kanzi::Matrix4x4 Class Reference

Matrix with 4x4 elements. More...

#include <kanzi/core/math/matrix4x4.hpp>

Public Types
enum	FieldOfViewType { FieldOfViewType::XFov, FieldOfViewType::YFov }
	Field of view type of a camera. More...

Public Member Functions
Vector4	getColumn (size_t index) const
	Gets the column of a matrix. More...
optional< Vector3 >	getRotationAngle () const
	Calculates Euler rotation angles of the matrix. More...
Vector4	getRow (size_t index) const
	Gets the row of a matrix. More...
Vector3	getScale () const
	Get scale as a vector. More...
Vector3	getTranslation () const
	Get translation. More...
float	getTranslationX () const
	Get translation on X axis. More...
float	getTranslationY () const
	Get translation on Y axis. More...
float	getTranslationZ () const
	Get translation on Z axis. More...
Vector3	getXAxis () const
	Get X axis. More...
Vector3	getYAxis () const
	Get Y axis. More...
Vector3	getZAxis () const
	Get Z axis. More...
	Matrix4x4 ()
	Default constructor, initializes the matrix to identity matrix. More...
	Matrix4x4 (float x0, float x1, float x2, float x3, float x4, float x5, float x6, float x7, float x8, float x9, float x10, float x11, float x12, float x13, float x14, float x15)
	Constructs the matrix from elements in column-major order. More...
	Matrix4x4 (const Vector3 &x, const Vector3 &y, const Vector3 &z, const Vector3 &translation)
	Constructs the matrix from four column vectors. More...
	Matrix4x4 (const Vector4 &x, const Vector4 &y, const Vector4 &z, const Vector4 &translation)
	Constructs the matrix from four column vectors. More...
Vector3	operator* (const Vector3 &vector) const
	Multiply a 3-component vector with this matrix. More...
Vector4	operator* (const Vector4 &vector) const
	Multiply a 4-component vector with this matrix. More...
Matrix4x4 &	operator*= (const Matrix4x4 &m)
	Modifies this matrix by multiplying it with another matrix. More...
Matrix4x4 &	operator+= (const Matrix4x4 &v)
	Modifies this matrix by adding another matrix. More...
Matrix4x4 &	operator-= (const Matrix4x4 &v)
	Modifies this matrix by subtracting another matrix from this matrix. More...
const float &	operator[] (size_t index) const
	Access to individual elements of the matrix. More...
float &	operator[] (size_t index)
	Access to individual elements of the matrix. More...
void	scale (const Vector3 &scale)
	Scales this matrix. More...
void	scaleUniform (float scale)
	Scales this matrix. More...
void	setColumn (size_t index, const Vector4 &column)
	Sets the column of a matrix. More...
void	setRow (size_t index, const Vector4 &row)
	Sets the row of a matrix. More...
void	setTranslation (Vector3 translation)
	Set translation. More...
void	setTranslationX (float translationX)
	Set translation on X axis. More...
void	setTranslationY (float translationY)
	Set translation on Y axis. More...
void	setTranslationZ (float translationZ)
	Set translation on Z axis. More...
void	setXAxis (Vector3 v)
	Set X axis. More...
void	setYAxis (Vector3 v)
	Set Y axis. More...
void	setZAxis (Vector3 v)
	Set Z axis. More...
void	translate (const Vector3 &translate)
	Translates this matrix. More...
Matrix4x4	transposed () const
	Applies a transpose to a matrix. More...

