mirror of
https://github.com/classilla/tenfourfox.git
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1566 lines
50 KiB
C++
1566 lines
50 KiB
C++
/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 2 -*-
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
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#ifndef MOZILLA_GFX_MATRIX_H_
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#define MOZILLA_GFX_MATRIX_H_
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#include "Types.h"
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#include "Rect.h"
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#include "Point.h"
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#include "Quaternion.h"
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#include <iosfwd>
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#include <math.h>
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#include "mozilla/Attributes.h"
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#include "mozilla/DebugOnly.h"
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#include "mozilla/FloatingPoint.h"
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namespace mozilla {
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namespace gfx {
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static bool FuzzyEqual(Float aV1, Float aV2) {
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// XXX - Check if fabs does the smart thing and just negates the sign bit.
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return fabs(aV2 - aV1) < 1e-6;
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}
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class Matrix
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{
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public:
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Matrix()
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: _11(1.0f), _12(0)
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, _21(0), _22(1.0f)
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, _31(0), _32(0)
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{}
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Matrix(Float a11, Float a12, Float a21, Float a22, Float a31, Float a32)
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: _11(a11), _12(a12)
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, _21(a21), _22(a22)
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, _31(a31), _32(a32)
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{}
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Float _11, _12;
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Float _21, _22;
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Float _31, _32;
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MOZ_ALWAYS_INLINE Matrix Copy() const
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{
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return Matrix(*this);
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}
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friend std::ostream& operator<<(std::ostream& aStream, const Matrix& aMatrix);
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Point operator *(const Point &aPoint) const
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{
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Point retPoint;
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retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31;
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retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32;
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return retPoint;
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}
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Size operator *(const Size &aSize) const
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{
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Size retSize;
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retSize.width = aSize.width * _11 + aSize.height * _21;
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retSize.height = aSize.width * _12 + aSize.height * _22;
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return retSize;
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}
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GFX2D_API Rect TransformBounds(const Rect& rect) const;
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static Matrix Translation(Float aX, Float aY)
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{
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return Matrix(1.0f, 0.0f, 0.0f, 1.0f, aX, aY);
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}
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static Matrix Translation(Point aPoint)
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{
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return Translation(aPoint.x, aPoint.y);
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}
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/**
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* Apply a translation to this matrix.
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*
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* The "Pre" in this method's name means that the translation is applied
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* -before- this matrix's existing transformation. That is, any vector that
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* is multiplied by the resulting matrix will first be translated, then be
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* transformed by the original transform.
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*
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* Calling this method will result in this matrix having the same value as
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* the result of:
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*
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* Matrix::Translation(x, y) * this
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*
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* (Note that in performance critical code multiplying by the result of a
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* Translation()/Scaling() call is not recommended since that results in a
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* full matrix multiply involving 12 floating-point multiplications. Calling
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* this method would be preferred since it only involves four floating-point
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* multiplications.)
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*/
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Matrix &PreTranslate(Float aX, Float aY)
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{
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_31 += _11 * aX + _21 * aY;
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_32 += _12 * aX + _22 * aY;
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return *this;
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}
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Matrix &PreTranslate(const Point &aPoint)
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{
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return PreTranslate(aPoint.x, aPoint.y);
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}
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/**
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* Similar to PreTranslate, but the translation is applied -after- this
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* matrix's existing transformation instead of before it.
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*
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* This method is generally less used than PreTranslate since typically code
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* want to adjust an existing user space to device space matrix to create a
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* transform to device space from a -new- user space (translated from the
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* previous user space). In that case consumers will need to use the Pre*
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* variants of the matrix methods rather than using the Post* methods, since
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* the Post* methods add a transform to the device space end of the
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* transformation.
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*/
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Matrix &PostTranslate(Float aX, Float aY)
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{
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_31 += aX;
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_32 += aY;
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return *this;
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}
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Matrix &PostTranslate(const Point &aPoint)
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{
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return PostTranslate(aPoint.x, aPoint.y);
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}
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static Matrix Scaling(Float aScaleX, Float aScaleY)
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{
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return Matrix(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f);
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}
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/**
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* Similar to PreTranslate, but applies a scale instead of a translation.
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*/
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Matrix &PreScale(Float aX, Float aY)
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{
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_11 *= aX;
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_12 *= aX;
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_21 *= aY;
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_22 *= aY;
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return *this;
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}
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/**
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* Similar to PostTranslate, but applies a scale instead of a translation.
