t::Matrix4x4 Class Reference

The \(4 \times 4\) matrix class. More...

#include <Matrix4x4.hpp>

Public Member Functions
	Matrix4x4 (double _n11, double _n12, double _n13, double _n14, double _n21, double _n22, double _n23, double _n24, double _n31, double _n32, double _n33, double _n34, double _n41, double _n42, double _n43, double _n44)
	Creates a new \(4 \times 4\) matrix with the specified elements.
Matrix4x4	clone () const
	Returns a copy of this matrix.
Matrix4x4 &	copy (const Matrix4x4 &source)
	Copies the elements of another \(4 \times 4\) matrix into this matrix.
Matrix4x4 &	set (double _n11, double _n12, double _n13, double _n14, double _n21, double _n22, double _n23, double _n24, double _n31, double _n32, double _n33, double _n34, double _n41, double _n42, double _n43, double _n44)
	Sets the elements of this matrix.
double	get (int row, int column) const
	Gets the element at the specified row and column of this matrix with bounds checking.
Matrix4x4 &	set (int row, int column, int value)
	Sets the element at the specified row and column of this matrix to the specified value.
Matrix4x4 &	reset ()
	Resets this matrix to the \(4 \times 4\) identity matrix.
double	determinant () const
	Returns the determinant of this matrix.
Matrix4x4	transpose () const
	Returns the transpose of this matrix.
Matrix4x4	inverse () const
	Returns the inverse of this matrix or the zero matrix if this matrix does not have an inverse.
Matrix3x3	topLeft3x3Matrix () const
	Returns the top-left \(3 \times 3\) matrix of this matrix.
double	operator[] (std::size_t index) const
	Returns the element at the specified index of this matrix without bounds checking and assuming row-major ordering.
Matrix4x4 &	operator+= (const Matrix4x4 &m)
	Adds the specified \(4 \times 4\) matrix to this matrix.
Matrix4x4 &	operator+= (double s)
	Adds the specified constant to all elements in this matrix.
Matrix4x4 &	operator-= (const Matrix4x4 &m)
	Substracts the specified \(4 \times 4\) matrix from this matrix.
Matrix4x4 &	operator-= (double s)
	Substracts the specified constant from all elements in this matrix.
Matrix4x4 &	operator*= (const Matrix4x4 &m)
	Multiplies this matrix with another \(4 \times 4\) matrix and copies the result into this instance.
Matrix4x4 &	operator*= (double s)
	Multiplies the elements of this matrix with the specified constant.
Matrix4x4 &	operator/= (const Matrix4x4 &m)
	Divides the elements of this matrix by the corresponding elements of the specified \(3 \times 3\) matrix.
Matrix4x4 &	operator/= (double s)
	Divides the elements of this matrix with the specified constant.

Static Public Member Functions
static Matrix4x4	identity ()
	Returns a \(4 \times 4\) identity matrix.
static Matrix4x4	zero ()
	Returns a \(4 \times 4\) zero matrix.
static Matrix4x4	fromTranslation (const Vector3 &distance)
	Returns a translation matrix for the specified translation for post-multiplication ( \(V' = AV\) where \(V\) is the homogeneous coordinates and \(A\) is the transformation matrix).
static Matrix4x4	fromRotation (const EulerRotation &angle)
	Returns a rotation matrix for the specified rotation for post-multiplication ( \(V' = AV\) where \(V\) is the homogeneous coordinates and \(A\) is the transformation matrix).
static Matrix4x4	fromScale (const Vector3 &scaleFactor)
	Returns a scale matrix for the specified scale factor.

Public Attributes
std::array< double, 16 >	elements
	The array containing the elements of this matrix in row-major order.

