Matrix 4x4 Sapphire-Maths class. More...

#include <Matrix4.hpp>

Inheritance diagram for SA::Mat4< T, major >:

Public Member Functions
template<typename TIn , MatrixMajor majorIn>
constexpr	Mat4 (const Mat4< TIn, majorIn > &_other) noexcept
	Value constructor from another Mat4 type.

template<typename TIn , MatrixMajor majorIn>
constexpr	Mat4 (const Mat3< TIn, majorIn > &_other) noexcept
	Value constructor from another Mat3 type.

constexpr bool	IsZero () const noexcept
	Whether this matrix is a zero matrix.

constexpr bool	IsIdentity () const noexcept
	Whether this matrix is an identity matrix.

constexpr bool	Equals (const Mat4 &_other, T _threshold=std::numeric_limits< T >::epsilon()) const noexcept
	Compare 2 Matrix.

constexpr bool	operator== (const Mat4 &_rhs) const noexcept
	Compare 2 matrix equality.

constexpr bool	operator!= (const Mat4 &_rhs) const noexcept
	Compare 2 matrix inequality.

T *	Data () noexcept
	Getter of matrix data

const T *	Data () const noexcept
	Const Getter of matrix data

T &	At (uint32_t _index)
	Getter of Value at index.

const T &	At (uint32_t _index) const
	Const Getter of Value at index.

T &	At (uint32_t _x, uint32_t _y)
	Getter of Value at (x;y).

const T &	At (uint32_t _x, uint32_t _y) const
	Const Getter of Value at (x;y).

T &	operator[] (uint32_t _index)
	Access operator by index.

const T &	operator[] (uint32_t _index) const
	Const Access operator by index.

Mat4 &	Transpose () noexcept
	Transpose this matrix.

constexpr Mat4	GetTransposed () const noexcept
	Transpose this matrix.

T	Determinant () const noexcept
	Compute the determinant of the matrix.

Mat4 &	Inverse ()
	Inverse this matrix.

Mat4	GetInversed () const
	Inverse this matrix.

template<typename TIn , MatrixMajor majorIn>
Mat4 &	operator= (const Mat4< TIn, majorIn > _rhs) noexcept
	Assignment operator from another Mat4 type.

constexpr Mat4	operator- () const noexcept
	Getter of the opposite signed matrix.

template<typename TIn >
Mat4	operator* (TIn _scale) const noexcept
	Scale each matrix component by _scale.

template<typename TIn >
Mat4	operator/ (TIn _scale) const
	Inverse Scale each matrix component by _scale.

Mat4	operator+ (const Mat4 &_rhs) const noexcept
	Add term by term matrix values.

Mat4	operator- (const Mat4 &_rhs) const noexcept
	Subtract term by term matrix values.

Mat4	operator* (const Mat4 &_rhs) const noexcept
	Multiply matrices.

Mat4	operator/ (const Mat4 &_rhs) const
	Inverse multiply matrices.

Vec3< T >	operator* (const Vec3< T > &_rhs) const noexcept
	transform this vector by this matrix.

Vec4< T >	operator* (const Vec4< T > &_rhs) const noexcept
	transform this vector by this matrix.

template<typename TIn >
Mat4 &	operator*= (TIn _scale) noexcept
	Scale each matrix component by _scale.

template<typename TIn >
Mat4 &	operator/= (TIn _scale)
	Inverse Scale each matrix component by _scale.

Mat4 &	operator+= (const Mat4 &_rhs) noexcept
	Add term by term matrix values.

Mat4 &	operator-= (const Mat4 &_rhs) noexcept
	Subtract term by term matrix values.

Mat4 &	operator*= (const Mat4 &_rhs) noexcept
	Multiply matrices.

Mat4 &	operator/= (const Mat4 &_rhs)
	Inverse multiply matrices.

Static Public Member Functions
static Mat4	Lerp (const Mat4 &_start, const Mat4 &_end, float _alpha) noexcept
	Clamped Lerp from _start to _end at _alpha.

static Mat4	LerpUnclamped (const Mat4 &_start, const Mat4 &_end, float _alpha) noexcept
	Unclamped Lerp from _start to _end at _alpha.

static Mat4	MakeTranslation (const Vec3< T > &_transl) noexcept
	Make translation matrix from vector3.

static Mat4	MakeRotation (const Quat< T > &_rot) noexcept
	Make rotation matrix from quaternion.

static Mat4	MakeScale (const Vec3< T > &_scale) noexcept
	Make scale matrix from vector3.

static Mat4	MakeLookAt (const Vec3< T > &_eye, const Vec3< T > &_target, const Vec3< T > &_up)
	Make LookAt matrix from center, target and up.

static Mat4	MakeInverseView (const Vec3< T > &_eye, const Vec3< T > &_forward, const Vec3< T > &_up)
	Make view matrix for camera.

static Mat4	MakePerspective (T _fov=T(90.0), T _aspect=T(1.0), T _near=T(0.35), T _far=T(10.0)) noexcept
	Make perspective matrix .

