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+/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
+/* vim: set ts=8 sts=2 et sw=2 tw=80: */
+/* This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
+
+/*
+ * A class used for intermediate representations of the -moz-transform property.
+ */
+
+#include "nsStyleTransformMatrix.h"
+#include "nsLayoutUtils.h"
+#include "nsPresContext.h"
+#include "mozilla/MotionPathUtils.h"
+#include "mozilla/ServoBindings.h"
+#include "mozilla/StyleAnimationValue.h"
+#include "mozilla/SVGUtils.h"
+#include "gfxMatrix.h"
+#include "gfxQuaternion.h"
+
+using namespace mozilla;
+using namespace mozilla::gfx;
+
+namespace nsStyleTransformMatrix {
+
+/* Note on floating point precision: The transform matrix is an array
+ * of single precision 'float's, and so are most of the input values
+ * we get from the style system, but intermediate calculations
+ * involving angles need to be done in 'double'.
+ */
+
+// Define UNIFIED_CONTINUATIONS here and in nsDisplayList.cpp
+// to have the transform property try
+// to transform content with continuations as one unified block instead of
+// several smaller ones. This is currently disabled because it doesn't work
+// correctly, since when the frames are initially being reflowed, their
+// continuations all compute their bounding rects independently of each other
+// and consequently get the wrong value.
+//#define UNIFIED_CONTINUATIONS
+
+void TransformReferenceBox::EnsureDimensionsAreCached() {
+ if (mIsCached) {
+ return;
+ }
+
+ MOZ_ASSERT(mFrame);
+
+ mIsCached = true;
+
+ if (mFrame->HasAnyStateBits(NS_FRAME_SVG_LAYOUT)) {
+ if (mFrame->StyleDisplay()->mTransformBox == StyleGeometryBox::FillBox) {
+ // Percentages in transforms resolve against the SVG bbox, and the
+ // transform is relative to the top-left of the SVG bbox.
+ nsRect bboxInAppUnits = nsLayoutUtils::ComputeGeometryBox(
+ const_cast<nsIFrame*>(mFrame), StyleGeometryBox::FillBox);
+ // The mRect of an SVG nsIFrame is its user space bounds *including*
+ // stroke and markers, whereas bboxInAppUnits is its user space bounds
+ // including fill only. We need to note the offset of the reference box
+ // from the frame's mRect in mX/mY.
+ mX = bboxInAppUnits.x - mFrame->GetPosition().x;
+ mY = bboxInAppUnits.y - mFrame->GetPosition().y;
+ mWidth = bboxInAppUnits.width;
+ mHeight = bboxInAppUnits.height;
+ } else {
+ // The value 'border-box' is treated as 'view-box' for SVG content.
+ MOZ_ASSERT(
+ mFrame->StyleDisplay()->mTransformBox == StyleGeometryBox::ViewBox ||
+ mFrame->StyleDisplay()->mTransformBox ==
+ StyleGeometryBox::BorderBox,
+ "Unexpected value for 'transform-box'");
+ // Percentages in transforms resolve against the width/height of the
+ // nearest viewport (or its viewBox if one is applied), and the
+ // transform is relative to {0,0} in current user space.
+ mX = -mFrame->GetPosition().x;
+ mY = -mFrame->GetPosition().y;
+ Size contextSize = SVGUtils::GetContextSize(mFrame);
+ mWidth = nsPresContext::CSSPixelsToAppUnits(contextSize.width);
+ mHeight = nsPresContext::CSSPixelsToAppUnits(contextSize.height);
+ }
+ return;
+ }
+
+ // If UNIFIED_CONTINUATIONS is not defined, this is simply the frame's
+ // bounding rectangle, translated to the origin. Otherwise, it is the
+ // smallest rectangle containing a frame and all of its continuations. For
+ // example, if there is a <span> element with several continuations split
+ // over several lines, this function will return the rectangle containing all
+ // of those continuations.
+
+ nsRect rect;
+
+#ifndef UNIFIED_CONTINUATIONS
+ rect = mFrame->GetRect();
+#else
+ // Iterate the continuation list, unioning together the bounding rects:
+ for (const nsIFrame* currFrame = mFrame->FirstContinuation();
+ currFrame != nullptr; currFrame = currFrame->GetNextContinuation()) {
+ // Get the frame rect in local coordinates, then translate back to the
+ // original coordinates:
+ rect.UnionRect(
+ result, nsRect(currFrame->GetOffsetTo(mFrame), currFrame->GetSize()));
+ }
+#endif
+
+ mX = 0;
+ mY = 0;
+ mWidth = rect.Width();
+ mHeight = rect.Height();
+}
+
+void TransformReferenceBox::Init(const nsRect& aDimensions) {
+ MOZ_ASSERT(!mFrame && !mIsCached);
+
+ mX = aDimensions.x;
+ mY = aDimensions.y;
+ mWidth = aDimensions.width;
+ mHeight = aDimensions.height;
+ mIsCached = true;
+}
+
+float ProcessTranslatePart(
+ const LengthPercentage& aValue, TransformReferenceBox* aRefBox,
+ TransformReferenceBox::DimensionGetter aDimensionGetter) {
+ return aValue.ResolveToCSSPixelsWith([&] {
+ return aRefBox && !aRefBox->IsEmpty()
+ ? CSSPixel::FromAppUnits((aRefBox->*aDimensionGetter)())
+ : CSSCoord(0);
+ });
+}
+
+/**
+ * Helper functions to process all the transformation function types.
