forked from mirrors/gecko-dev
d7e8a09c21
Updated with clang-format version 15.0.5 (taskcluster-MKK8dHUpQkGfPLA793lizg) # ignore-this-changeset Differential Revision: https://phabricator.services.mozilla.com/D168658
873 lines
31 KiB
C++
873 lines
31 KiB
C++
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
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/* vim: set ts=8 sts=2 et sw=2 tw=80: */
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/* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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/*
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* A class used for intermediate representations of the -moz-transform property.
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*/
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#include "nsStyleTransformMatrix.h"
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#include "nsLayoutUtils.h"
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#include "nsPresContext.h"
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#include "mozilla/MotionPathUtils.h"
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#include "mozilla/ServoBindings.h"
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#include "mozilla/StyleAnimationValue.h"
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#include "mozilla/SVGUtils.h"
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#include "gfxMatrix.h"
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#include "gfxQuaternion.h"
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using namespace mozilla;
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using namespace mozilla::gfx;
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namespace nsStyleTransformMatrix {
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/* Note on floating point precision: The transform matrix is an array
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* of single precision 'float's, and so are most of the input values
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* we get from the style system, but intermediate calculations
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* involving angles need to be done in 'double'.
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*/
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// Define UNIFIED_CONTINUATIONS here and in nsDisplayList.cpp
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// to have the transform property try
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// to transform content with continuations as one unified block instead of
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// several smaller ones. This is currently disabled because it doesn't work
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// correctly, since when the frames are initially being reflowed, their
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// continuations all compute their bounding rects independently of each other
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// and consequently get the wrong value.
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// #define UNIFIED_CONTINUATIONS
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void TransformReferenceBox::EnsureDimensionsAreCached() {
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if (mIsCached) {
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return;
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}
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MOZ_ASSERT(mFrame);
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mIsCached = true;
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if (mFrame->HasAnyStateBits(NS_FRAME_SVG_LAYOUT)) {
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if (mFrame->StyleDisplay()->mTransformBox == StyleGeometryBox::FillBox) {
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// Percentages in transforms resolve against the SVG bbox, and the
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// transform is relative to the top-left of the SVG bbox.
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nsRect bboxInAppUnits = nsLayoutUtils::ComputeGeometryBox(
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const_cast<nsIFrame*>(mFrame), StyleGeometryBox::FillBox);
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// The mRect of an SVG nsIFrame is its user space bounds *including*
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// stroke and markers, whereas bboxInAppUnits is its user space bounds
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// including fill only. We need to note the offset of the reference box
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// from the frame's mRect in mX/mY.
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mX = bboxInAppUnits.x - mFrame->GetPosition().x;
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mY = bboxInAppUnits.y - mFrame->GetPosition().y;
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mWidth = bboxInAppUnits.width;
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mHeight = bboxInAppUnits.height;
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} else {
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// The value 'border-box' is treated as 'view-box' for SVG content.
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MOZ_ASSERT(
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mFrame->StyleDisplay()->mTransformBox == StyleGeometryBox::ViewBox ||
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mFrame->StyleDisplay()->mTransformBox ==
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StyleGeometryBox::BorderBox,
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"Unexpected value for 'transform-box'");
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// Percentages in transforms resolve against the width/height of the
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// nearest viewport (or its viewBox if one is applied), and the
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// transform is relative to {0,0} in current user space.
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mX = -mFrame->GetPosition().x;
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mY = -mFrame->GetPosition().y;
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Size contextSize = SVGUtils::GetContextSize(mFrame);
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mWidth = nsPresContext::CSSPixelsToAppUnits(contextSize.width);
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mHeight = nsPresContext::CSSPixelsToAppUnits(contextSize.height);
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}
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return;
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}
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// If UNIFIED_CONTINUATIONS is not defined, this is simply the frame's
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// bounding rectangle, translated to the origin. Otherwise, it is the
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// smallest rectangle containing a frame and all of its continuations. For
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// example, if there is a <span> element with several continuations split
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// over several lines, this function will return the rectangle containing all
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// of those continuations.
