Quaternion implementation supporting Gimbal-Lock free rotations. More...

#include <quaternion.hpp>

Collaboration diagram for jau::math::Quaternion< Value_type, >:

Public Types
typedef const value_type *	const_iterator

typedef const value_type *	const_pointer

typedef const value_type &	const_reference

typedef value_type *	iterator

typedef value_type *	pointer

typedef value_type &	reference

typedef Value_type	value_type

typedef Vector3F< value_type, std::is_floating_point_v< Value_type > >	Vec3

Public Member Functions
constexpr	Quaternion () noexcept

constexpr	Quaternion (const Quaternion &o) noexcept=default

constexpr	Quaternion (const value_type x, const value_type y, const value_type z, const value_type w) noexcept

constexpr	Quaternion (Quaternion &&o) noexcept=default

constexpr Quaternion &	conjugate () noexcept
	Conjugates this quaternion `[-x, -y, -z, w]`. More...

constexpr value_type	dot (const Quaternion &quat) const noexcept
	Returns the dot product of this quaternion with the given quaternion. More...

constexpr value_type	dot (value_type x, value_type y, value_type z, value_type w) const noexcept
	Returns the dot product of this quaternion with the given x,y,z and m_w components. More...

constexpr Quaternion &	invert () noexcept
	Invert the quaternion If rotational, will produce a the inverse rotation. More...

constexpr bool	isIdentity () const noexcept
	Returns `true` if this quaternion has identity. More...

constexpr_cxx26 value_type	magnitude () const noexcept
	Return the magnitude of this quaternion, i.e. More...

constexpr value_type	magnitudeSquared () const noexcept
	See `magnitude()` for special handling of `epsilon`, which is not applied here. More...

constexpr Quaternion &	normalize () noexcept
	Normalize a quaternion required if to be used as a rotational quaternion. More...

constexpr Quaternion &	operator*= (const Quaternion &rhs) noexcept
	Multiply this quaternion: this = this * rhs, returns this. More...

constexpr Quaternion &	operator*= (const value_type rhs) noexcept
	Scale this quaternion by a scalar: this = this * rhs, returns this. More...

constexpr Quaternion &	operator+= (const Quaternion &rhs) noexcept
	Add a quaternion: this = this + rhs, returns this. More...

constexpr Quaternion &	operator-= (const Quaternion &rhs) noexcept
	Subtract a quaternion: this = this - rhs, returns this. More...

constexpr Quaternion &	operator= (const Quaternion &) noexcept=default

constexpr Quaternion &	operator= (Quaternion &&) noexcept=default

constexpr bool	operator== (const Quaternion &o) const noexcept

constexpr_cxx26 Quaternion &	rotateByAngleNormalAxis (const value_type angle, const value_type axisX, const value_type axisY, const value_type axisZ) noexcept
	Rotate this quaternion by the given angle and axis. More...

constexpr_cxx26 Quaternion &	rotateByAngleNormalAxis (const value_type angle, const Vec3 &axis) noexcept
	Rotate this quaternion by the given angle and axis. More...

constexpr_cxx26 Quaternion &	rotateByAngleX (const value_type angle) noexcept
	Rotate this quaternion around X axis with the given angle in radians. More...

constexpr Quaternion &	rotateByAngleX (const value_type sin, const value_type cos) noexcept
	Rotate this quaternion around X axis with the given angle's sin + cos values. More...

constexpr Quaternion &	rotateByAngleY (const value_type sin, const value_type cos) noexcept
	Rotate this quaternion around Y axis with the given angle's sin + cos values. More...

constexpr_cxx26 Quaternion &	rotateByAngleY (value_type angle) noexcept
	Rotate this quaternion around Y axis with the given angle in radians. More...

constexpr Quaternion &	rotateByAngleZ (const value_type sin, const value_type cos) noexcept
	Rotate this quaternion around Y axis with the given angle's sin + cos values. More...

constexpr_cxx26 Quaternion &	rotateByAngleZ (value_type angle) noexcept
	Rotate this quaternion around Z axis with the given angle in radians. More...

constexpr_cxx26 Quaternion &	rotateByEuler (const value_type bankX, const value_type headingY, const value_type attitudeZ) noexcept
	Rotates this quaternion from the given Euler rotation angles in radians. More...