Static Public Attributes
static const Mat4	Zero
	Zero Mat4 constant.

static const Mat4	Identity
	Identity Mat4 constant.

Detailed Description

template<typename T, MatrixMajor major = MatrixMajor::Default>
struct SA::Mat4< T, major >

Matrix 4x4 Sapphire-Maths class.

must be align at 32 for intrinsics.

Template Parameters

T	Type of the matrix.

Constructor & Destructor Documentation

◆ Mat4() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn , MatrixMajor majorIn>

constexpr SA::Mat4< T, major >::Mat4 ( const Mat4< TIn, majorIn > & _other )

constexprnoexcept

Value constructor from another Mat4 type.

Template Parameters

TIn	Type of the input Mat4.
majorIn	Major of the input Mat4.

Parameters

[in] _other Mat4 to construct from.

◆ Mat4() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn , MatrixMajor majorIn>

constexpr SA::Mat4< T, major >::Mat4 ( const Mat3< TIn, majorIn > & _other )

constexprnoexcept

Value constructor from another Mat3 type.

Template Parameters

TIn	Type of the input Mat3.
majorIn	Major of the input Mat4.

Parameters

[in] _other Mat3 to construct from.

Member Function Documentation

◆ At() [1/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

T & SA::Mat4< T, major >::At ( uint32_t _index )

Getter of Value at index.

Parameters

[in] _index Index to access.

Returns: element at index.

◆ At() [2/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

const T & SA::Mat4< T, major >::At ( uint32_t _index ) const

Const Getter of Value at index.

Parameters

[in] _index Index to access.

Returns: element at index.

◆ At() [3/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

T & SA::Mat4< T, major >::At	(	uint32_t	_x,
		uint32_t	_y )

Getter of Value at (x;y).

Parameters

[in]	_x	row index.
[in]	_y	column index.

Returns: element at index.

◆ At() [4/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

const T & SA::Mat4< T, major >::At	(	uint32_t	_x,
		uint32_t	_y ) const

Const Getter of Value at (x;y).

Parameters

[in]	_x	row index.
[in]	_y	column index.

Returns: element at index.

◆ Data() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

const T * SA::Mat4< T, major >::Data ( ) const

noexcept

Const Getter of matrix data

Returns: this matrix as a const T*.

◆ Data() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

T * SA::Mat4< T, major >::Data ( )

noexcept

Getter of matrix data

Returns: this matrix as a T*.

◆ Determinant()

template<typename T , MatrixMajor major = MatrixMajor::Default>

T SA::Mat4< T, major >::Determinant ( ) const

noexcept

Compute the determinant of the matrix.

Returns: Determinant of this matrix.

◆ Equals()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr bool SA::Mat4< T, major >::Equals	(	const Mat4< T, major > &	_other,
		T	_threshold = std::numeric_limits< T >::epsilon() ) const

constexprnoexcept

Compare 2 Matrix.

Parameters

[in]	_other	Other matrix to compare to.
[in]	_threshold	Allowed threshold to accept equality.

Returns: Whether this and _other are equal.

◆ GetInversed()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 SA::Mat4< T, major >::GetInversed ( ) const

Inverse this matrix.

Returns: new inversed matrix.

◆ GetTransposed()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr Mat4 SA::Mat4< T, major >::GetTransposed ( ) const

constexprnoexcept

Transpose this matrix.

Returns: new transposed matrix.

◆ Inverse()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::Inverse ( )

Inverse this matrix.

Returns: self inversed matrix.

◆ IsIdentity()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr bool SA::Mat4< T, major >::IsIdentity ( ) const

constexprnoexcept

Whether this matrix is an identity matrix.

Returns: True if this is an identity matrix.

◆ IsZero()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr bool SA::Mat4< T, major >::IsZero ( ) const

constexprnoexcept

Whether this matrix is a zero matrix.

Returns: True if this is a zero matrix.

◆ Lerp()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::Lerp	(	const Mat4< T, major > &	_start,
		const Mat4< T, major > &	_end,
		float	_alpha )

staticnoexcept

Clamped Lerp from _start to _end at _alpha.

Reference: https://en.wikipedia.org/wiki/Linear_interpolation

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ LerpUnclamped()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::LerpUnclamped	(	const Mat4< T, major > &	_start,
		const Mat4< T, major > &	_end,
		float	_alpha )

staticnoexcept

Unclamped Lerp from _start to _end at _alpha.

