The \(3 \times 3\) matrix class. More...

#include <Matrix3x3.hpp>

Public Member Functions
	Matrix3x3 (double _n11, double _n12, double _n13, double _n21, double _n22, double _n23, double _n31, double _n32, double _n33)
	Creates a new \(3 \times 3\) matrix with the specified elements.

Matrix3x3	clone () const
	Returns a copy of this matrix.

Matrix3x3 &	copy (const Matrix3x3 &source)
	Copies the elements of another \(3 \times 3\) matrix into this matrix.

Matrix3x3 &	set (double _n11, double _n12, double _n13, double _n21, double _n22, double _n23, double _n31, double _n32, double _n33)
	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.

Matrix3x3 &	set (int row, int column, int value)
	Sets the element at the specified row and column of this matrix to the specified value.

Matrix3x3 &	reset ()
	Resets this matrix to the \(3 \times 3\) identity matrix.

double	determinant () const
	Returns the determinant of this matrix.

Matrix3x3	transpose () const
	Returns the transpose of this matrix.

Matrix3x3	inverse () const
	Returns the inverse of this matrix or the zero matrix if this matrix does not have an inverse.

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.

Matrix3x3 &	operator+= (const Matrix3x3 &m)
	Adds the specified \(3 \times 3\) matrix to this matrix.

Matrix3x3 &	operator+= (double s)
	Adds the specified constant to all elements in this matrix.

Matrix3x3 &	operator-= (const Matrix3x3 &m)
	Substracts the specified \(3 \times 3\) matrix from this matrix.

Matrix3x3 &	operator-= (double s)
	Substracts the specified constant from all elements in this matrix.

Matrix3x3 &	operator*= (const Matrix3x3 &m)
	Multiplies this matrix with another \(3 \times 3\) matrix and copies the result into this instance.

Matrix3x3 &	operator*= (double s)
	Multiplies the elements of this matrix with the specified constant.

Matrix3x3 &	operator/= (const Matrix3x3 &m)
	Divides the elements of this matrix by the corresponding elements of the specified \(3 \times 3\) matrix.

Matrix3x3 &	operator/= (double s)
	Divides the elements of this matrix with the specified constant.

Static Public Member Functions
static Matrix3x3	identity ()
	Returns a \(3 \times 3\) identity matrix.

static Matrix3x3	zero ()
	Returns a \(3 \times 3\) zero matrix.

Public Attributes
std::array< double, 9 >	elements
	The array containing the elements of this matrix in row-major order.

Friends
bool	operator== (const Matrix3x3 &a, const Matrix3x3 &b)=default
	Returns whether two \(3 \times 3\) matrices are equal.

Matrix3x3	operator+ (const Matrix3x3 &a, const Matrix3x3 &b)
	Adds two \(3 \times 3\) matrices.

Matrix3x3	operator+ (const Matrix3x3 &a, double s)
	Adds a constant to all elements of a \(3 \times 3\) matrix.

Matrix3x3	operator+ (double s, const Matrix3x3 &a)
	Adds a constant to all elements of a \(3 \times 3\) matrix.

Matrix3x3	operator- (const Matrix3x3 &a, const Matrix3x3 &b)
	Substracts 2 \(3 \times 3\) matrices.

Matrix3x3	operator- (const Matrix3x3 &a, double s)
	Substracts a constant from all elements of a \(3 \times 3\) matrix.

Matrix3x3	operator- (double s, const Matrix3x3 &a)
	Substracts a \(3 \times 3\) matrix from a \(3 \times 3\) constant matrix.

Matrix3x3	operator* (const Matrix3x3 &a, const Matrix3x3 &b)
	Multiplies two \(3 \times 3\) matrices.

Matrix3x3	operator* (const Matrix3x3 &a, double s)
	Multiplies all elements of a \(3 \times 3\) matrix with a constant.

Matrix3x3	operator* (double s, const Matrix3x3 &a)
	Multiplies all elements of a \(3 \times 3\) matrix with a constant.

Vector3	operator* (const Matrix3x3 &a, const Vector3 &v)
	Multiplies a \(3 \times 3\) matrix with a 3D vector.

Matrix3x3	operator/ (const Matrix3x3 &a, const Matrix3x3 &b)
	Returns the element-wise division of two \(3 \times 3\) matrices.

Matrix3x3	operator/ (const Matrix3x3 &a, double s)
	Divides all elements of a \(3 \times 3\) matrix by a constant.

Matrix3x3	operator/ (double s, const Matrix3x3 &a)
	Returns the element-wise division of a \(3 \times 3\) constant matrix and a \(3 \times 3\) matrix.

Detailed Description

The \(3 \times 3\) matrix class.

