Class encapsulating a standard 4x4 homogeneous matrix. More...

#include <OgreMatrix4.h>

Public Member Functions
	Matrix4 ()
	Default constructor.

	Matrix4 (const Matrix3 &m3x3)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.

	Matrix4 (const Quaternion &rot)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.

	Matrix4 (const Real *arr)

	Matrix4 (Real m00, Real m01, Real m02, Real m03, Real m10, Real m11, Real m12, Real m13, Real m20, Real m21, Real m22, Real m23, Real m30, Real m31, Real m32, Real m33)

Matrix4	adjoint () const

Matrix4	concatenate (const Matrix4 &m2) const

Matrix4	concatenateAffine (const Matrix4 &m2) const
	Concatenate two affine matrices.

void	decomposition (Vector3 &position, Vector3 &scale, Quaternion &orientation) const
	Decompose a Matrix4 to orientation / scale / position.

Real	determinant () const

void	extract3x3Matrix (Matrix3 &m3x3) const
	Extracts the rotation / scaling part of the Matrix as a 3x3 matrix.

Quaternion	extractQuaternion () const
	Extracts the rotation / scaling part as a quaternion from the Matrix.

Vector3	getTrans () const
	Extracts the translation transformation part of the matrix.

bool	hasNegativeScale () const
	Determines if this matrix involves a negative scaling.

bool	hasScale () const
	Determines if this matrix involves a scaling.

Matrix4	inverse () const

Matrix4	inverseAffine (void) const
	Returns the inverse of the affine matrix.

bool	isAffine (void) const
	Check whether or not the matrix is affine matrix.

void	makeInverseTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building an inverse Matrix4 from orientation / scale / position.

void	makeTrans (const Vector3 &v)
	Builds a translation matrix.

void	makeTrans (Real tx, Real ty, Real tz)

void	makeTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building a Matrix4 from orientation / scale / position.

bool	operator!= (const Matrix4 &m2) const
	Tests 2 matrices for inequality.

Matrix4	operator* (const Matrix4 &m2) const
	Matrix concatenation using '*'.

Plane	operator* (const Plane &p) const

Vector3	operator* (const Vector3 &v) const
	Vector transformation using '*'.

Vector4	operator* (const Vector4 &v) const

Matrix4	operator* (Real scalar) const

Matrix4	operator+ (const Matrix4 &m2) const
	Matrix addition.

Matrix4	operator- (const Matrix4 &m2) const
	Matrix subtraction.

void	operator= (const Matrix3 &mat3)
	Assignment from 3x3 matrix.

bool	operator== (const Matrix4 &m2) const
	Tests 2 matrices for equality.

Real *	operator[] (size_t iRow)

const Real *	operator[] (size_t iRow) const

void	setScale (const Vector3 &v)
	Sets the scale part of the matrix.

void	setTrans (const Vector3 &v)
	Sets the translation transformation part of the matrix.

void	swap (Matrix4 &other)
	Exchange the contents of this matrix with another.

Vector3	transformAffine (const Vector3 &v) const
	3-D Vector transformation specially for an affine matrix.

Vector4	transformAffine (const Vector4 &v) const
	4-D Vector transformation specially for an affine matrix.

Vector3	transformDirectionAffine (const Vector3 &v) const
	3-D Vector transformation specially for an affine matrix.

Matrix4	transpose (void) const

Static Public Member Functions
static Matrix4	getScale (const Vector3 &v)
	Gets a scale matrix.

static Matrix4	getScale (Real s_x, Real s_y, Real s_z)
	Gets a scale matrix - variation for not using a vector.

static Matrix4	getTrans (const Vector3 &v)
	Gets a translation matrix.

static Matrix4	getTrans (Real t_x, Real t_y, Real t_z)
	Gets a translation matrix - variation for not using a vector.

Static Public Attributes
static const Matrix4	CLIPSPACE2DTOIMAGESPACE
	Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y.

static const Matrix4	IDENTITY

static const Matrix4	ZERO

static const Matrix4	ZEROAFFINE

Friends
class	ArrayMatrix4

class	ArrayMatrixAf4x3

_OgreExport friend std::ostream &	operator<< (std::ostream &o, const Matrix4 &mat)
	Function for writing to a stream.

class	SimpleMatrix4

class	SimpleMatrixAf4x3

Detailed Description

Class encapsulating a standard 4x4 homogeneous matrix.

