Vector 3 Sapphire-Maths class. More...

#include <Vector3.hpp>

Public Types
using	Type = T
	Type of the Vector.

Public Member Functions
	Vec3 ()=default
	Default constructor.

constexpr	Vec3 (T _x, T _y, T _z) noexcept
	Value constructor.

constexpr	Vec3 (T _scale) noexcept
	Scale Value constructor.

	Vec3 (Vec3 &&)=default
	Default move constructor.

	Vec3 (const Vec3 &)=default
	Default copy constructor.

template<typename TIn >
constexpr	Vec3 (const Vec3< TIn > &_other) noexcept
	Value constructor from another Vec3 type.

template<typename TIn >
constexpr	Vec3 (const Vec2< TIn > &_other, T _z=T(0)) noexcept
	Value constructor from Vec2.

template<typename TIn >
constexpr	Vec3 (const Vec4< TIn > &_other) noexcept
	Value constructor from Vec4.

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

constexpr bool	Equals (const Vec3 &_other, T _epsilon=std::numeric_limits< T >::epsilon()) const noexcept
	Compare 2 vector.

constexpr bool	operator== (const Vec3 &_rhs) const noexcept
	Compare 2 vector equality.

constexpr bool	operator!= (const Vec3 &_rhs) const noexcept
	Compare 2 vector inequality.

T *	Data () noexcept
	Getter of vector data

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

T &	operator[] (uint32_t _index)
	Access operator by index: x, y, z using 0, 1, 2.

const T &	operator[] (uint32_t _index) const
	Const Access operator by index: x, y, z using 0, 1, 2.

constexpr T	Length () const
	Getter of the length of this vector.

constexpr T	SqrLength () const noexcept
	Getter of the Squared Length of this vector.

Vec3 &	Normalize ()
	Normalize this vector.

Vec3	GetNormalized () const
	Normalize this vector.

constexpr bool	IsNormalized () const noexcept
	Whether this vector is normalized.

Vec3	Reflect (const Vec3 &_normal, float _elasticity=1.0f) const noexcept
	Reflect this vector over the normal.

Vec3	ProjectOnTo (const Vec3 &_other) const noexcept
	Project this vector onto an other vector.

Vec3	ProjectOnToNormal (const Vec3 &_normal) const noexcept
	Project this vector onto s normal.

Vec3 &	operator= (Vec3 &&)=default
	Default assignment move operator.

Vec3 &	operator= (const Vec3 &)=default
	Default assignment copy operator.

constexpr Vec3	operator- () const noexcept
	Getter of the opposite signed vector.

Vec3	operator* (T _scale) const noexcept
	Scale each vector axis by _scale.

Vec3	operator/ (T _scale) const
	Inverse Scale each vector axis by _scale.

constexpr Vec3	operator+ (const Vec3 &_rhs) const noexcept
	Add term by term vector values.

constexpr Vec3	operator- (const Vec3 &_rhs) const noexcept
	Subtract term by term vector values.

constexpr Vec3	operator* (const Vec3 &_rhs) const noexcept
	Multiply term by term vector values.

Vec3	operator/ (const Vec3 &_rhs) const
	Divide term by term vector values.

constexpr T	operator\| (const Vec3 &_rhs) const noexcept
	Compute the Dot product between this and _rhs.

constexpr Vec3	operator^ (const Vec3 &_rhs) const noexcept
	Compute the Cross product between this and _rhs.

Vec3 &	operator*= (T _scale) noexcept
	Scale each vector axis by _scale.

Vec3 &	operator/= (T _scale)
	Inverse Scale each vector axis by _scale.

Vec3 &	operator+= (const Vec3 &_rhs) noexcept
	Add term by term vector values.

Vec3 &	operator-= (const Vec3 &_rhs) noexcept
	Substract term by term vector values.

Vec3	operator*= (const Vec3 &_rhs) noexcept
	Multiply term by term vector values.

Vec3	operator/= (const Vec3 &_rhs)
	Divide term by term vector values.