Constructor & Destructor Documentation

◆ Matrix3x3()

t::Matrix3x3::Matrix3x3	(	double	_n11,
		double	_n12,
		double	_n13,
		double	_n21,
		double	_n22,
		double	_n23,
		double	_n31,
		double	_n32,
		double	_n33 )

inline

Creates a new \(3 \times 3\) 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.
_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.
_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.

Member Function Documentation

◆ clone()

Matrix3x3 t::Matrix3x3::clone ( ) const

inline

Returns a copy of this matrix.

Returns: A copy of this matrix.

◆ copy()

Matrix3x3 & t::Matrix3x3::copy ( const Matrix3x3 & source )

inline

Copies the elements of another \(3 \times 3\) matrix into this matrix.

Parameters

source The \(3 \times 3\) matrix to copy from.

Returns: This matrix.

◆ determinant()

double t::Matrix3x3::determinant ( ) const

inline

Returns the determinant of this matrix.

Returns: The determinant of this matrix.

◆ get()

double t::Matrix3x3::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.

Exceptions

std::out_of_range if the row or column is out of bounds.

See also: operator[] for accessing without bounds checking.

◆ identity()

static Matrix3x3 t::Matrix3x3::identity ( )

inlinestatic

Returns a \(3 \times 3\) identity matrix.

Returns: A \(3 \times 3\) identity matrix.

◆ inverse()

Matrix3x3 t::Matrix3x3::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]

Matrix3x3 & t::Matrix3x3::operator*= ( const Matrix3x3 & m )

inline

Multiplies this matrix with another \(3 \times 3\) matrix and copies the result into this instance.

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

Parameters

m	A \(3 \times 3\) matrix to multiply with.

Returns: This matrix.

◆ operator*=() [2/2]

Matrix3x3 & t::Matrix3x3::operator*= ( double s )

inline

Multiplies the elements of this matrix with the specified constant.

Parameters

s	A constant.

Returns: This matrix.

◆ operator+=() [1/2]

Matrix3x3 & t::Matrix3x3::operator+= ( const Matrix3x3 & m )

inline

Adds the specified \(3 \times 3\) matrix to this matrix.

Parameters

m	A \(3 \times 3\) matrix.

Returns: This matrix.

◆ operator+=() [2/2]

Matrix3x3 & t::Matrix3x3::operator+= ( double s )

inline

Adds the specified constant to all elements in this matrix.

Parameters

s	A constant.

Returns: This matrix.

◆ operator-=() [1/2]

Matrix3x3 & t::Matrix3x3::operator-= ( const Matrix3x3 & m )

inline

Substracts the specified \(3 \times 3\) matrix from this matrix.

Parameters

m	A \(3 \times 3\) matrix.

Returns: This matrix.

◆ operator-=() [2/2]

Matrix3x3 & t::Matrix3x3::operator-= ( double s )

inline

Substracts the specified constant from all elements in this matrix.

Parameters

s	A constant.

Returns: This matrix.

◆ operator/=() [1/2]

Matrix3x3 & t::Matrix3x3::operator/= ( const Matrix3x3 & m )

inline

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

Parameters

m	A \(3 \times 3\) matrix.

Returns: This matrix.

◆ operator/=() [2/2]

Matrix3x3 & t::Matrix3x3::operator/= ( double s )

inline

Divides the elements of this matrix with the specified constant.

Parameters

s	A constant.

Returns: This matrix.

◆ operator[]()

double t::Matrix3x3::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 \(3i + j\) 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()

Matrix3x3 & t::Matrix3x3::reset ( )

inline

Resets this matrix to the \(3 \times 3\) identity matrix.

Returns: This matrix.

◆ set() [1/2]

Matrix3x3 & t::Matrix3x3::set	(	double	_n11,
		double	_n12,
		double	_n13,
		double	_n21,
		double	_n22,
		double	_n23,
		double	_n31,
		double	_n32,
		double	_n33 )

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.
_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.
_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.

Returns: This matrix.

◆ set() [2/2]

Matrix3x3 & t::Matrix3x3::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.

◆ transpose()

Matrix3x3 t::Matrix3x3::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 Matrix3x3 t::Matrix3x3::zero ( )

inlinestatic

Returns a \(3 \times 3\) zero matrix.

Returns: A \(3 \times 3\) zero matrix.

Friends And Related Symbol Documentation

◆ operator* [1/4]

Matrix3x3 operator*	(	const Matrix3x3 &	a,
		const Matrix3x3 &	b )

friend

Multiplies two \(3 \times 3\) matrices.

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

Parameters

a	A \(3 \times 3\) matrix.
b	Another \(3 \times 3\) matrix.

Returns: The matrix product of a and b.

