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
- * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
- * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
- * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- */
-
-#include "config.h"
-
-#include <public/WebTransformationMatrix.h>
-
-#include "CCGeometryTestUtils.h"
-#include <gtest/gtest.h>
-#include <wtf/MathExtras.h>
-
-#define EXPECT_ROW1_EQ(a, b, c, d, matrix) \
- EXPECT_FLOAT_EQ((a), (matrix).m11()); \
- EXPECT_FLOAT_EQ((b), (matrix).m21()); \
- EXPECT_FLOAT_EQ((c), (matrix).m31()); \
- EXPECT_FLOAT_EQ((d), (matrix).m41());
-
-#define EXPECT_ROW2_EQ(a, b, c, d, matrix) \
- EXPECT_FLOAT_EQ((a), (matrix).m12()); \
- EXPECT_FLOAT_EQ((b), (matrix).m22()); \
- EXPECT_FLOAT_EQ((c), (matrix).m32()); \
- EXPECT_FLOAT_EQ((d), (matrix).m42());
-
-#define EXPECT_ROW3_EQ(a, b, c, d, matrix) \
- EXPECT_FLOAT_EQ((a), (matrix).m13()); \
- EXPECT_FLOAT_EQ((b), (matrix).m23()); \
- EXPECT_FLOAT_EQ((c), (matrix).m33()); \
- EXPECT_FLOAT_EQ((d), (matrix).m43());
-
-#define EXPECT_ROW4_EQ(a, b, c, d, matrix) \
- EXPECT_FLOAT_EQ((a), (matrix).m14()); \
- EXPECT_FLOAT_EQ((b), (matrix).m24()); \
- EXPECT_FLOAT_EQ((c), (matrix).m34()); \
- EXPECT_FLOAT_EQ((d), (matrix).m44()); \
-
-// 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, matrix, errorThreshold) \
- EXPECT_NEAR((a), (matrix).m11(), (errorThreshold)); \
- EXPECT_NEAR((b), (matrix).m21(), (errorThreshold)); \
- EXPECT_NEAR((c), (matrix).m31(), (errorThreshold)); \
- EXPECT_NEAR((d), (matrix).m41(), (errorThreshold));
-
-#define EXPECT_ROW2_NEAR(a, b, c, d, matrix, errorThreshold) \
- EXPECT_NEAR((a), (matrix).m12(), (errorThreshold)); \
- EXPECT_NEAR((b), (matrix).m22(), (errorThreshold)); \
- EXPECT_NEAR((c), (matrix).m32(), (errorThreshold)); \
- EXPECT_NEAR((d), (matrix).m42(), (errorThreshold));
-
-#define EXPECT_ROW3_NEAR(a, b, c, d, matrix, errorThreshold) \
- EXPECT_NEAR((a), (matrix).m13(), (errorThreshold)); \
- EXPECT_NEAR((b), (matrix).m23(), (errorThreshold)); \
- EXPECT_NEAR((c), (matrix).m33(), (errorThreshold)); \
- EXPECT_NEAR((d), (matrix).m43(), (errorThreshold));
-
-#define ERROR_THRESHOLD 1e-14
-#define LOOSE_ERROR_THRESHOLD 1e-7
-
-using namespace WebKit;
-
-namespace {
-
-static void initializeTestMatrix(WebTransformationMatrix& transform)
-{
- transform.setM11(10);
- transform.setM12(11);
- transform.setM13(12);
- transform.setM14(13);
- transform.setM21(14);
- transform.setM22(15);
- transform.setM23(16);
- transform.setM24(17);
- transform.setM31(18);
- transform.setM32(19);
- transform.setM33(20);
- transform.setM34(21);
- transform.setM41(22);
- transform.setM42(23);
- transform.setM43(24);
- transform.setM44(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(WebTransformationMatrix& transform)
-{
- transform.setM11(30);
- transform.setM12(31);
- transform.setM13(32);
- transform.setM14(33);
- transform.setM21(34);
- transform.setM22(35);
- transform.setM23(36);
- transform.setM24(37);
- transform.setM31(38);
- transform.setM32(39);
- transform.setM33(40);
- transform.setM34(41);
- transform.setM41(42);
- transform.setM42(43);
- transform.setM43(44);
- transform.setM44(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(WebTransformationMatrixTest, verifyDefaultConstructorCreatesIdentityMatrix)
-{
- WebTransformationMatrix 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(A.isIdentity());
-}
-
-TEST(WebTransformationMatrixTest, verifyConstructorFor2dElements)
-{
- WebTransformationMatrix A(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(WebTransformationMatrixTest, verifyConstructorForAllElements)
-{
- WebTransformationMatrix A(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(WebTransformationMatrixTest, verifyCopyConstructor)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
-
- // Copy constructor should produce exact same elements as matrix A.
