/* -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */ /* 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 "nsCSSValue.h" #include "nsLayoutUtils.h" #include "nsPresContext.h" #include "nsRuleNode.h" #include "nsSVGUtils.h" #include "nsCSSKeywords.h" #include "mozilla/StyleAnimationValue.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->GetStateBits() & NS_FRAME_SVG_LAYOUT) { if (!nsLayoutUtils::SVGTransformBoxEnabled()) { mX = -mFrame->GetPosition().x; mY = -mFrame->GetPosition().y; Size contextSize = nsSVGUtils::GetContextSize(mFrame); mWidth = nsPresContext::CSSPixelsToAppUnits(contextSize.width); mHeight = nsPresContext::CSSPixelsToAppUnits(contextSize.height); } else if (mFrame->StyleDisplay()->mTransformBox == NS_STYLE_TRANSFORM_BOX_FILL_BOX) { // Percentages in transforms resolve against the SVG bbox, and the // transform is relative to the top-left of the SVG bbox. gfxRect bbox = nsSVGUtils::GetBBox(const_cast<nsIFrame*>(mFrame)); nsRect bboxInAppUnits = nsLayoutUtils::RoundGfxRectToAppRect(bbox, mFrame->PresContext()->AppUnitsPerCSSPixel()); // 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 == NS_STYLE_TRANSFORM_BOX_VIEW_BOX || mFrame->StyleDisplay()->mTransformBox == NS_STYLE_TRANSFORM_BOX_BORDER_BOX, "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 = nsSVGUtils::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 nsSize& aDimensions) { MOZ_ASSERT(!mFrame && !mIsCached); mX = 0; mY = 0; mWidth = aDimensions.width; mHeight = aDimensions.height; mIsCached = true; } float ProcessTranslatePart(const nsCSSValue& aValue, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox* aRefBox, TransformReferenceBox::DimensionGetter aDimensionGetter) { nscoord offset = 0; float percent = 0.0f; if (aValue.GetUnit() == eCSSUnit_Percent) { percent = aValue.GetPercentValue(); } else if (aValue.GetUnit() == eCSSUnit_Pixel || aValue.GetUnit() == eCSSUnit_Number) { // Handle this here (even though nsRuleNode::CalcLength handles it // fine) so that callers are allowed to pass a null style context // and pres context to SetToTransformFunction if they know (as // StyleAnimationValue does) that all lengths within the transform // function have already been computed to pixels and percents. // // Raw numbers are treated as being pixels. // // Don't convert to aValue to AppUnits here to avoid precision issues. return aValue.GetFloatValue(); } else if (aValue.IsCalcUnit()) { nsRuleNode::ComputedCalc result = nsRuleNode::SpecifiedCalcToComputedCalc(aValue, aContext, aPresContext, aConditions); percent = result.mPercent; offset = result.mLength; } else { offset = nsRuleNode::CalcLength(aValue, aContext, aPresContext, aConditions); } float translation = NSAppUnitsToFloatPixels(offset, nsPresContext::AppUnitsPerCSSPixel()); // We want to avoid calling aDimensionGetter if there's no percentage to be // resolved (for performance reasons - see TransformReferenceBox). if (percent != 0.0f && aRefBox && !aRefBox->IsEmpty()) { translation += percent * NSAppUnitsToFloatPixels((aRefBox->*aDimensionGetter)(), nsPresContext::AppUnitsPerCSSPixel()); } return translation; } /** * 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 nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 7, "Invalid array!"); gfxMatrix result; /* Take the first four elements out of the array as floats and store * them. */ result._11 = aData->Item(1).GetFloatValue(); result._12 = aData->Item(2).GetFloatValue(); result._21 = aData->Item(3).GetFloatValue(); result._22 = aData->Item(4).GetFloatValue(); /* The last two elements have their length parts stored in aDelta * and their percent parts stored in aX[0] and aY[1]. */ result._31 = ProcessTranslatePart(aData->Item(5), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Width); result._32 = ProcessTranslatePart(aData->Item(6), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Height); aMatrix = result * aMatrix; } static void ProcessMatrix3D(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 17, "Invalid array!"); Matrix4x4 temp; temp._11 = aData->Item(1).GetFloatValue(); temp._12 = aData->Item(2).GetFloatValue(); temp._13 = aData->Item(3).GetFloatValue(); temp._14 = aData->Item(4).GetFloatValue(); temp._21 = aData->Item(5).GetFloatValue(); temp._22 = aData->Item(6).GetFloatValue(); temp._23 = aData->Item(7).GetFloatValue(); temp._24 = aData->Item(8).GetFloatValue(); temp._31 = aData->Item(9).GetFloatValue(); temp._32 = aData->Item(10).GetFloatValue(); temp._33 = aData->Item(11).GetFloatValue(); temp._34 = aData->Item(12).GetFloatValue(); temp._44 = aData->Item(16).GetFloatValue(); temp._41 = ProcessTranslatePart(aData->Item(13), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Width); temp._42 = ProcessTranslatePart(aData->Item(14), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Height); temp._43 = ProcessTranslatePart(aData->Item(15), aContext, aPresContext, aConditions, nullptr); aMatrix = temp * aMatrix; } /* Helper function to process two matrices that we need to interpolate between */ void ProcessInterpolateMatrix(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox, bool* aContains3dTransform) { NS_PRECONDITION(aData->Count() == 4, "Invalid array!"); Matrix4x4 matrix1, matrix2; if (aData->Item(1).GetUnit() == eCSSUnit_List) { matrix1 = nsStyleTransformMatrix::ReadTransforms(aData->Item(1).GetListValue(), aContext, aPresContext, aConditions, aRefBox, nsPresContext::AppUnitsPerCSSPixel(), aContains3dTransform); } if (aData->Item(2).GetUnit() == eCSSUnit_List) { matrix2 = ReadTransforms(aData->Item(2).GetListValue(), aContext, aPresContext, aConditions, aRefBox, nsPresContext::AppUnitsPerCSSPixel(), aContains3dTransform); } double progress = aData->Item(3).GetPercentValue(); aMatrix = StyleAnimationValue::InterpolateTransformMatrix(matrix1, matrix2, progress) * aMatrix; } /* Helper function to process a translatex function. */ static void ProcessTranslateX(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); Point3D temp; temp.x = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Width); aMatrix.PreTranslate(temp); } /* Helper function to process a translatey function. */ static void ProcessTranslateY(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); Point3D temp; temp.y = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Height); aMatrix.PreTranslate(temp); } static void ProcessTranslateZ(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); Point3D temp; temp.z = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, nullptr); aMatrix.PreTranslate(temp); } /* Helper function to process a translate function. */ static void ProcessTranslate(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 2 || aData->Count() == 3, "Invalid array!"); Point3D temp; temp.x = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Width); /* If we read in a Y component, set it appropriately */ if (aData->Count() == 3) { temp.y = ProcessTranslatePart(aData->Item(2), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Height); } aMatrix.PreTranslate(temp); } static void ProcessTranslate3D(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox) { NS_PRECONDITION(aData->Count() == 4, "Invalid array!"); Point3D temp; temp.x = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Width); temp.y = ProcessTranslatePart(aData->Item(2), aContext, aPresContext, aConditions, &aRefBox, &TransformReferenceBox::Height); temp.z = ProcessTranslatePart(aData->Item(3), aContext, aPresContext, aConditions, nullptr); 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); } /* Process a scalex function. */ static void ProcessScaleX(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Bad array!"); ProcessScaleHelper(aMatrix, aData->Item(1).GetFloatValue(), 1.0f, 1.0f); } /* Process a scaley function. */ static void ProcessScaleY(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Bad array!"); ProcessScaleHelper(aMatrix, 1.0f, aData->Item(1).GetFloatValue(), 1.0f); } static void ProcessScaleZ(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Bad array!"); ProcessScaleHelper(aMatrix, 1.0f, 1.0f, aData->Item(1).GetFloatValue()); } static void ProcessScale3D(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 4, "Bad array!"); ProcessScaleHelper(aMatrix, aData->Item(1).GetFloatValue(), aData->Item(2).GetFloatValue(), aData->Item(3).GetFloatValue()); } /* Process a scale function. */ static void ProcessScale(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2 || aData->Count() == 3, "Bad array!"); /* We either have one element or two. If we have one, it's for both X and Y. * Otherwise it's one for each. */ const nsCSSValue& scaleX = aData->Item(1); const nsCSSValue& scaleY = (aData->Count() == 2 ? scaleX : aData->Item(2)); ProcessScaleHelper(aMatrix, scaleX.GetFloatValue(), scaleY.GetFloatValue(), 1.0f); } /* Helper function that, given a set of angles, constructs the