# Ogre::Matrix4 Class Reference

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

`#include <OgreMatrix4.h>`

List of all members.

## 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.
Real * | operator[] (size_t iRow)
const Real *const | 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.
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 matrix.
Vector3 | transformAffine (const Vector3 &v) const
| 3-D Vector transformation specially for affine matrix.
Vector4 | transformAffine (const Vector4 &v) const
| 4-D Vector transformation specially for 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 | 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]
}; |

## Friends

_OgreExport friend std::ostream & | operator<< (std::ostream &o, const Matrix4 &m)
| 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 cummatative, 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 id 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 73 of file OgreMatrix4.h.

## Constructor & Destructor Documentation

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

Default constructor.

Note:
  It does NOT initialize the matrix for efficiency.

Definition at line 86 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 90 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 117 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 126 of file OgreMatrix4.h.

References Ogre::Quaternion::ToRotationMatrix().

## Member Function Documentation

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

Definition at line 135 of file OgreMatrix4.h.

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

Definition at line 141 of file OgreMatrix4.h.

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

Definition at line 147 of file OgreMatrix4.h.

References m.

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

Matrix concatenation using '*'.

Definition at line 175 of file OgreMatrix4.h.

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 189 of file OgreMatrix4.h.

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

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

Definition at line 201 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

Definition at line 210 of file OgreMatrix4.h.

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

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

Matrix addition.

Definition at line 227 of file OgreMatrix4.h.

References m.

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

Matrix subtraction.

Definition at line 256 of file OgreMatrix4.h.

References m.

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

Tests 2 matrices for equality.

Definition at line 284 of file OgreMatrix4.h.

References m.

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

Tests 2 matrices for inequality.

Definition at line 297 of file OgreMatrix4.h.

References m.

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

Assignment from 3x3 matrix.

Definition at line 310 of file OgreMatrix4.h.

References Ogre::Matrix3::m.

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

Definition at line 317 of file OgreMatrix4.h.

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

Sets the translation transformation part of the matrix.

Definition at line 332 of file OgreMatrix4.h.

References 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 341 of file OgreMatrix4.h.

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

Builds a translation matrix.

Definition at line 349 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 |
| ) |  |  |

Definition at line 357 of file OgreMatrix4.h.

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

Gets a translation matrix.

Definition at line 367 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 381 of file OgreMatrix4.h.

References m.

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

Sets the scale part of the matrix.

Definition at line 400 of file OgreMatrix4.h.

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

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

Gets a scale matrix.

Definition at line 409 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 |
| ) |  |  | `[static]`

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

Definition at line 422 of file OgreMatrix4.h.

References m.

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 436 of file OgreMatrix4.h.

References Ogre::Matrix3::m.

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

Determines if this matrix involves a scaling.

Definition at line 451 of file OgreMatrix4.h.

References Ogre::Math::RealEqual().

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

Determines if this matrix involves a negative scaling.

Definition at line 468 of file OgreMatrix4.h.

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

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

Definition at line 475 of file OgreMatrix4.h.

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

Definition at line 488 of file OgreMatrix4.h.

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

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

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

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.

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.

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 540 of file OgreMatrix4.h.

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

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.

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

Concatenate two affine matrix.

Note:
  The matrices must be affine matrix.

See also:
  Matrix4::isAffine.

Definition at line 555 of file OgreMatrix4.h.

References isAffine(), and m.

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

3-D Vector transformation specially for 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 585 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

4-D Vector transformation specially for affine matrix.

Note:
  The matrix must be an affine matrix.

See also:
  Matrix4::isAffine.

Definition at line 599 of file OgreMatrix4.h.

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

## Friends And Related Function Documentation

_OgreExport friend std::ostream& operator<< | ( | std::ostream & | o,
|  | const Matrix4 & | m |
| ) |  |  | `[friend]`

Function for writing to a stream.

Definition at line 500 of file OgreMatrix4.h.

## Member Data Documentation

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

Definition at line 78 of file OgreMatrix4.h.

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

Real Ogre::Matrix4::_m[16]

Definition at line 79 of file OgreMatrix4.h.

union { ... } `[protected]`

const Matrix4 Ogre::Matrix4::ZERO `[static]`

Definition at line 482 of file OgreMatrix4.h.

const Matrix4 Ogre::Matrix4::IDENTITY `[static]`

Definition at line 483 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 486 of file OgreMatrix4.h.

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

- OgreMatrix4.h

Copyright © 2008 Torus Knot Software Ltd
This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.
Last modified Sun Jul 26 11:34:02 2009