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nsRect rect;
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#ifndef UNIFIED_CONTINUATIONS
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rect = mFrame->GetRect();
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#else
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// Iterate the continuation list, unioning together the bounding rects:
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for (const nsIFrame* currFrame = mFrame->FirstContinuation();
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currFrame != nullptr; currFrame = currFrame->GetNextContinuation()) {
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// Get the frame rect in local coordinates, then translate back to the
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// original coordinates:
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rect.UnionRect(
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result, nsRect(currFrame->GetOffsetTo(mFrame), currFrame->GetSize()));
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}
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#endif
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mX = 0;
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mY = 0;
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mWidth = rect.Width();
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mHeight = rect.Height();
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}
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void TransformReferenceBox::Init(const nsRect& aDimensions) {
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MOZ_ASSERT(!mFrame && !mIsCached);
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mX = aDimensions.x;
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mY = aDimensions.y;
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mWidth = aDimensions.width;
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mHeight = aDimensions.height;
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mIsCached = true;
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}
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float ProcessTranslatePart(
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const LengthPercentage& aValue, TransformReferenceBox* aRefBox,
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TransformReferenceBox::DimensionGetter aDimensionGetter) {
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return aValue.ResolveToCSSPixelsWith([&] {
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return aRefBox && !aRefBox->IsEmpty()
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? CSSPixel::FromAppUnits((aRefBox->*aDimensionGetter)())
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: CSSCoord(0);
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});
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}
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/**
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* Helper functions to process all the transformation function types.
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*
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* These take a matrix parameter to accumulate the current matrix.
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*/
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/* Helper function to process a matrix entry. */
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static void ProcessMatrix(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp) {
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const auto& matrix = aOp.AsMatrix();
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gfxMatrix result;
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result._11 = matrix.a;
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result._12 = matrix.b;
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result._21 = matrix.c;
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result._22 = matrix.d;
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result._31 = matrix.e;
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result._32 = matrix.f;
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aMatrix = result * aMatrix;
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}
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static void ProcessMatrix3D(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp) {
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Matrix4x4 temp;
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const auto& matrix = aOp.AsMatrix3D();
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temp._11 = matrix.m11;
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temp._12 = matrix.m12;
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temp._13 = matrix.m13;
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temp._14 = matrix.m14;
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temp._21 = matrix.m21;
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temp._22 = matrix.m22;
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temp._23 = matrix.m23;
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temp._24 = matrix.m24;
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temp._31 = matrix.m31;
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temp._32 = matrix.m32;
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temp._33 = matrix.m33;
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temp._34 = matrix.m34;
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temp._41 = matrix.m41;
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temp._42 = matrix.m42;
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temp._43 = matrix.m43;
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temp._44 = matrix.m44;
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aMatrix = temp * aMatrix;
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}
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// For accumulation for transform functions, |aOne| corresponds to |aB| and
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// |aTwo| corresponds to |aA| for StyleAnimationValue::Accumulate().
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class Accumulate {
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public:
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template <typename T>
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static T operate(const T& aOne, const T& aTwo, double aCoeff) {
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return aOne + aTwo * aCoeff;
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}
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static Point4D operateForPerspective(const Point4D& aOne, const Point4D& aTwo,
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double aCoeff) {
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return (aOne - Point4D(0, 0, 0, 1)) +
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(aTwo - Point4D(0, 0, 0, 1)) * aCoeff + Point4D(0, 0, 0, 1);
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}
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static Point3D operateForScale(const Point3D& aOne, const Point3D& aTwo,
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double aCoeff) {
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// For scale, the identify element is 1, see AddTransformScale in
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// StyleAnimationValue.cpp.