appropriate * skew matrix. */ static void ProcessSkewHelper(Matrix4x4& aMatrix, double aXAngle, double aYAngle) { aMatrix.SkewXY(aXAngle, aYAngle); } /* Function that converts a skewx transform into a matrix. */ static void ProcessSkewX(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_ASSERTION(aData->Count() == 2, "Bad array!"); ProcessSkewHelper(aMatrix, aData->Item(1).GetAngleValueInRadians(), 0.0); } /* Function that converts a skewy transform into a matrix. */ static void ProcessSkewY(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_ASSERTION(aData->Count() == 2, "Bad array!"); ProcessSkewHelper(aMatrix, 0.0, aData->Item(1).GetAngleValueInRadians()); } /* Function that converts a skew transform into a matrix. */ static void ProcessSkew(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_ASSERTION(aData->Count() == 2 || aData->Count() == 3, "Bad array!"); double xSkew = aData->Item(1).GetAngleValueInRadians(); double ySkew = (aData->Count() == 2 ? 0.0 : aData->Item(2).GetAngleValueInRadians()); ProcessSkewHelper(aMatrix, xSkew, ySkew); } /* Function that converts a rotate transform into a matrix. */ static void ProcessRotateZ(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); double theta = aData->Item(1).GetAngleValueInRadians(); aMatrix.RotateZ(theta); } static void ProcessRotateX(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); double theta = aData->Item(1).GetAngleValueInRadians(); aMatrix.RotateX(theta); } static void ProcessRotateY(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); double theta = aData->Item(1).GetAngleValueInRadians(); aMatrix.RotateY(theta); } static void ProcessRotate3D(Matrix4x4& aMatrix, const nsCSSValue::Array* aData) { NS_PRECONDITION(aData->Count() == 5, "Invalid array!"); double theta = aData->Item(4).GetAngleValueInRadians(); float x = aData->Item(1).GetFloatValue(); float y = aData->Item(2).GetFloatValue(); float z = aData->Item(3).GetFloatValue(); Matrix4x4 temp; temp.SetRotateAxisAngle(x, y, z, theta); aMatrix = temp * aMatrix; } static void ProcessPerspective(Matrix4x4& aMatrix, const nsCSSValue::Array* aData, nsStyleContext *aContext, nsPresContext *aPresContext, RuleNodeCacheConditions& aConditions) { NS_PRECONDITION(aData->Count() == 2, "Invalid array!"); float depth = ProcessTranslatePart(aData->Item(1), aContext, aPresContext, aConditions, nullptr); ApplyPerspectiveToMatrix(aMatrix, depth); } /** * SetToTransformFunction is essentially a giant switch statement that fans * out to many smaller helper functions. */ static void MatrixForTransformFunction(Matrix4x4& aMatrix, const nsCSSValue::Array * aData, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox, bool* aContains3dTransform) { MOZ_ASSERT(aContains3dTransform); NS_PRECONDITION(aData, "Why did you want to get data from a null array?"); // It's OK if aContext and aPresContext are null if the caller already // knows that all length units have been converted to pixels (as // StyleAnimationValue does). /* Get the keyword for the transform. */ switch (TransformFunctionOf(aData)) { case eCSSKeyword_translatex: ProcessTranslateX(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_translatey: ProcessTranslateY(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_translatez: *aContains3dTransform = true; ProcessTranslateZ(aMatrix, aData, aContext, aPresContext, aConditions); break; case eCSSKeyword_translate: ProcessTranslate(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_translate3d: *aContains3dTransform = true; ProcessTranslate3D(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_scalex: ProcessScaleX(aMatrix, aData); break; case eCSSKeyword_scaley: ProcessScaleY(aMatrix, aData); break; case eCSSKeyword_scalez: *aContains3dTransform = true; ProcessScaleZ(aMatrix, aData); break; case eCSSKeyword_scale: ProcessScale(aMatrix, aData); break; case eCSSKeyword_scale3d: *aContains3dTransform = true; ProcessScale3D(aMatrix, aData); break; case eCSSKeyword_skewx: ProcessSkewX(aMatrix, aData); break; case eCSSKeyword_skewy: ProcessSkewY(aMatrix, aData); break; case eCSSKeyword_skew: ProcessSkew(aMatrix, aData); break; case eCSSKeyword_rotatex: *aContains3dTransform = true; ProcessRotateX(aMatrix, aData); break; case eCSSKeyword_rotatey: *aContains3dTransform = true; ProcessRotateY(aMatrix, aData); break; case eCSSKeyword_rotatez: *aContains3dTransform = true; MOZ_FALLTHROUGH; case eCSSKeyword_rotate: ProcessRotateZ(aMatrix, aData); break; case