Friends
bool	operator== (const Matrix4x4 &a, const Matrix4x4 &b)=default
	Returns whether two \(4 \times 4\) matrices are equal.
Matrix4x4	operator+ (const Matrix4x4 &a, const Matrix4x4 &b)
	Adds two \(4 \times 4\) matrices.
Matrix4x4	operator+ (const Matrix4x4 &a, double s)
	Adds a constant to all elements of a \(4 \times 4\) matrix.
Matrix4x4	operator+ (double s, const Matrix4x4 &a)
	Adds a constant to all elements of a \(4 \times 4\) matrix.
Matrix4x4	operator- (const Matrix4x4 &a, const Matrix4x4 &b)
	Substracts 2 \(4 \times 4\) matrices.
Matrix4x4	operator- (const Matrix4x4 &a, double s)
	Substracts a constant from all elements of a \(4 \times 4\) matrix.
Matrix4x4	operator- (double s, const Matrix4x4 &a)
	Substracts a \(4 \times 4\) matrix from a \(4 \times 4\) constant matrix.
Matrix4x4	operator* (const Matrix4x4 &a, const Matrix4x4 &b)
	Multiplies two \(4 \times 4\) matrices.
Matrix4x4	operator* (const Matrix4x4 &a, double s)
	Multiplies all elements of a \(4 \times 4\) matrix with a constant.
Matrix4x4	operator* (double s, const Matrix4x4 &a)
	Multiplies all elements of a \(4 \times 4\) matrix with a constant.
Vector4	operator* (const Matrix4x4 &a, const Vector4 &v)
	Multiplies a \(4 \times 4\) matrix with a four-dimensional vector.
Matrix4x4	operator/ (const Matrix4x4 &a, const Matrix4x4 &b)
	Returns the element-wise division of two \(4 \times 4\) matrices.
Matrix4x4	operator/ (const Matrix4x4 &a, double s)
	Divides all elements of a \(4 \times 4\) matrix by a constant.
Matrix4x4	operator/ (double s, const Matrix4x4 &a)
	Returns the element-wise division of a \(4 \times 4\) constant matrix and a \(4 \times 4\) matrix.

Detailed Description

The \(4 \times 4\) matrix class.

Constructor & Destructor Documentation

Matrix4x4()

t::Matrix4x4::Matrix4x4 ( double _n11, double _n12, double _n13, double _n14, double _n21, double _n22, double _n23, double _n24, double _n31, double _n32, double _n33, double _n34, double _n41, double _n42, double _n43, double _n44 )

inline

Creates a new \(4 \times 4\) matrix with the specified elements.

Parameters

_n11	The \((1, 1)\) element of the new matrix.
_n12	The \((1, 2)\) element of the new matrix.
_n13	The \((1, 3)\) element of the new matrix.
_n14	The \((1, 4)\) element of the new matrix.
_n21	The \((2, 1)\) element of the new matrix.
_n22	The \((2, 2)\) element of the new matrix.
_n23	The \((2, 3)\) element of the new matrix.
_n24	The \((2, 4)\) element of the new matrix.
_n31	The \((3, 1)\) element of the new matrix.
_n32	The \((3, 2)\) element of the new matrix.
_n33	The \((3, 3)\) element of the new matrix.
_n34	The \((3, 4)\) element of the new matrix.
_n41	The \((4, 1)\) element of the new matrix.
_n42	The \((4, 2)\) element of the new matrix.
_n43	The \((4, 3)\) element of the new matrix.
_n44	The \((4, 4)\) element of the new matrix.

Member Function Documentation

clone()

Matrix4x4 t::Matrix4x4::clone ( ) const

inline

Returns a copy of this matrix.

Returns

A copy of this matrix.

copy()

Matrix4x4 & t::Matrix4x4::copy ( const Matrix4x4 & source )

inline

Copies the elements of another \(4 \times 4\) matrix into this matrix.

Parameters

source

The \(4 \times 4\) matrix to copy from.

Returns

This matrix.

determinant()

double t::Matrix4x4::determinant ( ) const

inline

Returns the determinant of this matrix.