- WebTransformationMatrix 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(WebTransformationMatrixTest, verifyMatrixInversion)
-{
- // Invert a translation
- WebTransformationMatrix translation;
- translation.translate3d(2, 3, 4);
- EXPECT_TRUE(translation.isInvertible());
-
- WebTransformationMatrix inverseTranslation = translation.inverse();
- 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
- WebTransformationMatrix scale;
- scale.scale3d(4, 10, 100);
- EXPECT_TRUE(scale.isInvertible());
-
- WebTransformationMatrix inverseScale = scale.inverse();
- 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.
- WebTransformationMatrix notInvertible;
- notInvertible.setM11(0);
- notInvertible.setM22(0);
- notInvertible.setM33(0);
- notInvertible.setM44(0);
- EXPECT_FALSE(notInvertible.isInvertible());
-
- WebTransformationMatrix inverseOfNotInvertible;
- initializeTestMatrix(inverseOfNotInvertible); // initialize this to something non-identity, to make sure that assignment below actually took place.
- inverseOfNotInvertible = notInvertible.inverse();
- EXPECT_TRUE(inverseOfNotInvertible.isIdentity());
-}
-
-TEST(WebTransformationMatrixTest, verifyTo2DTransform)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
-
- WebTransformationMatrix B = A.to2dTransform();
-
- 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(WebTransformationMatrixTest, verifyAssignmentOperator)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
- WebTransformationMatrix B;
- initializeTestMatrix2(B);
- WebTransformationMatrix 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(WebTransformationMatrixTest, verifyEqualsBooleanOperator)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
-
- WebTransformationMatrix B;
- initializeTestMatrix(B);
- EXPECT_TRUE(A == B);
-
- // Modifying multiple elements should cause equals operator to return false.
- WebTransformationMatrix C;
- initializeTestMatrix2(C);
- EXPECT_FALSE(A == C);
-
- // Modifying any one individual element should cause equals operator to return false.
- WebTransformationMatrix D;
- D = A;
- D.setM11(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM12(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM13(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM14(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM21(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM22(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM23(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM24(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM31(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM32(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM33(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM34(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM41(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM42(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM43(0);
- EXPECT_FALSE(A == D);
-
- D = A;
- D.setM44(0);
- EXPECT_FALSE(A == D);
-}
-
-TEST(WebTransformationMatrixTest, verifyMultiplyOperator)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
-
- WebTransformationMatrix B;
- initializeTestMatrix2(B);
-
- WebTransformationMatrix 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(WebTransformationMatrixTest, verifyMatrixMultiplication)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
-
- WebTransformationMatrix B;
- initializeTestMatrix2(B);
-
- A.multiply(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(WebTransformationMatrixTest, verifyMakeIdentiy)
-{
- WebTransformationMatrix A;
- initializeTestMatrix(A);
- A.makeIdentity();
- 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(A.isIdentity());
-}
-
-TEST(WebTransformationMatrixTest, verifyTranslate)
-{
- WebTransformationMatrix A;
- A.translate(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 translate() post-multiplies the existing matrix.