Static Public Member Functions
static Matrix4x4	createFromHomogenousMatrix (const Matrix3x3 &matrix, float zTranslation)
	Creates a matrix from an existing homogeneous matrix and Z translation. More...
static Matrix4x4	createFromHomogenousMatrix (const Matrix3x3 &matrix)
	Creates a matrix from an existing homogeneous matrix. More...
static Matrix4x4	createIdentity ()
	Creates identity matrix. More...
static optional< Matrix4x4 >	createLookAtMatrix (Vector3 position, Vector3 lookAtPoint, Vector3 upVector)
	Creates a lookup transformation matrix, so that it is in a given position looking at the given point. More...
static Matrix4x4	createOrthogonalProjection (float left, float right, float bottom, float top, float near, float far)
	Creates projection matrix for orthogonal projection. More...
static Matrix4x4	createPerspectiveProjection (float near, float far, FieldOfViewType fovType, float fovInDegrees, float aspectRatio)
	Creates a perspective projection matrix for a symmetrical viewing volume. More...
static Matrix4x4	createPerspectiveProjection (float near, float far, Vector4 fovInDegrees)
	Creates a perspective projection matrix for a viewing volume. More...
static Matrix4x4	createRotation (float angleInRadians, Vector3 rotationAxis)
	Creates a rotation matrix over an arbitrary axis. More...
static Matrix4x4	createRotationInDegrees (float angleInDegrees, Vector3 rotationAxis)
	Creates a rotation matrix over an arbitrary axis. More...
static Matrix4x4	createScale (Vector3 scale)
	Creates a scaling matrix. More...
static Matrix4x4	createSRT (Vector3 scale, Vector3 rotationInRadians, Vector3 translation)
	Create an SRT matrix. More...
static Matrix4x4	createSubProjection (const Matrix4x4 &projection, float relativeOffsetX, float relativeOffsetY, float relativeSizeX, float relativeSizeY)
	Calculate sub-quad projection of an existing projection matrix. More...
static Matrix4x4	createTranslation (Vector3 translation)
	Creates translation matrix. More...
static Matrix4x4	createTranslation (float x, float y, float z)
	Creates translation matrix. More...
static Matrix4x4	createXRotationInDegrees (float angleInDegrees)
	Creates a X rotation matrix. More...
static Matrix4x4	createXRotationInRadians (float angleInRadians)
	Creates a X rotation matrix. More...
static Matrix4x4	createYRotationInDegrees (float angleInDegrees)
	Creates a Y rotation matrix. More...
static Matrix4x4	createYRotationInRadians (float angleInRadians)
	Creates a Y rotation matrix. More...
static Matrix4x4	createZRotationInDegrees (float angleInDegrees)
	Creates a Z rotation matrix. More...
static Matrix4x4	createZRotationInRadians (float angleInRadians)
	Creates a Z rotation matrix. More...

Friends
bool	operator!= (const Matrix4x4 &left, const Matrix4x4 &right)
	Inequality operator. More...
Matrix4x4	operator+ (Matrix4x4 lhs, const Matrix4x4 &rhs)
	Creates a new matrix by adding an existing matrix to another one. More...
Matrix4x4	operator- (Matrix4x4 lhs, const Matrix4x4 &rhs)
	Creates a new matrix by subtracting an existing matrix from another one. More...
bool	operator== (const Matrix4x4 &left, const Matrix4x4 &right)
	Equality operator. More...

Detailed Description

Matrix with 4x4 elements.

Member Enumeration Documentation

enum kanzi::Matrix4x4::FieldOfViewType

strong

Field of view type of a camera.

Enumerator
XFov	Field of view is specified in the x axis direction.
YFov	Field of view is specified in the y axis direction.

Constructor & Destructor Documentation

kanzi::Matrix4x4::Matrix4x4 ( )

inlineexplicit

Default constructor, initializes the matrix to identity matrix.

kanzi::Matrix4x4::Matrix4x4 ( float  x0, float  x1, float  x2, float  x3, float  x4, float  x5, float  x6, float  x7, float  x8, float  x9, float  x10, float  x11, float  x12, float  x13, float  x14, float  x15  )

inlineexplicit

Constructs the matrix from elements in column-major order.

kanzi::Matrix4x4::Matrix4x4 ( const Vector3 &  x, const Vector3 &  y, const Vector3 &  z, const Vector3 &  translation  )

inlineexplicit

Constructs the matrix from four column vectors.

kanzi::Matrix4x4::Matrix4x4 ( const Vector4 &  x, const Vector4 &  y, const Vector4 &  z, const Vector4 &  translation  )

inlineexplicit

Constructs the matrix from four column vectors.

Member Function Documentation

const float& kanzi::Matrix4x4::operator[] ( size_t  index ) const

inline

Access to individual elements of the matrix.

Elements are stored in column-major order.

Parameters

index

Index of the accessed element. Possible values are numbers from 0 to 15.

Returns

float& kanzi::Matrix4x4::operator[] ( size_t  index )

inline

Access to individual elements of the matrix.

Elements are stored in column-major order.

Parameters

index

Index of the accessed element. Possible values are numbers from 0 to 15.