Quaternion &	rotateByEuler (const Vec3 &angradXYZ) noexcept
	Rotates this quaternion from the given Euler rotation array `angradXYZ` in radians. More...

Vec3	rotateVector (const Vec3 &in) noexcept

Vec3 &	rotateVector (const Vec3 &in, Vec3 &out) noexcept

constexpr Quaternion &	set (const value_type x, const value_type y, const value_type z, const value_type w) noexcept
	Set all values of this quaternion using the given components. More...

Quaternion &	setFromAngleAxis (const value_type angle, const Vec3 &vector) noexcept

constexpr_cxx26 Quaternion &	setFromAngleNormalAxis (const value_type angle, const Vec3 &vector) noexcept

constexpr Quaternion &	setFromAxes (const Vec3 &xAxis, const Vec3 &yAxis, const Vec3 &zAxis) noexcept
	Initializes this quaternion to represent a rotation formed by the given three orthogonal axes. More...

constexpr_cxx26 Quaternion &	setFromEuler (const value_type bankX, const value_type headingY, const value_type attitudeZ) noexcept
	Initializes this quaternion from the given Euler rotation angles in radians. More...

constexpr_cxx26 Quaternion &	setFromEuler (const Vec3 &angradXYZ) noexcept
	Initializes this quaternion from the given Euler rotation array `angradXYZ` in radians. More...

constexpr Quaternion &	setFromMat (const Mat4f &m) noexcept
	Compute the quaternion from a 3x3 column rotation matrix from mat4f instance. More...

constexpr Quaternion &	setFromMat (const value_type m00, const value_type m01, const value_type m02, const value_type m10, const value_type m11, const value_type m12, const value_type m20, const value_type m21, const value_type m22) noexcept
	Compute the quaternion from a 3x3 column rotation matrix. More...

constexpr_cxx26 Quaternion &	setFromNormalVectors (const Vec3 &v1, const Vec3 &v2) noexcept
	Initialize this quaternion from two normalized vectors. More...

constexpr_cxx26 Quaternion &	setFromVectors (const Vec3 &v1, const Vec3 &v2) noexcept
	Initialize this quaternion from two vectors. More...

constexpr Quaternion &	setIdentity () noexcept

Quaternion &	setLookAt (const Vec3 &directionIn, const Vec3 &upIn, Vec3 &xAxisOut, Vec3 &yAxisOut, Vec3 &zAxisOut) noexcept
	Set this quaternion to equal the rotation required to point the z-axis at direction and the y-axis to up. More...

constexpr_cxx26 Quaternion &	setSlerp (const Quaternion &a, const Quaternion &b, const value_type changeAmnt) noexcept
	Set this quaternion to a spherical linear interpolation between the given start and end quaternions by the given change amount. More...

constexpr void	setW (value_type w) noexcept

constexpr void	setX (value_type x) noexcept

constexpr void	setY (value_type y) noexcept

constexpr void	setZ (value_type z) noexcept

constexpr_cxx26 value_type	toAngleAxis (Vec3 &axis) const noexcept
	Transform the rotational quaternion to axis based rotation angles. More...

constexpr void	toAxes (Vec3 &xAxis, Vec3 &yAxis, Vec3 &zAxis) const noexcept
	Extracts this quaternion's orthogonal rotation axes. More...

constexpr void	toAxes (Vec3 &xAxis, Vec3 &yAxis, Vec3 &zAxis, Matrix4< value_type > &tmp) const noexcept
	Extracts this quaternion's orthogonal rotation axes. More...

constexpr_cxx26 Vec3	toEuler () noexcept
	Transform this quaternion to Euler rotation angles in radians (pitchX, yawY and rollZ). More...

constexpr Mat4f	toMatrix () const noexcept
	Transform this quaternion to a normalized 4x4 column matrix representing the rotation. More...

constexpr Mat4f &	toMatrix (Mat4f &m) const noexcept
	Transform this quaternion to a normalized 4x4 column matrix representing the rotation, see toMatrix(). More...