- A.makeIdentity();
- A.scale(5);
- A.translate(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(WebTransformationMatrixTest, verifyTranslate3d)
-{
- WebTransformationMatrix A;
- A.translate3d(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 translate3d() post-multiplies the existing matrix.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.translate3d(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(WebTransformationMatrixTest, verifyTranslateRight3d)
-{
- WebTransformationMatrix A;
- A.translateRight3d(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);
-
- // Note carefully, all other operations do post-multiply, this one is unique.
- // Verify that translateRight3d() PRE-multiplies the existing matrix.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.translateRight3d(2, 3, 4);
- 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(WebTransformationMatrixTest, verifyScale)
-{
- WebTransformationMatrix A;
- A.scale(5);
- EXPECT_ROW1_EQ(5, 0, 0, 0, A);
- EXPECT_ROW2_EQ(0, 5, 0, 0, A);
- EXPECT_ROW3_EQ(0, 0, 1, 0, A);
- EXPECT_ROW4_EQ(0, 0, 0, 1, A);
-
- // Verify that scale() post-multiplies the existing matrix.
- A.makeIdentity();
- A.translate3d(2, 3, 4);
- A.scale(5);
- EXPECT_ROW1_EQ(5, 0, 0, 2, A);
- EXPECT_ROW2_EQ(0, 5, 0, 3, A);
- EXPECT_ROW3_EQ(0, 0, 1, 4, A);
- EXPECT_ROW4_EQ(0, 0, 0, 1, A);
-}
-
-TEST(WebTransformationMatrixTest, verifyNonUniformScale)
-{
- WebTransformationMatrix A;
- A.scaleNonUniform(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 scaleNonUniform() post-multiplies the existing matrix.
- A.makeIdentity();
- A.translate3d(2, 3, 4);
- A.scaleNonUniform(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(WebTransformationMatrixTest, verifyScale3d)
-{
- WebTransformationMatrix A;
- A.scale3d(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.
- A.makeIdentity();
- A.translate3d(2, 3, 4);
- A.scale3d(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(WebTransformationMatrixTest, verifyRotate)
-{
- WebTransformationMatrix A;
- A.rotate(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 rotate() post-multiplies the existing matrix.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.rotate(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(WebTransformationMatrixTest, verifyRotate3d)
-{
- WebTransformationMatrix A;
-
- // Check rotation about z-axis
- A.makeIdentity();
- A.rotate3d(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
- A.makeIdentity();
- A.rotate3d(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.
- A.makeIdentity();
- A.rotate3d(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.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.rotate3d(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(WebTransformationMatrixTest, verifyRotate3dOrderOfCompositeRotations)
-{
- // 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.
-
- WebTransformationMatrix A;
- A.makeIdentity();
- A.rotate3d(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(WebTransformationMatrixTest, verifyRotateAxisAngle3d)
-{
- WebTransformationMatrix A;
-
- // Check rotation about z-axis
- A.makeIdentity();
- A.rotate3d(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
- A.makeIdentity();
- A.rotate3d(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.
- A.makeIdentity();
- A.rotate3d(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.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.rotate3d(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(WebTransformationMatrixTest, verifyRotateAxisAngle3dForArbitraryAxis)
-{
- // Check rotation about an arbitrary non-axis-aligned vector.
- WebTransformationMatrix A;
- A.rotate3d(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(WebTransformationMatrixTest, verifyRotateAxisAngle3dForDegenerateAxis)
-{
- // Check rotation about a degenerate zero vector.
- // It is expected to default to rotation about the z-axis.
- WebTransformationMatrix A;
- A.rotate3d(0, 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);
-}
-
-TEST(WebTransformationMatrixTest, verifySkewX)
-{
- WebTransformationMatrix A;
- A.skewX(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.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.skewX(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(WebTransformationMatrixTest, verifySkewY)
-{
- WebTransformationMatrix A;
- A.skewY(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.