Returns

Vector4 kanzi::Matrix4x4::getRow ( size_t  index ) const

inline

Gets the row of a matrix.

Parameters

index

Index of the accessed row.

Returns

The row.

Vector4 kanzi::Matrix4x4::getColumn ( size_t  index ) const

inline

Gets the column of a matrix.

Parameters

index

Index of the accessed column.

Returns

The column.

void kanzi::Matrix4x4::setRow ( size_t  index, const Vector4 &  row  )

inline

Sets the row of a matrix.

Parameters

index	Index of the accessed row.
row	The value to set to the row.

void kanzi::Matrix4x4::setColumn ( size_t  index, const Vector4 &  column  )

inline

Sets the column of a matrix.

Parameters

index	Index of the accessed column.
column	The value to set to the column.

Vector3 kanzi::Matrix4x4::getXAxis ( ) const

inline

Get X axis.

Vector3 kanzi::Matrix4x4::getYAxis ( ) const

inline

Get Y axis.

Vector3 kanzi::Matrix4x4::getZAxis ( ) const

inline

Get Z axis.

Vector3 kanzi::Matrix4x4::getScale

(

)

const

Get scale as a vector.

optional<Vector3> kanzi::Matrix4x4::getRotationAngle

(

)

const

Calculates Euler rotation angles of the matrix.

Kanzi Engine represents Euler angles as Tait-Bryan angles where the rotations are applied in the order x, y and z.

Returns

Euler angles in radians, or nullopt if the matrix is not decomposable.

void kanzi::Matrix4x4::scale ( const Vector3 &  scale )

inline

Scales this matrix.

Parameters

scale

Scaling vector.

void kanzi::Matrix4x4::scaleUniform ( float  scale )

inline

Scales this matrix.

Parameters

scale

Uniform scaling value.

void kanzi::Matrix4x4::translate ( const Vector3 &  translate )

inline

Translates this matrix.

Parameters

translate

Translation vector.

void kanzi::Matrix4x4::setXAxis ( Vector3  v )

inline

Set X axis.

Parameters

v	X axis vector.

void kanzi::Matrix4x4::setYAxis ( Vector3  v )

inline

Set Y axis.

Parameters

v	Y axis vector.

void kanzi::Matrix4x4::setZAxis ( Vector3  v )

inline

Set Z axis.

Parameters

v	Z axis vector.

Vector3 kanzi::Matrix4x4::getTranslation ( ) const

inline

Get translation.

Returns

Translation vector.

void kanzi::Matrix4x4::setTranslation ( Vector3  translation )

inline

Set translation.

Parameters

translation

Translation vector.

float kanzi::Matrix4x4::getTranslationX ( ) const

inline

Get translation on X axis.

Returns

Translation X component.

void kanzi::Matrix4x4::setTranslationX ( float  translationX )

inline

Set translation on X axis.

Parameters

translationX

Translation X component.

float kanzi::Matrix4x4::getTranslationY ( ) const

inline

Get translation on Y axis.

Returns

Translation Y component.

void kanzi::Matrix4x4::setTranslationY ( float  translationY )

inline

Set translation on Y axis.

Parameters

translationY

Translation Y component.

float kanzi::Matrix4x4::getTranslationZ ( ) const

inline

Get translation on Z axis.

Returns

Translation Z component.

void kanzi::Matrix4x4::setTranslationZ ( float  translationZ )

inline

Set translation on Z axis.

Parameters

translationZ

Translation Y component.

Matrix4x4& kanzi::Matrix4x4::operator+= ( const Matrix4x4 &  v )

inline

Modifies this matrix by adding another matrix.

Parameters

v	Another matrix.

Returns

This matrix.

Matrix4x4& kanzi::Matrix4x4::operator-= ( const Matrix4x4 &  v )

inline

Modifies this matrix by subtracting another matrix from this matrix.

Parameters

v	Another matrix.

Returns

This matrix.

Vector3 kanzi::Matrix4x4::operator* ( const Vector3 &  vector ) const

inline

Multiply a 3-component vector with this matrix.

Parameters

vector

A Vector3.

Returns

Result of the multiplication.

Vector4 kanzi::Matrix4x4::operator* ( const Vector4 &  vector ) const

inline

Multiply a 4-component vector with this matrix.

Parameters

vector

A Vector4.