Remarks: OGRE uses column vectors when applying matrix multiplications, This means a vector is represented as a single column, 4-row matrix. This has the effect that the transformations implemented by the matrices happens right-to-left e.g. if vector V is to be transformed by M1 then M2 then M3, the calculation would be M3 * M2 * M1 * V. The order that matrices are concatenated is vital since matrix multiplication is not commutative, i.e. you can get a different result if you concatenate in the wrong order.

: The use of column vectors and right-to-left ordering is the standard in most mathematical texts, and is the same as used in OpenGL. It is, however, the opposite of Direct3D, which has inexplicably chosen to differ from the accepted standard and uses row vectors and left-to-right matrix multiplication.

: OGRE deals with the differences between D3D and OpenGL etc. internally when operating through different render systems. OGRE users only need to conform to standard maths conventions, i.e. right-to-left matrix multiplication, (OGRE transposes matrices it passes to D3D to compensate).

The generic form M * V which shows the layout of the matrix entries is shown below:

        [ m[0][0]  m[0][1]  m[0][2]  m[0][3] ]   {x}
        | m[1][0]  m[1][1]  m[1][2]  m[1][3] | * {y}
        | m[2][0]  m[2][1]  m[2][2]  m[2][3] |   {z}
        [ m[3][0]  m[3][1]  m[3][2]  m[3][3] ]   {1}

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

Ogre::Matrix4::Matrix4 ( )

inline

Default constructor.

Note: It does NOT initialize the matrix for efficiency.

◆ Matrix4() [2/5]

Ogre::Matrix4::Matrix4	(	Real	m00,
		Real	m01,
		Real	m02,
		Real	m03,
		Real	m10,
		Real	m11,
		Real	m12,
		Real	m13,
		Real	m20,
		Real	m21,
		Real	m22,
		Real	m23,
		Real	m30,
		Real	m31,
		Real	m32,
		Real	m33
	)

inline

◆ Matrix4() [3/5]

Ogre::Matrix4::Matrix4 ( const Real * arr )

inline

◆ Matrix4() [4/5]

Ogre::Matrix4::Matrix4 ( const Matrix3 & m3x3 )

inline

Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.

◆ Matrix4() [5/5]

Ogre::Matrix4::Matrix4 ( const Quaternion & rot )

inline

Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.

Member Function Documentation

◆ adjoint()

Matrix4 Ogre::Matrix4::adjoint ( ) const

◆ concatenate()

Matrix4 Ogre::Matrix4::concatenate ( const Matrix4 & m2 ) const

inline

References m.

◆ concatenateAffine()

Matrix4 Ogre::Matrix4::concatenateAffine ( const Matrix4 & m2 ) const

inline

Concatenate two affine matrices.

Note: The matrices must be affine matrix.

See also: Matrix4::isAffine.

◆ decomposition()

void Ogre::Matrix4::decomposition	(	Vector3 &	position,
		Vector3 &	scale,
		Quaternion &	orientation
	)		const

Decompose a Matrix4 to orientation / scale / position.

◆ determinant()

Real Ogre::Matrix4::determinant ( ) const

◆ extract3x3Matrix()

void Ogre::Matrix4::extract3x3Matrix ( Matrix3 & m3x3 ) const

inline

Extracts the rotation / scaling part of the Matrix as a 3x3 matrix.

Parameters

m3x3	Destination Matrix3

◆ extractQuaternion()

Quaternion Ogre::Matrix4::extractQuaternion ( ) const

inline

Extracts the rotation / scaling part as a quaternion from the Matrix.

◆ getScale() [1/2]

static Matrix4 Ogre::Matrix4::getScale ( const Vector3 & v )

inlinestatic

Gets a scale matrix.

References m.

◆ getScale() [2/2]

static Matrix4 Ogre::Matrix4::getScale	(	Real	s_x,
		Real	s_y,
		Real	s_z
	)

inlinestatic

Gets a scale matrix - variation for not using a vector.

References m.

◆ getTrans() [1/3]

Vector3 Ogre::Matrix4::getTrans ( ) const

inline

Extracts the translation transformation part of the matrix.

◆ getTrans() [2/3]

static Matrix4 Ogre::Matrix4::getTrans ( const Vector3 & v )

inlinestatic

Gets a translation matrix.

References m.