Static Public Member Functions
static constexpr T	Dot (const Vec3 &_lhs, const Vec3 &_rhs) noexcept
	Compute the Dot product between _lhs and _rhs.

static constexpr Vec3< T >	Cross (const Vec3 &_lhs, const Vec3 &_rhs) noexcept
	Compute the Cross product between _lhs and _rhs.

static Deg< T >	Angle (const Vec3 &_start, const Vec3 &_end, const Vec3 &_normal=Vec3::Up) noexcept
	Compute the Signed Angle between _lhs and _rhs.

static Deg< T >	AngleUnsigned (const Vec3 &_start, const Vec3 &_end) noexcept
	Compute the Unsigned Angle between _lhs and _rhs.

static constexpr T	Dist (const Vec3 &_start, const Vec3 &_end)
	Compute the Distance between _lhs and _rhs.

static constexpr T	SqrDist (const Vec3 &_start, const Vec3 &_end) noexcept
	Compute the Squared Distance between _lhs and _rhs.

static constexpr Vec3	Dir (const Vec3 &_start, const Vec3 &_end) noexcept
	Compute the Non-Normalized Direction from _lhs and _rhs.

static constexpr Vec3	DirN (const Vec3 &_start, const Vec3 &_end)
	Compute the Normalized Direction from _start to _end.

static Vec3	Lerp (const Vec3 &_start, const Vec3 &_end, float _alpha) noexcept
	Clamped Lerp from _start to _end at _alpha.

static Vec3	LerpUnclamped (const Vec3 &_start, const Vec3 &_end, float _alpha) noexcept
	Unclamped Lerp from _start to _end at _alpha.

static Vec3	SLerp (const Vec3 &_start, const Vec3 &_end, float _alpha) noexcept
	Clamped SLerp from _start to _end at _alpha.

static Vec3	SLerpUnclamped (const Vec3 &_start, const Vec3 &_end, float _alpha) noexcept
	Unclamped SLerp from _start to _end at _alpha.

Public Attributes
T	x = T()
	Vector's X component (axis value).

T	y = T()
	Vector's Y component (axis value).

T	z = T()
	Vector's Z component (axis value).

Static Public Attributes
static const Vec3	Zero
	Zero vector constant {0, 0, 0}.

static const Vec3	One
	One vector constant {1, 1, 1}.

static const Vec3	Right
	Right vector constant {1, 0, 0}.

static const Vec3	Left
	Left vector constant {-1, 0, 0}.

static const Vec3	Up
	Up vector constant {0, 1, 0}.

static const Vec3	Down
	Down vector constant {0, -1, 0}.

static const Vec3	Forward
	Down vector constant {0, 0, 1}.

static const Vec3	Backward
	Down vector constant {0, 0, -1}.

Detailed Description

template<typename T>
struct SA::Vec3< T >

Vector 3 Sapphire-Maths class.

Template Parameters

T	Type of the vector.

Constructor & Destructor Documentation

◆ Vec3() [1/5]

template<typename T >

constexpr SA::Vec3< T >::Vec3	(	T	_x,
		T	_y,
		T	_z )

constexprnoexcept

Value constructor.

Parameters

[in]	_x	X axis value.
[in]	_y	Y axis value.
[in]	_z	Z axis value.

◆ Vec3() [2/5]

template<typename T >

constexpr SA::Vec3< T >::Vec3 ( T _scale )

constexprnoexcept

Scale Value constructor.

Parameters

[in] _scale Axis value to apply on all axis.

◆ Vec3() [3/5]

template<typename T >

template<typename TIn >

constexpr SA::Vec3< T >::Vec3 ( const Vec3< TIn > & _other )

constexprnoexcept

Value constructor from another Vec3 type.

Template Parameters

TIn	Type of the input Vec3.

Parameters

[in] _other Vec3 to construct from.

◆ Vec3() [4/5]

template<typename T >

template<typename TIn >

constexpr SA::Vec3< T >::Vec3	(	const Vec2< TIn > &	_other,
		T	_z = T(0) )

constexprnoexcept

Value constructor from Vec2.

Template Parameters

TIn	Type of the in Vec2.

Parameters

[in]	_other	Vec2 to construct from.
[in]	_z	Z axis value.

◆ Vec3() [5/5]

template<typename T >

template<typename TIn >

constexpr SA::Vec3< T >::Vec3 ( const Vec4< TIn > & _other )

constexprnoexcept

Value constructor from Vec4.

Template Parameters

TIn	Type of the in Vec4.

Parameters

[in] _other Vec4 to construct from.

Member Function Documentation

◆ Angle()

template<typename T >

static Deg< T > SA::Vec3< T >::Angle	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end,
		const Vec3< T > &	_normal = Vec3< T >::Up )

staticnoexcept

Compute the Signed Angle between _lhs and _rhs.