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*/
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Matrix &PostScale(Float aScaleX, Float aScaleY)
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{
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_11 *= aScaleX;
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_12 *= aScaleY;
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_21 *= aScaleX;
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_22 *= aScaleY;
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_31 *= aScaleX;
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_32 *= aScaleY;
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return *this;
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}
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GFX2D_API static Matrix Rotation(Float aAngle);
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/**
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* Similar to PreTranslate, but applies a rotation instead of a translation.
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*/
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Matrix &PreRotate(Float aAngle)
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{
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return *this = Matrix::Rotation(aAngle) * *this;
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}
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bool Invert()
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{
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// Compute co-factors.
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Float A = _22;
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Float B = -_21;
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Float C = _21 * _32 - _22 * _31;
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Float D = -_12;
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Float E = _11;
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Float F = _31 * _12 - _11 * _32;
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Float det = Determinant();
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if (!det) {
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return false;
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}
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Float inv_det = 1 / det;
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_11 = inv_det * A;
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_12 = inv_det * D;
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_21 = inv_det * B;
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_22 = inv_det * E;
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_31 = inv_det * C;
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_32 = inv_det * F;
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return true;
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}
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Matrix Inverse() const
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{
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Matrix clone = *this;
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DebugOnly<bool> inverted = clone.Invert();
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MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix");
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return clone;
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}
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Float Determinant() const
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{
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return _11 * _22 - _12 * _21;
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}
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Matrix operator*(const Matrix &aMatrix) const
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{
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Matrix resultMatrix;
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resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21;
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resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22;
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resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21;
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resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22;
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resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + aMatrix._31;
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resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + aMatrix._32;
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return resultMatrix;
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}
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Matrix& operator*=(const Matrix &aMatrix)
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{
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*this = *this * aMatrix;
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return *this;
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}
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/**
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* Multiplies in the opposite order to operator=*.
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*/
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Matrix &PreMultiply(const Matrix &aMatrix)
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{
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*this = aMatrix * *this;
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return *this;
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}
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/* Returns true if the other matrix is fuzzy-equal to this matrix.
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* Note that this isn't a cheap comparison!
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*/
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bool operator==(const Matrix& other) const
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{
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return FuzzyEqual(_11, other._11) && FuzzyEqual(_12, other._12) &&
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FuzzyEqual(_21, other._21) && FuzzyEqual(_22, other._22) &&
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FuzzyEqual(_31, other._31) && FuzzyEqual(_32, other._32);
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}
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bool operator!=(const Matrix& other) const
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{
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return !(*this == other);
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}
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bool ExactlyEquals(const Matrix& o) const
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{
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return _11 == o._11 && _12 == o._12 &&
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_21 == o._21 && _22 == o._22 &&
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_31 == o._31 && _32 == o._32;
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}
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/* Verifies that the matrix contains no Infs or NaNs. */
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bool IsFinite() const
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{
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return mozilla::IsFinite(_11) && mozilla::IsFinite(_12) &&
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mozilla::IsFinite(_21) && mozilla::IsFinite(_22) &&
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mozilla::IsFinite(_31) && mozilla::IsFinite(_32);
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}
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/* Returns true if the matrix is a rectilinear transformation (i.e.
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* grid-aligned rectangles are transformed to grid-aligned rectangles)
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*/
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bool IsRectilinear() const {
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if (FuzzyEqual(_12, 0) && FuzzyEqual(_21, 0)) {
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return true;
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} else if (FuzzyEqual(_22, 0) && FuzzyEqual(_11, 0)) {
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return true;
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}
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return false;
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}
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/**
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* Returns true if the matrix is anything other than a straight
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* translation by integers.
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*/
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bool HasNonIntegerTranslation() const {
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return HasNonTranslation() ||
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!FuzzyEqual(_31, floor(_31 + 0.5)) ||
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!FuzzyEqual(_32, floor(_32 + 0.5));
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}
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/**
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* Returns true if the matrix only has an integer translation.
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*/
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bool HasOnlyIntegerTranslation() const {
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return !HasNonIntegerTranslation();
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}
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/**
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* Returns true if the matrix has any transform other
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* than a straight translation.
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*/
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bool HasNonTranslation() const {
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return !FuzzyEqual(_11, 1.0) || !FuzzyEqual(_22, 1.0) ||
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!FuzzyEqual(_12, 0.0) || !FuzzyEqual(_21, 0.0);
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}
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/**
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* Returns true if the matrix has any transform other
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* than a translation or a -1 y scale (y axis flip)
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*/
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bool HasNonTranslationOrFlip() const {
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return !FuzzyEqual(_11, 1.0) ||
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(!FuzzyEqual(_22, 1.0) && !FuzzyEqual(_22, -1.0)) ||
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!FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
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}
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/* Returns true if the matrix is an identity matrix.