Reference: https://en.wikipedia.org/wiki/Linear_interpolation

Parameters

_start	Starting point of the lerp.
_end	Ending point of the lerp.
_alpha	Alpha of the lerp.

Returns: interpolation between _start and _end. return _start when _alpha == 0.0f and _end when _alpha == 1.0f.

◆ MakeInverseView()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakeInverseView	(	const Vec3< T > &	_eye,
		const Vec3< T > &	_forward,
		const Vec3< T > &	_up )

static

Make view matrix for camera.

Parameters

_eye	Camera's world position
_forward	Camera forward vector
_up	Camera's up vector.

Returns: Inverse View matrix.

Make inverse view matrix for camera.

Parameters

_eye	Camera's world position
_forward	Camera forward vector
_up	Camera's up vector.

Returns: Inverse View matrix.

◆ MakeLookAt()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakeLookAt	(	const Vec3< T > &	_eye,
		const Vec3< T > &	_target,
		const Vec3< T > &	_up )

static

Make LookAt matrix from center, target and up.

Parameters

[in]	_eye	Center (camera).
[in]	_target	Target to look at.
[in]	_up	Up vector (camera).

Returns: LookAt matrix.

◆ MakePerspective()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakePerspective	(	T	_fov = T(90.0),
		T	_aspect = T(1.0),
		T	_near = T(0.35),
		T	_far = T(10.0) )

staticnoexcept

Make perspective matrix .

Parameters

[in]	_fov	Perspective FOV.
[in]	_aspect	Aspect ratio (width/height).
[in]	_near	Near frustum.
[in]	_far	Far frustum.

Returns: perspective matrix.

◆ MakeRotation()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakeRotation ( const Quat< T > & _rot )

staticnoexcept

Make rotation matrix from quaternion.

Parameters

[in] _rot quaternion to use for rotation.

Returns: rotation matrix.

◆ MakeScale()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakeScale ( const Vec3< T > & _scale )

staticnoexcept

Make scale matrix from vector3.

Parameters

[in] _scale Vector for scaling.

Returns: scale matrix.

◆ MakeTranslation()

template<typename T , MatrixMajor major = MatrixMajor::Default>

static Mat4 SA::Mat4< T, major >::MakeTranslation ( const Vec3< T > & _transl )

staticnoexcept

Make translation matrix from vector3.

Parameters

[in] _transl Vector to translate

Returns: translation matrix.

◆ operator!=()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr bool SA::Mat4< T, major >::operator!= ( const Mat4< T, major > & _rhs ) const

constexprnoexcept

Compare 2 matrix inequality.

Parameters

[in] _rhs Other matrix to compare to.

Returns: Whether this and _rhs are non-equal.

◆ operator*() [1/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 SA::Mat4< T, major >::operator* ( const Mat4< T, major > & _rhs ) const

noexcept

Multiply matrices.

Parameters

[in] _rhs Matrix to multiply to.

Returns: new matrix result.

◆ operator*() [2/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Vec3< T > SA::Mat4< T, major >::operator* ( const Vec3< T > & _rhs ) const

noexcept

transform this vector by this matrix.

Ignore 4th row/column component.

Parameters

[in] _rhs Vector to transform.

Returns: Transformed vector.

◆ operator*() [3/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Vec4< T > SA::Mat4< T, major >::operator* ( const Vec4< T > & _rhs ) const

noexcept

transform this vector by this matrix.

Parameters

[in] _rhs Vector to transform.

Returns: Transformed vector.

◆ operator*() [4/4]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn >

Mat4 SA::Mat4< T, major >::operator* ( TIn _scale ) const

noexcept

Scale each matrix component by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Scale value to apply on all components.

Returns: new matrix scaled.

◆ operator*=() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::operator*= ( const Mat4< T, major > & _rhs )

noexcept

Multiply matrices.

Parameters

[in] _rhs Matrix to multiply to.

Returns: self matrix result.

◆ operator*=() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn >

Mat4 & SA::Mat4< T, major >::operator*= ( TIn _scale )

noexcept

Scale each matrix component by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Scale value to apply on all components.

Returns: self matrix scaled.

◆ operator+()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 SA::Mat4< T, major >::operator+ ( const Mat4< T, major > & _rhs ) const

noexcept

Add term by term matrix values.

Parameters

[in] _rhs Matrix to add.

Returns: new matrix result.

◆ operator+=()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::operator+= ( const Mat4< T, major > & _rhs )

noexcept

Add term by term matrix values.

Parameters

[in] _rhs Matrix to add.

Returns: self matrix result.

