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Matrix.h
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Matrix.h
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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
#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 inline 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;
}
template <class T>
class BaseMatrix {
// Alias that maps to either Point or PointDouble depending on whether T is a
// float or a double.
typedef PointTyped<UnknownUnits, T> MatrixPoint;
// Same for size and rect
typedef SizeTyped<UnknownUnits, T> MatrixSize;
typedef RectTyped<UnknownUnits, T> MatrixRect;
public:
BaseMatrix() : _11(1.0f), _12(0), _21(0), _22(1.0f), _31(0), _32(0) {}
BaseMatrix(T a11, T a12, T a21, T a22, T a31, T a32)
: _11(a11), _12(a12), _21(a21), _22(a22), _31(a31), _32(a32) {}
union {
struct {
T _11, _12;
T _21, _22;
T _31, _32;
};
T components[6];
};
MOZ_ALWAYS_INLINE BaseMatrix Copy() const { return BaseMatrix<T>(*this); }
friend std::ostream& operator<<(std::ostream& aStream,
const BaseMatrix& aMatrix) {
return aStream << "[ " << aMatrix._11 << " " << aMatrix._12 << "; "
<< aMatrix._21 << " " << aMatrix._22 << "; " << aMatrix._31
<< " " << aMatrix._32 << "; ]";
}
MatrixPoint TransformPoint(const MatrixPoint& aPoint) const {
MatrixPoint retPoint;
retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31;
retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32;
return retPoint;
}
MatrixSize TransformSize(const MatrixSize& aSize) const {
MatrixSize retSize;
retSize.width = aSize.width * _11 + aSize.height * _21;
retSize.height = aSize.width * _12 + aSize.height * _22;
return retSize;
}
/**
* In most cases you probably want to use TransformBounds. This function
* just transforms the top-left and size separately and constructs a rect
* from those results.
*/
MatrixRect TransformRect(const MatrixRect& aRect) const {
return MatrixRect(TransformPoint(aRect.TopLeft()),
TransformSize(aRect.Size()));
}
GFX2D_API MatrixRect TransformBounds(const MatrixRect& aRect) const {
int i;
MatrixPoint quad[4];
T min_x, max_x;
T 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 (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 MatrixRect(min_x, min_y, max_x - min_x, max_y - min_y);
}
static BaseMatrix<T> Translation(T aX, T aY) {
return BaseMatrix<T>(1.0f, 0.0f, 0.0f, 1.0f, aX, aY);
}
static BaseMatrix<T> Translation(MatrixPoint 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:
*
* BaseMatrix<T>::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.)
*/
BaseMatrix<T>& PreTranslate(T aX, T aY) {
_31 += _11 * aX + _21 * aY;
_32 += _12 * aX + _22 * aY;
return *this;
}
BaseMatrix<T>& PreTranslate(const MatrixPoint& 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.
*/
BaseMatrix<T>& PostTranslate(T aX, T aY) {
_31 += aX;
_32 += aY;
return *this;
}
BaseMatrix<T>& PostTranslate(const MatrixPoint& aPoint) {
return PostTranslate(aPoint.x, aPoint.y);
}
static BaseMatrix<T> Scaling(T aScaleX, T aScaleY) {
return BaseMatrix<T>(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f);
}
/**
* Similar to PreTranslate, but applies a scale instead of a translation.
*/
BaseMatrix<T>& PreScale(T aX, T aY) {
_11 *= aX;
_12 *= aX;
_21 *= aY;
_22 *= aY;
return *this;
}
/**
* Similar to PostTranslate, but applies a scale instead of a translation.
*/
BaseMatrix<T>& PostScale(T aScaleX, T aScaleY) {
_11 *= aScaleX;
_12 *= aScaleY;
_21 *= aScaleX;
_22 *= aScaleY;
_31 *= aScaleX;
_32 *= aScaleY;
return *this;
}
GFX2D_API static BaseMatrix<T> Rotation(T aAngle);
/**
* Similar to PreTranslate, but applies a rotation instead of a translation.