Parameters

[in]	_start	Left hand side operand to compute angle with.
[in]	_end	Right hand side operand to compute angle with.
[in]	_normal	Normal of the plan between _lhs and _rhs, used to determine angle's sign.

Returns: Signed Angle between _start and _end.

◆ AngleUnsigned()

template<typename T >

static Deg< T > SA::Vec3< T >::AngleUnsigned	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end )

staticnoexcept

Compute the Unsigned Angle between _lhs and _rhs.

Parameters

[in]	_start	Left hand side operand to compute angle with.
[in]	_end	Right hand side operand to compute angle with.

Returns: Unsigned Angle between _start and _end.

◆ Cross()

template<typename T >

static constexpr Vec3< T > SA::Vec3< T >::Cross	(	const Vec3< T > &	_lhs,
		const Vec3< T > &	_rhs )

staticconstexprnoexcept

Compute the Cross product between _lhs and _rhs.

Parameters

[in]	_lhs	Left hand side operand to compute cross product with.
[in]	_rhs	Right hand side operand to compute cross product with.

Returns: Cross product between _lhs and _rhs.

◆ Data() [1/2]

template<typename T >

const T * SA::Vec3< T >::Data ( ) const

noexcept

Const Getter of vector data

Returns: this vector as a const T*.

◆ Data() [2/2]

template<typename T >

T * SA::Vec3< T >::Data ( )

noexcept

Getter of vector data

Returns: this vector as a T*.

◆ Dir()

template<typename T >

static constexpr Vec3 SA::Vec3< T >::Dir	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end )

staticconstexprnoexcept

Compute the Non-Normalized Direction from _lhs and _rhs.

Direction get not normalized. Use DirN instead.

Parameters

[in]	_start	Left hand side operand to compute direction from.
[in]	_end	Right hand side operand to compute direction to

Returns: Non-Normalized Direction from _start and _end.

◆ DirN()

template<typename T >

static constexpr Vec3 SA::Vec3< T >::DirN	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end )

staticconstexpr

Compute the Normalized Direction from _start to _end.

Parameters

[in]	_start	Starting point to compute direction from.
[in]	_end	ending point to compute direction to.

Returns: Normalized Direction from _start to _end.

◆ Dist()

template<typename T >

static constexpr T SA::Vec3< T >::Dist	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end )

staticconstexpr

Compute the Distance between _lhs and _rhs.

Parameters

[in]	_start	Left hand side operand to compute distance with.
[in]	_end	Right hand side operand to compute distance with.

Returns: Distance between _start and _end.

◆ Dot()

template<typename T >

static constexpr T SA::Vec3< T >::Dot	(	const Vec3< T > &	_lhs,
		const Vec3< T > &	_rhs )

staticconstexprnoexcept

Compute the Dot product between _lhs and _rhs.

Parameters

[in]	_lhs	Left hand side operand to compute dot product with.
[in]	_rhs	Right hand side operand to compute dot product with.

Returns: Dot product between _lhs and _rhs.

◆ Equals()

template<typename T >

constexpr bool SA::Vec3< T >::Equals	(	const Vec3< T > &	_other,
		T	_epsilon = std::numeric_limits< T >::epsilon() ) const

constexprnoexcept

Compare 2 vector.

Parameters

[in]	_other	Other vector to compare to.
[in]	_epsilon	Epsilon value for threshold comparison.

Returns: Whether this and _other are equal.

◆ GetNormalized()

template<typename T >

Vec3 SA::Vec3< T >::GetNormalized ( ) const

Normalize this vector.

Returns: new normalized vector.

◆ IsNormalized()

template<typename T >

constexpr bool SA::Vec3< T >::IsNormalized ( ) const

constexprnoexcept

Whether this vector is normalized.

Returns: True if this vector is normalized, otherwise false.

◆ IsZero()

template<typename T >

constexpr bool SA::Vec3< T >::IsZero ( ) const

constexprnoexcept

Whether this vector is a zero vector.

Returns: True if this is a zero vector.

◆ Length()

template<typename T >

constexpr T SA::Vec3< T >::Length ( ) const

constexpr

Getter of the length of this vector.

Returns: Length of this vector.

◆ Lerp()

template<typename T >

static Vec3 SA::Vec3< T >::Lerp	(	const Vec3< T > &	_start,
		const Vec3< T > &	_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 >

static Vec3 SA::Vec3< T >::LerpUnclamped	(	const Vec3< T > &	_start,
		const Vec3< T > &	_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.