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return (aOne - Point3D(1, 1, 1)) + (aTwo - Point3D(1, 1, 1)) * aCoeff +
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Point3D(1, 1, 1);
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}
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static Matrix4x4 operateForRotate(const gfxQuaternion& aOne,
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const gfxQuaternion& aTwo, double aCoeff) {
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if (aCoeff == 0.0) {
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return aOne.ToMatrix();
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}
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double theta = acos(mozilla::clamped(aTwo.w, -1.0, 1.0));
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double scale = (theta != 0.0) ? 1.0 / sin(theta) : 0.0;
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theta *= aCoeff;
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scale *= sin(theta);
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gfxQuaternion result = gfxQuaternion(scale * aTwo.x, scale * aTwo.y,
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scale * aTwo.z, cos(theta)) *
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aOne;
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return result.ToMatrix();
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}
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static Matrix4x4 operateForFallback(const Matrix4x4& aMatrix1,
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const Matrix4x4& aMatrix2,
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double aProgress) {
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return aMatrix1;
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}
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static Matrix4x4 operateByServo(const Matrix4x4& aMatrix1,
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const Matrix4x4& aMatrix2, double aCount) {
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Matrix4x4 result;
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Servo_MatrixTransform_Operate(MatrixTransformOperator::Accumulate,
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&aMatrix1.components, &aMatrix2.components,
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aCount, &result.components);
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return result;
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}
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};
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class Interpolate {
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public:
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template <typename T>
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static T operate(const T& aOne, const T& aTwo, double aCoeff) {
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return aOne + (aTwo - aOne) * aCoeff;
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}
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static Point4D operateForPerspective(const Point4D& aOne, const Point4D& aTwo,
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double aCoeff) {
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return aOne + (aTwo - aOne) * aCoeff;
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}
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static Point3D operateForScale(const Point3D& aOne, const Point3D& aTwo,
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double aCoeff) {
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return aOne + (aTwo - aOne) * aCoeff;
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}
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static Matrix4x4 operateForRotate(const gfxQuaternion& aOne,
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const gfxQuaternion& aTwo, double aCoeff) {
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return aOne.Slerp(aTwo, aCoeff).ToMatrix();
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}
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static Matrix4x4 operateForFallback(const Matrix4x4& aMatrix1,
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const Matrix4x4& aMatrix2,
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double aProgress) {
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return aProgress < 0.5 ? aMatrix1 : aMatrix2;
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}
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static Matrix4x4 operateByServo(const Matrix4x4& aMatrix1,
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const Matrix4x4& aMatrix2, double aProgress) {
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Matrix4x4 result;
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Servo_MatrixTransform_Operate(MatrixTransformOperator::Interpolate,
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&aMatrix1.components, &aMatrix2.components,
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aProgress, &result.components);
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return result;
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}
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};
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template <typename Operator>
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static void ProcessMatrixOperator(Matrix4x4& aMatrix,
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const StyleTransform& aFrom,
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const StyleTransform& aTo, float aProgress,
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TransformReferenceBox& aRefBox) {
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float appUnitPerCSSPixel = AppUnitsPerCSSPixel();
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Matrix4x4 matrix1 = ReadTransforms(aFrom, aRefBox, appUnitPerCSSPixel);
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Matrix4x4 matrix2 = ReadTransforms(aTo, aRefBox, appUnitPerCSSPixel);
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aMatrix = Operator::operateByServo(matrix1, matrix2, aProgress) * aMatrix;
