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Diffstat (limited to 'layout/style/nsStyleTransformMatrix.cpp')
| -rw-r--r-- | layout/style/nsStyleTransformMatrix.cpp | 873 |
1 files changed, 873 insertions, 0 deletions
diff --git a/layout/style/nsStyleTransformMatrix.cpp b/layout/style/nsStyleTransformMatrix.cpp new file mode 100644 index 0000000000..cefe1adaab --- /dev/null +++ b/layout/style/nsStyleTransformMatrix.cpp @@ -0,0 +1,873 @@ +/* -*- 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 StyleGenericPerspectiveFunction<Length>& aPerspective) { + if (aPerspective.IsNone()) { + return; + } + float p = aPerspective.AsLength().ToCSSPixels(); + if (!std::isinf(p)) { + aMatrix.Perspective(std::max(p, 1.0f)); + } +} + +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 |