◆ Normalize()

template<typename T >

Vec3 & SA::Vec3< T >::Normalize ( )

Normalize this vector.

Returns: self vector normalized.

◆ operator!=()

template<typename T >

constexpr bool SA::Vec3< T >::operator!= ( const Vec3< T > & _rhs ) const

constexprnoexcept

Compare 2 vector inequality.

Parameters

[in] _rhs Other vector to compare to.

Returns: Whether this and _rhs are non-equal.

◆ operator*() [1/2]

template<typename T >

constexpr Vec3 SA::Vec3< T >::operator* ( const Vec3< T > & _rhs ) const

constexprnoexcept

Multiply term by term vector values.

Parameters

[in] _rhs Vector to multiply.

Returns: new vector result.

◆ operator*() [2/2]

template<typename T >

Vec3 SA::Vec3< T >::operator* ( T _scale ) const

noexcept

Scale each vector axis by _scale.

Parameters

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

Returns: new vector scaled.

◆ operator*=() [1/2]

template<typename T >

Vec3 SA::Vec3< T >::operator*= ( const Vec3< T > & _rhs )

noexcept

Multiply term by term vector values.

Parameters

[in] _rhs Vector to multiply.

Returns: self vector result.

◆ operator*=() [2/2]

template<typename T >

Vec3 & SA::Vec3< T >::operator*= ( T _scale )

noexcept

Scale each vector axis by _scale.

Parameters

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

Returns: self vector scaled.

◆ operator+()

template<typename T >

constexpr Vec3 SA::Vec3< T >::operator+ ( const Vec3< T > & _rhs ) const

constexprnoexcept

Add term by term vector values.

Parameters

[in] _rhs Vector to add.

Returns: new vector result.

◆ operator+=()

template<typename T >

Vec3 & SA::Vec3< T >::operator+= ( const Vec3< T > & _rhs )

noexcept

Add term by term vector values.

Parameters

[in] _rhs Vector to add.

Returns: self vector result.

◆ operator-() [1/2]

template<typename T >

constexpr Vec3 SA::Vec3< T >::operator- ( ) const

constexprnoexcept

Getter of the opposite signed vector.

Returns: new opposite signed vector.

◆ operator-() [2/2]

template<typename T >

constexpr Vec3 SA::Vec3< T >::operator- ( const Vec3< T > & _rhs ) const

constexprnoexcept

Subtract term by term vector values.

Parameters

[in] _rhs Vector to substract.

Returns: new vector result.

◆ operator-=()

template<typename T >

Vec3 & SA::Vec3< T >::operator-= ( const Vec3< T > & _rhs )

noexcept

Substract term by term vector values.

Parameters

[in] _rhs Vector to substract.

Returns: self vector result.

◆ operator/() [1/2]

template<typename T >

Vec3 SA::Vec3< T >::operator/ ( const Vec3< T > & _rhs ) const

Divide term by term vector values.

Parameters

[in] _rhs Vector to divide.

Returns: new vector result.

◆ operator/() [2/2]

template<typename T >

Vec3 SA::Vec3< T >::operator/ ( T _scale ) const

Inverse Scale each vector axis by _scale.

Parameters

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

Returns: new vector inverse-scaled.

◆ operator/=() [1/2]

template<typename T >

Vec3 SA::Vec3< T >::operator/= ( const Vec3< T > & _rhs )

Divide term by term vector values.

Parameters

[in] _rhs Vector to divide.

Returns: self vector result.

◆ operator/=() [2/2]

template<typename T >

Vec3 & SA::Vec3< T >::operator/= ( T _scale )

Inverse Scale each vector axis by _scale.

Parameters

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

Returns: self vector inverse-scaled.

◆ operator=() [1/2]

template<typename T >

Vec3 & SA::Vec3< T >::operator= ( const Vec3< T > & )

default

Default assignment copy operator.

Returns: self vector assigned.

◆ operator=() [2/2]

template<typename T >

Vec3 & SA::Vec3< T >::operator= ( Vec3< T > && )

default

Default assignment move operator.

Returns: self vector assigned.

◆ operator==()

template<typename T >

constexpr bool SA::Vec3< T >::operator== ( const Vec3< T > & _rhs ) const

constexprnoexcept

Compare 2 vector equality.

Parameters

[in] _rhs Other vector to compare to.