std::string	toString () const noexcept

constexpr value_type	w () const noexcept

constexpr value_type	x () const noexcept

constexpr value_type	y () const noexcept

constexpr value_type	z () const noexcept

Static Public Attributes
static constexpr const value_type	allowed_deviation = value_type(8.4) * std::numeric_limits<value_type>::epsilon()
	Quaternion Epsilon, used with equals method to determine if two Quaternions are close enough to be considered equal. More...

static constexpr const value_type	half = one/two

static constexpr const value_type	one = value_type(1)

static constexpr const value_type	two = value_type(2)

static constexpr const value_type	zero = value_type(0)

Detailed Description

template<typename Value_type, std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>
class jau::math::Quaternion< Value_type, >

Quaternion implementation supporting Gimbal-Lock free rotations.

All matrix operation provided are in column-major order, as specified in the OpenGL fixed function pipeline, i.e. compatibility profile. See FloatUtil.

See Matrix-FAQ

See euclideanspace.com-Quaternion

Definition at line 62 of file quaternion.hpp.

Member Typedef Documentation

◆ value_type

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef Value_type jau::math::Quaternion< Value_type, >::value_type

Definition at line 64 of file quaternion.hpp.

◆ pointer

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef value_type* jau::math::Quaternion< Value_type, >::pointer

Definition at line 65 of file quaternion.hpp.

◆ const_pointer

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef const value_type* jau::math::Quaternion< Value_type, >::const_pointer

Definition at line 66 of file quaternion.hpp.

◆ reference

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef value_type& jau::math::Quaternion< Value_type, >::reference

Definition at line 67 of file quaternion.hpp.

◆ const_reference

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef const value_type& jau::math::Quaternion< Value_type, >::const_reference

Definition at line 68 of file quaternion.hpp.

◆ iterator

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef value_type* jau::math::Quaternion< Value_type, >::iterator

Definition at line 69 of file quaternion.hpp.

◆ const_iterator

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef const value_type* jau::math::Quaternion< Value_type, >::const_iterator

Definition at line 70 of file quaternion.hpp.

◆ Vec3

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

typedef Vector3F<value_type, std::is_floating_point_v<Value_type> > jau::math::Quaternion< Value_type, >::Vec3

Definition at line 72 of file quaternion.hpp.

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr jau::math::Quaternion< Value_type, >::Quaternion ( )

inlineconstexprnoexcept

Definition at line 92 of file quaternion.hpp.

◆ Quaternion() [2/4]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr jau::math::Quaternion< Value_type, >::Quaternion	(	const value_type	x,
		const value_type	y,
		const value_type	z,
		const value_type	w
	)

inlineconstexprnoexcept

Definition at line 95 of file quaternion.hpp.

◆ Quaternion() [3/4]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr jau::math::Quaternion< Value_type, >::Quaternion ( const Quaternion< Value_type, > & o )

constexprdefaultnoexcept

◆ Quaternion() [4/4]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr jau::math::Quaternion< Value_type, >::Quaternion ( Quaternion< Value_type, > && o )

constexprdefaultnoexcept

Member Function Documentation

◆ operator=() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator= ( const Quaternion< Value_type, > & )

constexprdefaultnoexcept

◆ operator=() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator= ( Quaternion< Value_type, > && )

constexprdefaultnoexcept

◆ magnitudeSquared()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::magnitudeSquared ( ) const

inlineconstexprnoexcept

See magnitude() for special handling of epsilon, which is not applied here.

Returns: the squared magnitude of this quaternion.

Definition at line 108 of file quaternion.hpp.

◆ magnitude()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 value_type jau::math::Quaternion< Value_type, >::magnitude ( ) const

inlinenoexcept

Return the magnitude of this quaternion, i.e.

sqrt(magnitudeSquared())

A magnitude of zero shall equal identity, as performed by normalize().

Implementation Details:

returns 0f if magnitudeSquared() is is zero using epsilon
returns 1f if magnitudeSquared() is equals 1f using epsilon

Definition at line 126 of file quaternion.hpp.

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◆ w()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::w ( ) const

inlineconstexprnoexcept

Definition at line 137 of file quaternion.hpp.

◆ setW()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::setW ( value_type w )

inlineconstexprnoexcept

Definition at line 139 of file quaternion.hpp.

