Ogre::Matrix4 Class Reference
[Math]

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

#include <OgreMatrix4.h>

Public Member Functions
	Matrix4 ()
	Default constructor.
	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.
	Matrix4 (const Quaternion &rot)
	Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.
void	swap (Matrix4 &other)
	Exchange the contents of this matrix with another.
Real *	operator[] (size_t iRow)
const Real *	operator[] (size_t iRow) const
Matrix4	concatenate (const Matrix4 &m2) const
Matrix4	operator* (const Matrix4 &m2) const
	Matrix concatenation using '*'.
Vector3	operator* (const Vector3 &v) const
	Vector transformation using '*'.
Vector4	operator* (const Vector4 &v) const
Plane	operator* (const Plane &p) const
Matrix4	operator+ (const Matrix4 &m2) const
	Matrix addition.
Matrix4	operator- (const Matrix4 &m2) const
	Matrix subtraction.
bool	operator== (const Matrix4 &m2) const
	Tests 2 matrices for equality.
bool	operator!= (const Matrix4 &m2) const
	Tests 2 matrices for inequality.
void	operator= (const Matrix3 &mat3)
	Assignment from 3x3 matrix.
Matrix4	transpose (void) const
void	setTrans (const Vector3 &v)
	Sets the translation transformation part of the matrix.
Vector3	getTrans () const
	Extracts the translation transformation part of the matrix.
void	makeTrans (const Vector3 &v)
	Builds a translation matrix.
void	makeTrans (Real tx, Real ty, Real tz)
void	setScale (const Vector3 &v)
	Sets the scale part of the matrix.
void	extract3x3Matrix (Matrix3 &m3x3) const
	Extracts the rotation / scaling part of the Matrix as a 3x3 matrix.
bool	hasScale () const
	Determines if this matrix involves a scaling.
bool	hasNegativeScale () const
	Determines if this matrix involves a negative scaling.
Quaternion	extractQuaternion () const
	Extracts the rotation / scaling part as a quaternion from the Matrix.
Matrix4	operator* (Real scalar) const
Matrix4	adjoint () const
Real	determinant () const
Matrix4	inverse () const
void	makeTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building a Matrix4 from orientation / scale / position.
void	makeInverseTransform (const Vector3 &position, const Vector3 &scale, const Quaternion &orientation)
	Building an inverse Matrix4 from orientation / scale / position.
void	decomposition (Vector3 &position, Vector3 &scale, Quaternion &orientation) const
	Decompose a Matrix4 to orientation / scale / position.
bool	isAffine (void) const
	Check whether or not the matrix is affine matrix.
Matrix4	inverseAffine (void) const
	Returns the inverse of the affine matrix.
Matrix4	concatenateAffine (const Matrix4 &m2) const
	Concatenate two affine matrices.
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.
Static Public Member Functions
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 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 Public Attributes
static const Matrix4	ZERO
static const Matrix4	ZEROAFFINE
static const Matrix4	IDENTITY
static const Matrix4	CLIPSPACE2DTOIMAGESPACE
	Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y.
Protected Attributes
union {
Real m [4][4]
Real _m [16]
};
	The matrix entries, indexed by [row][col].
Friends
_OgreExport friend std::ostream &	operator<< (std::ostream &o, const Matrix4 &mat)
	Function for writing to a stream.

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 ( )

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
	)

Definition at line 95 of file OgreMatrix4.h.

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

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 )

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

Definition at line 174 of file OgreMatrix4.h.

References m.

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

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

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

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

Definition at line 502 of file OgreMatrix4.h.

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

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

Definition at line 449 of file OgreMatrix4.h.

References m.

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

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::getTrans	(	Real	t_x,
		Real	t_y,
		Real	t_z
	)			`[static]`

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

Definition at line 408 of file OgreMatrix4.h.

References m.

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

Gets a translation matrix.

Definition at line 394 of file OgreMatrix4.h.

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

Vector3 Ogre::Matrix4::getTrans ( ) const

Extracts the translation transformation part of the matrix.

Definition at line 368 of file OgreMatrix4.h.

bool Ogre::Matrix4::hasNegativeScale ( ) const

Determines if this matrix involves a negative scaling.

Definition at line 495 of file OgreMatrix4.h.

bool Ogre::Matrix4::hasScale ( ) const

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

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	(	Real	tx,
		Real	ty,
		Real	tz
	)

Definition at line 384 of file OgreMatrix4.h.

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

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::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

Tests 2 matrices for inequality.

Definition at line 324 of file OgreMatrix4.h.

References m.

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

Definition at line 516 of file OgreMatrix4.h.

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

Definition at line 237 of file OgreMatrix4.h.

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

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

Definition at line 228 of file OgreMatrix4.h.

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

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

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.

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

Matrix concatenation using '*'.

Definition at line 202 of file OgreMatrix4.h.

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

Matrix addition.

Definition at line 254 of file OgreMatrix4.h.

References m.

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

Matrix subtraction.

Definition at line 283 of file OgreMatrix4.h.