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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];
};
template <class T2>
explicit BaseMatrix(const BaseMatrix<T2>& aOther)
: _11(aOther._11),
_12(aOther._12),
_21(aOther._21),
_22(aOther._22),
_31(aOther._31),
_32(aOther._32) {}
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 + 0.5f)) ||
!FuzzyEqual(_32, floor(_32 + 0.5f));
}
/**
* 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 <class SourceUnits, class TargetUnits, class T>
class Matrix4x4Typed {
public:
typedef PointTyped<SourceUnits, T> SourcePoint;
typedef PointTyped<TargetUnits, T> TargetPoint;
typedef Point3DTyped<SourceUnits, T> SourcePoint3D;
typedef Point3DTyped<TargetUnits, T> TargetPoint3D;
typedef Point4DTyped<SourceUnits, T> SourcePoint4D;
typedef Point4DTyped<TargetUnits, T> TargetPoint4D;
typedef RectTyped<SourceUnits, T> SourceRect;
typedef RectTyped<TargetUnits, T> 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(T a11, T a12, T a13, T a14, T a21, T a22, T a23, T a24, T a31,
T a32, T a33, T a34, T a41, T a42, T a43, T 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 T aArray[16]) {
memcpy(components, aArray, sizeof(components));
}
Matrix4x4Typed(const Matrix4x4Typed& aOther) {
memcpy(components, aOther.components, sizeof(components));
}
template <class T2>
explicit Matrix4x4Typed(
const Matrix4x4Typed<SourceUnits, TargetUnits, T2>& aOther)
: _11(aOther._11),
_12(aOther._12),
_13(aOther._13),
_14(aOther._14),
_21(aOther._21),
_22(aOther._22),
_23(aOther._23),
_24(aOther._24),
_31(aOther._31),
_32(aOther._32),
_33(aOther._33),
_34(aOther._34),
_41(aOther._41),
_42(aOther._42),
_43(aOther._43),
_44(aOther._44) {}
union {
struct {
T _11, _12, _13, _14;
T _21, _22, _23, _24;
T _31, _32, _33, _34;
T _41, _42, _43, _44;
};
T components[16];
};
friend std::ostream& operator<<(std::ostream& aStream,
const Matrix4x4Typed& aMatrix) {
const T* 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;
}
Point4DTyped<UnknownUnits, T>& operator[](int aIndex) {
MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
return *reinterpret_cast<Point4DTyped<UnknownUnits, T>*>((&_11) +
4 * aIndex);
}
const Point4DTyped<UnknownUnits, T>& operator[](int aIndex) const {
MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
return *reinterpret_cast<const Point4DTyped<UnknownUnits, T>*>((&_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(BaseMatrix<T>* 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;
}
BaseMatrix<T> As2D() const {
MOZ_ASSERT(Is2D(), "Matrix is not a 2D affine transform");
return BaseMatrix<T>(_11, _12, _21, _22, _41, _42);
}
bool CanDraw2D(BaseMatrix<T>* 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) {
T 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 than 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>* dstPointStart = points[0];
Point4DTyped<UnknownUnits, F>* dstPoint = dstPointStart;
*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.
// For each clipping plane, we intersect the plane with all polygon edges.
// Each pass can increase or decrease the number of points that make up the
// current clipped polygon. We double buffer that set of points, alternating
// between points[0] and points[1].
for (int plane = 0; plane < 4; plane++) {
planeNormals[plane].Normalize();
Point4DTyped<UnknownUnits, F>* srcPoint = dstPointStart;
Point4DTyped<UnknownUnits, F>* srcPointEnd = dstPoint;
dstPointStart = points[~plane & 1];
dstPoint = dstPointStart;
// Iterate over the polygon edges. In each iteration the current edge is
// the edge from prevPoint to srcPoint. If the two end points lie on
// different sides of the plane, we have an intersection. Otherwise, the
// edge is either completely "inside" the half-space created by the
// clipping plane, and we add srcPoint, or it is completely "outside", and
// we discard srcPoint.
// We may create duplicated points in the polygon. We keep those around
// until all clipping is done and then filter out duplicates at the end.
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) {
// No polygon points were produced, so the polygon has been
// completely clipped away by the current clipping plane. Exit.
break;
}
}
Point4DTyped<UnknownUnits, F>* srcPoint = dstPointStart;
Point4DTyped<UnknownUnits, F>* srcPointEnd = dstPoint;
size_t vertCount = 0;
while (srcPoint < srcPointEnd) {
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 (vertCount == 0 || p != aVerts[vertCount - 1]) {
aVerts[vertCount++] = p;
}
srcPoint++;
}
return vertCount;
}
static const int kTransformAndClipRectMaxVerts = 32;
static Matrix4x4Typed From2D(const BaseMatrix<T>& 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;