Returns

The determinant of this matrix.

fromRotation()

static Matrix4x4 t::Matrix4x4::fromRotation ( const EulerRotation & angle )

inlinestatic

Returns a rotation matrix for the specified rotation for post-multiplication ( \(V' = AV\) where \(V\) is the homogeneous coordinates and \(A\) is the transformation matrix).

If you want to use pre-multiplication i.e. \(V' = VA\), transpose the returned matrix.

Parameters

angle

An Euler rotation.

Returns

The rotation matrix for angle.

fromScale()

static Matrix4x4 t::Matrix4x4::fromScale ( const Vector3 & scaleFactor )

inlinestatic

Returns a scale matrix for the specified scale factor.

Parameters

scaleFactor

The scale factor along the x, y, and z axes.

Returns

The scale matrix for scaleFactor.

fromTranslation()

static Matrix4x4 t::Matrix4x4::fromTranslation ( const Vector3 & distance )

inlinestatic

Returns a translation matrix for the specified translation for post-multiplication ( \(V' = AV\) where \(V\) is the homogeneous coordinates and \(A\) is the transformation matrix).

If you want to use pre-multiplication i.e. \(V' = VA\), transpose the returned matrix.

Parameters

distance

The distance to translate along the x, y, and z axes.

Returns

The translation matrix for distance.

get()

double t::Matrix4x4::get ( int row, int column ) const

inline

Gets the element at the specified row and column of this matrix with bounds checking.

Parameters

row	The 0-based index of the row of the element.
column	The 0-based index of the column of the element.

Returns

The element at the specified row and column of this matrix.

See also

operator[] for accessing without bounds checking.

identity()

static Matrix4x4 t::Matrix4x4::identity ( )

inlinestatic

Returns a \(4 \times 4\) identity matrix.

Returns

A \(4 \times 4\) identity matrix.

inverse()

Matrix4x4 t::Matrix4x4::inverse ( ) const

inline

Returns the inverse of this matrix or the zero matrix if this matrix does not have an inverse.

The inverse of a matrix \(A\) is the matrix \(A^{-1}\) such that \(AA^{-1} = I\) where \(I\) is the identity matrix. A matrix does not have an inverse if its determinant is zero.

Note that this method does not modify this instance.

Returns

The inverse of this matrix.

operator*=() [1/2]

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

inline

Multiplies this matrix with another \(4 \times 4\) matrix and copies the result into this instance.

Note that this is not an element-wise multiplication, but matrix multiplication.

Parameters

m	A \(4 \times 4\) matrix to multiply with.

Returns

This matrix.

operator*=() [2/2]

Matrix4x4 & t::Matrix4x4::operator*= ( double s )

inline

Multiplies the elements of this matrix with the specified constant.

Parameters

s	A constant.

Returns

This matrix.

operator+=() [1/2]

Matrix4x4 & t::Matrix4x4::operator+= ( const Matrix4x4 & m )

inline

Adds the specified \(4 \times 4\) matrix to this matrix.

Parameters

m	A \(4 \times 4\) matrix.

Returns

This matrix.

operator+=() [2/2]

Matrix4x4 & t::Matrix4x4::operator+= ( double s )

inline

Adds the specified constant to all elements in this matrix.

Parameters

s	A constant.

Returns

This matrix.

operator-=() [1/2]

Matrix4x4 & t::Matrix4x4::operator-= ( const Matrix4x4 & m )

inline

Substracts the specified \(4 \times 4\) matrix from this matrix.

Parameters

m	A \(4 \times 4\) matrix.

Returns

This matrix.

operator-=() [2/2]

Matrix4x4 & t::Matrix4x4::operator-= ( double s )

inline

Substracts the specified constant from all elements in this matrix.

Parameters

s	A constant.

Returns

This matrix.

operator/=() [1/2]

Matrix4x4 & t::Matrix4x4::operator/= ( const Matrix4x4 & m )

inline

Divides the elements of this matrix by the corresponding elements of the specified \(3 \times 3\) matrix.

Parameters

m	A \(4 \times 4\) matrix.