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- A.skewY(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(WebTransformationMatrixTest, verifyApplyPerspective)
-{
- WebTransformationMatrix A;
- A.applyPerspective(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 applyPerspective() post-multiplies the existing matrix.
- A.makeIdentity();
- A.translate3d(2, 3, 4);
- A.applyPerspective(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(WebTransformationMatrixTest, verifyHasPerspective)
-{
- WebTransformationMatrix A;
- A.applyPerspective(1);
- EXPECT_TRUE(A.hasPerspective());
-
- A.makeIdentity();
- A.applyPerspective(0);
- EXPECT_FALSE(A.hasPerspective());
-
- A.makeIdentity();
- A.setM34(-0.3);
- EXPECT_TRUE(A.hasPerspective());
-
- // FIXME: WebCore only checkes m34() for perspective, but that is probably
- // wrong. https://bugs.webkit.org/show_bug.cgi?id=83088. For now, this test
- // case expects the exact behavior as implemented by WebCore, but this should
- // probably be changed so that if the entire bottom row is not exactly
- // (0, 0, 0, 1), then hasPerspective should return true.
-
- A.makeIdentity();
- A.setM14(-1);
- EXPECT_FALSE(A.hasPerspective());
-
- A.makeIdentity();
- A.setM24(-1);
- EXPECT_FALSE(A.hasPerspective());
-
- A.makeIdentity();
- A.setM44(0.5);
- EXPECT_FALSE(A.hasPerspective());
-}
-
-TEST(WebTransformationMatrixTest, verifyIsInvertible)
-{
- WebTransformationMatrix A;
-
- // Translations, rotations, scales, skews and arbitrary combinations of them are invertible.
- A.makeIdentity();
- EXPECT_TRUE(A.isInvertible());
-
- A.makeIdentity();
- A.translate3d(2, 3, 4);
- EXPECT_TRUE(A.isInvertible());
-
- A.makeIdentity();
- A.scale3d(6, 7, 8);
- EXPECT_TRUE(A.isInvertible());
-
- A.makeIdentity();
- A.rotate3d(10, 20, 30);
- EXPECT_TRUE(A.isInvertible());
-
- A.makeIdentity();
- A.skewX(45);
- EXPECT_TRUE(A.isInvertible());
-
- // 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.
- A.makeIdentity();
- A.applyPerspective(1);
- EXPECT_TRUE(A.isInvertible());
-
- // A "pure" perspective matrix derived by similar triangles, with m44() set to zero
- // (i.e. camera positioned at the origin), is not invertible.
- A.makeIdentity();
- A.applyPerspective(1);
- A.setM44(0);
- EXPECT_FALSE(A.isInvertible());
-
- // Adding more to a non-invertible matrix will not make it invertible in the general case.
- A.makeIdentity();
- A.applyPerspective(1);
- A.setM44(0);
- A.scale3d(6, 7, 8);
- A.rotate3d(10, 20, 30);
- A.translate3d(6, 7, 8);
- EXPECT_FALSE(A.isInvertible());
-
- // A degenerate matrix of all zeros is not invertible.
- A.makeIdentity();
- A.setM11(0);
- A.setM22(0);
- A.setM33(0);
- A.setM44(0);
- EXPECT_FALSE(A.isInvertible());
-}
-
-TEST(WebTransformationMatrixTest, verifyIsIdentity)
-{
- WebTransformationMatrix A;
-
- initializeTestMatrix(A);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- EXPECT_TRUE(A.isIdentity());
-
- // Modifying any one individual element should cause the matrix to no longer be identity.
