Ogre::Matrix4 Class Reference

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

#include <OgreMatrix4.h>

Collaboration diagram for Ogre::Matrix4:

Public Member Functions
	Matrix4 ()
	Default constructor. More...
	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 (const Matrix3 &m3x3)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix. More...
	Matrix4 (const Quaternion &rot)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion. More...
Matrix4	adjoint () const
Matrix4	concatenate (const Matrix4 &m2) const
Matrix4	concatenateAffine (const Matrix4 &m2) const
	Concatenate two affine matrices. More...
void	decomposition (Vector3 &position, Vector3 &scale, Quaternion &orientation) const
	Decompose a Matrix4 to orientation / scale / position. More...
Real	determinant () const
void	extract3x3Matrix (Matrix3 &m3x3) const
	Extracts the rotation / scaling part of the Matrix as a 3x3 matrix. More...
Quaternion	extractQuaternion () const
	Extracts the rotation / scaling part as a quaternion from the Matrix. More...
Vector3	getTrans () const
	Extracts the translation transformation part of the matrix. More...
bool	hasNegativeScale () const
	Determines if this matrix involves a negative scaling. More...
bool	hasScale () const
	Determines if this matrix involves a scaling. More...
Matrix4	inverse () const
Matrix4	inverseAffine (void) const
	Returns the inverse of the affine matrix. More...
bool	isAffine (void) const
	Check whether or not the matrix is affine matrix. More...
void	makeInverseTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building an inverse Matrix4 from orientation / scale / position. More...
void	makeTrans (const Vector3 &v)
	Builds a translation matrix. More...
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. More...
bool	operator!= (const Matrix4 &m2) const
	Tests 2 matrices for inequality. More...
Matrix4	operator* (const Matrix4 &m2) const
	Matrix concatenation using '*'. More...
Vector3	operator* (const Vector3 &v) const
	Vector transformation using '*'. More...
Vector4	operator* (const Vector4 &v) const
Plane	operator* (const Plane &p) const
Matrix4	operator* (Real scalar) const
Matrix4	operator+ (const Matrix4 &m2) const
	Matrix addition. More...
Matrix4	operator- (const Matrix4 &m2) const
	Matrix subtraction. More...
void	operator= (const Matrix3 &mat3)
	Assignment from 3x3 matrix. More...
bool	operator== (const Matrix4 &m2) const
	Tests 2 matrices for equality. More...
Real *	operator[] (size_t iRow)
const Real *	operator[] (size_t iRow) const
void	setScale (const Vector3 &v)
	Sets the scale part of the matrix. More...
void	setTrans (const Vector3 &v)
	Sets the translation transformation part of the matrix. More...
void	swap (Matrix4 &other)
	Exchange the contents of this matrix with another. More...
Vector3	transformAffine (const Vector3 &v) const
	3-D Vector transformation specially for an affine matrix. More...
Vector4	transformAffine (const Vector4 &v) const
	4-D Vector transformation specially for an affine matrix. More...
Matrix4	transpose (void) const

Static Public Member Functions
static Matrix4	getScale (const Vector3 &v)
	Gets a scale matrix. More...
static Matrix4	getScale (Real s_x, Real s_y, Real s_z)
	Gets a scale matrix - variation for not using a vector. More...
static Matrix4	getTrans (const Vector3 &v)
	Gets a translation matrix. More...
static Matrix4	getTrans (Real t_x, Real t_y, Real t_z)
	Gets a translation matrix - variation for not using a vector. More...

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

Protected Attributes
union {
Real   _m [16]
Real   m [4][4]
};
	The matrix entries, indexed by [row][col]. More...

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

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}
    

Definition at line 78 of file OgreMatrix4.h.

Constructor & Destructor Documentation

Ogre::Matrix4::Matrix4 ( )

inline

Default constructor.

Note

It does NOT initialize the matrix for efficiency.

Definition at line 91 of file OgreMatrix4.h.

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

Definition at line 95 of file OgreMatrix4.h.

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

inline

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

Definition at line 122 of file OgreMatrix4.h.

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

inline

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

Definition at line 131 of file OgreMatrix4.h.

References Ogre::Quaternion::ToRotationMatrix().

Member Function Documentation

Matrix4 Ogre::Matrix4::adjoint

(

)

const

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

inline

Definition at line 174 of file OgreMatrix4.h.

References m.

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

inline

Concatenate two affine matrices.

Note

The matrices must be affine matrix.

See also

Matrix4::isAffine.

Definition at line 587 of file OgreMatrix4.h.

References isAffine(), and m.

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

Decompose a Matrix4 to orientation / scale / position.