+ *
+ * These take a matrix parameter to accumulate the current matrix.
+ */
+
+/* Helper function to process a matrix entry. */
+static void ProcessMatrix(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp) {
+ const auto& matrix = aOp.AsMatrix();
+ gfxMatrix result;
+
+ result._11 = matrix.a;
+ result._12 = matrix.b;
+ result._21 = matrix.c;
+ result._22 = matrix.d;
+ result._31 = matrix.e;
+ result._32 = matrix.f;
+
+ aMatrix = result * aMatrix;
+}
+
+static void ProcessMatrix3D(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp) {
+ Matrix4x4 temp;
+
+ const auto& matrix = aOp.AsMatrix3D();
+
+ temp._11 = matrix.m11;
+ temp._12 = matrix.m12;
+ temp._13 = matrix.m13;
+ temp._14 = matrix.m14;
+ temp._21 = matrix.m21;
+ temp._22 = matrix.m22;
+ temp._23 = matrix.m23;
+ temp._24 = matrix.m24;
+ temp._31 = matrix.m31;
+ temp._32 = matrix.m32;
+ temp._33 = matrix.m33;
+ temp._34 = matrix.m34;
+
+ temp._41 = matrix.m41;
+ temp._42 = matrix.m42;
+ temp._43 = matrix.m43;
+ temp._44 = matrix.m44;
+
+ aMatrix = temp * aMatrix;
+}
+
+// For accumulation for transform functions, |aOne| corresponds to |aB| and
+// |aTwo| corresponds to |aA| for StyleAnimationValue::Accumulate().
+class Accumulate {
+ public:
+ template <typename T>
+ static T operate(const T& aOne, const T& aTwo, double aCoeff) {
+ return aOne + aTwo * aCoeff;
+ }
+
+ static Point4D operateForPerspective(const Point4D& aOne, const Point4D& aTwo,
+ double aCoeff) {
+ return (aOne - Point4D(0, 0, 0, 1)) +
+ (aTwo - Point4D(0, 0, 0, 1)) * aCoeff + Point4D(0, 0, 0, 1);
+ }
+ static Point3D operateForScale(const Point3D& aOne, const Point3D& aTwo,
+ double aCoeff) {
+ // For scale, the identify element is 1, see AddTransformScale in
+ // StyleAnimationValue.cpp.
+ return (aOne - Point3D(1, 1, 1)) + (aTwo - Point3D(1, 1, 1)) * aCoeff +
+ Point3D(1, 1, 1);
+ }
+
+ static Matrix4x4 operateForRotate(const gfxQuaternion& aOne,
+ const gfxQuaternion& aTwo, double aCoeff) {
+ if (aCoeff == 0.0) {
+ return aOne.ToMatrix();
+ }
+
+ double theta = acos(mozilla::clamped(aTwo.w, -1.0, 1.0));
+ double scale = (theta != 0.0) ? 1.0 / sin(theta) : 0.0;
+ theta *= aCoeff;
+ scale *= sin(theta);
+
+ gfxQuaternion result = gfxQuaternion(scale * aTwo.x, scale * aTwo.y,
+ scale * aTwo.z, cos(theta)) *
+ aOne;
+ return result.ToMatrix();
+ }
+
+ static Matrix4x4 operateForFallback(const Matrix4x4& aMatrix1,
+ const Matrix4x4& aMatrix2,
+ double aProgress) {
+ return aMatrix1;
+ }
+
+ static Matrix4x4 operateByServo(const Matrix4x4& aMatrix1,
+ const Matrix4x4& aMatrix2, double aCount) {
+ Matrix4x4 result;
+ Servo_MatrixTransform_Operate(MatrixTransformOperator::Accumulate,
+ &aMatrix1.components, &aMatrix2.components,
+ aCount, &result.components);
+ return result;
+ }
+};
+
+class Interpolate {
+ public:
+ template <typename T>
+ static T operate(const T& aOne, const T& aTwo, double aCoeff) {
+ return aOne + (aTwo - aOne) * aCoeff;
+ }
+
+ static Point4D operateForPerspective(const Point4D& aOne, const Point4D& aTwo,
+ double aCoeff) {
+ return aOne + (aTwo - aOne) * aCoeff;
+ }
+
+ static Point3D operateForScale(const Point3D& aOne, const Point3D& aTwo,
+ double aCoeff) {
+ return aOne + (aTwo - aOne) * aCoeff;
+ }
+
+ static Matrix4x4 operateForRotate(const gfxQuaternion& aOne,
+ const gfxQuaternion& aTwo, double aCoeff) {
+ return aOne.Slerp(aTwo, aCoeff).ToMatrix();
+ }
+
+ static Matrix4x4 operateForFallback(const Matrix4x4& aMatrix1,
+ const Matrix4x4& aMatrix2,
+ double aProgress) {
+ return aProgress < 0.5 ? aMatrix1 : aMatrix2;
