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Diffstat (limited to 'gfx/2d/Matrix.h')
| -rw-r--r-- | gfx/2d/Matrix.h | 1676 |
1 files changed, 1676 insertions, 0 deletions
diff --git a/gfx/2d/Matrix.h b/gfx/2d/Matrix.h new file mode 100644 index 000000000..22a01ca10 --- /dev/null +++ b/gfx/2d/Matrix.h @@ -0,0 +1,1676 @@ +/* -*- Mode: C++; tab-width: 20; 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/. */ + +#ifndef MOZILLA_GFX_MATRIX_H_ +#define MOZILLA_GFX_MATRIX_H_ + +#include "Types.h" +#include "Triangle.h" +#include "Rect.h" +#include "Point.h" +#include "Quaternion.h" +#include <iosfwd> +#include <math.h> +#include "mozilla/Attributes.h" +#include "mozilla/DebugOnly.h" +#include "mozilla/FloatingPoint.h" + +namespace mozilla { +namespace gfx { + +static bool FuzzyEqual(Float aV1, Float aV2) { + // XXX - Check if fabs does the smart thing and just negates the sign bit. + return fabs(aV2 - aV1) < 1e-6; +} + +class Matrix +{ +public: + Matrix() + : _11(1.0f), _12(0) + , _21(0), _22(1.0f) + , _31(0), _32(0) + {} + Matrix(Float a11, Float a12, Float a21, Float a22, Float a31, Float a32) + : _11(a11), _12(a12) + , _21(a21), _22(a22) + , _31(a31), _32(a32) + {} + union { + struct { + Float _11, _12; + Float _21, _22; + Float _31, _32; + }; + Float components[6]; + }; + + MOZ_ALWAYS_INLINE Matrix Copy() const + { + return Matrix(*this); + } + + friend std::ostream& operator<<(std::ostream& aStream, const Matrix& aMatrix); + + Point TransformPoint(const Point &aPoint) const + { + Point retPoint; + + retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31; + retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32; + + return retPoint; + } + + Size TransformSize(const Size &aSize) const + { + Size retSize; + + retSize.width = aSize.width * _11 + aSize.height * _21; + retSize.height = aSize.width * _12 + aSize.height * _22; + + return retSize; + } + + GFX2D_API Rect TransformBounds(const Rect& rect) const; + + static Matrix Translation(Float aX, Float aY) + { + return Matrix(1.0f, 0.0f, 0.0f, 1.0f, aX, aY); + } + + static Matrix Translation(Point aPoint) + { + return Translation(aPoint.x, aPoint.y); + } + + /** + * Apply a translation to this matrix. + * + * The "Pre" in this method's name means that the translation is applied + * -before- this matrix's existing transformation. That is, any vector that + * is multiplied by the resulting matrix will first be translated, then be + * transformed by the original transform. + * + * Calling this method will result in this matrix having the same value as + * the result of: + * + * Matrix::Translation(x, y) * this + * + * (Note that in performance critical code multiplying by the result of a + * Translation()/Scaling() call is not recommended since that results in a + * full matrix multiply involving 12 floating-point multiplications. Calling + * this method would be preferred since it only involves four floating-point + * multiplications.) + */ + Matrix &PreTranslate(Float aX, Float aY) + { + _31 += _11 * aX + _21 * aY; + _32 += _12 * aX + _22 * aY; + + return *this; + } + + Matrix &PreTranslate(const Point &aPoint) + { + return PreTranslate(aPoint.x, aPoint.y); + } + + /** + * Similar to PreTranslate, but the translation is applied -after- this + * matrix's existing transformation instead of before it. + * + * This method is generally less used than PreTranslate since typically code + * want to adjust an existing user space to device space matrix to create a + * transform to device space from a -new- user space (translated from the + * previous user space). In that case consumers will need to use the Pre* + * variants of the matrix methods rather than using the Post* methods, since + * the Post* methods add a transform to the device space end of the + * transformation. + */ + Matrix &PostTranslate(Float aX, Float aY) + { + _31 += aX; + _32 += aY; + return *this; + } + + Matrix &PostTranslate(const Point &aPoint) + { + return PostTranslate(aPoint.x, aPoint.y); + } + + static Matrix Scaling(Float aScaleX, Float aScaleY) + { + return Matrix(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f); + } + + /** + * Similar to PreTranslate, but applies a scale instead of a translation. + */ + Matrix &PreScale(Float aX, Float aY) + { + _11 *= aX; + _12 *= aX; + _21 *= aY; + _22 *= aY; + + return *this; + } + + /** + * Similar to PostTranslate, but applies a scale instead of a translation. + */ + Matrix &PostScale(Float aScaleX, Float aScaleY) + { + _11 *= aScaleX; + _12 *= aScaleY; + _21 *= aScaleX; + _22 *= aScaleY; + _31 *= aScaleX; + _32 *= aScaleY; + + return *this; + } + + GFX2D_API static Matrix Rotation(Float aAngle); + + /** + * Similar to PreTranslate, but applies a rotation instead of a translation. + */ + Matrix &PreRotate(Float aAngle) + { + return *this = Matrix::Rotation(aAngle) * *this; + } + + bool Invert() + { + // Compute co-factors. + Float A = _22; + Float B = -_21; + Float C = _21 * _32 - _22 * _31; + Float D = -_12; + Float E = _11; + Float F = _31 * _12 - _11 * _32; + + Float det = Determinant(); + + if (!det) { + return false; + } + + Float inv_det = 1 / det; + + _11 = inv_det * A; + _12 = inv_det * D; + _21 = inv_det * B; + _22 = inv_det * E; + _31 = inv_det * C; + _32 = inv_det * F; + + return true; + } + + Matrix Inverse() const + { + Matrix clone = *this; + DebugOnly<bool> inverted = clone.Invert(); + MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix"); + return clone; + } + + Float Determinant() const + { + return _11 * _22 - _12 * _21; + } + + Matrix operator*(const Matrix &aMatrix) const + { + Matrix resultMatrix; + + resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21; + resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22; + resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21; + resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22; + resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + aMatrix._31; + resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + aMatrix._32; + + return resultMatrix; + } + + Matrix& operator*=(const Matrix &aMatrix) + { + *this = *this * aMatrix; + return *this; + } + + /** + * Multiplies in the opposite order to operator=*. + */ + Matrix &PreMultiply(const Matrix &aMatrix) + { + *this = aMatrix * *this; + return *this; + } + + /* Returns true if the other matrix is fuzzy-equal to this matrix. + * Note that this isn't a cheap comparison! + */ + bool operator==(const Matrix& other) const + { + return FuzzyEqual(_11, other._11) && FuzzyEqual(_12, other._12) && + FuzzyEqual(_21, other._21) && FuzzyEqual(_22, other._22) && + FuzzyEqual(_31, other._31) && FuzzyEqual(_32, other._32); + } + + bool operator!