Returns

This matrix.

operator/=() [2/2]

Matrix4x4 & t::Matrix4x4::operator/= ( double s )

inline

Divides the elements of this matrix with the specified constant.

Parameters

s	A constant.

Returns

This matrix.

operator[]()

double t::Matrix4x4::operator[] ( std::size_t index ) const

inline

Returns the element at the specified index of this matrix without bounds checking and assuming row-major ordering.

The element at row \(i\) and column \(j\) of this matrix has the index \(4i + j\) assuming \(i\) and \(j\) are zero-based.

Parameters

index

The 0-based index of the element in row-major order.

Returns

The element at the specified index of this matrix.

See also

get for accessing with bounds checking.

reset()

Matrix4x4 & t::Matrix4x4::reset ( )

inline

Resets this matrix to the \(4 \times 4\) identity matrix.

Returns

This matrix.

set() [1/2]

Matrix4x4 & t::Matrix4x4::set ( double _n11, double _n12, double _n13, double _n14, double _n21, double _n22, double _n23, double _n24, double _n31, double _n32, double _n33, double _n34, double _n41, double _n42, double _n43, double _n44 )

inline

Sets the elements of this matrix.

Parameters

_n11	The new \((1, 1)\) element of this matrix.
_n12	The new \((1, 2)\) element of this matrix.
_n13	The new \((1, 3)\) element of this matrix.
_n14	The new \((1, 4)\) element of this matrix.
_n21	The new \((2, 1)\) element of this matrix.
_n22	The new \((2, 2)\) element of this matrix.
_n23	The new \((2, 3)\) element of this matrix.
_n24	The new \((2, 4)\) element of this matrix.
_n31	The new \((3, 1)\) element of this matrix.
_n32	The new \((3, 2)\) element of this matrix.
_n33	The new \((3, 3)\) element of this matrix.
_n34	The new \((3, 4)\) element of this matrix.
_n41	The new \((4, 1)\) element of this matrix.
_n42	The new \((4, 2)\) element of this matrix.
_n43	The new \((4, 3)\) element of this matrix.
_n44	The new \((4, 4)\) element of this matrix.

Returns

This matrix.

set() [2/2]

Matrix4x4 & t::Matrix4x4::set ( int row, int column, int value )

inline

Sets the element at the specified row and column of this matrix to the specified value.

Parameters

row	The 0-based index of the row of the element.
column	The 0-based index of the column of the element.
value	The new value for the element.

Returns

This matrix.

topLeft3x3Matrix()

Matrix3x3 t::Matrix4x4::topLeft3x3Matrix ( ) const

inline

Returns the top-left \(3 \times 3\) matrix of this matrix.

For a transformation matrix, this method may be used to extract the rotation and scale components of the transformation, while discarding the translation component.

Returns

The top-left \(3 \times 3\) matrix of this matrix.

transpose()

Matrix4x4 t::Matrix4x4::transpose ( ) const

inline

Returns the transpose of this matrix.

Note that this method does not modify this instance.

Returns

The transpose of this matrix.

zero()

static Matrix4x4 t::Matrix4x4::zero ( )

inlinestatic

Returns a \(4 \times 4\) zero matrix.

Returns

A \(4 \times 4\) zero matrix.

Friends And Related Symbol Documentation

operator* [1/4]

Matrix4x4 operator* ( const Matrix4x4 & a, const Matrix4x4 & b )

friend

Multiplies two \(4 \times 4\) matrices.

Note that this is not an element-wise multiplication, but matrix multiplication.

Parameters

a	A \(4 \times 4\) matrix.
b	Another \(4 \times 4\) matrix.

Returns

The matrix product of a and b.

operator* [2/4]

Vector4 operator* ( const Matrix4x4 & a, const Vector4 & v )

friend

Multiplies a \(4 \times 4\) matrix with a four-dimensional vector.

Parameters

a	A \(4 \times 4\) matrix.
v	A four-dimensional vector.