+ }
+
+ static Matrix4x4 operateByServo(const Matrix4x4& aMatrix1,
+ const Matrix4x4& aMatrix2, double aProgress) {
+ Matrix4x4 result;
+ Servo_MatrixTransform_Operate(MatrixTransformOperator::Interpolate,
+ &aMatrix1.components, &aMatrix2.components,
+ aProgress, &result.components);
+ return result;
+ }
+};
+
+template <typename Operator>
+static void ProcessMatrixOperator(Matrix4x4& aMatrix,
+ const StyleTransform& aFrom,
+ const StyleTransform& aTo, float aProgress,
+ TransformReferenceBox& aRefBox) {
+ float appUnitPerCSSPixel = AppUnitsPerCSSPixel();
+ Matrix4x4 matrix1 = ReadTransforms(aFrom, aRefBox, appUnitPerCSSPixel);
+ Matrix4x4 matrix2 = ReadTransforms(aTo, aRefBox, appUnitPerCSSPixel);
+ aMatrix = Operator::operateByServo(matrix1, matrix2, aProgress) * aMatrix;
+}
+
+/* Helper function to process two matrices that we need to interpolate between
+ */
+void ProcessInterpolateMatrix(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp,
+ TransformReferenceBox& aRefBox) {
+ const auto& args = aOp.AsInterpolateMatrix();
+ ProcessMatrixOperator<Interpolate>(aMatrix, args.from_list, args.to_list,
+ args.progress._0, aRefBox);
+}
+
+void ProcessAccumulateMatrix(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp,
+ TransformReferenceBox& aRefBox) {
+ const auto& args = aOp.AsAccumulateMatrix();
+ ProcessMatrixOperator<Accumulate>(aMatrix, args.from_list, args.to_list,
+ args.count, aRefBox);
+}
+
+/* Helper function to process a translatex function. */
+static void ProcessTranslateX(Matrix4x4& aMatrix,
+ const LengthPercentage& aLength,
+ TransformReferenceBox& aRefBox) {
+ Point3D temp;
+ temp.x =
+ ProcessTranslatePart(aLength, &aRefBox, &TransformReferenceBox::Width);
+ aMatrix.PreTranslate(temp);
+}
+
+/* Helper function to process a translatey function. */
+static void ProcessTranslateY(Matrix4x4& aMatrix,
+ const LengthPercentage& aLength,
+ TransformReferenceBox& aRefBox) {
+ Point3D temp;
+ temp.y =
+ ProcessTranslatePart(aLength, &aRefBox, &TransformReferenceBox::Height);
+ aMatrix.PreTranslate(temp);
+}
+
+static void ProcessTranslateZ(Matrix4x4& aMatrix, const Length& aLength) {
+ Point3D temp;
+ temp.z = aLength.ToCSSPixels();
+ aMatrix.PreTranslate(temp);
+}
+
+/* Helper function to process a translate function. */
+static void ProcessTranslate(Matrix4x4& aMatrix, const LengthPercentage& aX,
+ const LengthPercentage& aY,
+ TransformReferenceBox& aRefBox) {
+ Point3D temp;
+ temp.x = ProcessTranslatePart(aX, &aRefBox, &TransformReferenceBox::Width);
+ temp.y = ProcessTranslatePart(aY, &aRefBox, &TransformReferenceBox::Height);
+ aMatrix.PreTranslate(temp);
+}
+
+static void ProcessTranslate3D(Matrix4x4& aMatrix, const LengthPercentage& aX,
+ const LengthPercentage& aY, const Length& aZ,
+ TransformReferenceBox& aRefBox) {
+ Point3D temp;
+
+ temp.x = ProcessTranslatePart(aX, &aRefBox, &TransformReferenceBox::Width);
+ temp.y = ProcessTranslatePart(aY, &aRefBox, &TransformReferenceBox::Height);
+ temp.z = aZ.ToCSSPixels();
+
+ aMatrix.PreTranslate(temp);
+}
+
+/* Helper function to set up a scale matrix. */
+static void ProcessScaleHelper(Matrix4x4& aMatrix, float aXScale, float aYScale,
+ float aZScale) {
+ aMatrix.PreScale(aXScale, aYScale, aZScale);
+}
+
+static void ProcessScale3D(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp) {
+ const auto& scale = aOp.AsScale3D();
+ ProcessScaleHelper(aMatrix, scale._0, scale._1, scale._2);
+}
+
+/* Helper function that, given a set of angles, constructs the appropriate
+ * skew matrix.
