#include <MRMatrix3.h>

Classes
struct	QR

Public Types
using	ValueType = T

using	VectorType = Vector3<T>

Public Member Functions
constexpr	Matrix3 () noexcept=default

constexpr	Matrix3 (const Vector3< T > &x, const Vector3< T > &y, const Vector3< T > &z)
	initializes matrix from its 3 rows

template<typename U >
constexpr	Matrix3 (const Matrix3< U > &m)

constexpr const Vector3< T > &	operator[] (int row) const noexcept
	row access

constexpr Vector3< T > &	operator[] (int row) noexcept

constexpr Vector3< T >	col (int i) const noexcept
	column access

constexpr T	trace () const noexcept
	computes trace of the matrix

constexpr T	normSq () const noexcept
	compute sum of squared matrix elements

constexpr T	norm () const noexcept

constexpr T	det () const noexcept
	computes determinant of the matrix

constexpr Matrix3< T >	inverse () const noexcept
	computes inverse matrix

constexpr Matrix3< T >	transposed () const noexcept
	computes transposed matrix

constexpr Vector3< T >	toEulerAngles () const noexcept
	returns 3 Euler angles, assuming this is a rotation matrix composed as follows: R=R(z)R(y)R(x)

QR	qr () const noexcept
	decompose this matrix on the product Q*R, where Q is orthogonal and R is upper triangular

Matrix3 &	operator+= (const Matrix3< T > &b)

Matrix3 &	operator-= (const Matrix3< T > &b)

Matrix3 &	operator*= (T b)

Matrix3 &	operator/= (T b)

Static Public Member Functions
static constexpr Matrix3	zero () noexcept

static constexpr Matrix3	identity () noexcept

static constexpr Matrix3	scale (T s) noexcept
	returns a matrix that scales uniformly

static constexpr Matrix3	scale (T sx, T sy, T sz) noexcept
	returns a matrix that has its own scale along each axis

static constexpr Matrix3	scale (const Vector3< T > &s) noexcept

static constexpr Matrix3	rotation (const Vector3< T > &axis, T angle) noexcept
	creates matrix representing rotation around given axis on given angle

static constexpr Matrix3	rotation (const Vector3< T > &from, const Vector3< T > &to) noexcept
	creates matrix representing rotation that after application to (from) makes (to) vector

static constexpr Matrix3	rotationFromEuler (const Vector3< T > &eulerAngles) noexcept

static constexpr Matrix3	approximateLinearRotationMatrixFromEuler (const Vector3< T > &eulerAngles) noexcept
	returns linear by angles approximation of the rotation matrix, which is close to true rotation matrix for small angles

static constexpr Matrix3	fromRows (const Vector3< T > &x, const Vector3< T > &y, const Vector3< T > &z) noexcept
	constructs a matrix from its 3 rows

static constexpr Matrix3	fromColumns (const Vector3< T > &x, const Vector3< T > &y, const Vector3< T > &z) noexcept

Public Attributes
Vector3< T >	x { 1, 0, 0 }
	rows, identity matrix by default

Vector3< T >	y { 0, 1, 0 }

Vector3< T >	z { 0, 0, 1 }

Related Symbols
(Note that these are not member symbols.)

template<typename T >
Vector3< T >	operator* (const Matrix3< T > &a, const Vector3< T > &b)
	x = a * b

template<typename T >
T	dot (const Matrix3< T > &a, const Matrix3< T > &b)
	double-dot product: x = a : b

template<typename T >
Matrix3< T >	operator* (const Matrix3< T > &a, const Matrix3< T > &b)
	product of two matrices

template<typename T >
Matrix3< T >	outer (const Vector3< T > &a, const Vector3< T > &b)
	x = a * b^T

Detailed Description

template<typename T>
struct MR::Matrix3< T >

arbitrary 3x3 matrix

Member Typedef Documentation

◆ ValueType

template<typename T >

using MR::Matrix3< T >::ValueType = T

◆ VectorType

template<typename T >

using MR::Matrix3< T >::VectorType = Vector3<T>

Constructor & Destructor Documentation

◆ Matrix3() [1/3]

template<typename T >

constexpr MR::Matrix3< T >::Matrix3 ( )

constexprdefaultnoexcept

◆ Matrix3() [2/3]

template<typename T >

constexpr MR::Matrix3< T >::Matrix3	(	const Vector3< T > &	x,
		const Vector3< T > &	y,
		const Vector3< T > &	z )

inlineconstexpr

initializes matrix from its 3 rows

◆ Matrix3() [3/3]

template<typename T >

template<typename U >

constexpr MR::Matrix3< T >::Matrix3 ( const Matrix3< U > & m )

inlineexplicitconstexpr

Member Function Documentation

◆ approximateLinearRotationMatrixFromEuler()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::approximateLinearRotationMatrixFromEuler ( const Vector3< T > & eulerAngles )

staticconstexprnoexcept

returns linear by angles approximation of the rotation matrix, which is close to true rotation matrix for small angles

◆ col()

template<typename T >

constexpr Vector3< T > MR::Matrix3< T >::col ( int i ) const

inlineconstexprnoexcept

column access

◆ det()

template<typename T >

constexpr T MR::Matrix3< T >::det ( ) const

constexprnoexcept

computes determinant of the matrix

◆ fromColumns()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::fromColumns	(	const Vector3< T > &	x,
		const Vector3< T > &	y,
		const Vector3< T > &	z )

inlinestaticconstexprnoexcept

constructs a matrix from its 3 columns; use this method to get the matrix that transforms basis vectors ( plusX, plusY, plusZ ) into vectors ( x, y, z ) respectively