Returns

Result of the multiplication.

Matrix4x4& kanzi::Matrix4x4::operator*=

(

const Matrix4x4 &

m

)

Modifies this matrix by multiplying it with another matrix.

Parameters

m	Another matrix.

Returns

This matrix.

static Matrix4x4 kanzi::Matrix4x4::createTranslation ( Vector3  translation )

inlinestatic

Creates translation matrix.

Parameters

translation

Translation vector.

Returns

Translation matrix.

static Matrix4x4 kanzi::Matrix4x4::createTranslation ( float  x, float  y, float  z  )

inlinestatic

Creates translation matrix.

Parameters

x	X component of the Translation vector.
y	Y component of the Translation vector.
z	Z component of the Translation vector.

Returns

Translation matrix.

static Matrix4x4 kanzi::Matrix4x4::createIdentity ( )

inlinestatic

Creates identity matrix.

Returns

Identity matrix.

static Matrix4x4 kanzi::Matrix4x4::createFromHomogenousMatrix ( const Matrix3x3 &  matrix, float  zTranslation  )

inlinestatic

Creates a matrix from an existing homogeneous matrix and Z translation.

Parameters

matrix	Homogeneous matrix.
zTranslation	X translation.

Returns

Newly constructed matrix.

static Matrix4x4 kanzi::Matrix4x4::createFromHomogenousMatrix ( const Matrix3x3 &  matrix )

inlinestatic

Creates a matrix from an existing homogeneous matrix.

0.0f is used for the Z translation.

Parameters

matrix

Homogeneous matrix.

Returns

Newly constructed matrix.

static Matrix4x4 kanzi::Matrix4x4::createRotation ( float  angleInRadians, Vector3  rotationAxis  )

static

Creates a rotation matrix over an arbitrary axis.

Similar to the matrix used by glRotatef. The rotation axis needs not be normalized.

Parameters

angleInRadians	Rotation angle in radians.
rotationAxis	Arbitrary rotation axis.

Returns

Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createRotationInDegrees ( float  angleInDegrees, Vector3  rotationAxis  )

inlinestatic

Creates a rotation matrix over an arbitrary axis.

Similar to the matrix used by glRotatef. The rotation axis needs not be normalized.

Parameters

angleInDegrees	Rotation angle in degrees.
rotationAxis	Arbitrary rotation axis.

Returns

Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createXRotationInRadians ( float  angleInRadians )

static

Creates a X rotation matrix.

Parameters

angleInRadians

Rotation angle in radians.

Returns

X Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createXRotationInDegrees ( float  angleInDegrees )

inlinestatic

Creates a X rotation matrix.

Parameters

angleInDegrees

Rotation angle in degrees.

Returns

X Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createYRotationInRadians ( float  angleInRadians )

static

Creates a Y rotation matrix.

Parameters

angleInRadians

Rotation angle in radians.

Returns

Y Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createYRotationInDegrees ( float  angleInDegrees )

inlinestatic

Creates a Y rotation matrix.

Parameters

angleInDegrees

Rotation angle in degrees.

Returns

Y Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createZRotationInRadians ( float  angleInRadians )

static

Creates a Z rotation matrix.

Parameters

angleInRadians

Rotation angle in radians.

Returns

Z Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createZRotationInDegrees ( float  angleInDegrees )

inlinestatic

Creates a Z rotation matrix.

Parameters

angleInDegrees

Rotation angle in degrees.

Returns

Z Rotation matrix.

static Matrix4x4 kanzi::Matrix4x4::createScale ( Vector3  scale )

static

Creates a scaling matrix.

Parameters

scale

Scaling vector.

Returns

Scaled matrix.

static Matrix4x4 kanzi::Matrix4x4::createOrthogonalProjection ( float  left, float  right, float  bottom, float  top, float  near, float  far  )

static

Creates projection matrix for orthogonal projection.

Parameters

left	Viewing box left.
right	Viewing box right.
bottom	Viewing box bottom.
top	Viewing box top.
near	Camera near value.
far	Camera far value.

Returns

A newly constructed projection matrix.

static Matrix4x4 kanzi::Matrix4x4::createPerspectiveProjection ( float  near, float  far, FieldOfViewType  fovType, float  fovInDegrees, float  aspectRatio  )

static

Creates a perspective projection matrix for a symmetrical viewing volume.