+ */
+static void ProcessSkewHelper(Matrix4x4& aMatrix, const StyleAngle& aXAngle,
+ const StyleAngle& aYAngle) {
+ aMatrix.SkewXY(aXAngle.ToRadians(), aYAngle.ToRadians());
+}
+
+static void ProcessRotate3D(Matrix4x4& aMatrix, float aX, float aY, float aZ,
+ const StyleAngle& aAngle) {
+ Matrix4x4 temp;
+ temp.SetRotateAxisAngle(aX, aY, aZ, aAngle.ToRadians());
+ aMatrix = temp * aMatrix;
+}
+
+static void ProcessPerspective(Matrix4x4& aMatrix, const Length& aLength) {
+ float depth = aLength.ToCSSPixels();
+ ApplyPerspectiveToMatrix(aMatrix, depth);
+}
+
+static void MatrixForTransformFunction(Matrix4x4& aMatrix,
+ const StyleTransformOperation& aOp,
+ TransformReferenceBox& aRefBox) {
+ /* Get the keyword for the transform. */
+ switch (aOp.tag) {
+ case StyleTransformOperation::Tag::TranslateX:
+ ProcessTranslateX(aMatrix, aOp.AsTranslateX(), aRefBox);
+ break;
+ case StyleTransformOperation::Tag::TranslateY:
+ ProcessTranslateY(aMatrix, aOp.AsTranslateY(), aRefBox);
+ break;
+ case StyleTransformOperation::Tag::TranslateZ:
+ ProcessTranslateZ(aMatrix, aOp.AsTranslateZ());
+ break;
+ case StyleTransformOperation::Tag::Translate:
+ ProcessTranslate(aMatrix, aOp.AsTranslate()._0, aOp.AsTranslate()._1,
+ aRefBox);
+ break;
+ case StyleTransformOperation::Tag::Translate3D:
+ return ProcessTranslate3D(aMatrix, aOp.AsTranslate3D()._0,
+ aOp.AsTranslate3D()._1, aOp.AsTranslate3D()._2,
+ aRefBox);
+ break;
+ case StyleTransformOperation::Tag::ScaleX:
+ ProcessScaleHelper(aMatrix, aOp.AsScaleX(), 1.0f, 1.0f);
+ break;
+ case StyleTransformOperation::Tag::ScaleY:
+ ProcessScaleHelper(aMatrix, 1.0f, aOp.AsScaleY(), 1.0f);
+ break;
+ case StyleTransformOperation::Tag::ScaleZ:
+ ProcessScaleHelper(aMatrix, 1.0f, 1.0f, aOp.AsScaleZ());
+ break;
+ case StyleTransformOperation::Tag::Scale:
+ ProcessScaleHelper(aMatrix, aOp.AsScale()._0, aOp.AsScale()._1, 1.0f);
+ break;
+ case StyleTransformOperation::Tag::Scale3D:
+ ProcessScale3D(aMatrix, aOp);
+ break;
+ case StyleTransformOperation::Tag::SkewX:
+ ProcessSkewHelper(aMatrix, aOp.AsSkewX(), StyleAngle::Zero());
+ break;
+ case StyleTransformOperation::Tag::SkewY:
+ ProcessSkewHelper(aMatrix, StyleAngle::Zero(), aOp.AsSkewY());
+ break;
+ case StyleTransformOperation::Tag::Skew:
+ ProcessSkewHelper(aMatrix, aOp.AsSkew()._0, aOp.AsSkew()._1);
+ break;
+ case StyleTransformOperation::Tag::RotateX:
+ aMatrix.RotateX(aOp.AsRotateX().ToRadians());
+ break;
+ case StyleTransformOperation::Tag::RotateY:
+ aMatrix.RotateY(aOp.AsRotateY().ToRadians());
+ break;
+ case StyleTransformOperation::Tag::RotateZ:
+ aMatrix.RotateZ(aOp.AsRotateZ().ToRadians());
+ break;
+ case StyleTransformOperation::Tag::Rotate:
+ aMatrix.RotateZ(aOp.AsRotate().ToRadians());
+ break;
+ case StyleTransformOperation::Tag::Rotate3D:
+ ProcessRotate3D(aMatrix, aOp.AsRotate3D()._0, aOp.AsRotate3D()._1,
+ aOp.AsRotate3D()._2, aOp.AsRotate3D()._3);
+ break;
+ case StyleTransformOperation::Tag::Matrix:
+ ProcessMatrix(aMatrix, aOp);
+ break;
+ case StyleTransformOperation::Tag::Matrix3D:
+ ProcessMatrix3D(aMatrix, aOp);
+ break;
+ case StyleTransformOperation::Tag::InterpolateMatrix:
+ ProcessInterpolateMatrix(aMatrix, aOp, aRefBox);
+ break;
+ case StyleTransformOperation::Tag::AccumulateMatrix:
+ ProcessAccumulateMatrix(aMatrix, aOp, aRefBox);
+ break;
+ case StyleTransformOperation::Tag::Perspective:
+ ProcessPerspective(aMatrix, aOp.AsPerspective());
+ break;
+ default:
+ MOZ_ASSERT_UNREACHABLE("Unknown transform function!");
+ }
+}
+
+Matrix4x4 ReadTransforms(const StyleTransform& aTransform,
+ TransformReferenceBox& aRefBox,
+ float aAppUnitsPerMatrixUnit) {
+ Matrix4x4 result;
+
+ for (const StyleTransformOperation& op : aTransform.Operations()) {
+ MatrixForTransformFunction(result, op, aRefBox);
+ }
+
+ float scale = float(AppUnitsPerCSSPixel()) / aAppUnitsPerMatrixUnit;
+ result.PreScale(1 / scale, 1 / scale, 1 / scale);
+ result.PostScale(scale, scale, scale);
+
+ return result;
+}
+
+static void ProcessTranslate(Matrix4x4& aMatrix,
+ const StyleTranslate& aTranslate,
+ TransformReferenceBox& aRefBox) {
+ switch (aTranslate.tag) {
+ case StyleTranslate::Tag::None:
+ return;
+ case StyleTranslate::Tag::Translate:
+ return ProcessTranslate3D(aMatrix, aTranslate.AsTranslate()._0,
+ aTranslate.AsTranslate()._1,
+ aTranslate.AsTranslate()._2, aRefBox);
+ default:
+ MOZ_ASSERT_UNREACHABLE("Huh?");
+ }
+}
+
+static void ProcessRotate(Matrix4x4& aMatrix, const StyleRotate& aRotate) {
+ switch (aRotate.tag) {
+ case StyleRotate::Tag::None:
+ return;
+ case StyleRotate::Tag::Rotate:
+ aMatrix.RotateZ(aRotate.AsRotate().ToRadians());
+ return;
+ case StyleRotate::Tag::Rotate3D:
+ return ProcessRotate3D(aMatrix, aRotate.AsRotate3D()._0,
+ aRotate.AsRotate3D()._1, aRotate.AsRotate3D()._2,
+ aRotate.AsRotate3D()._3);
+ default:
+ MOZ_ASSERT_UNREACHABLE("Huh?");
+ }
+}
+
+static void ProcessScale(Matrix4x4& aMatrix, const StyleScale& aScale) {
+ switch (aScale.tag) {
+ case StyleScale::Tag::None:
+ return;
+ case StyleScale::Tag::Scale:
+ return ProcessScaleHelper(aMatrix, aScale.AsScale()._0,
+ aScale.AsScale()._1, aScale.AsScale()._2);
+ default:
+ MOZ_ASSERT_UNREACHABLE("Huh?");
+ }
+}
+
+Matrix4x4 ReadTransforms(const StyleTranslate& aTranslate,
+ const StyleRotate& aRotate, const StyleScale& aScale,
+ const Maybe<ResolvedMotionPathData>& aMotion,
+ const StyleTransform& aTransform,
+ TransformReferenceBox& aRefBox,
+ float aAppUnitsPerMatrixUnit) {
+ Matrix4x4 result;
+
+ ProcessTranslate(result, aTranslate, aRefBox);
+ ProcessRotate(result, aRotate);
+ ProcessScale(result, aScale);
+
+ if (aMotion.isSome()) {
+ // Create the equivalent translate and rotate function, according to the
+ // order in spec. We combine the translate and then the rotate.
+ // https://drafts.fxtf.org/motion-1/#calculating-path-transform
+ //
+ // Besides, we have to shift the object by the delta between anchor-point
+ // and transform-origin, to make sure we rotate the object according to
+ // anchor-point.
+ result.PreTranslate(aMotion->mTranslate.x + aMotion->mShift.x,
+ aMotion->mTranslate.y + aMotion->mShift.y, 0.0);
+ if (aMotion->mRotate != 0.0) {
+ result.RotateZ(aMotion->mRotate);
+ }
+ // Shift the origin back to transform-origin.