◆ operator* [2/4]

Vector3 operator*	(	const Matrix3x3 &	a,
		const Vector3 &	v )

friend

Multiplies a \(3 \times 3\) matrix with a 3D vector.

Parameters

a	A \(3 \times 3\) matrix.
v	A 3D vector.

Returns: The product of a and v.

◆ operator* [3/4]

Matrix3x3 operator*	(	const Matrix3x3 &	a,
		double	s )

friend

Multiplies all elements of a \(3 \times 3\) matrix with a constant.

Parameters

a	A \(3 \times 3\) matrix.
s	A constant.

Returns: The resulting matrix when multiplying all elements of a with s.

◆ operator* [4/4]

Matrix3x3 operator*	(	double	s,
		const Matrix3x3 &	a )

friend

Multiplies all elements of a \(3 \times 3\) matrix with a constant.

Parameters

s	A constant.
a	A \(3 \times 3\) matrix.

Returns: The resulting matrix when multiplying all elements of a with s.

◆ operator+ [1/3]

Matrix3x3 operator+	(	const Matrix3x3 &	a,
		const Matrix3x3 &	b )

friend

Adds two \(3 \times 3\) matrices.

Parameters

a	A \(3 \times 3\) matrix.
b	Another \(3 \times 3\) matrix.

Returns: The sum of a and b.

◆ operator+ [2/3]

Matrix3x3 operator+	(	const Matrix3x3 &	a,
		double	s )

friend

Adds a constant to all elements of a \(3 \times 3\) matrix.

Parameters

a	A \(3 \times 3\) matrix.
s	A constant.

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

◆ operator+ [3/3]

Matrix3x3 operator+	(	double	s,
		const Matrix3x3 &	a )

friend

Adds a constant to all elements of a \(3 \times 3\) matrix.

Parameters

s	A constant.
a	A \(3 \times 3\) matrix.

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

◆ operator- [1/3]

Matrix3x3 operator-	(	const Matrix3x3 &	a,
		const Matrix3x3 &	b )

friend

Substracts 2 \(3 \times 3\) matrices.

Parameters

a	A \(3 \times 3\) matrix.
b	Another \(3 \times 3\) matrix.

Returns: The difference of a and b.

◆ operator- [2/3]

Matrix3x3 operator-	(	const Matrix3x3 &	a,
		double	s )

friend

Substracts a constant from all elements of a \(3 \times 3\) matrix.

Parameters

a	A \(3 \times 3\) matrix.
s	A constant.

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

◆ operator- [3/3]

Matrix3x3 operator-	(	double	s,
		const Matrix3x3 &	a )

friend

Substracts a \(3 \times 3\) matrix from a \(3 \times 3\) constant matrix.

Parameters

s	A constant for a \(3 \times 3\) constant matrix.
a	A \(3 \times 3\) matrix.

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

◆ operator/ [1/3]

Matrix3x3 operator/	(	const Matrix3x3 &	a,
		const Matrix3x3 &	b )

friend

Returns the element-wise division of two \(3 \times 3\) matrices.

Parameters

a	A \(3 \times 3\) matrix.
b	Another \(3 \times 3\) matrix.

Returns: The element-wise division of a and b.

◆ operator/ [2/3]

Matrix3x3 operator/	(	const Matrix3x3 &	a,
		double	s )

friend

Divides all elements of a \(3 \times 3\) matrix by a constant.

Parameters

a	A \(3 \times 3\) matrix.
s	A constant.

Returns: The resulting matrix when dividing all elements of a by s.

◆ operator/ [3/3]

Matrix3x3 operator/	(	double	s,
		const Matrix3x3 &	a )

friend

Returns the element-wise division of a \(3 \times 3\) constant matrix and a \(3 \times 3\) matrix.

Parameters

s	A constant for a \(3 \times 3\) constant matrix.
a	Another \(3 \times 3\) matrix.

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

◆ operator==

bool operator==	(	const Matrix3x3 &	a,
		const Matrix3x3 &	b )

friend

Returns whether two \(3 \times 3\) matrices are equal.

Parameters

a	A \(3 \times 3\) matrix.
b	Another \(3 \times 3\) matrix.

Returns: true if a equals b, false otherwise.

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

include/math/Matrix3x3.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix3x3()

Member Function Documentation

◆ clone()

◆ copy()

◆ determinant()

◆ get()

◆ identity()

◆ inverse()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator[]()

◆ reset()

◆ set() [1/2]

◆ set() [2/2]

◆ transpose()

◆ zero()

Friends And Related Symbol Documentation

◆ operator* [1/4]

◆ operator* [2/4]

◆ operator* [3/4]

◆ operator* [4/4]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/ [1/3]

◆ operator/ [2/3]

◆ operator/ [3/3]

◆ operator==