eCSSKeyword_rotate3d: *aContains3dTransform = true; ProcessRotate3D(aMatrix, aData); break; case eCSSKeyword_matrix: ProcessMatrix(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_matrix3d: *aContains3dTransform = true; ProcessMatrix3D(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox); break; case eCSSKeyword_interpolatematrix: ProcessInterpolateMatrix(aMatrix, aData, aContext, aPresContext, aConditions, aRefBox, aContains3dTransform); break; case eCSSKeyword_perspective: *aContains3dTransform = true; ProcessPerspective(aMatrix, aData, aContext, aPresContext, aConditions); break; default: NS_NOTREACHED("Unknown transform function!"); } } /** * Return the transform function, as an nsCSSKeyword, for the given * nsCSSValue::Array from a transform list. */ nsCSSKeyword TransformFunctionOf(const nsCSSValue::Array* aData) { MOZ_ASSERT(aData->Item(0).GetUnit() == eCSSUnit_Enumerated); return aData->Item(0).GetKeywordValue(); } void SetIdentityMatrix(nsCSSValue::Array* aMatrix) { MOZ_ASSERT(aMatrix, "aMatrix should be non-null"); nsCSSKeyword tfunc = TransformFunctionOf(aMatrix); MOZ_ASSERT(tfunc == eCSSKeyword_matrix || tfunc == eCSSKeyword_matrix3d, "Only accept matrix and matrix3d"); if (tfunc == eCSSKeyword_matrix) { MOZ_ASSERT(aMatrix->Count() == 7, "Invalid matrix"); Matrix m; for (size_t i = 0; i < 6; ++i) { aMatrix->Item(i + 1).SetFloatValue(m.components[i], eCSSUnit_Number); } return; } MOZ_ASSERT(aMatrix->Count() == 17, "Invalid matrix3d"); Matrix4x4 m; for (size_t i = 0; i < 16; ++i) { aMatrix->Item(i + 1).SetFloatValue(m.components[i], eCSSUnit_Number); } } Matrix4x4 ReadTransforms(const nsCSSValueList* aList, nsStyleContext* aContext, nsPresContext* aPresContext, RuleNodeCacheConditions& aConditions, TransformReferenceBox& aRefBox, float aAppUnitsPerMatrixUnit, bool* aContains3dTransform) { Matrix4x4 result; for (const nsCSSValueList* curr = aList; curr != nullptr; curr = curr->mNext) { const nsCSSValue &currElem = curr->mValue; if (currElem.GetUnit() != eCSSUnit_Function) { NS_ASSERTION(currElem.GetUnit() == eCSSUnit_None && !aList->mNext, "stream should either be a list of functions or a " "lone None"); continue; } NS_ASSERTION(currElem.GetArrayValue()->Count() >= 1, "Incoming function is too short!"); /* Read in a single transform matrix. */ MatrixForTransformFunction(result, currElem.GetArrayValue(), aContext, aPresContext, aConditions, aRefBox, aContains3dTransform); } float scale = float(nsPresContext::AppUnitsPerCSSPixel()) / aAppUnitsPerMatrixUnit; result.PreScale(1/scale, 1/scale, 1/scale); result.PostScale(scale, scale, scale); return result; } /* * 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; // A*D - B*C should now be 1 or -1 NS_ASSERTION(0.99 < Abs(A*D - B*C) && Abs(A*D - B*C) < 1.01, "determinant should now be 1 or -1"); if (A * D < B * C) { 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::XYSHEAR] = 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::XYSHEAR] = local[0].DotProduct(local[1]); local[1] -= local[0] * aShear[ShearType::XYSHEAR]; /* Now, compute Y scale and normalize 2nd local. */ aScale.y = local[1].Length(); local[1] /= aScale.y; aShear[ShearType::XYSHEAR] /= aScale.y; /* Compute XZ and YZ shears, make 3rd local orthogonal */ aShear[ShearType::XZSHEAR] = local[0].DotProduct(local[2]); local[2] -= local[0] * aShear[ShearType::XZSHEAR]; aShear[ShearType::YZSHEAR] = local[1].DotProduct(local[2]); local[2] -= local[1] * aShear[ShearType::YZSHEAR]; /* Next, get Z scale and normalize 3rd local. */ aScale.z = local[2].Length(); local[2] /= aScale.z; aShear[ShearType::XZSHEAR] /= aScale.z; aShear[ShearType::YZSHEAR] /= 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; } Matrix CSSValueArrayTo2DMatrix(nsCSSValue::Array* aArray) { MOZ_ASSERT(aArray && TransformFunctionOf(aArray) == eCSSKeyword_matrix && aArray->Count() == 7); Matrix m(aArray->Item(1).GetFloatValue(), aArray->Item(2).GetFloatValue(), aArray->Item(3).GetFloatValue(), aArray->Item(4).GetFloatValue(), aArray->Item(5).GetFloatValue(), aArray->Item(6).GetFloatValue()); return m; } Matrix4x4 CSSValueArrayTo3DMatrix(nsCSSValue::Array* aArray) { MOZ_ASSERT(aArray && TransformFunctionOf(aArray) == eCSSKeyword_matrix3d && aArray->Count() == 17); gfx::Float array[16]; for (size_t i = 0; i < 16; ++i) { array[i] = aArray->Item(i+1).GetFloatValue(); } Matrix4x4 m(array); return m; } } // namespace nsStyleTransformMatrix