| OGRE 1.10.11 Object-Oriented Graphics Rendering Engine

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Ogre::Matrix4 Class Reference
Core » Math

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

`#include <OgreMatrix4.h>`

## 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...
Vector3 | transformDirectionAffine (const Vector3 &v) const
| 3-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

## 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}

## Constructor & Destructor Documentation

## ◆ Matrix4() [1/4]

Ogre::Matrix4::Matrix4 | ( |  | ) |
| inline

Default constructor.

Note
  It does NOT initialize the matrix for efficiency.

## ◆ Matrix4() [2/4]

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() [3/4]

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() [4/4]

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

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

References Ogre::Quaternion::ToRotationMatrix().

## Member Function Documentation

## ◆ swap()

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

Exchange the contents of this matrix with another.

References m, and std::swap().

## ◆ operator[]() [1/2]

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

## ◆ operator[]() [2/2]

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

## ◆ concatenate()

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

References m.

## ◆ operator*() [1/5]

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

Matrix concatenation using '*'.

## ◆ operator*() [2/5]

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*() [3/5]

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

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

## ◆ operator*() [4/5]

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

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

## ◆ 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==()

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

Tests 2 matrices for equality.

References m.

## ◆ operator!=()

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

Tests 2 matrices for inequality.

References m.

## ◆ operator=()

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

Assignment from 3x3 matrix.

## ◆ transpose()

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

Referenced by operator*().

## ◆ setTrans()

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

Sets the translation transformation part of the matrix.

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

## ◆ getTrans() [1/3]

Vector3 Ogre::Matrix4::getTrans | ( |  | ) | const
| inline

Extracts the translation transformation part of the matrix.

## ◆ makeTrans() [1/2]

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

Builds a translation matrix.

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

## ◆ makeTrans() [2/2]

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

## ◆ getTrans() [2/3]

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

Gets a translation matrix.

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

## ◆ getTrans() [3/3]

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

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

References m.

## ◆ setScale()

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

Sets the scale part of the matrix.

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

## ◆ getScale() [1/2]

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

Gets a scale matrix.

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

## ◆ getScale() [2/2]

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

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

References m.

## ◆ 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

## ◆ hasScale()

bool Ogre::Matrix4::hasScale | ( |  | ) | const
| inline

Determines if this matrix involves a scaling.

References Ogre::Math::RealEqual().

## ◆ hasNegativeScale()

bool Ogre::Matrix4::hasNegativeScale | ( |  | ) | const
| inline

Determines if this matrix involves a negative scaling.

## ◆ extractQuaternion()

Quaternion Ogre::Matrix4::extractQuaternion | ( |  | ) | const
| inline

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

## ◆ operator*() [5/5]

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

## ◆ adjoint()

Matrix4 Ogre::Matrix4::adjoint | ( |  | ) | const

## ◆ determinant()

Real Ogre::Matrix4::determinant | ( |  | ) | const

## ◆ inverse()

Matrix4 Ogre::Matrix4::inverse | ( |  | ) | const

## ◆ 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.

## ◆ 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.

## ◆ decomposition()

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

Decompose a Matrix4 to orientation / scale / position.

## ◆ 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 concatenateAffine(), and Ogre::AxisAlignedBox::transformAffine().

## ◆ 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.

## ◆ 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.

References isAffine(), and m.

## ◆ 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.

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

## ◆ 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.

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

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.

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

## Friends And Related Function Documentation

## ◆ operator<<

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

Function for writing to a stream.

## Member Data Documentation

## ◆ m

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

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

## ◆ _m

Real Ogre::Matrix4::_m[16]

## ◆ ZERO

const Matrix4 Ogre::Matrix4::ZERO
| static

## ◆ ZEROAFFINE

const Matrix4 Ogre::Matrix4::ZEROAFFINE
| static

## ◆ IDENTITY

const Matrix4 Ogre::Matrix4::IDENTITY
| static

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

## ◆ CLIPSPACE2DTOIMAGESPACE

const Matrix4 Ogre::Matrix4::CLIPSPACE2DTOIMAGESPACE
| static

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

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

- OgreMatrix4.h