=(const Matrix& other) const + { + return !(*this == other); + } + + bool ExactlyEquals(const Matrix& o) const + { + return _11 == o._11 && _12 == o._12 && + _21 == o._21 && _22 == o._22 && + _31 == o._31 && _32 == o._32; + } + + /* Verifies that the matrix contains no Infs or NaNs. */ + bool IsFinite() const + { + return mozilla::IsFinite(_11) && mozilla::IsFinite(_12) && + mozilla::IsFinite(_21) && mozilla::IsFinite(_22) && + mozilla::IsFinite(_31) && mozilla::IsFinite(_32); + } + + /* Returns true if the matrix is a rectilinear transformation (i.e. + * grid-aligned rectangles are transformed to grid-aligned rectangles) + */ + bool IsRectilinear() const { + if (FuzzyEqual(_12, 0) && FuzzyEqual(_21, 0)) { + return true; + } else if (FuzzyEqual(_22, 0) && FuzzyEqual(_11, 0)) { + return true; + } + + return false; + } + + /** + * Returns true if the matrix is anything other than a straight + * translation by integers. + */ + bool HasNonIntegerTranslation() const { + return HasNonTranslation() || + !FuzzyEqual(_31, floor(_31 + Float(0.5))) || + !FuzzyEqual(_32, floor(_32 + Float(0.5))); + } + + /** + * Returns true if the matrix only has an integer translation. + */ + bool HasOnlyIntegerTranslation() const { + return !HasNonIntegerTranslation(); + } + + /** + * Returns true if the matrix has any transform other + * than a straight translation. + */ + bool HasNonTranslation() const { + return !FuzzyEqual(_11, 1.0) || !FuzzyEqual(_22, 1.0) || + !FuzzyEqual(_12, 0.0) || !FuzzyEqual(_21, 0.0); + } + + /** + * Returns true if the matrix has any transform other + * than a translation or a -1 y scale (y axis flip) + */ + bool HasNonTranslationOrFlip() const { + return !FuzzyEqual(_11, 1.0) || + (!FuzzyEqual(_22, 1.0) && !FuzzyEqual(_22, -1.0)) || + !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0); + } + + /* Returns true if the matrix is an identity matrix. + */ + bool IsIdentity() const + { + return _11 == 1.0f && _12 == 0.0f && + _21 == 0.0f && _22 == 1.0f && + _31 == 0.0f && _32 == 0.0f; + } + + /* Returns true if the matrix is singular. + */ + bool IsSingular() const + { + Float det = Determinant(); + return !mozilla::IsFinite(det) || det == 0; + } + + GFX2D_API Matrix &NudgeToIntegers(); + + bool IsTranslation() const + { + return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) && + FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f); + } + + static bool FuzzyIsInteger(Float aValue) + { + return FuzzyEqual(aValue, floorf(aValue + 0.5f)); + } + + bool IsIntegerTranslation() const + { + return IsTranslation() && FuzzyIsInteger(_31) && FuzzyIsInteger(_32); + } + + bool IsAllIntegers() const + { + return FuzzyIsInteger(_11) && FuzzyIsInteger(_12) && + FuzzyIsInteger(_21) && FuzzyIsInteger(_22) && + FuzzyIsInteger(_31) && FuzzyIsInteger(_32); + } + + Point GetTranslation() const { + return Point(_31, _32); + } + + /** + * Returns true if matrix is multiple of 90 degrees rotation with flipping, + * scaling and translation. + */ + bool PreservesAxisAlignedRectangles() const { + return ((FuzzyEqual(_11, 0.0) && FuzzyEqual(_22, 0.0)) + || (FuzzyEqual(_12, 0.0) && FuzzyEqual(_21, 0.0))); + } + + /** + * Returns true if the matrix has any transform other + * than a translation or scale; this is, if there is + * rotation. + */ + bool HasNonAxisAlignedTransform() const { + return !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0); + } + + /** + * Returns true if the matrix has negative scaling (i.e. flip). + */ + bool HasNegativeScaling() const { + return (_11 < 0.0) || (_22 < 0.0); + } +}; + +// Helper functions used by Matrix4x4Typed defined in Matrix.cpp +double +SafeTangent(double aTheta); +double +FlushToZero(double aVal); + +template<class Units, class F> +Point4DTyped<Units, F> +ComputePerspectivePlaneIntercept(const Point4DTyped<Units, F>& aFirst, + const Point4DTyped<Units, F>& aSecond) +{ + // This function will always return a point with a w value of 0. + // The X, Y, and Z components will point towards an infinite vanishing + // point. + + // We want to interpolate aFirst and aSecond to find the point intersecting + // with the w=0 plane. + + // Since we know what we want the w component to be, we can rearrange the + // interpolation equation and solve for t. + float t = -aFirst.w / (aSecond.w - aFirst.w); + + // Use t to find the remainder of the components + return aFirst + (aSecond - aFirst) * t; +} + + +template <typename SourceUnits, typename TargetUnits> +class Matrix4x4Typed +{ +public: + typedef PointTyped<SourceUnits> SourcePoint; + typedef PointTyped<TargetUnits> TargetPoint; + typedef Point3DTyped<SourceUnits> SourcePoint3D; + typedef Point3DTyped<TargetUnits> TargetPoint3D; + typedef Point4DTyped<SourceUnits> SourcePoint4D; + typedef Point4DTyped<TargetUnits> TargetPoint4D; + typedef RectTyped<SourceUnits> SourceRect; + typedef RectTyped<TargetUnits> TargetRect; + + Matrix4x4Typed() + : _11(1.0f), _12(0.0f), _13(0.0f), _14(0.0f) + , _21(0.0f), _22(1.0f), _23(0.0f), _24(0.0f) + , _31(0.0f), _32(0.0f), _33(1.0f), _34(0.0f) + , _41(0.0f), _42(0.0f), _43(0.0f), _44(1.0f) + {} + + Matrix4x4Typed(Float a11, Float a12, Float a13, Float a14, + Float a21, Float a22, Float a23, Float a24, + Float a31, Float a32, Float a33, Float a34, + Float a41, Float a42, Float a43, Float a44) + : _11(a11), _12(a12), _13(a13), _14(a14) + , _21(a21), _22(a22), _23(a23), _24(a24) + , _31(a31), _32(a32), _33(a33), _34(a34) + , _41(a41), _42(a42), _43(a43), _44(a44) + {} + + explicit Matrix4x4Typed(const Float aArray[16]) + { + memcpy(components, aArray, sizeof(components)); + } + + Matrix4x4Typed(const Matrix4x4Typed& aOther) + { + memcpy(this, &aOther, sizeof(*this)); + } + + union { + struct { + Float _11, _12, _13, _14; + Float _21, _22, _23, _24; + Float _31, _32, _33, _34; + Float _41, _42, _43, _44; + }; + Float components[16]; + }; + + friend std::ostream& operator<<(std::ostream& aStream, const Matrix4x4Typed& aMatrix) + { + const Float *f = &aMatrix._11; + aStream << "[ " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4; + aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4; + aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4; + aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ]" << std::endl; + return