◆ getTrans() [3/3]

static Matrix4 Ogre::Matrix4::getTrans	(	Real	t_x,
		Real	t_y,
		Real	t_z
	)

inlinestatic

Gets a translation matrix - variation for not using a vector.

References m.

◆ hasNegativeScale()

bool Ogre::Matrix4::hasNegativeScale ( ) const

inline

Determines if this matrix involves a negative scaling.

◆ hasScale()

bool Ogre::Matrix4::hasScale ( ) const

inline

Determines if this matrix involves a scaling.

References Ogre::Math::RealEqual().

◆ inverse()

Matrix4 Ogre::Matrix4::inverse ( ) const

◆ inverseAffine()

Matrix4 Ogre::Matrix4::inverseAffine ( void ) const

Returns the inverse of the affine matrix.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

◆ isAffine()

bool Ogre::Matrix4::isAffine ( void ) const

inline

Check whether or not the matrix is affine matrix.

Remarks: An affine matrix is a 4x4 matrix with row 3 equal to (0, 0, 0, 1), e.g. no projective coefficients.

Referenced by Ogre::AxisAlignedBox::transformAffine().

◆ makeInverseTransform()

void Ogre::Matrix4::makeInverseTransform	(	const Vector3 &	position,
		const Vector3 &	scale,
		const Quaternion &	orientation
	)

Building an inverse Matrix4 from orientation / scale / position.

Remarks: As makeTransform except it build the inverse given the same data as makeTransform, so performing -translation, -rotate, 1/scale in that order.

◆ makeTrans() [1/2]

void Ogre::Matrix4::makeTrans ( const Vector3 & v )

inline

Builds a translation matrix.

◆ makeTrans() [2/2]

void Ogre::Matrix4::makeTrans	(	Real	tx,
		Real	ty,
		Real	tz
	)

inline

◆ makeTransform()

void Ogre::Matrix4::makeTransform	(	const Vector3 &	position,
		const Vector3 &	scale,
		const Quaternion &	orientation
	)

Building a Matrix4 from orientation / scale / position.

Remarks: Transform is performed in the order scale, rotate, translation, i.e. translation is independent of orientation axes, scale does not affect size of translation, rotation and scaling are always centered on the origin.

◆ operator!=()

bool Ogre::Matrix4::operator!= ( const Matrix4 & m2 ) const

inline

Tests 2 matrices for inequality.

◆ operator*() [1/5]

Matrix4 Ogre::Matrix4::operator* ( const Matrix4 & m2 ) const

inline

Matrix concatenation using '*'.

◆ operator*() [2/5]

Plane Ogre::Matrix4::operator* ( const Plane & p ) const

inline

◆ operator*() [3/5]

Vector3 Ogre::Matrix4::operator* ( const Vector3 & v ) const

inline

Vector transformation using '*'.

Remarks: Transforms the given 3-D vector by the matrix, projecting the result back into w = 1.

Note: This means that the initial w is considered to be 1.0, and then all the tree elements of the resulting 3-D vector are divided by the resulting w.

References Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

◆ operator*() [4/5]

Vector4 Ogre::Matrix4::operator* ( const Vector4 & v ) const

inline

◆ operator*() [5/5]

Matrix4 Ogre::Matrix4::operator* ( Real scalar ) const

inline

◆ operator+()

Matrix4 Ogre::Matrix4::operator+ ( const Matrix4 & m2 ) const

inline

Matrix addition.

References m.

◆ operator-()

Matrix4 Ogre::Matrix4::operator- ( const Matrix4 & m2 ) const

inline

Matrix subtraction.

References m.

◆ operator=()

void Ogre::Matrix4::operator= ( const Matrix3 & mat3 )

inline

Assignment from 3x3 matrix.

◆ operator==()

bool Ogre::Matrix4::operator== ( const Matrix4 & m2 ) const

inline

Tests 2 matrices for equality.

◆ operator[]() [1/2]

Real * Ogre::Matrix4::operator[] ( size_t iRow )

inline

◆ operator[]() [2/2]

const Real * Ogre::Matrix4::operator[] ( size_t iRow ) const

inline

◆ setScale()

void Ogre::Matrix4::setScale ( const Vector3 & v )

inline

Sets the scale part of the matrix.

◆ setTrans()

void Ogre::Matrix4::setTrans ( const Vector3 & v )

inline

Sets the translation transformation part of the matrix.