◆ operator-() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr Mat4 SA::Mat4< T, major >::operator- ( ) const

constexprnoexcept

Getter of the opposite signed matrix.

Returns: new opposite signed matrix.

◆ operator-() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 SA::Mat4< T, major >::operator- ( const Mat4< T, major > & _rhs ) const

noexcept

Subtract term by term matrix values.

Parameters

[in] _rhs Matrix to substract.

Returns: new matrix result.

◆ operator-=()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::operator-= ( const Mat4< T, major > & _rhs )

noexcept

Subtract term by term matrix values.

Parameters

[in] _rhs Matrix to substract.

Returns: self matrix result.

◆ operator/() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 SA::Mat4< T, major >::operator/ ( const Mat4< T, major > & _rhs ) const

Inverse multiply matrices.

Parameters

[in] _rhs Matrix to inverse multiply to.

Returns: new matrix result.

◆ operator/() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn >

Mat4 SA::Mat4< T, major >::operator/ ( TIn _scale ) const

Inverse Scale each matrix component by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Inverse scale value to apply on all components.

Returns: new matrix inverse-scaled.

◆ operator/=() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::operator/= ( const Mat4< T, major > & _rhs )

Inverse multiply matrices.

Parameters

[in] _rhs Matrix to inverse multiply to.

Returns: self matrix result.

◆ operator/=() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn >

Mat4 & SA::Mat4< T, major >::operator/= ( TIn _scale )

Inverse Scale each matrix component by _scale.

Template Parameters

TIn	Type of the input scale.

Parameters

[in] _scale Inverse scale value to apply on all components.

Returns: self matrix inverse-scaled.

◆ operator=()

template<typename T , MatrixMajor major = MatrixMajor::Default>

template<typename TIn , MatrixMajor majorIn>

Mat4 & SA::Mat4< T, major >::operator= ( const Mat4< TIn, majorIn > _rhs )

noexcept

Assignment operator from another Mat4 type.

Template Parameters

TIn	Type of the input Mat4.
majorIn	Major of the input Mat4.

Parameters

[in] _rhs Mat4 to assign from.

◆ operator==()

template<typename T , MatrixMajor major = MatrixMajor::Default>

constexpr bool SA::Mat4< T, major >::operator== ( const Mat4< T, major > & _rhs ) const

constexprnoexcept

Compare 2 matrix equality.

Parameters

[in] _rhs Other matrix to compare to.

Returns: Whether this and _rhs are equal.

◆ operator[]() [1/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

T & SA::Mat4< T, major >::operator[] ( uint32_t _index )

Access operator by index.

Parameters

[in] _index Index to access.

Returns: T value at index.

◆ operator[]() [2/2]

template<typename T , MatrixMajor major = MatrixMajor::Default>

const T & SA::Mat4< T, major >::operator[] ( uint32_t _index ) const

Const Access operator by index.

Parameters

[in] _index Index to access.

Returns: T value at index.

◆ Transpose()

template<typename T , MatrixMajor major = MatrixMajor::Default>

Mat4 & SA::Mat4< T, major >::Transpose ( )

noexcept

Transpose this matrix.

Returns: self transposed matrix.

Member Data Documentation

◆ Identity

template<typename T , MatrixMajor major = MatrixMajor::Default>

const Mat4 SA::Mat4< T, major >::Identity

static

Identity Mat4 constant.

{1, 0, 0, 0} {0, 1, 0, 0} {0, 0, 1, 0} {0, 0, 0, 1}

◆ Zero

template<typename T , MatrixMajor major = MatrixMajor::Default>

const Mat4 SA::Mat4< T, major >::Zero

static

Zero Mat4 constant.

{0, 0, 0, 0} {0, 0, 0, 0} {0, 0, 0, 0} {0, 0, 0, 0}

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

Include/SA/Maths/Matrix/Matrix3.hpp
Include/SA/Maths/Matrix/Matrix4.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Mat4() [1/2]

◆ Mat4() [2/2]

Member Function Documentation

◆ At() [1/4]

◆ At() [2/4]

◆ At() [3/4]

◆ At() [4/4]

◆ Data() [1/2]

◆ Data() [2/2]

◆ Determinant()

◆ Equals()

◆ GetInversed()

◆ GetTransposed()

◆ Inverse()

◆ IsIdentity()

◆ IsZero()

◆ Lerp()

◆ LerpUnclamped()

◆ MakeInverseView()

◆ MakeLookAt()

◆ MakePerspective()

◆ MakeRotation()

◆ MakeScale()

◆ MakeTranslation()

◆ operator!=()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ Transpose()

Member Data Documentation

◆ Identity

◆ Zero