aStream; + } + + Point4D& operator[](int aIndex) + { + MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index"); + return *reinterpret_cast<Point4D*>((&_11)+4*aIndex); + } + const Point4D& operator[](int aIndex) const + { + MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index"); + return *reinterpret_cast<const Point4D*>((&_11)+4*aIndex); + } + + /** + * Returns true if the matrix is isomorphic to a 2D affine transformation. + */ + bool Is2D() const + { + if (_13 != 0.0f || _14 != 0.0f || + _23 != 0.0f || _24 != 0.0f || + _31 != 0.0f || _32 != 0.0f || _33 != 1.0f || _34 != 0.0f || + _43 != 0.0f || _44 != 1.0f) { + return false; + } + return true; + } + + bool Is2D(Matrix* aMatrix) const { + if (!Is2D()) { + return false; + } + if (aMatrix) { + aMatrix->_11 = _11; + aMatrix->_12 = _12; + aMatrix->_21 = _21; + aMatrix->_22 = _22; + aMatrix->_31 = _41; + aMatrix->_32 = _42; + } + return true; + } + + Matrix As2D() const + { + MOZ_ASSERT(Is2D(), "Matrix is not a 2D affine transform"); + + return Matrix(_11, _12, _21, _22, _41, _42); + } + + bool CanDraw2D(Matrix* aMatrix = nullptr) const { + if (_14 != 0.0f || + _24 != 0.0f || + _44 != 1.0f) { + return false; + } + if (aMatrix) { + aMatrix->_11 = _11; + aMatrix->_12 = _12; + aMatrix->_21 = _21; + aMatrix->_22 = _22; + aMatrix->_31 = _41; + aMatrix->_32 = _42; + } + return true; + } + + Matrix4x4Typed& ProjectTo2D() { + _31 = 0.0f; + _32 = 0.0f; + _13 = 0.0f; + _23 = 0.0f; + _33 = 1.0f; + _43 = 0.0f; + _34 = 0.0f; + // Some matrices, such as those derived from perspective transforms, + // can modify _44 from 1, while leaving the rest of the fourth column + // (_14, _24) at 0. In this case, after resetting the third row and + // third column above, the value of _44 functions only to scale the + // coordinate transform divide by W. The matrix can be converted to + // a true 2D matrix by normalizing out the scaling effect of _44 on + // the remaining components ahead of time. + if (_14 == 0.0f && _24 == 0.0f && + _44 != 1.0f && _44 != 0.0f) { + Float scale = 1.0f / _44; + _11 *= scale; + _12 *= scale; + _21 *= scale; + _22 *= scale; + _41 *= scale; + _42 *= scale; + _44 = 1.0f; + } + return *this; + } + + template<class F> + Point4DTyped<TargetUnits, F> + ProjectPoint(const PointTyped<SourceUnits, F>& aPoint) const { + // Find a value for z that will transform to 0. + + // The transformed value of z is computed as: + // z' = aPoint.x * _13 + aPoint.y * _23 + z * _33 + _43; + + // Solving for z when z' = 0 gives us: + F z = -(aPoint.x * _13 + aPoint.y * _23 + _43) / _33; + + // Compute the transformed point + return this->TransformPoint(Point4DTyped<SourceUnits, F>(aPoint.x, aPoint.y, z, 1)); + } + + template<class F> + RectTyped<TargetUnits, F> + ProjectRectBounds(const RectTyped<SourceUnits, F>& aRect, const RectTyped<TargetUnits, F>& aClip) const + { + // This function must never return std::numeric_limits<Float>::max() or any + // other arbitrary large value in place of inifinity. This often occurs when + // aRect is an inversed projection matrix or when aRect is transformed to be + // partly behind and in front of the camera (w=0 plane in homogenous + // coordinates) - See Bug 1035611 + + // Some call-sites will call RoundGfxRectToAppRect which clips both the + // extents and dimensions of the rect to be bounded by nscoord_MAX. + // If we return a Rect that, when converted to nscoords, has a width or height + // greater than nscoord_MAX, RoundGfxRectToAppRect will clip the overflow + // off both the min and max end of the rect after clipping the extents of the + // rect, resulting in a translation of the rect towards the infinite end. + + // The bounds returned by ProjectRectBounds are expected to be clipped only on + // the edges beyond the bounds of the coordinate system; otherwise, the + // clipped bounding box would be smaller than the correct one and result + // bugs such as incorrect culling (eg. Bug 1073056) + + // To address this without requiring all code to work in homogenous + // coordinates or interpret infinite values correctly, a specialized + // clipping function is integrated into ProjectRectBounds. + + // Callers should pass an aClip value that represents the extents to clip + // the result to, in the same coordinate system as aRect. + Point4DTyped<TargetUnits, F> points[4]; + + points[0] = ProjectPoint(aRect.TopLeft()); + points[1] = ProjectPoint(aRect.TopRight()); + points[2] = ProjectPoint(aRect.BottomRight()); + points[3] = ProjectPoint(aRect.BottomLeft()); + + F min_x = std::numeric_limits<F>::max(); + F min_y = std::numeric_limits<F>::max(); + F max_x = -std::numeric_limits<F>::max(); + F max_y = -std::numeric_limits<F>::max(); + + for (int i=0; i<4; i++) { + // Only use points that exist above the w=0 plane + if (points[i].HasPositiveWCoord()) { + PointTyped<TargetUnits, F> point2d = aClip.ClampPoint(points[i].As2DPoint()); + min_x = std::min<F>(point2d.x, min_x); + max_x = std::max<F>(point2d.x, max_x); + min_y = std::min<F>(point2d.y, min_y); + max_y = std::max<F>(point2d.y, max_y); + } + + int next = (i == 3) ? 0 : i + 1; + if (points[i].HasPositiveWCoord() != points[next].HasPositiveWCoord()) { + // If the line between two points crosses the w=0 plane, then interpolate + // to find the point of intersection with the w=0 plane and use that + // instead. + Point4DTyped<TargetUnits, F> intercept = + ComputePerspectivePlaneIntercept(points[i], points[next]); + // Since intercept.w will always be 0 here, we interpret x,y,z as a + // direction towards an infinite vanishing point. + if (intercept.x < 0.0f) { + min_x = aClip.x; + } else if (intercept.x > 0.0f) { + max_x = aClip.XMost(); + } + if (intercept.y < 0.0f) { + min_y = aClip.y; + } else if (intercept.y > 0.0f) { + max_y = aClip.YMost(); + } + } + } + + if (max_x < min_x || max_y < min_y) { + return RectTyped<TargetUnits, F>(0, 0, 0, 0); + } + + return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y); + } + + /** + * TransformAndClipBounds transforms aRect as a bounding box, while clipping + * the transformed bounds to the extents of aClip. + */ + template<class F> + RectTyped<TargetUnits, F> TransformAndClipBounds(const RectTyped<SourceUnits, F>& aRect, + const RectTyped<TargetUnits, F>& aClip) const + { + PointTyped<UnknownUnits, F> verts[kTransformAndClipRectMaxVerts]; + size_t vertCount = TransformAndClipRect(aRect, aClip, verts); + + F min_x = std::numeric_limits<F>::max(); + F