Real Ogre::Matrix4::determinant

(

)

const

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

inline

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

Parameters

m3x3	Destination Matrix3

Definition at line 463 of file OgreMatrix4.h.

References Ogre::Matrix3::m.

Quaternion Ogre::Matrix4::extractQuaternion ( ) const

inline

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

Definition at line 502 of file OgreMatrix4.h.

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

inlinestatic

Gets a scale matrix.

Definition at line 436 of file OgreMatrix4.h.

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

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.

Definition at line 449 of file OgreMatrix4.h.

References m.

Vector3 Ogre::Matrix4::getTrans ( ) const

inline

Extracts the translation transformation part of the matrix.

Definition at line 368 of file OgreMatrix4.h.

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

inlinestatic

Gets a translation matrix.

Definition at line 394 of file OgreMatrix4.h.

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

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.

Definition at line 408 of file OgreMatrix4.h.

References m.

bool Ogre::Matrix4::hasNegativeScale ( ) const

inline

Determines if this matrix involves a negative scaling.

Definition at line 495 of file OgreMatrix4.h.

bool Ogre::Matrix4::hasScale ( ) const

inline

Determines if this matrix involves a scaling.

Definition at line 478 of file OgreMatrix4.h.

References Ogre::Math::RealEqual().

Matrix4 Ogre::Matrix4::inverse

(

)

const

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.

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.

Definition at line 572 of file OgreMatrix4.h.

Referenced by concatenateAffine(), and Ogre::AxisAlignedBox::transformAffine().

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.

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

inline

Builds a translation matrix.

Definition at line 376 of file OgreMatrix4.h.

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

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

inline

Definition at line 384 of file OgreMatrix4.h.

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.

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

inline

Tests 2 matrices for inequality.

Definition at line 324 of file OgreMatrix4.h.

References m.

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

inline

Matrix concatenation using '*'.

Definition at line 202 of file OgreMatrix4.h.

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.

Definition at line 216 of file OgreMatrix4.h.

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

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

inline

Definition at line 228 of file OgreMatrix4.h.

References Ogre::Vector4::w, Ogre::Vector4::x, Ogre::Vector4::y, and Ogre::Vector4::z.

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

inline

Definition at line 237 of file OgreMatrix4.h.

References Ogre::Plane::d, Ogre::Plane::normal, Ogre::Vector3::normalise(), transpose(), Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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

inline

Definition at line 516 of file OgreMatrix4.h.

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

inline

Matrix addition.

Definition at line 254 of file OgreMatrix4.h.

References m.

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

inline

Matrix subtraction.

Definition at line 283 of file OgreMatrix4.h.

References m.

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

inline

Assignment from 3x3 matrix.

Definition at line 337 of file OgreMatrix4.h.

References Ogre::Matrix3::m.

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

inline

Tests 2 matrices for equality.

Definition at line 311 of file OgreMatrix4.h.

References m.

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

inline

Definition at line 162 of file OgreMatrix4.h.

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

inline

Definition at line 168 of file OgreMatrix4.h.

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

inline

Sets the scale part of the matrix.

Definition at line 427 of file OgreMatrix4.h.

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

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

inline

Sets the translation transformation part of the matrix.

Definition at line 359 of file OgreMatrix4.h.

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

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

inline

Exchange the contents of this matrix with another.

Definition at line 142 of file OgreMatrix4.h.

References m, and std::swap().

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.

Definition at line 617 of file OgreMatrix4.h.

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

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

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.

Definition at line 631 of file OgreMatrix4.h.

References Ogre::Vector4::w, Ogre::Vector4::x, Ogre::Vector4::y, and Ogre::Vector4::z.

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

inline

Definition at line 344 of file OgreMatrix4.h.

Referenced by operator*().

Friends And Related Function Documentation

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

friend

Function for writing to a stream.

Definition at line 528 of file OgreMatrix4.h.

Member Data Documentation

union { ... }

The matrix entries, indexed by [row][col].

Real Ogre::Matrix4::_m[16]

Definition at line 84 of file OgreMatrix4.h.

const Matrix4 Ogre::Matrix4::CLIPSPACE2DTOIMAGESPACE

static

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

Definition at line 514 of file OgreMatrix4.h.

const Matrix4 Ogre::Matrix4::IDENTITY

static

Definition at line 511 of file OgreMatrix4.h.

Referenced by Ogre::InstancedEntity::_getParentNodeFullTransform().

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

Definition at line 83 of file OgreMatrix4.h.

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

const Matrix4 Ogre::Matrix4::ZERO

static

Definition at line 509 of file OgreMatrix4.h.

const Matrix4 Ogre::Matrix4::ZEROAFFINE

static

Definition at line 510 of file OgreMatrix4.h.

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

• OgreMatrix4.h