A general-purpose 4x4 matrix, defined in a right-handed coordinate system. More...

#include <luciad/cartesian/Matrix4x4.h>

Public Member Functions
	Matrix4x4 ()
	Default constructor.
Matrix4x4	add (const Matrix4x4 &other) const
	Returns the sum of two matrices.
size_t	getHash () const
	Returns the hash of this matrix.
double	getValue (size_t column, size_t row) const
	Returns the value from the given column and row.
std::optional< Matrix4x4 >	inverse () const
	Returns the inverse of this matrix, or std::nullopt if this matrix is not invertible.
bool	isAffineTransformation () const
	Returns whether this arbitrary matrix represents a valid 3D affine transformation.
Coordinate	multiply (const Coordinate &point) const
	Applies this matrix as an affine transformation to a point.
Matrix4x4	multiply (const Matrix4x4 &other) const
	Returns the product of two matrices.
Matrix4x4	multiply (double scalar) const
	Returns the element-wise product between this matrix and a scalar.
bool	operator!= (const Matrix4x4 &other) const
Coordinate	operator* (const Coordinate &point) const
Matrix4x4	operator* (const Matrix4x4 &other) const
Matrix4x4	operator* (double scalar) const
Matrix4x4 &	operator*= (const Matrix4x4 &other)
Matrix4x4 &	operator*= (double scalar)
Matrix4x4	operator+ (const Matrix4x4 &other) const
Matrix4x4 &	operator+= (const Matrix4x4 &other)
Matrix4x4	operator- (const Matrix4x4 &other) const
Matrix4x4 &	operator-= (const Matrix4x4 &other)
bool	operator== (const Matrix4x4 &other) const
void	setValue (size_t column, size_t row, double value)
	Sets the value at the given column and row.
Matrix4x4	subtract (const Matrix4x4 &other) const
	Returns the difference of two matrices.
Coordinate	transformPoint (const Coordinate &point) const
	Applies this matrix as an affine transformation to a point.
Coordinate	transformVector (const Coordinate &vector) const
	Applies this matrix as an affine transformation to a vector.
Matrix4x4	transpose () const
	Returns the transpose of this matrix.

Static Public Member Functions
static Matrix4x4	create (const std::vector< double > &values)
	Creates a new 4x4 matrix with the given values.
static Matrix4x4	identity ()
	Creates a new identity matrix.
static Matrix4x4	rotate (const Coordinate &axis, Angle angle)
	Creates a new rotation matrix around a given vector.
static Matrix4x4	rotateX (Angle angle)
	Creates a new rotation matrix around the x-axis.
static Matrix4x4	rotateY (Angle angle)
	Creates a new rotation matrix around the y-axis.
static Matrix4x4	rotateZ (Angle angle)
	Creates a new rotation matrix around the z-axis.
static Matrix4x4	scale (double scalar)
	Creates a new scaling matrix in all 3 dimensions.
static Matrix4x4	scale (double x, double y, double z)
	Creates a new scaling matrix.
static Matrix4x4	translate (const Coordinate &translation)
	Creates a new translation matrix.
static Matrix4x4	translate (double x, double y, double z)
	Creates a new translation matrix.

Detailed Description

A general-purpose 4x4 matrix, defined in a right-handed coordinate system.

A common use case for this class is to represent affine 3D transformations, such as translations, scalings, and rotations.

Since: 2026.1

Constructor & Destructor Documentation

◆ Matrix4x4()

luciad::Matrix4x4::Matrix4x4 ( )

Default constructor.

Constructs the identity matrix.

Member Function Documentation

◆ add()

Matrix4x4 luciad::Matrix4x4::add ( const Matrix4x4 & other ) const

Returns the sum of two matrices.

Parameters

other the other matrix.

Returns: the sum of the two matrices.

◆ create()

Matrix4x4 luciad::Matrix4x4::create ( const std::vector< double > & values )

static

Creates a new 4x4 matrix with the given values.

The values are expected in column-major order. For example, a list like [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] will become the following matrix:

  [ 0   4   8  12 ]
  [ 1   5   9  13 ]
  [ 2   6  10  14 ]
  [ 3   7  11  15 ]

Parameters

values a list of 16 values, in column-major order.