min_y = std::numeric_limits<F>::max(); + F max_x = -std::numeric_limits<F>::max(); + F max_y = -std::numeric_limits<F>::max(); + for (size_t i=0; i < vertCount; i++) { + min_x = std::min(min_x, verts[i].x); + max_x = std::max(max_x, verts[i].x); + min_y = std::min(min_y, verts[i].y); + max_y = std::max(max_y, verts[i].y); + } + + if (max_x < min_x || max_y < min_y) { + return RectTyped<TargetUnits, F>(0, 0, 0, 0); + } + + return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y); + } + + template<class F> + RectTyped<TargetUnits, F> TransformAndClipBounds(const TriangleTyped<SourceUnits, F>& aTriangle, + const RectTyped<TargetUnits, F>& aClip) const + { + return TransformAndClipBounds(aTriangle.BoundingBox(), aClip); + } + + /** + * TransformAndClipRect projects a rectangle and clips against view frustum + * clipping planes in homogenous space so that its projected vertices are + * constrained within the 2d rectangle passed in aClip. + * The resulting vertices are populated in aVerts. aVerts must be + * pre-allocated to hold at least kTransformAndClipRectMaxVerts Points. + * The vertex count is returned by TransformAndClipRect. It is possible to + * emit fewer that 3 vertices, indicating that aRect will not be visible + * within aClip. + */ + template<class F> + size_t TransformAndClipRect(const RectTyped<SourceUnits, F>& aRect, + const RectTyped<TargetUnits, F>& aClip, + PointTyped<TargetUnits, F>* aVerts) const + { + // Initialize a double-buffered array of points in homogenous space with + // the input rectangle, aRect. + Point4DTyped<UnknownUnits, F> points[2][kTransformAndClipRectMaxVerts]; + Point4DTyped<UnknownUnits, F>* dstPoint = points[0]; + + *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.x, aRect.y, 0, 1)); + *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.y, 0, 1)); + *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.YMost(), 0, 1)); + *dstPoint++ = TransformPoint(Point4DTyped<UnknownUnits, F>(aRect.x, aRect.YMost(), 0, 1)); + + // View frustum clipping planes are described as normals originating from + // the 0,0,0,0 origin. + Point4DTyped<UnknownUnits, F> planeNormals[4]; + planeNormals[0] = Point4DTyped<UnknownUnits, F>(1.0, 0.0, 0.0, -aClip.x); + planeNormals[1] = Point4DTyped<UnknownUnits, F>(-1.0, 0.0, 0.0, aClip.XMost()); + planeNormals[2] = Point4DTyped<UnknownUnits, F>(0.0, 1.0, 0.0, -aClip.y); + planeNormals[3] = Point4DTyped<UnknownUnits, F>(0.0, -1.0, 0.0, aClip.YMost()); + + // Iterate through each clipping plane and clip the polygon. + // In each pass, we double buffer, alternating between points[0] and + // points[1]. + for (int plane=0; plane < 4; plane++) { + planeNormals[plane].Normalize(); + Point4DTyped<UnknownUnits, F>* srcPoint = points[plane & 1]; + Point4DTyped<UnknownUnits, F>* srcPointEnd = dstPoint; + + dstPoint = points[~plane & 1]; + Point4DTyped<UnknownUnits, F>* dstPointStart = dstPoint; + + Point4DTyped<UnknownUnits, F>* prevPoint = srcPointEnd - 1; + F prevDot = planeNormals[plane].DotProduct(*prevPoint); + while (srcPoint < srcPointEnd && ((dstPoint - dstPointStart) < kTransformAndClipRectMaxVerts)) { + F nextDot = planeNormals[plane].DotProduct(*srcPoint); + + if ((nextDot >= 0.0) != (prevDot >= 0.0)) { + // An intersection with the clipping plane has been detected. + // Interpolate to find the intersecting point and emit it. + F t = -prevDot / (nextDot - prevDot); + *dstPoint++ = *srcPoint * t + *prevPoint * (1.0 - t); + } + + if (nextDot >= 0.0) { + // Emit any source points that are on the positive side of the + // clipping plane. + *dstPoint++ = *srcPoint; + } + + prevPoint = srcPoint++; + prevDot = nextDot; + } + + if (dstPoint == dstPointStart) { + break; + } + } + + size_t dstPointCount = 0; + size_t srcPointCount = dstPoint - points[0]; + for (Point4DTyped<UnknownUnits, F>* srcPoint = points[0]; srcPoint < points[0] + srcPointCount; srcPoint++) { + + PointTyped<TargetUnits, F> p; + if (srcPoint->w == 0.0) { + // If a point lies on the intersection of the clipping planes at + // (0,0,0,0), we must avoid a division by zero w component. + p = PointTyped<TargetUnits, F>(0.0, 0.0); + } else { + p = srcPoint->As2DPoint(); + } + // Emit only unique points + if (dstPointCount == 0 || p != aVerts[dstPointCount - 1]) { + aVerts[dstPointCount++] = p; + } + } + + return dstPointCount; + } + + static const int kTransformAndClipRectMaxVerts = 32; + + static Matrix4x4Typed From2D(const Matrix &aMatrix) { + Matrix4x4Typed matrix; + matrix._11 = aMatrix._11; + matrix._12 = aMatrix._12; + matrix._21 = aMatrix._21; + matrix._22 = aMatrix._22; + matrix._41 = aMatrix._31; + matrix._42 = aMatrix._32; + return matrix; + } + + bool Is2DIntegerTranslation() const + { + return Is2D() && As2D().IsIntegerTranslation(); + } + + TargetPoint4D TransposeTransform4D(const SourcePoint4D& aPoint) const + { + Float x = aPoint.x * _11 + aPoint.y * _12 + aPoint.z * _13 + aPoint.w * _14; + Float y = aPoint.x * _21 + aPoint.y * _22 + aPoint.z * _23 + aPoint.w * _24; + Float z = aPoint.x * _31 + aPoint.y * _32 + aPoint.z * _33 + aPoint.w * _34; + Float w = aPoint.x * _41 + aPoint.y * _42 + aPoint.z * _43 + aPoint.w * _44; + + return TargetPoint4D(x, y, z, w); + } + + template<class F> + Point4DTyped<TargetUnits, F> TransformPoint(const Point4DTyped<SourceUnits, F>& aPoint) const + { + Point4DTyped<TargetUnits, F> retPoint; + + retPoint.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + aPoint.w * _41; + retPoint.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + aPoint.w * _42; + retPoint.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + aPoint.w * _43; + retPoint.w = aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + aPoint.w * _44; + + return retPoint; + } + + template<class F> + Point3DTyped<TargetUnits, F> TransformPoint(const Point3DTyped<SourceUnits, F>& aPoint) const + { + Point3DTyped<TargetUnits, F> result; + result.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + _41; + result.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + _42; + result.