+ result.PreTranslate(-aMotion->mShift.x, -aMotion->mShift.y, 0.0);
+ }
+
+ for (const StyleTransformOperation& op : aTransform.Operations()) {
+ MatrixForTransformFunction(result, op, aRefBox);
+ }
+
+ float scale = float(AppUnitsPerCSSPixel()) / aAppUnitsPerMatrixUnit;
+ result.PreScale(1 / scale, 1 / scale, 1 / scale);
+ result.PostScale(scale, scale, scale);
+
+ return result;
+}
+
+mozilla::CSSPoint Convert2DPosition(const mozilla::LengthPercentage& aX,
+ const mozilla::LengthPercentage& aY,
+ const CSSSize& aSize) {
+ return {
+ aX.ResolveToCSSPixels(aSize.width),
+ aY.ResolveToCSSPixels(aSize.height),
+ };
+}
+
+CSSPoint Convert2DPosition(const LengthPercentage& aX,
+ const LengthPercentage& aY,
+ TransformReferenceBox& aRefBox) {
+ return {
+ aX.ResolveToCSSPixelsWith(
+ [&] { return CSSPixel::FromAppUnits(aRefBox.Width()); }),
+ aY.ResolveToCSSPixelsWith(
+ [&] { return CSSPixel::FromAppUnits(aRefBox.Height()); }),
+ };
+}
+
+Point Convert2DPosition(const LengthPercentage& aX, const LengthPercentage& aY,
+ TransformReferenceBox& aRefBox,
+ int32_t aAppUnitsPerPixel) {
+ float scale = mozilla::AppUnitsPerCSSPixel() / float(aAppUnitsPerPixel);
+ CSSPoint p = Convert2DPosition(aX, aY, aRefBox);
+ return {p.x * scale, p.y * scale};
+}
+
+/*
+ * The relevant section of the transitions specification:
+ * http://dev.w3.org/csswg/css3-transitions/#animation-of-property-types-
+ * defers all of the details to the 2-D and 3-D transforms specifications.
+ * For the 2-D transforms specification (all that's relevant for us, right
+ * now), the relevant section is:
+ * http://dev.w3.org/csswg/css3-2d-transforms/#animation
+ * This, in turn, refers to the unmatrix program in Graphics Gems,
+ * available from http://tog.acm.org/resources/GraphicsGems/ , and in
+ * particular as the file GraphicsGems/gemsii/unmatrix.c
+ * in http://tog.acm.org/resources/GraphicsGems/AllGems.tar.gz
+ *
+ * The unmatrix reference is for general 3-D transform matrices (any of the
+ * 16 components can have any value).
+ *
+ * For CSS 2-D transforms, we have a 2-D matrix with the bottom row constant:
+ *
+ * [ A C E ]
+ * [ B D F ]
+ * [ 0 0 1 ]
+ *
+ * For that case, I believe the algorithm in unmatrix reduces to:
+ *
+ * (1) If A * D - B * C == 0, the matrix is singular. Fail.
+ *
+ * (2) Set translation components (Tx and Ty) to the translation parts of
+ * the matrix (E and F) and then ignore them for the rest of the time.
+ * (For us, E and F each actually consist of three constants: a
+ * length, a multiplier for the width, and a multiplier for the
+ * height. This actually requires its own decomposition, but I'll
+ * keep that separate.)
+ *
+ * (3) Let the X scale (Sx) be sqrt(A^2 + B^2). Then divide both A and B
+ * by it.
+ *
+ * (4) Let the XY shear (K) be A * C + B * D. From C, subtract A times
+ * the XY shear. From D, subtract B times the XY shear.
+ *
+ * (5) Let the Y scale (Sy) be sqrt(C^2 + D^2). Divide C, D, and the XY
+ * shear (K) by it.
+ *
+ * (6) At this point, A * D - B * C is either 1 or -1. If it is -1,
+ * negate the XY shear (K), the X scale (Sx), and A, B, C, and D.
+ * (Alternatively, we could negate the XY shear (K) and the Y scale
+ * (Sy).)
+ *
+ * (7) Let the rotation be R = atan2(B, A).
+ *
+ * Then the resulting decomposed transformation is:
+ *
+ * translate(Tx, Ty) rotate(R) skewX(atan(K)) scale(Sx, Sy)
+ *
+ * An interesting result of this is that all of the simple transform
+ * functions (i.e., all functions other than matrix()), in isolation,
+ * decompose back to themselves except for:
+ * 'skewY(φ)', which is 'matrix(1, tan(φ), 0, 1, 0, 0)', which decomposes
+ * to 'rotate(φ) skewX(φ) scale(sec(φ), cos(φ))' since (ignoring the
+ * alternate sign possibilities that would get fixed in step 6):
+ * In step 3, the X scale factor is sqrt(1+tan²(φ)) = sqrt(sec²(φ)) =
+ * sec(φ). Thus, after step 3, A = 1/sec(φ) = cos(φ) and B = tan(φ) / sec(φ) =
+ * sin(φ). In step 4, the XY shear is sin(φ). Thus, after step 4, C =
+ * -cos(φ)sin(φ) and D = 1 - sin²(φ) = cos²(φ). Thus, in step 5, the Y scale is
+ * sqrt(cos²(φ)(sin²(φ) + cos²(φ)) = cos(φ). Thus, after step 5, C = -sin(φ), D
+ * = cos(φ), and the XY shear is tan(φ). Thus, in step 6, A * D - B * C =
+ * cos²(φ) + sin²(φ) = 1. In step 7, the rotation is thus φ.