◆ x()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::x ( ) const

inlineconstexprnoexcept

Definition at line 141 of file quaternion.hpp.

◆ setX()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::setX ( value_type x )

inlineconstexprnoexcept

Definition at line 143 of file quaternion.hpp.

◆ y()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::y ( ) const

inlineconstexprnoexcept

Definition at line 145 of file quaternion.hpp.

◆ setY()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::setY ( value_type y )

inlineconstexprnoexcept

Definition at line 147 of file quaternion.hpp.

◆ z()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::z ( ) const

inlineconstexprnoexcept

Definition at line 149 of file quaternion.hpp.

◆ setZ()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::setZ ( value_type z )

inlineconstexprnoexcept

Definition at line 151 of file quaternion.hpp.

◆ dot() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::dot	(	value_type	x,
		value_type	y,
		value_type	z,
		value_type	w
	)		const

inlineconstexprnoexcept

Returns the dot product of this quaternion with the given x,y,z and m_w components.

Definition at line 156 of file quaternion.hpp.

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◆ dot() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr value_type jau::math::Quaternion< Value_type, >::dot ( const Quaternion< Value_type, > & quat ) const

inlineconstexprnoexcept

Returns the dot product of this quaternion with the given quaternion.

Definition at line 163 of file quaternion.hpp.

◆ isIdentity()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr bool jau::math::Quaternion< Value_type, >::isIdentity ( ) const

inlineconstexprnoexcept

Returns true if this quaternion has identity.

Implementation uses epsilon to compare W against 1f and X, Y and Z against zero.

Definition at line 176 of file quaternion.hpp.

◆ setIdentity()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::setIdentity ( )

inlineconstexprnoexcept

Definition at line 185 of file quaternion.hpp.

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◆ normalize()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::normalize ( )

inlineconstexprnoexcept

Normalize a quaternion required if to be used as a rotational quaternion.

Implementation Details:

setIdentity() if magnitude() is is zero using epsilon

Returns: this quaternion for chaining.

Definition at line 200 of file quaternion.hpp.

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◆ conjugate()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::conjugate ( )

inlineconstexprnoexcept

Conjugates this quaternion [-x, -y, -z, w].

Returns: this quaternion for chaining.

See also: Matrix-FAQ Q49

Definition at line 219 of file quaternion.hpp.

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◆ invert()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::invert ( )

inlineconstexprnoexcept

Invert the quaternion If rotational, will produce a the inverse rotation.

Implementation Details:

conjugates if magnitudeSquared() is is equals 1f using epsilon

Returns: this quaternion for chaining.

See also: Matrix-FAQ Q50

Definition at line 237 of file quaternion.hpp.

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◆ set()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::set	(	const value_type	x,
		const value_type	y,
		const value_type	z,
		const value_type	w
	)

inlineconstexprnoexcept

Set all values of this quaternion using the given components.

Returns: this quaternion for chaining.

Definition at line 255 of file quaternion.hpp.

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◆ operator+=()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator+= ( const Quaternion< Value_type, > & rhs )

inlineconstexprnoexcept

Add a quaternion: this = this + rhs, returns this.

Parameters

q	quaternion

Returns: this quaternion for chaining.

See also: euclideanspace.com-QuaternionAdd

Definition at line 270 of file quaternion.hpp.

◆ operator-=()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator-= ( const Quaternion< Value_type, > & rhs )

inlineconstexprnoexcept

Subtract a quaternion: this = this - rhs, returns this.

Parameters

q	quaternion

Returns: this quaternion for chaining.

See also: euclideanspace.com-QuaternionAdd

Definition at line 285 of file quaternion.hpp.

◆ operator*=() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator*= ( const Quaternion< Value_type, > & rhs )

inlineconstexprnoexcept

Multiply this quaternion: this = this * rhs, returns this.

Parameters

q	a quaternion to multiply with

Returns: this quaternion for chaining.

See also: Matrix-FAQ Q53; euclideanspace.com-QuaternionMul

Definition at line 301 of file quaternion.hpp.

◆ operator*=() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::operator*= ( const value_type rhs )

inlineconstexprnoexcept

Scale this quaternion by a scalar: this = this * rhs, returns this.

