mirror of
https://github.com/mozilla/gecko-dev.git
synced 2024-10-30 13:45:27 +00:00
1081 lines
32 KiB
C++
1081 lines
32 KiB
C++
/* -*- 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 "Rect.h"
|
|
#include "Point.h"
|
|
#include <iosfwd>
|
|
#include <math.h>
|
|
#include "mozilla/Attributes.h"
|
|
#include "mozilla/DebugOnly.h"
|
|
#include "mozilla/FloatingPoint.h"
|
|
|
|
namespace mozilla {
|
|
namespace gfx {
|
|
|
|
class Quaternion;
|
|
|
|
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)
|
|
{}
|
|
Float _11, _12;
|
|
Float _21, _22;
|
|
Float _31, _32;
|
|
|
|
MOZ_ALWAYS_INLINE Matrix Copy() const
|
|
{
|
|
return Matrix(*this);
|
|
}
|
|
|
|
friend std::ostream& operator<<(std::ostream& aStream, const Matrix& aMatrix);
|
|
|
|
Point operator *(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 operator *(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);
|
|
}
|
|
|
|
/* 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 + 0.5)) ||
|
|
!FuzzyEqual(_32, floor(_32 + 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
|
|
{
|
|
return Determinant() == 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);
|
|
}
|
|
};
|
|
|
|
class Matrix4x4
|
|
{
|
|
public:
|
|
Matrix4x4()
|
|
: _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)
|
|
{}
|
|
|
|
Matrix4x4(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)
|
|
{}
|
|
|
|
Matrix4x4(const Matrix4x4& aOther)
|
|
{
|
|
memcpy(this, &aOther, sizeof(*this));
|
|
}
|
|
|
|
Float _11, _12, _13, _14;
|
|
Float _21, _22, _23, _24;
|
|
Float _31, _32, _33, _34;
|
|
Float _41, _42, _43, _44;
|
|
|
|
friend std::ostream& operator<<(std::ostream& aStream, const Matrix4x4& aMatrix);
|
|
|
|
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;
|
|
}
|
|
|
|
Matrix4x4& ProjectTo2D() {
|
|
_31 = 0.0f;
|
|
_32 = 0.0f;
|
|
_13 = 0.0f;
|
|
_23 = 0.0f;
|
|
_33 = 1.0f;
|
|
_43 = 0.0f;
|
|
_34 = 0.0f;
|
|
return *this;
|
|
}
|
|
|
|
Point4D ProjectPoint(const Point& 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:
|
|
float z = -(aPoint.x * _13 + aPoint.y * _23 + _43) / _33;
|
|
|
|
// Compute the transformed point
|
|
return *this * Point4D(aPoint.x, aPoint.y, z, 1);
|
|
}
|
|
|
|
Rect ProjectRectBounds(const Rect& aRect, const Rect &aClip) const;
|
|
|
|
/**
|
|
* TransformAndClipBounds transforms aRect as a bounding box, while clipping
|
|
* the transformed bounds to the extents of aClip.
|
|
*/
|
|
template<class F>
|
|
RectTyped<UnknownUnits, F> TransformAndClipBounds(const RectTyped<UnknownUnits, F>& aRect, const RectTyped<UnknownUnits, F>& aClip) const;
|
|
|
|
/**
|
|
* 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<UnknownUnits, F>& aRect,
|
|
const RectTyped<UnknownUnits, F>& aClip,
|
|
PointTyped<UnknownUnits, F>* aVerts) const;
|
|
static const size_t kTransformAndClipRectMaxVerts = 32;
|
|
|
|
static Matrix4x4 From2D(const Matrix &aMatrix) {
|
|
Matrix4x4 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();
|
|
}
|
|
|
|
Point4D TransposeTransform4D(const Point4D& 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 Point4D(x, y, z, w);
|
|
}
|
|
|
|
template<class F>
|
|
Point4DTyped<UnknownUnits, F> operator *(const Point4DTyped<UnknownUnits, F>& aPoint) const
|
|
{
|
|
Point4DTyped<UnknownUnits, F> retPoint;
|
|
|
|
retPoint.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + _41;
|
|
retPoint.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + _42;
|
|
retPoint.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + _43;
|
|
retPoint.w = aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + _44;
|
|
|
|
return retPoint;
|
|
}
|
|
|
|
template<class F>
|
|
Point3DTyped<UnknownUnits, F> operator *(const Point3DTyped<UnknownUnits, F>& aPoint) const
|
|
{
|
|
Point4DTyped<UnknownUnits, F> temp(aPoint.x, aPoint.y, aPoint.z, 1);
|
|
|
|
temp = *this * temp;
|
|
temp /= temp.w;
|
|
|
|
return Point3DTyped<UnknownUnits, F>(temp.x, temp.y, temp.z);
|
|
}
|
|
|
|
template<class F>
|
|
PointTyped<UnknownUnits, F> operator *(const PointTyped<UnknownUnits, F> &aPoint) const
|
|
{
|
|
Point4DTyped<UnknownUnits, F> temp(aPoint.x, aPoint.y, 0, 1);
|
|
|
|
temp = *this * temp;
|
|
temp /= temp.w;
|
|
|
|
return PointTyped<UnknownUnits, F>(temp.x, temp.y);
|
|
}
|
|
|
|
template<class F>
|
|
GFX2D_API RectTyped<UnknownUnits, F> TransformBounds(const RectTyped<UnknownUnits, F>& aRect) const;
|
|
|
|
static Matrix4x4 Translation(Float aX, Float aY, Float aZ)
|
|
{
|
|
return Matrix4x4(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 Matrix4x4 Translation(const Point3D& aP)
|
|
{
|
|
return Translation(aP.x, aP.y, aP.z);
|
|
}
|
|
|
|
/**
|
|
* 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.)