+ *
+ * skew(θ, φ), which is matrix(1, tan(φ), tan(θ), 1, 0, 0), which decomposes
+ * to 'rotate(φ) skewX(θ + φ) scale(sec(φ), cos(φ))' since (ignoring
+ * the alternate sign possibilities that would get fixed in step 6):
+ * In step 3, the X scale factor is sqrt(1+tan²(φ)) = sqrt(sec²(φ)) =
+ * sec(φ). Thus, after step 3, A = 1/sec(φ) = cos(φ) and B = tan(φ) / sec(φ) =
+ * sin(φ). In step 4, the XY shear is cos(φ)tan(θ) + sin(φ). Thus, after step 4,
+ * C = tan(θ) - cos(φ)(cos(φ)tan(θ) + sin(φ)) = tan(θ)sin²(φ) - cos(φ)sin(φ)
+ * D = 1 - sin(φ)(cos(φ)tan(θ) + sin(φ)) = cos²(φ) - sin(φ)cos(φ)tan(θ)
+ * Thus, in step 5, the Y scale is sqrt(C² + D²) =
+ * sqrt(tan²(θ)(sin⁴(φ) + sin²(φ)cos²(φ)) -
+ * 2 tan(θ)(sin³(φ)cos(φ) + sin(φ)cos³(φ)) +
+ * (sin²(φ)cos²(φ) + cos⁴(φ))) =
+ * sqrt(tan²(θ)sin²(φ) - 2 tan(θ)sin(φ)cos(φ) + cos²(φ)) =
+ * cos(φ) - tan(θ)sin(φ) (taking the negative of the obvious solution so
+ * we avoid flipping in step 6).
+ * After step 5, C = -sin(φ) and D = cos(φ), and the XY shear is
+ * (cos(φ)tan(θ) + sin(φ)) / (cos(φ) - tan(θ)sin(φ)) =
+ * (dividing both numerator and denominator by cos(φ))
+ * (tan(θ) + tan(φ)) / (1 - tan(θ)tan(φ)) = tan(θ + φ).
+ * (See http://en.wikipedia.org/wiki/List_of_trigonometric_identities .)
+ * Thus, in step 6, A * D - B * C = cos²(φ) + sin²(φ) = 1.
+ * In step 7, the rotation is thus φ.
+ *
+ * To check this result, we can multiply things back together:
+ *
+ * [ cos(φ) -sin(φ) ] [ 1 tan(θ + φ) ] [ sec(φ) 0 ]
+ * [ sin(φ) cos(φ) ] [ 0 1 ] [ 0 cos(φ) ]
+ *
+ * [ cos(φ) cos(φ)tan(θ + φ) - sin(φ) ] [ sec(φ) 0 ]
+ * [ sin(φ) sin(φ)tan(θ + φ) + cos(φ) ] [ 0 cos(φ) ]
+ *
+ * but since tan(θ + φ) = (tan(θ) + tan(φ)) / (1 - tan(θ)tan(φ)),
+ * cos(φ)tan(θ + φ) - sin(φ)
+ * = cos(φ)(tan(θ) + tan(φ)) - sin(φ) + sin(φ)tan(θ)tan(φ)
+ * = cos(φ)tan(θ) + sin(φ) - sin(φ) + sin(φ)tan(θ)tan(φ)
+ * = cos(φ)tan(θ) + sin(φ)tan(θ)tan(φ)
+ * = tan(θ) (cos(φ) + sin(φ)tan(φ))
+ * = tan(θ) sec(φ) (cos²(φ) + sin²(φ))
+ * = tan(θ) sec(φ)
+ * and
+ * sin(φ)tan(θ + φ) + cos(φ)
+ * = sin(φ)(tan(θ) + tan(φ)) + cos(φ) - cos(φ)tan(θ)tan(φ)
+ * = tan(θ) (sin(φ) - sin(φ)) + sin(φ)tan(φ) + cos(φ)
+ * = sec(φ) (sin²(φ) + cos²(φ))
+ * = sec(φ)
+ * so the above is:
+ * [ cos(φ) tan(θ) sec(φ) ] [ sec(φ) 0 ]
+ * [ sin(φ) sec(φ) ] [ 0 cos(φ) ]
+ *
+ * [ 1 tan(θ) ]
+ * [ tan(φ) 1 ]
+ */
+
+/*
+ * Decompose2DMatrix implements the above decomposition algorithm.
+ */
+
+bool Decompose2DMatrix(const Matrix& aMatrix, Point3D& aScale,
+ ShearArray& aShear, gfxQuaternion& aRotate,
+ Point3D& aTranslate) {
+ float A = aMatrix._11, B = aMatrix._12, C = aMatrix._21, D = aMatrix._22;
+ if (A * D == B * C) {
+ // singular matrix
+ return false;
+ }
+
+ float scaleX = sqrt(A * A + B * B);
+ A /= scaleX;
+ B /= scaleX;
+
+ float XYshear = A * C + B * D;
+ C -= A * XYshear;
+ D -= B * XYshear;
+
+ float scaleY = sqrt(C * C + D * D);
+ C /= scaleY;
+ D /= scaleY;
+ XYshear /= scaleY;
+
+ float determinant = A * D - B * C;
+ // Determinant should now be 1 or -1.