Parameters

near	Camera near value.
far	Camera far value.
fovType	Tells whether the fovInDegrees parameter is xfov or yfov.
fovInDegrees	Field of view in degrees.
aspectRatio	The aspect ratio of the viewport.

Returns

Perspective projection matrix.

static Matrix4x4 kanzi::Matrix4x4::createPerspectiveProjection ( float  near, float  far, Vector4  fovInDegrees  )

static

Creates a perspective projection matrix for a viewing volume.

Parameters

near	Camera near value.
far	Camera far value.
fovInDegrees	Field of view in degrees, specified in order left, right, up, down. Angles to the right of center and upwards of center are positive.

Returns

Perspective projection matrix.

static Matrix4x4 kanzi::Matrix4x4::createSubProjection ( const Matrix4x4 &  projection, float  relativeOffsetX, float  relativeOffsetY, float  relativeSizeX, float  relativeSizeY  )

static

Calculate sub-quad projection of an existing projection matrix.

This is a specific solution for an axis-aligned case.

Old projection matrix = [P00 0 P02 P03] [ 0 P11 P12 P13] [ 0 0 P22 P23] [ 0 0 -1 0]

Traslated and scaled: (x, y) |–> (Ox, Oy) + (Sx * x, Sy * y) [Sx P00, 0, Ox P22 + Sx P02, Ox P23] [ 0, Sy P11, Oy P22 + Sy P12, Oy P23] [ 0, 0, P22, P23] [ 0, 0, -1, 0]

Parameters

projection	Projection matrix.
relativeOffsetX	X offset of sub-quad as portion of the size of the projection area.
relativeOffsetY	Y offset of sub-quad as portion of the size of the projection area.
relativeSizeX	Projection area X size in regard to sub-quad area size.
relativeSizeY	Projection area Y size in regard to sub-quad area size.

Returns

Modified projection matrix.

static optional<Matrix4x4> kanzi::Matrix4x4::createLookAtMatrix ( Vector3  position, Vector3  lookAtPoint, Vector3  upVector  )

static

Creates a lookup transformation matrix, so that it is in a given position looking at the given point.

Parameters

position	The new translation of the node.
lookAtPoint	A point where the node is looking at.
upVector	The new up vector of the node.

Returns

Lookup matrix if position is not the same as lookAtPoint and upVector is not null, nullopt otherwise.

static Matrix4x4 kanzi::Matrix4x4::createSRT ( Vector3  scale, Vector3  rotationInRadians, Vector3  translation  )

static

Create an SRT matrix.

Parameters

scale	Scales by axises.
rotationInRadians	Rotation component in radians.
translation	Translation component.

Returns

Newly constructed matrix.

Matrix4x4 kanzi::Matrix4x4::transposed ( ) const

inline

Applies a transpose to a matrix.

Returns

Newly constructed transpose matrix.

Friends And Related Function Documentation

Matrix4x4 operator+ ( Matrix4x4  lhs, const Matrix4x4 &  rhs  )

friend

Creates a new matrix by adding an existing matrix to another one.

Parameters

lhs	First matrix, left hand side.
rhs	Second matrix, right hand side.

Returns

A new matrix resulting from the addition of the right hand side to the left hand side.

Matrix4x4 operator- ( Matrix4x4  lhs, const Matrix4x4 &  rhs  )

friend

Creates a new matrix by subtracting an existing matrix from another one.

Parameters

lhs	First matrix, left hand side.
rhs	Second matrix, right hand side.

Returns

A new matrix resulting from the subtraction of the right hand side from the left hand side.

bool operator== ( const Matrix4x4 &  left, const Matrix4x4 &  right  )

friend

Equality operator.

Compares two matrices for equality. Note that this is a floating point comparison without any tolerance, so you probably don't want to use this.

Parameters

left	Left hand side matrix.
right	Right hand side matrix.

Returns

True if vectors are equal.

bool operator!= ( const Matrix4x4 &  left, const Matrix4x4 &  right  )

friend

Inequality operator.

Compares two matrices for inequality. Note that this is a floating point comparison without any tolerance, so you probably don't want to use this.

Parameters

left	Left-hand side matrix.
right	Right-hand side matrix.

Returns

True if matrices are not equal, false if they are.

---

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

• kanzi/core/math/matrix4x4.hpp