Parameters

n	a value_type constant

Returns: this quaternion for chaining.

See also: euclideanspace.com-QuaternionScale

Definition at line 315 of file quaternion.hpp.

◆ rotateByAngleNormalAxis() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleNormalAxis	(	const value_type	angle,
		const value_type	axisX,
		const value_type	axisY,
		const value_type	axisZ
	)

inlinenoexcept

Rotate this quaternion by the given angle and axis.

The axis must be a normalized vector.

A rotational quaternion is made from the given angle and axis.

Parameters

angle	in radians
axisX	x-coord of rotation axis
axisY	y-coord of rotation axis
axisZ	m_z-coord of rotation axis

Returns: this quaternion for chaining.

Definition at line 338 of file quaternion.hpp.

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◆ rotateByAngleNormalAxis() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleNormalAxis	(	const value_type	angle,
		const Vec3 &	axis
	)

inlinenoexcept

Rotate this quaternion by the given angle and axis.

The axis must be a normalized vector.

A rotational quaternion is made from the given angle and axis.

Parameters

angle	in radians
axis	Vec3 coord of rotation axis

Returns: this quaternion for chaining.

Definition at line 368 of file quaternion.hpp.

◆ rotateByAngleX() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleX ( const value_type angle )

inlinenoexcept

Rotate this quaternion around X axis with the given angle in radians.

Parameters

angle in radians

Returns: this quaternion for chaining.

Definition at line 378 of file quaternion.hpp.

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◆ rotateByAngleX() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleX	(	const value_type	sin,
		const value_type	cos
	)

inlineconstexprnoexcept

Rotate this quaternion around X axis with the given angle's sin + cos values.

Definition at line 383 of file quaternion.hpp.

◆ rotateByAngleY() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleY ( value_type angle )

inlinenoexcept

Rotate this quaternion around Y axis with the given angle in radians.

Parameters

angle in radians

Returns: this quaternion for chaining.

Definition at line 396 of file quaternion.hpp.

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◆ rotateByAngleY() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleY	(	const value_type	sin,
		const value_type	cos
	)

inlineconstexprnoexcept

Rotate this quaternion around Y axis with the given angle's sin + cos values.

Definition at line 401 of file quaternion.hpp.

◆ rotateByAngleZ() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleZ ( value_type angle )

inlinenoexcept

Rotate this quaternion around Z axis with the given angle in radians.

Parameters

angle in radians

Returns: this quaternion for chaining.

Definition at line 414 of file quaternion.hpp.

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◆ rotateByAngleZ() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::rotateByAngleZ	(	const value_type	sin,
		const value_type	cos
	)

inlineconstexprnoexcept

Rotate this quaternion around Y axis with the given angle's sin + cos values.

Definition at line 419 of file quaternion.hpp.

◆ rotateByEuler() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Quaternion & jau::math::Quaternion< Value_type, >::rotateByEuler ( const Vec3 & angradXYZ )

inlinenoexcept

Rotates this quaternion from the given Euler rotation array angradXYZ in radians.

The angradXYZ array is laid out in natural order:

x - bank
y - heading
z - attitude

For details see rotateByEuler(value_type, value_type, value_type).

Parameters

angradXYZ euler angle array in radians

Returns: this quaternion for chaining.

See also: rotateByEuler(value_type, value_type, value_type)

Definition at line 441 of file quaternion.hpp.

◆ rotateByEuler() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::rotateByEuler	(	const value_type	bankX,
		const value_type	headingY,
		const value_type	attitudeZ
	)

inlinenoexcept

Rotates this quaternion from the given Euler rotation angles in radians.

The rotations are applied in the given order and using chained rotation per axis:

y - heading - rotateByAngleY(value_type)
z - attitude - rotateByAngleZ(value_type)
x - bank - rotateByAngleX(value_type)

Implementation Details:

NOP if all angles are is zero using epsilon
result is normalize()ed

Parameters

bankX	the Euler pitch angle in radians. (rotation about the X axis)
headingY	the Euler yaw angle in radians. (rotation about the Y axis)
attitudeZ	the Euler roll angle in radians. (rotation about the Z axis)

Returns: this quaternion for chaining.

