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
optional< Vector3 >	getRotationAngle () const
	Calculates Euler rotation angles of the 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	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

◆ FieldOfViewType

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

◆ Matrix4x4() [1/4]

kanzi::Matrix4x4::Matrix4x4 ( )

inlineexplicit

Default constructor, initializes the matrix to identity matrix.

◆ Matrix4x4() [2/4]

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.

◆ Matrix4x4() [3/4]

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

inlineexplicit

Constructs the matrix from four column vectors.

◆ Matrix4x4() [4/4]

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

◆ operator[]() [1/2]

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

◆ operator[]() [2/2]

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

◆ getXAxis()

Vector3 kanzi::Matrix4x4::getXAxis ( ) const

inline

Get X axis.

◆ getYAxis()

Vector3 kanzi::Matrix4x4::getYAxis ( ) const

inline

Get Y axis.

◆ getZAxis()

Vector3 kanzi::Matrix4x4::getZAxis ( ) const

inline

Get Z axis.

◆ getScale()

Vector3 kanzi::Matrix4x4::getScale ( ) const

Get scale as a vector.

◆ getRotationAngle()

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.

◆ scale()

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

inline

Scales this matrix.

Parameters

scale Scaling vector.

◆ scaleUniform()

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

inline

Scales this matrix.

Parameters

scale Uniform scaling value.

◆ translate()

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

inline

Translates this matrix.

Parameters

translate Translation vector.

◆ setXAxis()

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

inline

Set X axis.

Parameters

v	X axis vector.

◆ setYAxis()

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

inline

Set Y axis.

Parameters

v	Y axis vector.

◆ setZAxis()

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

inline

Set Z axis.

Parameters

v	Z axis vector.

◆ getTranslation()

Vector3 kanzi::Matrix4x4::getTranslation ( ) const

inline

Get translation.

Returns: Translation vector.

◆ setTranslation()

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

inline

Set translation.

Parameters

translation Translation vector.

◆ getTranslationX()

float kanzi::Matrix4x4::getTranslationX ( ) const

inline

Get translation on X axis.

Returns: Translation X component.

◆ setTranslationX()

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

inline

Set translation on X axis.

Parameters

translationX Translation X component.

◆ getTranslationY()

float kanzi::Matrix4x4::getTranslationY ( ) const

inline

Get translation on Y axis.

Returns: Translation Y component.

◆ setTranslationY()

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

inline

Set translation on Y axis.

Parameters

translationY Translation Y component.

◆ getTranslationZ()

float kanzi::Matrix4x4::getTranslationZ ( ) const

inline

Get translation on Z axis.

Returns: Translation Z component.

◆ setTranslationZ()

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

inline

Set translation on Z axis.

Parameters

translationZ Translation Y component.

◆ operator+=()

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

inline

Modifies this matrix by adding another matrix.

Parameters

v	Another matrix.

Returns: This matrix.

◆ operator-=()

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.

◆ operator*() [1/2]

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.

◆ operator*() [2/2]

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.

◆ operator*=()

Matrix4x4& kanzi::Matrix4x4::operator*= ( const Matrix4x4 & m )

Modifies this matrix by multiplying it with another matrix.

Parameters

m	Another matrix.

Returns: This matrix.

◆ createTranslation() [1/2]

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

inlinestatic

Creates translation matrix.

Parameters

translation Translation vector.

Returns: Translation matrix.

◆ createTranslation() [2/2]

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.

◆ createIdentity()

static Matrix4x4 kanzi::Matrix4x4::createIdentity ( )

inlinestatic

Creates identity matrix.

Returns: Identity matrix.

◆ createFromHomogenousMatrix() [1/2]

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.

◆ createFromHomogenousMatrix() [2/2]

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.

◆ createRotation()

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.

◆ createRotationInDegrees()

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.

◆ createXRotationInRadians()

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

static

Creates a X rotation matrix.

Parameters

angleInRadians Rotation angle in radians.

Returns: X Rotation matrix.

◆ createXRotationInDegrees()

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

inlinestatic

Creates a X rotation matrix.

Parameters

angleInDegrees Rotation angle in degrees.

Returns: X Rotation matrix.

◆ createYRotationInRadians()

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

static

Creates a Y rotation matrix.

Parameters

angleInRadians Rotation angle in radians.

Returns: Y Rotation matrix.

◆ createYRotationInDegrees()

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

inlinestatic

Creates a Y rotation matrix.

Parameters

angleInDegrees Rotation angle in degrees.

Returns: Y Rotation matrix.

◆ createZRotationInRadians()

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

static

Creates a Z rotation matrix.

Parameters

angleInRadians Rotation angle in radians.

Returns: Z Rotation matrix.

◆ createZRotationInDegrees()

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

inlinestatic

Creates a Z rotation matrix.

Parameters

angleInDegrees Rotation angle in degrees.

Returns: Z Rotation matrix.

◆ createScale()

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

static

Creates a scaling matrix.

Parameters

scale Scaling vector.

Returns: Scaled matrix.

◆ createOrthogonalProjection()

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.

◆ createPerspectiveProjection() [1/2]

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.

◆ createPerspectiveProjection() [2/2]

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.

◆ createSubProjection()

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.

◆ createLookAtMatrix()

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.

◆ createSRT()

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.

◆ transposed()

Matrix4x4 kanzi::Matrix4x4::transposed ( ) const

inline

Applies a transpose to a matrix.

Returns: Newly constructed transpose matrix.

Friends And Related Function Documentation

◆ operator+

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.

◆ operator-

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.

◆ operator==

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.

◆ operator!=

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

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Enumeration Documentation

◆ FieldOfViewType

Constructor & Destructor Documentation

◆ Matrix4x4() [1/4]

◆ Matrix4x4() [2/4]

◆ Matrix4x4() [3/4]

◆ Matrix4x4() [4/4]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ getXAxis()

◆ getYAxis()

◆ getZAxis()

◆ getScale()

◆ getRotationAngle()

◆ scale()

◆ scaleUniform()

◆ translate()

◆ setXAxis()

◆ setYAxis()

◆ setZAxis()

◆ getTranslation()

◆ setTranslation()

◆ getTranslationX()

◆ setTranslationX()

◆ getTranslationY()

◆ setTranslationY()

◆ getTranslationZ()

◆ setTranslationZ()

◆ operator+=()

◆ operator-=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ createTranslation() [1/2]

◆ createTranslation() [2/2]

◆ createIdentity()

◆ createFromHomogenousMatrix() [1/2]

◆ createFromHomogenousMatrix() [2/2]

◆ createRotation()

◆ createRotationInDegrees()

◆ createXRotationInRadians()

◆ createXRotationInDegrees()

◆ createYRotationInRadians()

◆ createYRotationInDegrees()

◆ createZRotationInRadians()

◆ createZRotationInDegrees()

◆ createScale()

◆ createOrthogonalProjection()

◆ createPerspectiveProjection() [1/2]

◆ createPerspectiveProjection() [2/2]

◆ createSubProjection()

◆ createLookAtMatrix()

◆ createSRT()

◆ transposed()

Friends And Related Function Documentation

◆ operator+

◆ operator-

◆ operator==

◆ operator!=