Returns: a new 4x4 matrix with the given values.

Exceptions

luciad::InvalidArgumentException when the list does not contain exactly 16 values.

◆ getHash()

size_t luciad::Matrix4x4::getHash ( ) const

Returns the hash of this matrix.

Returns: the hash of this matrix.

◆ getValue()

double luciad::Matrix4x4::getValue	(	size_t	column,
		size_t	row ) const

Returns the value from the given column and row.

Parameters

column	the column.
row	the row.

Returns: the value from the given column and row.

◆ identity()

Matrix4x4 luciad::Matrix4x4::identity ( )

static

Creates a new identity matrix.

  [ 1 0 0 0 ]
  [ 0 1 0 0 ]
  [ 0 0 1 0 ]
  [ 0 0 0 1 ]

Returns: a new identity matrix.

◆ inverse()

std::optional< Matrix4x4 > luciad::Matrix4x4::inverse ( ) const

Returns the inverse of this matrix, or std::nullopt if this matrix is not invertible.

Returns: the inverse of this matrix, or std::nullopt if this matrix is not invertible.

◆ isAffineTransformation()

bool luciad::Matrix4x4::isAffineTransformation ( ) const

Returns whether this arbitrary matrix represents a valid 3D affine transformation.

This is equivalent to checking whether the matrix has the following form:

  [ . . . . ]
  [ . . . . ]
  [ . . . . ]
  [ 0 0 0 1 ]

Returns: whether this matrix is an affine transformation.

◆ multiply() [1/3]

Coordinate luciad::Matrix4x4::multiply ( const Coordinate & point ) const

Applies this matrix as an affine transformation to a point.

This method does the same as transformPoint.

Parameters

point the point.

Returns: the transformed point.

◆ multiply() [2/3]

Matrix4x4 luciad::Matrix4x4::multiply ( const Matrix4x4 & other ) const

Returns the product of two matrices.

Parameters

other the other matrix.

Returns: the product of the two matrices.

◆ multiply() [3/3]

Matrix4x4 luciad::Matrix4x4::multiply ( double scalar ) const

Returns the element-wise product between this matrix and a scalar.

Parameters

scalar the scalar.

Returns: the element-wise product between this matrix and the scalar.

◆ operator!=()

bool luciad::Matrix4x4::operator!= ( const Matrix4x4 & other ) const

◆ operator*() [1/3]

Coordinate luciad::Matrix4x4::operator* ( const Coordinate & point ) const

◆ operator*() [2/3]

Matrix4x4 luciad::Matrix4x4::operator* ( const Matrix4x4 & other ) const

◆ operator*() [3/3]

Matrix4x4 luciad::Matrix4x4::operator* ( double scalar ) const

◆ operator*=() [1/2]

Matrix4x4 & luciad::Matrix4x4::operator*= ( const Matrix4x4 & other )

◆ operator*=() [2/2]

Matrix4x4 & luciad::Matrix4x4::operator*= ( double scalar )

◆ operator+()

Matrix4x4 luciad::Matrix4x4::operator+ ( const Matrix4x4 & other ) const

◆ operator+=()

Matrix4x4 & luciad::Matrix4x4::operator+= ( const Matrix4x4 & other )

◆ operator-()

Matrix4x4 luciad::Matrix4x4::operator- ( const Matrix4x4 & other ) const

◆ operator-=()

Matrix4x4 & luciad::Matrix4x4::operator-= ( const Matrix4x4 & other )

◆ operator==()

bool luciad::Matrix4x4::operator== ( const Matrix4x4 & other ) const

◆ rotate()

Matrix4x4 luciad::Matrix4x4::rotate	(	const Coordinate &	axis,
		Angle	angle )

static

Creates a new rotation matrix around a given vector.

Note: the rotation happens counterclockwise. When imagining the vector as an arrow, looking at the arrowhead coming towards you makes the rotation appear counterclockwise.

Parameters

axis	the vector to rotate around.
angle	the amount to rotate.