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + _43; + + result /= (aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + _44); + + return result; + } + + template<class F> + PointTyped<TargetUnits, F> TransformPoint(const PointTyped<SourceUnits, F> &aPoint) const + { + Point4DTyped<SourceUnits, F> temp(aPoint.x, aPoint.y, 0, 1); + return TransformPoint(temp).As2DPoint(); + } + + template<class F> + GFX2D_API RectTyped<TargetUnits, F> TransformBounds(const RectTyped<SourceUnits, F>& aRect) const + { + Point4DTyped<TargetUnits, F> verts[4]; + verts[0] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.x, aRect.y, 0.0, 1.0)); + verts[1] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.y, 0.0, 1.0)); + verts[2] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.YMost(), 0.0, 1.0)); + verts[3] = TransformPoint(Point4DTyped<SourceUnits, F>(aRect.x, aRect.YMost(), 0.0, 1.0)); + + PointTyped<TargetUnits, F> quad[4]; + F min_x, max_x; + F min_y, max_y; + + quad[0] = TransformPoint(aRect.TopLeft()); + quad[1] = TransformPoint(aRect.TopRight()); + quad[2] = TransformPoint(aRect.BottomLeft()); + quad[3] = TransformPoint(aRect.BottomRight()); + + min_x = max_x = quad[0].x; + min_y = max_y = quad[0].y; + + for (int i = 1; i < 4; i++) { + if (quad[i].x < min_x) { + min_x = quad[i].x; + } + if (quad[i].x > max_x) { + max_x = quad[i].x; + } + + if (quad[i].y < min_y) { + min_y = quad[i].y; + } + if (quad[i].y > max_y) { + max_y = quad[i].y; + } + } + + return RectTyped<TargetUnits, F>(min_x, min_y, max_x - min_x, max_y - min_y); + } + + static Matrix4x4Typed Translation(Float aX, Float aY, Float aZ) + { + return Matrix4x4Typed(1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + aX, aY, aZ, 1.0f); + } + + static Matrix4x4Typed Translation(const TargetPoint3D& aP) + { + return Translation(aP.x, aP.y, aP.z); + } + + static Matrix4x4Typed Translation(const TargetPoint& aP) + { + return Translation(aP.x, aP.y, 0); + } + + /** + * Apply a translation to this matrix. + * + * The "Pre" in this method's name means that the translation is applied + * -before- this matrix's existing transformation. That is, any vector that + * is multiplied by the resulting matrix will first be translated, then be + * transformed by the original transform. + * + * Calling this method will result in this matrix having the same value as + * the result of: + * + * Matrix4x4::Translation(x, y) * this + * + * (Note that in performance critical code multiplying by the result of a + * Translation()/Scaling() call is not recommended since that results in a + * full matrix multiply involving 64 floating-point multiplications. Calling + * this method would be preferred since it only involves 12 floating-point + * multiplications.) + */ + Matrix4x4Typed &PreTranslate(Float aX, Float aY, Float aZ) + { + _41 += aX * _11 + aY * _21 + aZ * _31; + _42 += aX * _12 + aY * _22 + aZ * _32; + _43 += aX * _13 + aY * _23 + aZ * _33; + _44 += aX * _14 + aY * _24 + aZ * _34; + + return *this; + } + + Matrix4x4Typed &PreTranslate(const Point3D& aPoint) { + return PreTranslate(aPoint.x, aPoint.y, aPoint.z); + } + + /** + * Similar to PreTranslate, but the translation is applied -after- this + * matrix's existing transformation instead of before it. + * + * This method is generally less used than PreTranslate since typically code + * wants to adjust an existing user space to device space matrix to create a + * transform to device space from a -new- user space (translated from the + * previous user space). In that case consumers will need to use the Pre* + * variants of the matrix methods rather than using the Post* methods, since + * the Post* methods add a transform to the device space end of the + * transformation. + */ + Matrix4x4Typed &PostTranslate(Float aX, Float aY, Float aZ) + { + _11 += _14 * aX; + _21 += _24 * aX; + _31 += _34 * aX; + _41 += _44 * aX; + _12 += _14 * aY; + _22 += _24 * aY; + _32 += _34 * aY; + _42 += _44 * aY; + _13 += _14 * aZ; + _23 += _24 * aZ; + _33 += _34 * aZ; + _43 += _44 * aZ; + + return *this; + } + + Matrix4x4Typed &PostTranslate(const TargetPoint3D& aPoint) { + return PostTranslate(aPoint.x, aPoint.y, aPoint.z); + } + + Matrix4x4Typed &PostTranslate(const TargetPoint& aPoint) { + return PostTranslate(aPoint.x, aPoint.y, 0); + } + + static Matrix4x4Typed Scaling(Float aScaleX, Float aScaleY, float aScaleZ) + { + return Matrix4x4Typed(aScaleX, 0.0f, 0.0f, 0.0f, + 0.0f, aScaleY, 0.0f, 0.0f, + 0.0f, 0.0f, aScaleZ, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f); + } + + /** + * Similar to PreTranslate, but applies a scale instead of a translation. + */ + Matrix4x4Typed &PreScale(Float aX, Float aY, Float aZ) + { + _11 *= aX; + _12 *= aX; + _13 *= aX; + _14 *= aX; + _21 *= aY; + _22 *= aY; + _23 *= aY; + _24 *= aY; + _31 *= aZ; + _32 *= aZ; + _33 *= aZ; + _34 *= aZ; + + return *this; + } + + /** + * Similar to PostTranslate, but applies a scale instead of a translation. + */ + Matrix4x4Typed &PostScale(Float aScaleX, Float aScaleY, Float aScaleZ) + { + _11 *= aScaleX; + _21 *= aScaleX; + _31 *= aScaleX; + _41 *= aScaleX; + _12 *= aScaleY; + _22 *= aScaleY; + _32 *= aScaleY; + _42 *= aScaleY; + _13 *= aScaleZ; + _23 *= aScaleZ; + _33 *= aScaleZ; + _43 *= aScaleZ; + + return *this; + } + + void SkewXY(Float aSkew) + { + (*this)[1] += (*this)[0] * aSkew; + } + + void SkewXZ(Float aSkew) + { + (*this)[2] += (*this)[0] * aSkew; + } + + void SkewYZ(Float aSkew) + { + (*this)[2] += (*this)[1] * aSkew; + } + + Matrix4x4Typed &ChangeBasis(const Point3D& aOrigin) + { + return ChangeBasis(aOrigin.x, aOrigin.y, aOrigin.z); + } + + Matrix4x4Typed &ChangeBasis(Float aX, Float aY, Float aZ) + { + // Translate to the origin before applying this matrix + PreTranslate(-aX, -aY, -aZ); + + // Translate back into position after applying this matrix + PostTranslate(aX, aY, aZ); + + return *this; + } + + Matrix4x4Typed& Transpose() { + std::swap(_12, _21); + std::swap(_13, _31); + std::swap(_14, _41); + + std::swap(_23, _32); + std::swap(_24, _42); + + std::swap(_34, _43); + + return *this; + } + + bool operator==(const Matrix4x4Typed& o) const + { + // XXX would be nice to memcmp here, but that breaks IEEE 754 semantics + return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 && + _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 && + _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 && + _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44; + } + + bool operator!=(const Matrix4x4Typed& o) const + { + return !