◆ fromRows()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::fromRows	(	const Vector3< T > &	x,
		const Vector3< T > &	y,
		const Vector3< T > &	z )

inlinestaticconstexprnoexcept

constructs a matrix from its 3 rows

◆ identity()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::identity ( )

inlinestaticconstexprnoexcept

◆ inverse()

template<typename T >

constexpr Matrix3< T > MR::Matrix3< T >::inverse ( ) const

constexprnoexcept

computes inverse matrix

◆ norm()

template<typename T >

constexpr T MR::Matrix3< T >::norm ( ) const

inlineconstexprnoexcept

◆ normSq()

template<typename T >

constexpr T MR::Matrix3< T >::normSq ( ) const

inlineconstexprnoexcept

compute sum of squared matrix elements

◆ operator*=()

template<typename T >

Matrix3 & MR::Matrix3< T >::operator*= ( T b )

inline

◆ operator+=()

template<typename T >

Matrix3 & MR::Matrix3< T >::operator+= ( const Matrix3< T > & b )

inline

◆ operator-=()

template<typename T >

Matrix3 & MR::Matrix3< T >::operator-= ( const Matrix3< T > & b )

inline

◆ operator/=()

template<typename T >

Matrix3 & MR::Matrix3< T >::operator/= ( T b )

inline

◆ operator[]() [1/2]

template<typename T >

constexpr const Vector3< T > & MR::Matrix3< T >::operator[] ( int row ) const

inlineconstexprnoexcept

row access

◆ operator[]() [2/2]

template<typename T >

constexpr Vector3< T > & MR::Matrix3< T >::operator[] ( int row )

inlineconstexprnoexcept

◆ qr()

template<typename T >

QR MR::Matrix3< T >::qr ( ) const

noexcept

decompose this matrix on the product Q*R, where Q is orthogonal and R is upper triangular

◆ rotation() [1/2]

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::rotation	(	const Vector3< T > &	axis,
		T	angle )

staticconstexprnoexcept

creates matrix representing rotation around given axis on given angle

◆ rotation() [2/2]

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::rotation	(	const Vector3< T > &	from,
		const Vector3< T > &	to )

staticconstexprnoexcept

creates matrix representing rotation that after application to (from) makes (to) vector

◆ rotationFromEuler()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::rotationFromEuler ( const Vector3< T > & eulerAngles )

staticconstexprnoexcept

creates matrix representing rotation from 3 Euler angles: R=R(z)*R(y)*R(x) see more https://en.wikipedia.org/wiki/Euler_angles#Conventions_by_intrinsic_rotations

◆ scale() [1/3]

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::scale ( const Vector3< T > & s )

inlinestaticconstexprnoexcept

◆ scale() [2/3]

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::scale ( T s )

inlinestaticconstexprnoexcept

returns a matrix that scales uniformly

◆ scale() [3/3]

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::scale	(	T	sx,
		T	sy,
		T	sz )

inlinestaticconstexprnoexcept

returns a matrix that has its own scale along each axis

◆ toEulerAngles()

template<typename T >

constexpr Vector3< T > MR::Matrix3< T >::toEulerAngles ( ) const

constexprnoexcept

returns 3 Euler angles, assuming this is a rotation matrix composed as follows: R=R(z)*R(y)*R(x)

◆ trace()

template<typename T >

constexpr T MR::Matrix3< T >::trace ( ) const

inlineconstexprnoexcept

computes trace of the matrix

◆ transposed()

template<typename T >

constexpr Matrix3< T > MR::Matrix3< T >::transposed ( ) const

constexprnoexcept

computes transposed matrix

◆ zero()

template<typename T >

static constexpr Matrix3 MR::Matrix3< T >::zero ( )

inlinestaticconstexprnoexcept

Friends And Related Symbol Documentation

◆ dot()

template<typename T >

T dot	(	const Matrix3< T > &	a,
		const Matrix3< T > &	b )

◆ operator*() [1/2]

template<typename T >

Matrix3< T > operator*	(	const Matrix3< T > &	a,
		const Matrix3< T > &	b )

◆ operator*() [2/2]

template<typename T >

Vector3< T > operator*	(	const Matrix3< T > &	a,
		const Vector3< T > &	b )

◆ outer()

template<typename T >

Matrix3< T > outer	(	const Vector3< T > &	a,
		const Vector3< T > &	b )

Member Data Documentation

◆ x

template<typename T >

Vector3<T> MR::Matrix3< T >::x { 1, 0, 0 }

rows, identity matrix by default

◆ y

template<typename T >

Vector3<T> MR::Matrix3< T >::y { 0, 1, 0 }

◆ z

template<typename T >

Vector3<T> MR::Matrix3< T >::z { 0, 0, 1 }

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

MRMatrix3.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Related Symbols

Detailed Description

Member Typedef Documentation

◆ ValueType

◆ VectorType

Constructor & Destructor Documentation

◆ Matrix3() [1/3]

◆ Matrix3() [2/3]

◆ Matrix3() [3/3]

Member Function Documentation

◆ approximateLinearRotationMatrixFromEuler()

◆ col()

◆ det()

◆ fromColumns()

◆ fromRows()

◆ identity()

◆ inverse()

◆ norm()

◆ normSq()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ qr()

◆ rotation() [1/2]

◆ rotation() [2/2]

◆ rotationFromEuler()

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ toEulerAngles()

◆ trace()

◆ transposed()

◆ zero()

Friends And Related Symbol Documentation

◆ dot()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ outer()

Member Data Documentation

◆ x

◆ y

◆ z