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*/
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bool IsIdentity() const
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{
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return _11 == 1.0f && _12 == 0.0f &&
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_21 == 0.0f && _22 == 1.0f &&
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_31 == 0.0f && _32 == 0.0f;
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}
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/* Returns true if the matrix is singular.
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*/
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bool IsSingular() const
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{
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return Determinant() == 0;
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}
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GFX2D_API Matrix &NudgeToIntegers();
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bool IsTranslation() const
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{
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return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) &&
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FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f);
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}
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static bool FuzzyIsInteger(Float aValue)
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{
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return FuzzyEqual(aValue, floorf(aValue + 0.5f));
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}
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bool IsIntegerTranslation() const
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{
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return IsTranslation() && FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
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}
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bool IsAllIntegers() const
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{
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return FuzzyIsInteger(_11) && FuzzyIsInteger(_12) &&
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FuzzyIsInteger(_21) && FuzzyIsInteger(_22) &&
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FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
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}
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Point GetTranslation() const {
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return Point(_31, _32);
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}
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/**
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* Returns true if matrix is multiple of 90 degrees rotation with flipping,
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* scaling and translation.
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*/
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bool PreservesAxisAlignedRectangles() const {
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return ((FuzzyEqual(_11, 0.0) && FuzzyEqual(_22, 0.0))
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|| (FuzzyEqual(_12, 0.0) && FuzzyEqual(_21, 0.0)));
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}
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/**
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* Returns true if the matrix has any transform other
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* than a translation or scale; this is, if there is
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* rotation.
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*/
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bool HasNonAxisAlignedTransform() const {
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return !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
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}
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/**
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* Returns true if the matrix has negative scaling (i.e. flip).
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*/
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bool HasNegativeScaling() const {
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return (_11 < 0.0) || (_22 < 0.0);
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}
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};
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// Helper functions used by Matrix4x4Typed defined in Matrix.cpp
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double
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SafeTangent(double aTheta);
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double
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FlushToZero(double aVal);
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template<class Units, class F>
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Point4DTyped<Units, F>
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ComputePerspectivePlaneIntercept(const Point4DTyped<Units, F>& aFirst,
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const Point4DTyped<Units, F>& aSecond)
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{
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// This function will always return a point with a w value of 0.
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// The X, Y, and Z components will point towards an infinite vanishing
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// point.
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// We want to interpolate aFirst and aSecond to find the point intersecting
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// with the w=0 plane.
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// Since we know what we want the w component to be, we can rearrange the
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// interpolation equation and solve for t.
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float t = -aFirst.w / (aSecond.w - aFirst.w);
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// Use t to find the remainder of the components
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return aFirst + (aSecond - aFirst) * t;
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}
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template <typename SourceUnits, typename TargetUnits>
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class Matrix4x4Typed
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{
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public:
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typedef PointTyped<SourceUnits> SourcePoint;
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typedef PointTyped<TargetUnits> TargetPoint;
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typedef Point3DTyped<SourceUnits> SourcePoint3D;
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typedef Point3DTyped<TargetUnits> TargetPoint3D;
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typedef Point4DTyped<SourceUnits> SourcePoint4D;
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typedef Point4DTyped<TargetUnits> TargetPoint4D;
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typedef RectTyped<SourceUnits> SourceRect;
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typedef RectTyped<TargetUnits> TargetRect;
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Matrix4x4Typed()
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: _11(1.0f), _12(0.0f), _13(0.0f), _14(0.0f)
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, _21(0.0f), _22(1.0f), _23(0.0f), _24(0.0f)
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, _31(0.0f), _32(0.0f), _33(1.0f), _34(0.0f)
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, _41(0.0f), _42(0.0f), _43(0.0f), _44(1.0f)
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{}
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Matrix4x4Typed(Float a11, Float a12, Float a13, Float a14,
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Float a21, Float a22, Float a23, Float a24,
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Float a31, Float a32, Float a33, Float a34,
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Float a41, Float a42, Float a43, Float a44)
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: _11(a11), _12(a12), _13(a13), _14(a14)
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, _21(a21), _22(a22), _23(a23), _24(a24)
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, _31(a31), _32(a32), _33(a33), _34(a34)
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, _41(a41), _42(a42), _43(a43), _44(a44)
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{}
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Matrix4x4Typed(const Matrix4x4Typed& aOther)
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{
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memcpy(this, &aOther, sizeof(*this));
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}
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Float _11, _12, _13, _14;
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Float _21, _22, _23, _24;
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Float _31, _32, _33, _34;
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Float _41, _42, _43, _44;
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friend std::ostream& operator<<(std::ostream& aStream, const Matrix4x4Typed& aMatrix)
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{
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const Float *f = &aMatrix._11;
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aStream << "[ " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
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aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
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aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ;" << std::endl; f += 4;
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aStream << " " << f[0] << " " << f[1] << " " << f[2] << " " << f[3] << " ]" << std::endl;
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return aStream;
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}
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Point4D& operator[](int aIndex)
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{
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MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
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return *reinterpret_cast<Point4D*>((&_11)+4*aIndex);
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}
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const Point4D& operator[](int aIndex) const
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{
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MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
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return *reinterpret_cast<const Point4D*>((&_11)+4*aIndex);
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}
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/**
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* Returns true if the matrix is isomorphic to a 2D affine transformation.