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}
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/* Helper function to process two matrices that we need to interpolate between
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*/
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void ProcessInterpolateMatrix(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp,
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TransformReferenceBox& aRefBox) {
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const auto& args = aOp.AsInterpolateMatrix();
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ProcessMatrixOperator<Interpolate>(aMatrix, args.from_list, args.to_list,
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args.progress._0, aRefBox);
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}
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void ProcessAccumulateMatrix(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp,
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TransformReferenceBox& aRefBox) {
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const auto& args = aOp.AsAccumulateMatrix();
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ProcessMatrixOperator<Accumulate>(aMatrix, args.from_list, args.to_list,
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args.count, aRefBox);
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}
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/* Helper function to process a translatex function. */
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static void ProcessTranslateX(Matrix4x4& aMatrix,
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const LengthPercentage& aLength,
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TransformReferenceBox& aRefBox) {
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Point3D temp;
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temp.x =
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ProcessTranslatePart(aLength, &aRefBox, &TransformReferenceBox::Width);
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aMatrix.PreTranslate(temp);
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}
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/* Helper function to process a translatey function. */
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static void ProcessTranslateY(Matrix4x4& aMatrix,
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const LengthPercentage& aLength,
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TransformReferenceBox& aRefBox) {
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Point3D temp;
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temp.y =
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ProcessTranslatePart(aLength, &aRefBox, &TransformReferenceBox::Height);
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aMatrix.PreTranslate(temp);
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}
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static void ProcessTranslateZ(Matrix4x4& aMatrix, const Length& aLength) {
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Point3D temp;
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temp.z = aLength.ToCSSPixels();
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aMatrix.PreTranslate(temp);
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}
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/* Helper function to process a translate function. */
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static void ProcessTranslate(Matrix4x4& aMatrix, const LengthPercentage& aX,
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const LengthPercentage& aY,
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TransformReferenceBox& aRefBox) {
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Point3D temp;
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temp.x = ProcessTranslatePart(aX, &aRefBox, &TransformReferenceBox::Width);
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temp.y = ProcessTranslatePart(aY, &aRefBox, &TransformReferenceBox::Height);
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aMatrix.PreTranslate(temp);
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}
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static void ProcessTranslate3D(Matrix4x4& aMatrix, const LengthPercentage& aX,
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const LengthPercentage& aY, const Length& aZ,
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TransformReferenceBox& aRefBox) {
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Point3D temp;
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temp.x = ProcessTranslatePart(aX, &aRefBox, &TransformReferenceBox::Width);
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temp.y = ProcessTranslatePart(aY, &aRefBox, &TransformReferenceBox::Height);
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temp.z = aZ.ToCSSPixels();
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aMatrix.PreTranslate(temp);
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}
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/* Helper function to set up a scale matrix. */
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static void ProcessScaleHelper(Matrix4x4& aMatrix, float aXScale, float aYScale,
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float aZScale) {
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aMatrix.PreScale(aXScale, aYScale, aZScale);
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}
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static void ProcessScale3D(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp) {
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const auto& scale = aOp.AsScale3D();
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ProcessScaleHelper(aMatrix, scale._0, scale._1, scale._2);
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}
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/* Helper function that, given a set of angles, constructs the appropriate
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* skew matrix.