+ if (0.99 > Abs(determinant) || Abs(determinant) > 1.01) {
+ return false;
+ }
+
+ if (determinant < 0) {
+ A = -A;
+ B = -B;
+ C = -C;
+ D = -D;
+ XYshear = -XYshear;
+ scaleX = -scaleX;
+ }
+
+ float rotate = atan2f(B, A);
+ aRotate = gfxQuaternion(0, 0, sin(rotate / 2), cos(rotate / 2));
+ aShear[ShearType::XY] = XYshear;
+ aScale.x = scaleX;
+ aScale.y = scaleY;
+ aTranslate.x = aMatrix._31;
+ aTranslate.y = aMatrix._32;
+ return true;
+}
+
+/**
+ * Implementation of the unmatrix algorithm, specified by:
+ *
+ * http://dev.w3.org/csswg/css3-2d-transforms/#unmatrix
+ *
+ * This, in turn, refers to the unmatrix program in Graphics Gems,
+ * available from http://tog.acm.org/resources/GraphicsGems/ , and in
+ * particular as the file GraphicsGems/gemsii/unmatrix.c
+ * in http://tog.acm.org/resources/GraphicsGems/AllGems.tar.gz
+ */
+bool Decompose3DMatrix(const Matrix4x4& aMatrix, Point3D& aScale,
+ ShearArray& aShear, gfxQuaternion& aRotate,
+ Point3D& aTranslate, Point4D& aPerspective) {
+ Matrix4x4 local = aMatrix;
+
+ if (local[3][3] == 0) {
+ return false;
+ }
+
+ /* Normalize the matrix */
+ local.Normalize();
+
+ /**
+ * perspective is used to solve for perspective, but it also provides
+ * an easy way to test for singularity of the upper 3x3 component.
+ */
+ Matrix4x4 perspective = local;
+ Point4D empty(0, 0, 0, 1);
+ perspective.SetTransposedVector(3, empty);
+
+ if (perspective.Determinant() == 0.0) {
+ return false;
+ }
+
+ /* First, isolate perspective. */
+ if (local[0][3] != 0 || local[1][3] != 0 || local[2][3] != 0) {
+ /* aPerspective is the right hand side of the equation. */
+ aPerspective = local.TransposedVector(3);
+
+ /**
+ * Solve the equation by inverting perspective and multiplying
+ * aPerspective by the inverse.
+ */
+ perspective.Invert();
+ aPerspective = perspective.TransposeTransform4D(aPerspective);
+
+ /* Clear the perspective partition */
+ local.SetTransposedVector(3, empty);
+ } else {
+ aPerspective = Point4D(0, 0, 0, 1);
+ }
+
+ /* Next take care of translation */
+ for (int i = 0; i < 3; i++) {
+ aTranslate[i] = local[3][i];
+ local[3][i] = 0;
+ }
+
+ /* Now get scale and shear. */
+
+ /* Compute X scale factor and normalize first row. */
+ aScale.x = local[0].Length();
+ local[0] /= aScale.x;
+
+ /* Compute XY shear factor and make 2nd local orthogonal to 1st. */
+ aShear[ShearType::XY] = local[0].DotProduct(local[1]);
+ local[1] -= local[0] * aShear[ShearType::XY];
+
+ /* Now, compute Y scale and normalize 2nd local. */
+ aScale.y = local[1].Length();
+ local[1] /= aScale.y;
+ aShear[ShearType::XY] /= aScale.y;
+
+ /* Compute XZ and YZ shears, make 3rd local orthogonal */
+ aShear[ShearType::XZ] = local[0].DotProduct(local[2]);
+ local[2] -= local[0] * aShear[ShearType::XZ];
+ aShear[ShearType::YZ] = local[1].DotProduct(local[2]);
+ local[2] -= local[1] * aShear[ShearType::YZ];
+
+ /* Next, get Z scale and normalize 3rd local. */
+ aScale.z = local[2].Length();
+ local[2] /= aScale.z;
+
+ aShear[ShearType::XZ] /= aScale.z;
+ aShear[ShearType::YZ] /= aScale.z;
+
+ /**
+ * At this point, the matrix (in locals) is orthonormal.
+ * Check for a coordinate system flip. If the determinant
+ * is -1, then negate the matrix and the scaling factors.
+ */
+ if (local[0].DotProduct(local[1].CrossProduct(local[2])) < 0) {
+ aScale *= -1;
+ for (int i = 0; i < 3; i++) {
+ local[i] *= -1;
+ }
+ }
+
+ /* Now, get the rotations out */
+ aRotate = gfxQuaternion(local);
+
+ return true;
+}
+
+} // namespace nsStyleTransformMatrix
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