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*/
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bool Is2D() const
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{
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if (_13 != 0.0f || _14 != 0.0f ||
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_23 != 0.0f || _24 != 0.0f ||
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_31 != 0.0f || _32 != 0.0f || _33 != 1.0f || _34 != 0.0f ||
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_43 != 0.0f || _44 != 1.0f) {
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return false;
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}
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return true;
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}
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bool Is2D(Matrix* aMatrix) const {
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if (!Is2D()) {
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return false;
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}
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if (aMatrix) {
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aMatrix->_11 = _11;
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aMatrix->_12 = _12;
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aMatrix->_21 = _21;
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aMatrix->_22 = _22;
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aMatrix->_31 = _41;
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aMatrix->_32 = _42;
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}
|
|
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;
|
|
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 * 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);
|
|
}
|
|
|
|
/**
|
|
* 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++ = *this * Point4DTyped<UnknownUnits, F>(aRect.x, aRect.y, 0, 1);
|
|
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.y, 0, 1);
|
|
*dstPoint++ = *this * Point4DTyped<UnknownUnits, F>(aRect.XMost(), aRect.YMost(), 0, 1);
|
|
*dstPoint++ = *this * 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> operator *(const Point4DTyped<SourceUnits, F>& aPoint) const
|
|
{
|
|
Point4DTyped<TargetUnits, 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<TargetUnits, F> operator *(const Point3DTyped<SourceUnits, F>& aPoint) const
|
|
{
|
|
Point4DTyped<SourceUnits, F> temp(aPoint.x, aPoint.y, aPoint.z, 1);
|
|
|
|
Point4DTyped<TargetUnits, F> result = *this * temp;
|
|
result /= result.w;
|
|
|
|
return Point3DTyped<TargetUnits, F>(result.x, result.y, result.z);
|
|
}
|
|
|
|
template<class F>
|
|
PointTyped<TargetUnits, F> operator *(const PointTyped<SourceUnits, F> &aPoint) const
|
|
{
|
|
Point4DTyped<SourceUnits, F> temp(aPoint.x, aPoint.y, 0, 1);
|
|
Point4DTyped<TargetUnits, F> result = *this * temp;
|
|
return result.As2DPoint();
|
|
}
|
|
|
|
template<class F>
|
|
GFX2D_API RectTyped<TargetUnits, F> TransformBounds(const RectTyped<SourceUnits, F>& aRect) const
|
|
{
|
|
Point4DTyped<TargetUnits, F> verts[4];
|
|
verts[0] = *this * Point4DTyped<SourceUnits, F>(aRect.x, aRect.y, 0.0, 1.0);
|
|
verts[1] = *this * Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.y, 0.0, 1.0);
|
|
verts[2] = *this * Point4DTyped<SourceUnits, F>(aRect.XMost(), aRect.YMost(), 0.0, 1.0);
|
|
verts[3] = *this * 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] = *this * aRect.TopLeft();
|
|
quad[1] = *this * aRect.TopRight();
|
|
quad[2] = *this * aRect.BottomLeft();
|
|
quad[3] = *this * 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 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.)
|
|
*/
|
|
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 Point3D& aPoint) {
|
|
return PostTranslate(aPoint.x, aPoint.y, aPoint.z);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
// 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.
|
|
Matrix4x4Typed &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& 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;
|
|
}
|
|
|
|
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 = *this * Point3D(0, 0, 0);
|
|
Point3D b = *this * Point3D(0, 1, 0);
|
|
Point3D c = *this * 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);
|
|
}
|
|
|
|
/**
|
|
* 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;
|
|
}
|
|
|
|
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_ */
|