- A.makeIdentity();
- A.setM11(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM12(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM13(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM14(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM21(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM22(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM23(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM24(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM31(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM32(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM33(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM34(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM41(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM42(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM43(2);
- EXPECT_FALSE(A.isIdentity());
-
- A.makeIdentity();
- A.setM44(2);
- EXPECT_FALSE(A.isIdentity());
-}
-
-TEST(WebTransformationMatrixTest, verifyIsIdentityOrTranslation)
-{
- WebTransformationMatrix A;
-
- initializeTestMatrix(A);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- EXPECT_TRUE(A.isIdentityOrTranslation());
-
- // Modifying any non-translation components should cause isIdentityOrTranslation() to
- // return false. NOTE: m41(), m42(), and m43() are the translation components, so
- // modifying them should still return true for isIdentityOrTranslation().
- A.makeIdentity();
- A.setM11(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM12(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM13(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM14(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM21(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM22(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM23(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM24(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM31(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM32(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM33(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM34(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-
- // Note carefully - expecting true here.
- A.makeIdentity();
- A.setM41(2);
- EXPECT_TRUE(A.isIdentityOrTranslation());
-
- // Note carefully - expecting true here.
- A.makeIdentity();
- A.setM42(2);
- EXPECT_TRUE(A.isIdentityOrTranslation());
-
- // Note carefully - expecting true here.
- A.makeIdentity();
- A.setM43(2);
- EXPECT_TRUE(A.isIdentityOrTranslation());
-
- A.makeIdentity();
- A.setM44(2);
- EXPECT_FALSE(A.isIdentityOrTranslation());
-}
-
-TEST(WebTransformationMatrixTest, verifyIsIntegerTranslation)
-{
- WebTransformationMatrix A;
-
- A.makeIdentity();
- A.translate(2, 3);
- EXPECT_TRUE(A.isIntegerTranslation());
-
- A.makeIdentity();
- A.translate(2, 3);
- EXPECT_TRUE(A.isIntegerTranslation());
-
- A.makeIdentity();
- A.translate(2.00001, 3);
- EXPECT_FALSE(A.isIntegerTranslation());
-
- A.makeIdentity();
- A.translate(2, 2.99999);
- EXPECT_FALSE(A.isIntegerTranslation());
-
- // Stacking many integer translations should ideally not accumulate any precision error.
- A.makeIdentity();
- for (int i = 0; i < 100000; ++i)
- A.translate(2, 3);
- EXPECT_TRUE(A.isIntegerTranslation());
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForTranslation)
-{
- WebTransformationMatrix from;
- from.translate3d(100, 200, 100);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.translate3d(200, 100, 300);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- to.makeIdentity();
- to.translate3d(200, 100, 300);
- to.blend(from, 0.25);
- EXPECT_ROW1_EQ(1, 0, 0, 125, to);
- EXPECT_ROW2_EQ(0, 1, 0, 175, to);
- EXPECT_ROW3_EQ(0, 0, 1, 150, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.translate3d(200, 100, 300);
- to.blend(from, 0.5);
- EXPECT_ROW1_EQ(1, 0, 0, 150, to);
- EXPECT_ROW2_EQ(0, 1, 0, 150, to);
- EXPECT_ROW3_EQ(0, 0, 1, 200, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.translate3d(200, 100, 300);
- to.blend(from, 1);
- EXPECT_ROW1_EQ(1, 0, 0, 200, to);
- EXPECT_ROW2_EQ(0, 1, 0, 100, to);
- EXPECT_ROW3_EQ(0, 0, 1, 300, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForScale)
-{
- WebTransformationMatrix from;
- from.scale3d(100, 200, 100);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.scale3d(200, 100, 300);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- to.makeIdentity();
- to.scale3d(200, 100, 300);
- to.blend(from, 0.25);
- EXPECT_ROW1_EQ(125, 0, 0, 0, to);
- EXPECT_ROW2_EQ(0, 175, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 150, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.scale3d(200, 100, 300);
- to.blend(from, 0.5);
- EXPECT_ROW1_EQ(150, 0, 0, 0, to);
- EXPECT_ROW2_EQ(0, 150, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 200, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.scale3d(200, 100, 300);
- to.blend(from, 1);
- EXPECT_ROW1_EQ(200, 0, 0, 0, to);
- EXPECT_ROW2_EQ(0, 100, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 300, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForSkewX)
-{
- WebTransformationMatrix from;
- from.skewX(0);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.skewX(45);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- to.makeIdentity();
- to.skewX(45);
- to.blend(from, 0.5);
- EXPECT_ROW1_EQ(1, 0.5, 0, 0, to);
- EXPECT_ROW2_EQ(0, 1, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.skewX(45);
- to.blend(from, 0.25);
- EXPECT_ROW1_EQ(1, 0.25, 0, 0, to);
- EXPECT_ROW2_EQ(0, 1, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.skewX(45);
- to.blend(from, 1);
- EXPECT_ROW1_EQ(1, 1, 0, 0, to);
- EXPECT_ROW2_EQ(0, 1, 0, 0, to);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForSkewY)
-{
- // NOTE CAREFULLY: Decomposition of skew and rotation terms of the matrix is
- // inherently underconstrained, and so it does not always compute the originally
- // intended skew parameters. The current implementation uses QR decomposition, which
- // decomposes the shear into a rotation + non-uniform scale.