Returns

The product of a and v.

operator* [3/4]

Matrix4x4 operator* ( const Matrix4x4 & a, double s )

friend

Multiplies all elements of a \(4 \times 4\) matrix with a constant.

Parameters

a	A \(4 \times 4\) matrix.
s	A constant.

Returns

The resulting matrix when multiplying the elements of a with s.

operator* [4/4]

Matrix4x4 operator* ( double s, const Matrix4x4 & a )

friend

Multiplies all elements of a \(4 \times 4\) matrix with a constant.

Parameters

s	A constant.
a	A \(4 \times 4\) matrix.

Returns

The resulting matrix when multiplying the elements of a with s.

operator+ [1/3]

Matrix4x4 operator+ ( const Matrix4x4 & a, const Matrix4x4 & b )

friend

Adds two \(4 \times 4\) matrices.

Parameters

a	A \(4 \times 4\) matrix.
b	Another \(4 \times 4\) matrix.

Returns

The sum of a and b.

operator+ [2/3]

Matrix4x4 operator+ ( const Matrix4x4 & a, double s )

friend

Adds a constant to all elements of a \(4 \times 4\) matrix.

Parameters

a	A \(4 \times 4\) matrix.
s	A constant.

Returns

The resulting matrix when adding s to all elements of a.

operator+ [3/3]

Matrix4x4 operator+ ( double s, const Matrix4x4 & a )

friend

Adds a constant to all elements of a \(4 \times 4\) matrix.

Parameters

s	A constant.
a	A \(4 \times 4\) matrix.

Returns

The resulting matrix when adding s to all elements of a.

operator- [1/3]

Matrix4x4 operator- ( const Matrix4x4 & a, const Matrix4x4 & b )

friend

Substracts 2 \(4 \times 4\) matrices.

Parameters

a	A \(4 \times 4\) matrix.
b	Another \(4 \times 4\) matrix.

Returns

The difference of a and b.

operator- [2/3]

Matrix4x4 operator- ( const Matrix4x4 & a, double s )

friend

Substracts a constant from all elements of a \(4 \times 4\) matrix.

Parameters

a	A \(4 \times 4\) matrix.
s	A constant.

Returns

The resulting matrix when substracting s from all elements of a.

operator- [3/3]

Matrix4x4 operator- ( double s, const Matrix4x4 & a )

friend

Substracts a \(4 \times 4\) matrix from a \(4 \times 4\) constant matrix.

Parameters

s	A constant for a \(4 \times 4\) constant matrix.
a	A \(4 \times 4\) matrix.

Returns

The resulting matrix when substracting a from the constant matrix of s.

operator/ [1/3]

Matrix4x4 operator/ ( const Matrix4x4 & a, const Matrix4x4 & b )

friend

Returns the element-wise division of two \(4 \times 4\) matrices.

Parameters

a	A \(4 \times 4\) matrix.
b	Another \(4 \times 4\) matrix.

Returns

The element-wise division of a and b.

operator/ [2/3]

Matrix4x4 operator/ ( const Matrix4x4 & a, double s )

friend

Divides all elements of a \(4 \times 4\) matrix by a constant.

Parameters

a	A \(4 \times 4\) matrix.
s	A constant.

Returns

The resulting matrix when dividing the elements of a by s.

operator/ [3/3]

Matrix4x4 operator/ ( double s, const Matrix4x4 & a )

friend

Returns the element-wise division of a \(4 \times 4\) constant matrix and a \(4 \times 4\) matrix.

Parameters

s	A constant for a \(4 \times 4\) constant matrix.
a	Another \(4 \times 4\) matrix.

Returns

The element-wise division of the constant matrix and a.

operator==

bool operator== ( const Matrix4x4 & a, const Matrix4x4 & b )

friend

Returns whether two \(4 \times 4\) matrices are equal.

Parameters

a	A \(4 \times 4\) matrix.
b	Another \(4 \times 4\) matrix.

Returns

true if a equals b, false otherwise.

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

• include/math/Matrix4x4.hpp