Returns: a new rotation matrix around the given vector.

◆ rotateX()

Matrix4x4 luciad::Matrix4x4::rotateX ( Angle angle )

static

Creates a new rotation matrix around the x-axis.

Note: the rotation happens counterclockwise. Looking towards negative infinity on the x-axis makes the rotation appear counterclockwise.

Parameters

angle the amount to rotate.

Returns: a new rotation matrix around the x-axis.

◆ rotateY()

Matrix4x4 luciad::Matrix4x4::rotateY ( Angle angle )

static

Creates a new rotation matrix around the y-axis.

Note: the rotation happens counterclockwise. Looking towards negative infinity on the y-axis makes the rotation appear counterclockwise.

Parameters

angle the amount to rotate.

Returns: a new rotation matrix around the y-axis.

◆ rotateZ()

Matrix4x4 luciad::Matrix4x4::rotateZ ( Angle angle )

static

Creates a new rotation matrix around the z-axis.

Note: the rotation happens counterclockwise. Looking towards negative infinity on the z-axis makes the rotation appear counterclockwise.

Parameters

angle the amount to rotate.

Returns: a new rotation matrix around the z-axis.

◆ scale() [1/2]

Matrix4x4 luciad::Matrix4x4::scale ( double scalar )

static

Creates a new scaling matrix in all 3 dimensions.

Parameters

scalar the amount to scale.

Returns: a new scaling matrix.

◆ scale() [2/2]

Matrix4x4 luciad::Matrix4x4::scale	(	double	x,
		double	y,
		double	z )

static

Creates a new scaling matrix.

Parameters

x	the amount to scale on the x-axis.
y	the amount to scale on the y-axis.
z	the amount to scale on the z-axis.

Returns: a new scaling matrix.

◆ setValue()

void luciad::Matrix4x4::setValue	(	size_t	column,
		size_t	row,
		double	value )

Sets the value at the given column and row.

Parameters

column	the column.
row	the row.
value	the value.

◆ subtract()

Matrix4x4 luciad::Matrix4x4::subtract ( const Matrix4x4 & other ) const

Returns the difference of two matrices.

Parameters

other the other matrix.

Returns: the difference of the two matrices.

◆ transformPoint()

Coordinate luciad::Matrix4x4::transformPoint ( const Coordinate & point ) const

Applies this matrix as an affine transformation to a point.

This method does the same as the multiply operator.

Parameters

point the point.

Returns: the transformed point.

◆ transformVector()

Coordinate luciad::Matrix4x4::transformVector ( const Coordinate & vector ) const

Applies this matrix as an affine transformation to a vector.

Note: the main difference between transformVector and transformPoint is that transformVector does NOT apply translations, whereas transformPoint does.

Parameters

vector the vector.

Returns: the transformed vector.

◆ translate() [1/2]

Matrix4x4 luciad::Matrix4x4::translate ( const Coordinate & translation )

static

Creates a new translation matrix.

Parameters

translation the translation.

Returns: a new translation matrix.

◆ translate() [2/2]

Matrix4x4 luciad::Matrix4x4::translate	(	double	x,
		double	y,
		double	z )

static

Creates a new translation matrix.

Parameters

x	the translation on the x-axis.
y	the translation on the y-axis.
z	the translation on the z-axis.

Returns: a new translation matrix.

◆ transpose()

Matrix4x4 luciad::Matrix4x4::transpose ( ) const

Returns the transpose of this matrix.

Returns: the transpose of this matrix.

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Matrix4x4()

Member Function Documentation

◆ add()

◆ create()

◆ getHash()

◆ getValue()

◆ identity()

◆ inverse()

◆ isAffineTransformation()

◆ multiply() [1/3]

◆ multiply() [2/3]

◆ multiply() [3/3]

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator==()

◆ rotate()

◆ rotateX()

◆ rotateY()

◆ rotateZ()

◆ scale() [1/2]

◆ scale() [2/2]

◆ setValue()

◆ subtract()

◆ transformPoint()

◆ transformVector()

◆ translate() [1/2]

◆ translate() [2/2]

◆ transpose()