- //
- // It is unlikely that the decomposition implementation will need to change very
- // often, so to get any test coverage, the compromise is to verify the exact matrix
- // that the blend() operation produces.
- //
- // This problem also potentially exists for skewX, but the current QR decomposition
- // implementation just happens to decompose those test matrices intuitively.
-
- WebTransformationMatrix from;
- from.skewY(0);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.skewY(45);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- to.makeIdentity();
- to.skewY(45);
- to.blend(from, 0.25);
- EXPECT_ROW1_NEAR(1.0823489449280947471976333, 0.0464370719145053845178239, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0.2152925909665224513123150, 0.9541702441750861130032035, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.skewY(45);
- to.blend(from, 0.5);
- EXPECT_ROW1_NEAR(1.1152212925809066312865525, 0.0676495144007326631996335, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0.4619397844342648662419037, 0.9519009045724774464858342, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- // Unfortunately, this case suffers from uncomfortably large precision error.
- to.makeIdentity();
- to.skewY(45);
- to.blend(from, 1);
- EXPECT_ROW1_NEAR(1, 0, 0, 0, to, LOOSE_ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(1, 1, 0, 0, to, LOOSE_ERROR_THRESHOLD);
- EXPECT_ROW3_EQ(0, 0, 1, 0, to);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForRotationAboutX)
-{
- // Even though blending uses quaternions, axis-aligned rotations should blend the same
- // with quaternions or Euler angles. So we can test rotation blending by comparing
- // against manually specified matrices from Euler angles.
-
- WebTransformationMatrix from;
- from.rotate3d(1, 0, 0, 0);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.rotate3d(1, 0, 0, 90);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- double expectedRotationAngle = 22.5 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(1, 0, 0, 90);
- to.blend(from, 0.25);
- EXPECT_ROW1_NEAR(1, 0, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, cos(expectedRotationAngle), -sin(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, sin(expectedRotationAngle), cos(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- expectedRotationAngle = 45 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(1, 0, 0, 90);
- to.blend(from, 0.5);
- EXPECT_ROW1_NEAR(1, 0, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, cos(expectedRotationAngle), -sin(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, sin(expectedRotationAngle), cos(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.rotate3d(1, 0, 0, 90);
- to.blend(from, 1);
- EXPECT_ROW1_NEAR(1, 0, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, 0, -1, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, 1, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForRotationAboutY)
-{
- WebTransformationMatrix from;
- from.rotate3d(0, 1, 0, 0);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.rotate3d(0, 1, 0, 90);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- double expectedRotationAngle = 22.5 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(0, 1, 0, 90);
- to.blend(from, 0.25);
- EXPECT_ROW1_NEAR(cos(expectedRotationAngle), 0, sin(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, 1, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(-sin(expectedRotationAngle), 0, cos(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- expectedRotationAngle = 45 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(0, 1, 0, 90);
- to.blend(from, 0.5);