((*this) == o); + } + + template <typename NewTargetUnits> + Matrix4x4Typed<SourceUnits, NewTargetUnits> operator*(const Matrix4x4Typed<TargetUnits, NewTargetUnits> &aMatrix) const + { + Matrix4x4Typed<SourceUnits, NewTargetUnits> matrix; + + matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21 + _13 * aMatrix._31 + _14 * aMatrix._41; + matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21 + _23 * aMatrix._31 + _24 * aMatrix._41; + matrix._31 = _31 * aMatrix._11 + _32 * aMatrix._21 + _33 * aMatrix._31 + _34 * aMatrix._41; + matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + _43 * aMatrix._31 + _44 * aMatrix._41; + matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22 + _13 * aMatrix._32 + _14 * aMatrix._42; + matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22 + _23 * aMatrix._32 + _24 * aMatrix._42; + matrix._32 = _31 * aMatrix._12 + _32 * aMatrix._22 + _33 * aMatrix._32 + _34 * aMatrix._42; + matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + _43 * aMatrix._32 + _44 * aMatrix._42; + matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23 + _13 * aMatrix._33 + _14 * aMatrix._43; + matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23 + _23 * aMatrix._33 + _24 * aMatrix._43; + matrix._33 = _31 * aMatrix._13 + _32 * aMatrix._23 + _33 * aMatrix._33 + _34 * aMatrix._43; + matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + _43 * aMatrix._33 + _44 * aMatrix._43; + matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24 + _13 * aMatrix._34 + _14 * aMatrix._44; + matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24 + _23 * aMatrix._34 + _24 * aMatrix._44; + matrix._34 = _31 * aMatrix._14 + _32 * aMatrix._24 + _33 * aMatrix._34 + _34 * aMatrix._44; + matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + _43 * aMatrix._34 + _44 * aMatrix._44; + + return matrix; + } + + Matrix4x4Typed& operator*=(const Matrix4x4Typed<TargetUnits, TargetUnits> &aMatrix) + { + *this = *this * aMatrix; + return *this; + } + + /* Returns true if the matrix is an identity matrix. + */ + bool IsIdentity() const + { + return _11 == 1.0f && _12 == 0.0f && _13 == 0.0f && _14 == 0.0f && + _21 == 0.0f && _22 == 1.0f && _23 == 0.0f && _24 == 0.0f && + _31 == 0.0f && _32 == 0.0f && _33 == 1.0f && _34 == 0.0f && + _41 == 0.0f && _42 == 0.0f && _43 == 0.0f && _44 == 1.0f; + } + + bool IsSingular() const + { + return Determinant() == 0.0; + } + + Float Determinant() const + { + return _14 * _23 * _32 * _41 + - _13 * _24 * _32 * _41 + - _14 * _22 * _33 * _41 + + _12 * _24 * _33 * _41 + + _13 * _22 * _34 * _41 + - _12 * _23 * _34 * _41 + - _14 * _23 * _31 * _42 + + _13 * _24 * _31 * _42 + + _14 * _21 * _33 * _42 + - _11 * _24 * _33 * _42 + - _13 * _21 * _34 * _42 + + _11 * _23 * _34 * _42 + + _14 * _22 * _31 * _43 + - _12 * _24 * _31 * _43 + - _14 * _21 * _32 * _43 + + _11 * _24 * _32 * _43 + + _12 * _21 * _34 * _43 + - _11 * _22 * _34 * _43 + - _13 * _22 * _31 * _44 + + _12 * _23 * _31 * _44 + + _13 * _21 * _32 * _44 + - _11 * _23 * _32 * _44 + - _12 * _21 * _33 * _44 + + _11 * _22 * _33 * _44; + } + + // Invert() is not unit-correct. Prefer Inverse() where possible. + bool Invert() + { + Float det = Determinant(); + if (!det) { + return false; + } + + Matrix4x4Typed<SourceUnits, TargetUnits> result; + result._11 = _23 * _34 * _42 - _24 * _33 * _42 + _24 * _32 * _43 - _22 * _34 * _43 - _23 * _32 * _44 + _22 * _33 * _44; + result._12 = _14 * _33 * _42 - _13 * _34 * _42 - _14 * _32 * _43 + _12 * _34 * _43 + _13 * _32 * _44 - _12 * _33 * _44; + result._13 = _13 * _24 * _42 - _14 * _23 * _42 + _14 * _22 * _43 - _12 * _24 * _43 - _13 * _22 * _44 + _12 * _23 * _44; + result._14 = _14 * _23 * _32 - _13 * _24 * _32 - _14 * _22 * _33 + _12 * _24 * _33 + _13 * _22 * _34 - _12 * _23 * _34; + result._21 = _24 * _33 * _41 - _23 * _34 * _41 - _24 * _31 * _43 + _21 * _34 * _43 + _23 * _31 * _44 - _21 * _33 * _44; + result._22 = _13 * _34 * _41 - _14 * _33 * _41 + _14 * _31 * _43 - _11 * _34 * _43 - _13 * _31 * _44 + _11 * _33 * _44; + result._23 = _14 * _23 * _41 - _13 * _24 * _41 - _14 * _21 * _43 + _11 * _24 * _43 + _13 * _21 * _44 - _11 * _23 * _44; + result._24 = _13 * _24 * _31 - _14 * _23 * _31 + _14 * _21 * _33 - _11 * _24 * _33 - _13 * _21 * _34 + _11 * _23 * _34; + result._31 = _22 * _34 * _41 - _24 * _32 * _41 + _24 * _31 * _42 - _21 * _34 * _42 - _22 * _31 * _44 + _21 * _32 * _44; + result._32 = _14 * _32 * _41 - _12 * _34 * _41 - _14 * _31 * _42 + _11 * _34 * _42 + _12 * _31 * _44 - _11 * _32 * _44; + result._33 = _12 * _24 * _41 - _14 * _22 * _41 + _14 * _21 * _42 - _11 * _24 * _42 - _12 * _21 * _44 + _11 * _22 * _44; + result._34 = _14 * _22 * _31 - _12 * _24 * _31 - _14 * _21 * _32 + _11 * _24 * _32 + _12 * _21 * _34 - _11 * _22 * _34; + result._41 = _23 * _32 * _41 - _22 * _33 * _41 - _23 * _31 * _42 + _21 * _33 * _42 + _22 * _31 * _43 - _21 * _32 * _43; + result._42 = _12 * _33 * _41 - _13 * _32 * _41 + _13 * _31 * _42 - _11 * _33 * _42 - _12 * _31 * _43 + _11 * _32 * _43; + result._43 = _13 * _22 * _41 - _12 * _23 * _41 - _13 * _21 * _42 + _11 * _23 * _42 + _12 * _21 * _43 - _11 * _22 * _43; + result._44 = _12 * _23 * _31 - _13 * _22 * _31 + _13 * _21 * _32 - _11 * _23 * _32 - _12 * _21 * _33 + _11 * _22 * _33; + + result._11 /= det; + result._12 /= det; + result._13 /= det; + result._14 /= det; + result._21 /= det; + result._22 /= det; + result._23 /= det; + result._24 /= det; + result._31 /= det; + result._32 /= det; + result._33 /= det; + result._34 /= det; + result._41 /= det; + result._42 /= det; + result._43 /= det; + result._44 /= det; + *this = result; + + return true; + } + + Matrix4x4Typed<TargetUnits, SourceUnits> Inverse() const + { + typedef Matrix4x4Typed<TargetUnits, SourceUnits> InvertedMatrix; + InvertedMatrix clone = InvertedMatrix::FromUnknownMatrix(ToUnknownMatrix()); + DebugOnly<bool> inverted = clone.Invert(); + MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix"); + return clone; + } + + void Normalize() + { + for (int i = 0; i < 4; i++) { + for (int j = 0; j < 4; j++) { + (*this)[i][j] /= (*this)[3][3]; + } + } + } + + bool FuzzyEqual(const Matrix4x4Typed& o) const + { + return gfx::FuzzyEqual(_11, o._11) && gfx::FuzzyEqual(_12, o._12) && + gfx::FuzzyEqual(_13, o._13) && gfx::FuzzyEqual(_14, o._14) && + gfx::FuzzyEqual(_21, o._21) && gfx::FuzzyEqual(_22, o._22) && + gfx::FuzzyEqual(_23, o._23) && gfx::FuzzyEqual(_24, o._24) && + gfx::FuzzyEqual(_31, o._31) && gfx::FuzzyEqual(_32, o._32) && + gfx::FuzzyEqual(_33, o._33) && gfx::FuzzyEqual(_34, o._34) && + gfx::FuzzyEqual(_41, o._41) && gfx::FuzzyEqual(_42, o._42) && + gfx::FuzzyEqual(_43, o._43) && gfx::FuzzyEqual(_44, o._44); + } + + bool FuzzyEqualsMultiplicative(const Matrix4x4Typed& o) const + { + return ::mozilla::FuzzyEqualsMultiplicative(_11, o._11) && + ::mozilla::FuzzyEqualsMultiplicative(_12, o._12) && + ::mozilla::FuzzyEqualsMultiplicative(_13, o._13) && + ::mozilla::FuzzyEqualsMultiplicative(_14, o._14) && + ::mozilla::FuzzyEqualsMultiplicative(_21, o._21) && + ::mozilla::FuzzyEqualsMultiplicative(_22, o._22) && + ::mozilla::FuzzyEqualsMultiplicative(_23, o._23) && + ::mozilla::FuzzyEqualsMultiplicative(_24, o._24) && + ::mozilla::FuzzyEqualsMultiplicative(_31, o._31) && + ::mozilla::FuzzyEqualsMultiplicative(_32, o._32) && + ::mozilla::FuzzyEqualsMultiplicative(_33, o._33) && + ::mozilla::FuzzyEqualsMultiplicative(_34, o._34) && + ::mozilla::FuzzyEqualsMultiplicative(_41, o._41) && + ::mozilla::FuzzyEqualsMultiplicative(_42, o._42) && + ::mozilla::FuzzyEqualsMultiplicative(_43, o._43) && + ::mozilla::FuzzyEqualsMultiplicative(_44, o._44); + } + + bool IsBackfaceVisible() const + { + // Inverse()._33 < 0; + Float det = Determinant(); + Float __33 = _12*_24*_41 - _14*_22*_41 + + _14*_21*_42 - _11*_24*_42 - + _12*_21*_44 + _11*_22*_44; + return (__33 * det) < 0; + } + + Matrix4x4Typed &NudgeToIntegersFixedEpsilon() + { + NudgeToInteger(&_11); + NudgeToInteger(&_12); + NudgeToInteger(&_13); + NudgeToInteger(&_14); + NudgeToInteger(&_21); + NudgeToInteger(&_22); + NudgeToInteger(&_23); + NudgeToInteger(&_24); + NudgeToInteger(&_31); + NudgeToInteger(&_32); + NudgeToInteger(&_33); + NudgeToInteger(&_34); + static const float error = 1e-5f; + NudgeToInteger(&_41, error); + NudgeToInteger(&_42, error); + NudgeToInteger(&_43, error); + NudgeToInteger(&_44, error); + return *this; + } + + Point4D TransposedVector(int aIndex) const + { + MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index"); + return Point4D(*((&_11)+aIndex), *((&_21)+aIndex), *((&_31)+aIndex), *((&_41)+aIndex)); + } + + void SetTransposedVector(int aIndex, Point4D &aVector) + { + MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index"); + *((&_11)+aIndex) = aVector.x; + *((&_21)+aIndex) = aVector.y; + *((&_31)+aIndex) = aVector.z; + *((&_41)+aIndex) = aVector.w; + } + + // Sets this matrix to a rotation matrix given by aQuat. + // This quaternion *MUST* be normalized! + // Implemented in Quaternion.cpp + void SetRotationFromQuaternion(const Quaternion& q) + { + const Float x2 = q.x + q.x, y2 = q.y + q.y, z2 = q.z + q.z; + const Float xx = q.x * x2, xy = q.x * y2, xz = q.x * z2; + const Float yy = q.y * y2, yz = q.y * z2, zz = q.z * z2; + const Float wx = q.w * x2, wy = q.w * y2, wz = q.w * z2; + + _11 = 1.0f - (yy + zz); + _21 = xy + wz; + _31 = xz - wy; + _41 = 0.0f; + + _12 = xy - wz; + _22 = 1.0f - (xx + zz); + _32 = yz + wx; + _42 = 0.0f; + + _13 = xz + wy; + _23 = yz - wx; + _33 = 1.0f - (xx + yy); + _43 = 0.0f; + + _14 = _42 = _43 = 0.0f; + _44 = 1.0f; + } + + // Set all the members of the matrix to NaN + void SetNAN() + { + _11 = UnspecifiedNaN<Float>(); + _21 = UnspecifiedNaN<Float>(); + _31 = UnspecifiedNaN<Float>(); + _41 = UnspecifiedNaN<Float>(); + _12 = UnspecifiedNaN<Float>(); + _22 = UnspecifiedNaN<Float>(); + _32 = UnspecifiedNaN<Float>(); + _42 = UnspecifiedNaN<Float>(); + _13 = UnspecifiedNaN<Float>(); + _23 = UnspecifiedNaN<Float>(); + _33 = UnspecifiedNaN<Float>(); + _43 = UnspecifiedNaN<Float>(); + _14 = UnspecifiedNaN<Float>(); + _24 = UnspecifiedNaN<Float>(); + _34 = UnspecifiedNaN<Float>(); + _44 = UnspecifiedNaN<Float>(); + } + + void SkewXY(double aXSkew, double aYSkew) + { + // XXX Is double precision really necessary here + float tanX = SafeTangent(aXSkew); + float tanY = SafeTangent(aYSkew); + float temp; + + temp = _11; + _11 += tanY * _21; + _21 += tanX * temp; + + temp = _12; + _12 += tanY * _22; + _22 += tanX * temp; + + temp = _13; + _13 += tanY * _23; + _23 += tanX * temp; + + temp = _14; + _14 += tanY * _24; + _24 += tanX * temp; + } + + void RotateX(double aTheta) + { + // XXX Is double precision really necessary here + double cosTheta = FlushToZero(cos(aTheta)); + double sinTheta = FlushToZero(sin(aTheta)); + + float temp; + + temp = _21; + _21 = cosTheta * _21 + sinTheta * _31; + _31 = -sinTheta * temp + cosTheta * _31; + + temp = _22; + _22 = cosTheta * _22 + sinTheta * _32; + _32 = -sinTheta * temp + cosTheta * _32; + + temp = _23; + _23 = cosTheta * _23 + sinTheta * _33; + _33 = -sinTheta * temp + cosTheta * _33; + + temp = _24; + _24 = cosTheta * _24 + sinTheta * _34; + _34 = -sinTheta * temp + cosTheta * _34; + } + + void RotateY(double aTheta) + { + // XXX Is double precision really necessary here + double cosTheta = FlushToZero(cos(aTheta)); + double sinTheta = FlushToZero(sin(aTheta)); + + float temp; + + temp = _11; + _11 = cosTheta * _11 + -sinTheta * _31; + _31 = sinTheta * temp + cosTheta * _31; + + temp = _12; + _12 = cosTheta * _12 + -sinTheta * _32; + _32 = sinTheta * temp + cosTheta * _32; + + temp = _13; + _13 = cosTheta * _13 + -sinTheta * _33; + _33 = sinTheta * temp + cosTheta * _33; + + temp = _14; + _14 = cosTheta * _14 + -sinTheta * _34; + _34 = sinTheta * temp + cosTheta * _34; + } + + void RotateZ(double aTheta) + { + // XXX Is double precision really necessary here + double cosTheta = FlushToZero(cos(aTheta)); + double sinTheta = FlushToZero(sin(aTheta)); + + float temp; + + temp = _11; + _11 = cosTheta * _11 + sinTheta * _21; + _21 = -sinTheta * temp + cosTheta * _21; + + temp = _12; + _12 = cosTheta * _12 + sinTheta * _22; + _22 = -sinTheta * temp + cosTheta * _22; + + temp = _13; + _13 = cosTheta * _13 + sinTheta * _23; + _23 = -sinTheta * temp + cosTheta * _23; + + temp = _14; + _14 = cosTheta * _14 + sinTheta * _24; + _24 = -sinTheta * temp + cosTheta * _24; + } + + // Sets this matrix to a rotation matrix about a + // vector [x,y,z] by angle theta. The vector is normalized + // to a unit vector. + // https://www.w3.org/TR/css3-3d-transforms/#Rotate3dDefined + void SetRotateAxisAngle(double aX, double aY, double aZ, double aTheta) + { + Point3D vector(aX, aY, aZ); + if (!vector.Length()) { + return; + } + vector.Normalize(); + + double x = vector.x; + double y = vector.y; + double z = vector.z; + + double cosTheta = FlushToZero(cos(aTheta)); + double sinTheta = FlushToZero(sin(aTheta)); + + // sin(aTheta / 2) * cos(aTheta / 2) + double sc = sinTheta / 2; + // pow(sin(aTheta / 2), 2) + double sq = (1 - cosTheta) / 2; + + _11 = 1 - 2 * (y * y + z * z) * sq; + _12 = 2 * (x * y * sq + z * sc); + _13 = 2 * (x * z * sq - y * sc); + _14 = 0.0f; + _21 = 2 * (x * y * sq - z * sc); + _22 = 1 - 2 * (x * x + z * z) * sq; + _23 = 2 * (y * z * sq + x * sc); + _24 = 0.0f; + _31 = 2 * (x * z * sq + y * sc); + _32 = 2 * (y * z * sq - x * sc); + _33 = 1 - 2 * (x * x + y * y) * sq; + _34 = 0.0f; + _41 = 0.0f; + _42 = 0.0f; + _43 = 0.0f; + _44 = 1.0f; + } + + void Perspective(float aDepth) + { + MOZ_ASSERT(aDepth > 0.0f, "Perspective must be positive!"); + _31 += -1.0/aDepth * _41; + _32 += -1.0/aDepth * _42; + _33 += -1.0/aDepth * _43; + _34 += -1.0/aDepth * _44; + } + + Point3D GetNormalVector() const + { + // Define a plane in transformed space as the transformations + // of 3 points on the z=0 screen plane. + Point3D a = TransformPoint(Point3D(0, 0, 0)); + Point3D b = TransformPoint(Point3D(0, 1, 0)); + Point3D c = TransformPoint(Point3D(1, 0, 0)); + + // Convert to two vectors on the surface of the plane. + Point3D ab = b - a; + Point3D ac = c - a; + + return ac.CrossProduct(ab); + } + + /** + * Returns true if the matrix has any transform other + * than a straight translation. + */ + bool HasNonTranslation() const { + return !gfx::FuzzyEqual(_11, 1.0) || !gfx::FuzzyEqual(_22, 1.0) || + !gfx::FuzzyEqual(_12, 0.0) || !gfx::FuzzyEqual(_21, 0.0) || + !gfx::FuzzyEqual(_13, 0.0) || !gfx::FuzzyEqual(_23, 0.0) || + !gfx::FuzzyEqual(_31, 0.0) || !gfx::FuzzyEqual(_32, 0.0) || + !gfx::FuzzyEqual(_33, 1.0); + } + + /** + * Returns true if the matrix is anything other than a straight + * translation by integers. + */ + bool HasNonIntegerTranslation() const { + return HasNonTranslation() || + !gfx::FuzzyEqual(_41, floor(_41 + 0.5)) || + !gfx::FuzzyEqual(_42, floor(_42 + 0.5)) || + !gfx::FuzzyEqual(_43, floor(_43 + 0.5)); + } + + /** + * Return true if the matrix is with perspective (w). + */ + bool HasPerspectiveComponent() const { + return _14 != 0 || _24 != 0 || _34 != 0 || _44 != 1; + } + + /** + * Convert between typed and untyped matrices. + */ + Matrix4x4 ToUnknownMatrix() const { + return Matrix4x4{_11, _12, _13, _14, + _21, _22, _23, _24, + _31, _32, _33, _34, + _41, _42, _43, _44}; + } + static Matrix4x4Typed FromUnknownMatrix(const Matrix4x4& aUnknown) { + return Matrix4x4Typed{aUnknown._11, aUnknown._12, aUnknown._13, aUnknown._14, + aUnknown._21, aUnknown._22, aUnknown._23, aUnknown._24, + aUnknown._31, aUnknown._32, aUnknown._33, aUnknown._34, + aUnknown._41, aUnknown._42, aUnknown._43, aUnknown._44}; + } +}; + +typedef Matrix4x4Typed<UnknownUnits, UnknownUnits> Matrix4x4; + +class Matrix5x4 +{ +public: + Matrix5x4() + : _11(1.0f), _12(0), _13(0), _14(0) + , _21(0), _22(1.0f), _23(0), _24(0) + , _31(0), _32(0), _33(1.0f), _34(0) + , _41(0), _42(0), _43(0), _44(1.0f) + , _51(0), _52(0), _53(0), _54(0) + {} + Matrix5x4(Float a11, Float a12, Float a13, Float a14, + Float a21, Float a22, Float a23, Float a24, + Float a31, Float a32, Float a33, Float a34, + Float a41, Float a42, Float a43, Float a44, + Float a51, Float a52, Float a53, Float a54) + : _11(a11), _12(a12), _13(a13), _14(a14) + , _21(a21), _22(a22), _23(a23), _24(a24) + , _31(a31), _32(a32), _33(a33), _34(a34) + , _41(a41), _42(a42), _43(a43), _44(a44) + , _51(a51), _52(a52), _53(a53), _54(a54) + {} + + bool operator==(const Matrix5x4 &o) const + { + return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 && + _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 && + _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 && + _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44 && + _51 == o._51 && _52 == o._52 && _53 == o._53 && _54 == o._54; + } + + bool operator!=(const Matrix5x4 &aMatrix) const + { + return !(*this == aMatrix); + } + + Matrix5x4 operator*(const Matrix5x4 &aMatrix) const + { + Matrix5x4 resultMatrix; + + resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21 + this->_13 * aMatrix._31 + this->_14 * aMatrix._41; + resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22 + this->_13 * aMatrix._32 + this->_14 * aMatrix._42; + resultMatrix._13 = this->_11 * aMatrix._13 + this->_12 * aMatrix._23 + this->_13 * aMatrix._33 + this->_14 * aMatrix._43; + resultMatrix._14 = this->_11 * aMatrix._14 + this->_12 * aMatrix._24 + this->_13 * aMatrix._34 + this->_14 * aMatrix._44; + resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21 + this->_23 * aMatrix._31 + this->_24 * aMatrix._41; + resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22 + this->_23 * aMatrix._32 + this->_24 * aMatrix._42; + resultMatrix._23 = this->_21 * aMatrix._13 + this->_22 * aMatrix._23 + this->_23 * aMatrix._33 + this->_24 * aMatrix._43; + resultMatrix._24 = this->_21 * aMatrix._14 + this->_22 * aMatrix._24 + this->_23 * aMatrix._34 + this->_24 * aMatrix._44; + resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + this->_33 * aMatrix._31 + this->_34 * aMatrix._41; + resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + this->_33 * aMatrix._32 + this->_34 * aMatrix._42; + resultMatrix._33 = this->_31 * aMatrix._13 + this->_32 * aMatrix._23 + this->_33 * aMatrix._33 + this->_34 * aMatrix._43; + resultMatrix._34 = this->_31 * aMatrix._14 + this->_32 * aMatrix._24 + this->_33 * aMatrix._34 + this->_34 * aMatrix._44; + resultMatrix._41 = this->_41 * aMatrix._11 + this->_42 * aMatrix._21 + this->_43 * aMatrix._31 + this->_44 * aMatrix._41; + resultMatrix._42 = this->_41 * aMatrix._12 + this->_42 * aMatrix._22 + this->_43 * aMatrix._32 + this->_44 * aMatrix._42; + resultMatrix._43 = this->_41 * aMatrix._13 + this->_42 * aMatrix._23 + this->_43 * aMatrix._33 + this->_44 * aMatrix._43; + resultMatrix._44 = this->_41 * aMatrix._14 + this->_42 * aMatrix._24 + this->_43 * aMatrix._34 + this->_44 * aMatrix._44; + resultMatrix._51 = this->_51 * aMatrix._11 + this->_52 * aMatrix._21 + this->_53 * aMatrix._31 + this->_54 * aMatrix._41 + aMatrix._51; + resultMatrix._52 = this->_51 * aMatrix._12 + this->_52 * aMatrix._22 + this->_53 * aMatrix._32 + this->_54 * aMatrix._42 + aMatrix._52; + resultMatrix._53 = this->_51 * aMatrix._13 + this->_52 * aMatrix._23 + this->_53 * aMatrix._33 + this->_54 * aMatrix._43 + aMatrix._53; + resultMatrix._54 = this->_51 * aMatrix._14 + this->_52 * aMatrix._24 + this->_53 * aMatrix._34 + this->_54 * aMatrix._44 + aMatrix._54; + + return resultMatrix; + } + + Matrix5x4& operator*=(const Matrix5x4 &aMatrix) + { + *this = *this * aMatrix; + return *this; + } + + union { + struct { + Float _11, _12, _13, _14; + Float _21, _22, _23, _24; + Float _31, _32, _33, _34; + Float _41, _42, _43, _44; + Float _51, _52, _53, _54; + }; + Float components[20]; + }; +}; + +} // namespace gfx +} // namespace mozilla + +#endif /* MOZILLA_GFX_MATRIX_H_ */ |