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*/
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static void ProcessSkewHelper(Matrix4x4& aMatrix, const StyleAngle& aXAngle,
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const StyleAngle& aYAngle) {
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aMatrix.SkewXY(aXAngle.ToRadians(), aYAngle.ToRadians());
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}
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static void ProcessRotate3D(Matrix4x4& aMatrix, float aX, float aY, float aZ,
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const StyleAngle& aAngle) {
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Matrix4x4 temp;
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temp.SetRotateAxisAngle(aX, aY, aZ, aAngle.ToRadians());
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aMatrix = temp * aMatrix;
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}
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static void ProcessPerspective(
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Matrix4x4& aMatrix,
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const StyleGenericPerspectiveFunction<Length>& aPerspective) {
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if (aPerspective.IsNone()) {
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return;
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}
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float p = aPerspective.AsLength().ToCSSPixels();
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if (!std::isinf(p)) {
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aMatrix.Perspective(std::max(p, 1.0f));
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}
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}
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static void MatrixForTransformFunction(Matrix4x4& aMatrix,
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const StyleTransformOperation& aOp,
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TransformReferenceBox& aRefBox) {
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/* Get the keyword for the transform. */
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switch (aOp.tag) {
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case StyleTransformOperation::Tag::TranslateX:
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ProcessTranslateX(aMatrix, aOp.AsTranslateX(), aRefBox);
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break;
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case StyleTransformOperation::Tag::TranslateY:
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ProcessTranslateY(aMatrix, aOp.AsTranslateY(), aRefBox);
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break;
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case StyleTransformOperation::Tag::TranslateZ:
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ProcessTranslateZ(aMatrix, aOp.AsTranslateZ());
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break;
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case StyleTransformOperation::Tag::Translate:
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ProcessTranslate(aMatrix, aOp.AsTranslate()._0, aOp.AsTranslate()._1,
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aRefBox);
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break;
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case StyleTransformOperation::Tag::Translate3D:
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return ProcessTranslate3D(aMatrix, aOp.AsTranslate3D()._0,
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aOp.AsTranslate3D()._1, aOp.AsTranslate3D()._2,
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aRefBox);
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break;
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case StyleTransformOperation::Tag::ScaleX:
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ProcessScaleHelper(aMatrix, aOp.AsScaleX(), 1.0f, 1.0f);
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break;
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case StyleTransformOperation::Tag::ScaleY:
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ProcessScaleHelper(aMatrix, 1.0f, aOp.AsScaleY(), 1.0f);
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break;
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case StyleTransformOperation::Tag::ScaleZ:
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ProcessScaleHelper(aMatrix, 1.0f, 1.0f, aOp.AsScaleZ());
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break;
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case StyleTransformOperation::Tag::Scale:
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ProcessScaleHelper(aMatrix, aOp.AsScale()._0, aOp.AsScale()._1, 1.0f);
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break;
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case StyleTransformOperation::Tag::Scale3D:
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ProcessScale3D(aMatrix, aOp);
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break;
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case StyleTransformOperation::Tag::SkewX:
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ProcessSkewHelper(aMatrix, aOp.AsSkewX(), StyleAngle::Zero());
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break;
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case StyleTransformOperation::Tag::SkewY:
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ProcessSkewHelper(aMatrix, StyleAngle::Zero(), aOp.AsSkewY());
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break;
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case StyleTransformOperation::Tag::Skew:
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ProcessSkewHelper(aMatrix, aOp.AsSkew()._0, aOp.AsSkew()._1);
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break;
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case StyleTransformOperation::Tag::RotateX:
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aMatrix.RotateX(aOp.AsRotateX().ToRadians());
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break;
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case StyleTransformOperation::Tag::RotateY:
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aMatrix.RotateY(aOp.AsRotateY().ToRadians());
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break;
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case StyleTransformOperation::Tag::RotateZ:
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aMatrix.RotateZ(aOp.AsRotateZ().ToRadians());
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break;
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case StyleTransformOperation::Tag::Rotate:
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aMatrix.RotateZ(aOp.AsRotate().ToRadians());
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break;
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case StyleTransformOperation::Tag::Rotate3D:
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ProcessRotate3D(aMatrix, aOp.AsRotate3D()._0, aOp.AsRotate3D()._1,
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aOp.AsRotate3D()._2, aOp.AsRotate3D()._3);
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break;
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case StyleTransformOperation::Tag::Matrix:
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ProcessMatrix(aMatrix, aOp);
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break;
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case StyleTransformOperation::Tag::Matrix3D:
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ProcessMatrix3D(aMatrix, aOp);
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break;
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case StyleTransformOperation::Tag::InterpolateMatrix:
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ProcessInterpolateMatrix(aMatrix, aOp, aRefBox);
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break;
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case StyleTransformOperation::Tag::AccumulateMatrix:
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ProcessAccumulateMatrix(aMatrix, aOp, aRefBox);
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break;
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case StyleTransformOperation::Tag::Perspective:
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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
|