- EXPECT_ROW1_NEAR(cos(expectedRotationAngle), 0, sin(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, 1, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(-sin(expectedRotationAngle), 0, cos(expectedRotationAngle), 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.rotate3d(0, 1, 0, 90);
- to.blend(from, 1);
- EXPECT_ROW1_NEAR(0, 0, 1, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(0, 1, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(-1, 0, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-TEST(WebTransformationMatrixTest, verifyBlendForRotationAboutZ)
-{
- WebTransformationMatrix from;
- from.rotate3d(0, 0, 1, 0);
-
- WebTransformationMatrix to;
-
- to.makeIdentity();
- to.rotate3d(0, 0, 1, 90);
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- double expectedRotationAngle = 22.5 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(0, 0, 1, 90);
- to.blend(from, 0.25);
- EXPECT_ROW1_NEAR(cos(expectedRotationAngle), -sin(expectedRotationAngle), 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(sin(expectedRotationAngle), cos(expectedRotationAngle), 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, 0, 1, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- expectedRotationAngle = 45 * piDouble / 180.0;
- to.makeIdentity();
- to.rotate3d(0, 0, 1, 90);
- to.blend(from, 0.5);
- EXPECT_ROW1_NEAR(cos(expectedRotationAngle), -sin(expectedRotationAngle), 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(sin(expectedRotationAngle), cos(expectedRotationAngle), 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, 0, 1, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-
- to.makeIdentity();
- to.rotate3d(0, 0, 1, 90);
- to.blend(from, 1);
- EXPECT_ROW1_NEAR(0, -1, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW2_NEAR(1, 0, 0, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW3_NEAR(0, 0, 1, 0, to, ERROR_THRESHOLD);
- EXPECT_ROW4_EQ(0, 0, 0, 1, to);
-}
-
-
-TEST(WebTransformationMatrixTest, verifyBlendForCompositeTransform)
-{
- // Verify that the blending was done with a decomposition in correct order by blending
- // a composite transform.
- // Using matrix x vector notation (Ax = b, where x is column vector), the ordering should be:
- // perspective * translation * rotation * skew * scale
- //
- // It is not as important (or meaningful) to check intermediate interpolations; order
- // of operations will be tested well enough by the end cases that are easier to
- // specify.
-
- WebTransformationMatrix from;
- WebTransformationMatrix to;
-
- WebTransformationMatrix expectedEndOfAnimation;
- expectedEndOfAnimation.applyPerspective(1);
- expectedEndOfAnimation.translate3d(10, 20, 30);
- expectedEndOfAnimation.rotate3d(0, 0, 1, 25);
- expectedEndOfAnimation.skewY(45);
- expectedEndOfAnimation.scale3d(6, 7, 8);
-
- to = expectedEndOfAnimation;
- to.blend(from, 0);
- EXPECT_TRANSFORMATION_MATRIX_EQ(from, to);
-
- to = expectedEndOfAnimation;
- to.blend(from, 1);
-
- // Recomposing the matrix results in a normalized matrix, so to verify we need to
- // normalize the expectedEndOfAnimation before comparing elements. Normalizing means
- // dividing everything by expectedEndOfAnimation.m44().
- WebTransformationMatrix normalizedExpectedEndOfAnimation = expectedEndOfAnimation;
- WebTransformationMatrix normalizationMatrix;
- normalizationMatrix.setM11(1 / expectedEndOfAnimation.m44());
- normalizationMatrix.setM22(1 / expectedEndOfAnimation.m44());
- normalizationMatrix.setM33(1 / expectedEndOfAnimation.m44());
- normalizationMatrix.setM44(1 / expectedEndOfAnimation.m44());
- normalizedExpectedEndOfAnimation.multiply(normalizationMatrix);
-
- EXPECT_TRANSFORMATION_MATRIX_EQ(normalizedExpectedEndOfAnimation, to);
-}
-
-} // namespace
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