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gecko-dev/layout/style/nsStyleTransformMatrix.cpp

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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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