Returns: Whether this and _rhs are equal.

◆ operator[]() [1/2]

template<typename T >

T & SA::Vec3< T >::operator[] ( uint32_t _index )

Access operator by index: x, y, z using 0, 1, 2.

Parameters

[in] _index Index to access.

Returns: T value at index.

◆ operator[]() [2/2]

template<typename T >

const T & SA::Vec3< T >::operator[] ( uint32_t _index ) const

Const Access operator by index: x, y, z using 0, 1, 2.

Parameters

[in] _index Index to access.

Returns: T value at index.

◆ operator^()

template<typename T >

constexpr Vec3 SA::Vec3< T >::operator^ ( const Vec3< T > & _rhs ) const

constexprnoexcept

Compute the Cross product between this and _rhs.

Parameters

[in] _rhs Right hand side operand vector to compute cross product with.

Returns: Cross product between this vector and _other.

◆ operator|()

template<typename T >

constexpr T SA::Vec3< T >::operator| ( const Vec3< T > & _rhs ) const

constexprnoexcept

Compute the Dot product between this and _rhs.

Parameters

[in] _rhs Right hand side operand vector to compute dot product with.

Returns: Dot product between this vector and _other.

◆ ProjectOnTo()

template<typename T >

Vec3 SA::Vec3< T >::ProjectOnTo ( const Vec3< T > & _other ) const

noexcept

Project this vector onto an other vector.

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

Parameters

[in] _other Vector used for projection.

Returns: new vector projected.

◆ ProjectOnToNormal()

template<typename T >

Vec3 SA::Vec3< T >::ProjectOnToNormal ( const Vec3< T > & _normal ) const

noexcept

Project this vector onto s normal.

Assume _normal is normalized. Use GetProjectOnTo() for non normalized vector. Reference: https://en.wikipedia.org/wiki/Vector_projection

Parameters

[in] _normal Normal used for projection.

Returns: new vector projected.

◆ Reflect()

template<typename T >

Vec3 SA::Vec3< T >::Reflect	(	const Vec3< T > &	_normal,
		float	_elasticity = 1.0f ) const

noexcept

Reflect this vector over the normal.

Parameters

[in]	_normal	Normal used for reflection.
[in]	_elasticity	Elasticity reflection coefficient (use 1.0f for full reflection).

Returns: new vector reflected.

◆ SLerp()

template<typename T >

static Vec3 SA::Vec3< T >::SLerp	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end,
		float	_alpha )

staticnoexcept

Clamped SLerp from _start to _end at _alpha.

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

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.

◆ SLerpUnclamped()

template<typename T >

static Vec3 SA::Vec3< T >::SLerpUnclamped	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end,
		float	_alpha )

staticnoexcept

Unclamped SLerp from _start to _end at _alpha.

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

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.

◆ SqrDist()

template<typename T >

static constexpr T SA::Vec3< T >::SqrDist	(	const Vec3< T > &	_start,
		const Vec3< T > &	_end )

staticconstexprnoexcept

Compute the Squared Distance between _lhs and _rhs.

Parameters

[in]	_start	Left hand side operand to compute squared distance with.
[in]	_end	Right hand side operand to compute squared distance with.

Returns: Squared Distance between _start and _end.

◆ SqrLength()

template<typename T >

constexpr T SA::Vec3< T >::SqrLength ( ) const

constexprnoexcept

Getter of the Squared Length of this vector.

Returns: Squared Length of this vector.

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

Include/SA/Maths/Matrix/Matrix3.hpp
Include/SA/Maths/Space/Vector3.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Vec3() [1/5]

◆ Vec3() [2/5]

◆ Vec3() [3/5]

◆ Vec3() [4/5]

◆ Vec3() [5/5]

Member Function Documentation

◆ Angle()

◆ AngleUnsigned()

◆ Cross()

◆ Data() [1/2]

◆ Data() [2/2]

◆ Dir()

◆ DirN()

◆ Dist()

◆ Dot()

◆ Equals()

◆ GetNormalized()

◆ IsNormalized()

◆ IsZero()

◆ Length()

◆ Lerp()

◆ LerpUnclamped()

◆ Normalize()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ 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=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ operator^()

◆ operator|()

◆ ProjectOnTo()

◆ ProjectOnToNormal()

◆ Reflect()

◆ SLerp()

◆ SLerpUnclamped()

◆ SqrDist()

◆ SqrLength()