◆ swap()

void Ogre::Matrix4::swap ( Matrix4 & other )

inline

Exchange the contents of this matrix with another.

References m, and std::swap().

◆ transformAffine() [1/2]

Vector3 Ogre::Matrix4::transformAffine ( const Vector3 & v ) const

inline

3-D Vector transformation specially for an affine matrix.

Remarks: Transforms the given 3-D vector by the matrix, projecting the result back into w = 1.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

Referenced by Ogre::AxisAlignedBox::transformAffine().

◆ transformAffine() [2/2]

Vector4 Ogre::Matrix4::transformAffine ( const Vector4 & v ) const

inline

4-D Vector transformation specially for an affine matrix.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

◆ transformDirectionAffine()

Vector3 Ogre::Matrix4::transformDirectionAffine ( const Vector3 & v ) const

inline

3-D Vector transformation specially for an affine matrix.

Remarks: Transforms the given 3-D vector by the 3x3 submatrix, without adding translation, as should be transformed directions and normals.

Note: The matrix must be an affine matrix.

See also: Matrix4::isAffine.

◆ transpose()

Matrix4 Ogre::Matrix4::transpose ( void ) const

inline

Friends And Related Symbol Documentation

◆ ArrayMatrix4

friend class ArrayMatrix4

friend

◆ ArrayMatrixAf4x3

friend class ArrayMatrixAf4x3

friend

◆ operator<<

_OgreExport friend std::ostream & operator<<	(	std::ostream &	o,
		const Matrix4 &	mat
	)

friend

Function for writing to a stream.

◆ SimpleMatrix4

friend class SimpleMatrix4

friend

◆ SimpleMatrixAf4x3

friend class SimpleMatrixAf4x3

friend

Member Data Documentation

◆ _m

Real Ogre::Matrix4::_m[16]

Referenced by Ogre::ArrayMatrix4::createAllFromMatrix4(), Ogre::SimpleMatrix4::load(), Ogre::SimpleMatrixAf4x3::load(), Ogre::ArrayMatrix4::setAll(), Ogre::ArrayMatrixAf4x3::setAll(), Ogre::ArrayMatrix4::setFromMatrix4(), Ogre::SimpleMatrixAf4x3::store(), and Ogre::SimpleMatrixAf4x3::store4x3().

◆ CLIPSPACE2DTOIMAGESPACE

const Matrix4 Ogre::Matrix4::CLIPSPACE2DTOIMAGESPACE

static

Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y.

◆ IDENTITY

const Matrix4 Ogre::Matrix4::IDENTITY

static

◆ m

Real Ogre::Matrix4::m[4][4]

Referenced by concatenate(), getScale(), getScale(), getTrans(), getTrans(), operator+(), operator-(), and swap().

◆ ZERO

const Matrix4 Ogre::Matrix4::ZERO

static

◆ ZEROAFFINE

const Matrix4 Ogre::Matrix4::ZEROAFFINE

static

The documentation for this class was generated from the following file:

OgreMatrix4.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

◆ Matrix4() [2/5]

◆ Matrix4() [3/5]

◆ Matrix4() [4/5]

◆ Matrix4() [5/5]

Member Function Documentation

◆ adjoint()

◆ concatenate()

◆ concatenateAffine()

◆ decomposition()

◆ determinant()

◆ extract3x3Matrix()

◆ extractQuaternion()

◆ getScale() [1/2]

◆ getScale() [2/2]

◆ getTrans() [1/3]

◆ getTrans() [2/3]

◆ getTrans() [3/3]

◆ hasNegativeScale()

◆ hasScale()

◆ inverse()

◆ inverseAffine()

◆ isAffine()

◆ makeInverseTransform()

◆ makeTrans() [1/2]

◆ makeTrans() [2/2]

◆ makeTransform()

◆ operator!=()

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator+()

◆ operator-()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ setScale()

◆ setTrans()

◆ swap()

◆ transformAffine() [1/2]

◆ transformAffine() [2/2]

◆ transformDirectionAffine()

◆ transpose()

Friends And Related Symbol Documentation

◆ ArrayMatrix4

◆ ArrayMatrixAf4x3

◆ operator<<

◆ SimpleMatrix4

◆ SimpleMatrixAf4x3

Member Data Documentation

◆ _m

◆ CLIPSPACE2DTOIMAGESPACE

◆ IDENTITY

◆ m

◆ ZERO

◆ ZEROAFFINE