*/
BaseMatrix<T>& PreRotate(T aAngle) {
return *this = BaseMatrix<T>::Rotation(aAngle) * *this;
}
bool Invert() {
// Compute co-factors.
T A = _22;
T B = -_21;
T C = _21 * _32 - _22 * _31;
T D = -_12;
T E = _11;
T F = _31 * _12 - _11 * _32;
T det = Determinant();
if (!det) {
return false;
}
T 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;
}
BaseMatrix<T> Inverse() const {
BaseMatrix<T> clone = *this;
DebugOnly<bool> inverted = clone.Invert();
MOZ_ASSERT(inverted,
"Attempted to get the inverse of a non-invertible matrix");
return clone;
}
T Determinant() const { return _11 * _22 - _12 * _21; }
BaseMatrix<T> operator*(const BaseMatrix<T>& aMatrix) const {
BaseMatrix<T> 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;
}
BaseMatrix<T>& operator*=(const BaseMatrix<T>& aMatrix) {
*this = *this * aMatrix;
return *this;
}
/**
* Multiplies *this with aMatrix and returns the result.
*/
Matrix4x4 operator*(const Matrix4x4& aMatrix) const;
/**
* Multiplies in the opposite order to operator=*.
*/
BaseMatrix<T>& PreMultiply(const BaseMatrix<T>& aMatrix) {
*this = aMatrix * *this;
return *this;
}
/**
* Please explicitly use either FuzzyEquals or ExactlyEquals.
*/
bool operator==(const BaseMatrix<T>& other) const = delete;
bool operator!=(const BaseMatrix<T>& other) const = delete;
/* Returns true if the other matrix is fuzzy-equal to this matrix.
* Note that this isn't a cheap comparison!
*/
bool FuzzyEquals(const BaseMatrix<T>& o) const {
return FuzzyEqual(_11, o._11) && FuzzyEqual(_12, o._12) &&
FuzzyEqual(_21, o._21) && FuzzyEqual(_22, o._22) &&
FuzzyEqual(_31, o._31) && FuzzyEqual(_32, o._32);
}
bool ExactlyEquals(const BaseMatrix<T>& 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 + T(0.5))) ||
!FuzzyEqual(_32, floor(_32 + T(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 {
T det = Determinant();
return !mozilla::IsFinite(det) || det == 0;
}
GFX2D_API BaseMatrix<T>& NudgeToIntegers() {
NudgeToInteger(&_11);
NudgeToInteger(&_12);
NudgeToInteger(&_21);
NudgeToInteger(&_22);
NudgeToInteger(&_31);
NudgeToInteger(&_32);
return *this;
}
bool IsTranslation() const {
return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) &&
FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f);
}
static bool FuzzyIsInteger(T 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);
}
MatrixPoint GetTranslation() const { return MatrixPoint(_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); }
/**
* Computes the scale factors of this matrix; that is,
* the amounts each basis vector is scaled by.
* The xMajor parameter indicates if the larger scale is
* to be assumed to be in the X direction or not.
*/
MatrixSize ScaleFactors(bool xMajor) const {
T det = Determinant();
if (det == 0.0) {
return MatrixSize(0.0, 0.0);
}
MatrixSize sz = xMajor ? MatrixSize(1.0, 0.0) : MatrixSize(0.0, 1.0);
sz = TransformSize(sz);
T major = sqrt(sz.width * sz.width + sz.height * sz.height);
T minor = 0.0;
// ignore mirroring
if (det < 0.0) {
det = -det;
}
if (major) {
minor = det / major;
}
if (xMajor) {
return MatrixSize(major, minor);
}
return MatrixSize(minor, major);
}
};
typedef BaseMatrix<Float> Matrix;
typedef BaseMatrix<Double> MatrixDouble;
// 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 {
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.