# Ogre::Matrix4 Class Reference

Class encapsulating a standard 4x4 homogenous 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.
Quaternion | extractQuaternion () const
| Extracts the rotation / scaling part as a quaternion from the Matrix.
Matrix4 | operator * (Real scalar)
Matrix4 | adjoint () const
Real | determinant () const
Matrix4 | inverse () const

## Static Public Member Functions

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

## Static Public Attributes

const Matrix4 | ZERO
const Matrix4 | IDENTITY
const Matrix4 | CLIPSPACE2DTOIMAGESPACE
| Useful little matrix which takes 2D clipspace {-1, 1} to {0,1} and inverts the Y.

## 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 homogenous 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 tranformations 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 69 of file OgreMatrix4.h.

## Constructor & Destructor Documentation

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

Default constructor.

Note:
  It does NOT initialize the matrix for efficiency.

Definition at line 82 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 86 of file OgreMatrix4.h. References Ogre::Real.

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 113 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 122 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 143 of file OgreMatrix4.h. References m.

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 434 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 450 of file OgreMatrix4.h.

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 420 of file OgreMatrix4.h. References m, and Ogre::Real.

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

| Gets a scale matrix. Definition at line 407 of file OgreMatrix4.h. References m, Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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 379 of file OgreMatrix4.h. References m, and Ogre::Real.

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

| Gets a translation matrix. Definition at line 365 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 339 of file OgreMatrix4.h.

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

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

| Definition at line 355 of file OgreMatrix4.h. References Ogre::Real.

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

| Builds a translation matrix. Definition at line 347 of file OgreMatrix4.h. References Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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

| Definition at line 463 of file OgreMatrix4.h. References Ogre::Real.

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

| Definition at line 206 of file OgreMatrix4.h. References Ogre::Plane::d, Ogre::Plane::normal, Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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

| Definition at line 197 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 185 of file OgreMatrix4.h.

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

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

| Matrix concatenation using '*'. Definition at line 171 of file OgreMatrix4.h.

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

| Tests 2 matrices for inequality. Definition at line 295 of file OgreMatrix4.h. References m.

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

| Matrix addition. Definition at line 225 of file OgreMatrix4.h. References m.

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

| Matrix subtraction. Definition at line 254 of file OgreMatrix4.h. References m.

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

| Assignment from 3x3 matrix. Definition at line 308 of file OgreMatrix4.h. References Ogre::Matrix3::m.

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

| Tests 2 matrices for equality. Definition at line 282 of file OgreMatrix4.h. References m.

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

| Definition at line 137 of file OgreMatrix4.h. References Ogre::Real.

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

| Definition at line 131 of file OgreMatrix4.h. References Ogre::Real.

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

| Sets the scale part of the matrix. Definition at line 398 of file OgreMatrix4.h. References Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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

| Sets the translation transformation part of the matrix. Definition at line 330 of file OgreMatrix4.h. References Ogre::Vector3::x, Ogre::Vector3::y, and Ogre::Vector3::z.

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

| Definition at line 315 of file OgreMatrix4.h.

## 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 475 of file OgreMatrix4.h.

## Member Data Documentation

Real Ogre::Matrix4::_m[16]`[protected]`

| Definition at line 75 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 461 of file OgreMatrix4.h.

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

| Definition at line 458 of file OgreMatrix4.h.

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

| Definition at line 74 of file OgreMatrix4.h. Referenced by concatenate(), getScale(), getTrans(), operator!=(), operator+(), operator-(), and operator==().

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

| Definition at line 457 of file OgreMatrix4.h.

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

- OgreMatrix4.h

Copyright © 2000-2005 by The OGRE Team
Last modified Sun Nov 20 12:37:19 2005