|
|
*/
|
|
Matrix4x4 &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;
|
|
}
|
|
|
|
Matrix4x4 &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.
|
|
*/
|
|
Matrix4x4 &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;
|
|
}
|
|
|
|
Matrix4x4 &PostTranslate(const Point3D& aPoint) {
|
|
return PostTranslate(aPoint.x, aPoint.y, aPoint.z);
|
|
}
|
|
|
|
static Matrix4x4 Scaling(Float aScaleX, Float aScaleY, float aScaleZ)
|
|
{
|
|
return Matrix4x4(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.
|
|
*/
|
|
Matrix4x4 &PreScale(Float aX, Float aY, Float aZ)
|
|
{
|
|
_11 *= aX;
|
|
_12 *= aX;
|
|
_13 *= aX;
|
|
_21 *= aY;
|
|
_22 *= aY;
|
|
_23 *= aY;
|
|
_31 *= aZ;
|
|
_32 *= aZ;
|
|
_33 *= aZ;
|
|
|
|
return *this;
|
|
}
|
|
|
|
/**
|
|
* Similar to PostTranslate, but applies a scale instead of a translation.
|
|
*/
|
|
Matrix4x4 &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;
|
|
}
|
|
|
|
Matrix4x4 &ChangeBasis(const Point3D& aOrigin)
|
|
{
|
|
return ChangeBasis(aOrigin.x, aOrigin.y, aOrigin.z);
|
|
}
|
|
|
|
Matrix4x4 &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;
|
|
}
|
|
|
|
Matrix4x4& 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 Matrix4x4& 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 Matrix4x4& o) const
|
|
{
|
|
return !((*this) == o);
|
|
}
|
|
|
|
Matrix4x4 operator*(const Matrix4x4 &aMatrix) const
|
|
{
|
|
Matrix4x4 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;
|
|
}
|
|
|
|
Matrix4x4& operator*=(const Matrix4x4 &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;
|
|
}
|
|
|
|
bool Invert();
|
|
|
|
Matrix4x4 Inverse() const
|
|
{
|
|
Matrix4x4 clone = *this;
|
|
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 Matrix4x4& 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 Matrix4x4& 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;
|
|
}
|
|
|
|
Matrix4x4 &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;
|
|
}
|
|
|
|
// Nudge the 3D components to integer so that this matrix will become 2D if
|
|
// it's very close to already being 2D.
|
|
// This doesn't change the _41 and _42 components.
|
|
Matrix4x4 &NudgeTo2D()
|
|
{
|
|
NudgeToInteger(&_13);
|
|
NudgeToInteger(&_14);
|
|
NudgeToInteger(&_23);
|
|
NudgeToInteger(&_24);
|
|
NudgeToInteger(&_31);
|
|
NudgeToInteger(&_32);
|
|
NudgeToInteger(&_33);
|
|
NudgeToInteger(&_34);
|
|
NudgeToInteger(&_43);
|
|
NudgeToInteger(&_44);
|
|
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& aQuat);
|
|
|
|
// Set all the members of the matrix to NaN
|
|
void SetNAN();
|
|
|
|
void SkewXY(double aXSkew, double aYSkew);
|
|
|
|
void RotateX(double aTheta);
|
|
|
|
void RotateY(double aTheta);
|
|
|
|
void RotateZ(double aTheta);
|
|
|
|
void Perspective(float aDepth);
|
|
|
|
Point3D GetNormalVector() const;
|
|
};
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
};
|
|
|
|
} // namespace gfx
|
|
} // namespace mozilla
|
|
|
|
#endif /* MOZILLA_GFX_MATRIX_H_ */
|