See also: rotateByAngleY(value_type); rotateByAngleZ(value_type); rotateByAngleX(value_type); setFromEuler(value_type, value_type, value_type)

Definition at line 471 of file quaternion.hpp.

◆ rotateVector() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Vec3 jau::math::Quaternion< Value_type, >::rotateVector ( const Vec3 & in )

inlinenoexcept

Definition at line 488 of file quaternion.hpp.

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◆ rotateVector() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Vec3 & jau::math::Quaternion< Value_type, >::rotateVector	(	const Vec3 &	in,
		Vec3 &	out
	)

inlinenoexcept

Definition at line 501 of file quaternion.hpp.

◆ setSlerp()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setSlerp	(	const Quaternion< Value_type, > &	a,
		const Quaternion< Value_type, > &	b,
		const value_type	changeAmnt
	)

inlinenoexcept

Set this quaternion to a spherical linear interpolation between the given start and end quaternions by the given change amount.

Note: Method does not normalize this quaternion!

Parameters

a	start quaternion
b	end quaternion
changeAmnt	value_type between 0 and 1 representing interpolation.

Returns: this quaternion for chaining.

See also: euclideanspace.com-QuaternionSlerp

Definition at line 548 of file quaternion.hpp.

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◆ setLookAt()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Quaternion & jau::math::Quaternion< Value_type, >::setLookAt	(	const Vec3 &	directionIn,
		const Vec3 &	upIn,
		Vec3 &	xAxisOut,
		Vec3 &	yAxisOut,
		Vec3 &	zAxisOut
	)

inlinenoexcept

Set this quaternion to equal the rotation required to point the z-axis at direction and the y-axis to up.

Implementation generates a 3x3 matrix and is equal with ProjectFloat's lookAt(..).

Implementation Details:

result is normalize()ed

Parameters

directionIn	where to look at
upIn	a vector indicating the local up direction.
xAxisOut	vector storing the orthogonal x-axis of the coordinate system.
yAxisOut	vector storing the orthogonal y-axis of the coordinate system.
zAxisOut	vector storing the orthogonal m_z-axis of the coordinate system.

Returns: this quaternion for chaining.

See also: euclideanspace.com-LookUp

Definition at line 627 of file quaternion.hpp.

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◆ setFromVectors()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setFromVectors	(	const Vec3 &	v1,
		const Vec3 &	v2
	)

inlinenoexcept

Initialize this quaternion from two vectors.

  q = (s,v) = (v1•v2 , v1 × v2),
    angle = angle(v1, v2) = v1•v2
     axis = normal(v1 x v2)

<p<blockquote>‍

Implementation Details:

set_identity() if square vector-length is jau::is_zero2f(value_type, value_type) using epsilon

Parameters

v1	not normalized
v2	not normalized

Returns: this quaternion for chaining.

Definition at line 676 of file quaternion.hpp.

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◆ setFromNormalVectors()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setFromNormalVectors	(	const Vec3 &	v1,
		const Vec3 &	v2
	)

inlinenoexcept

Initialize this quaternion from two normalized vectors.

  q = (s,v) = (v1•v2 , v1 × v2),
    angle = angle(v1, v2) = v1•v2
     axis = v1 x v2

<p<blockquote>‍

Implementation Details:

setIdentity() if square vector-length is is zero using epsilon

Parameters

v1	normalized
v2	normalized

Returns: this quaternion for chaining.

Definition at line 730 of file quaternion.hpp.

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◆ setFromAngleAxis()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

Quaternion & jau::math::Quaternion< Value_type, >::setFromAngleAxis	(	const value_type	angle,
		const Vec3 &	vector
	)

inlinenoexcept

Definition at line 782 of file quaternion.hpp.

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◆ setFromAngleNormalAxis()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setFromAngleNormalAxis	(	const value_type	angle,
		const Vec3 &	vector
	)

inlinenoexcept

Definition at line 801 of file quaternion.hpp.

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◆ toAngleAxis()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 value_type jau::math::Quaternion< Value_type, >::toAngleAxis ( Vec3 & axis ) const

inlinenoexcept

Transform the rotational quaternion to axis based rotation angles.

Parameters

axis	storage for computed axis

Returns: the rotation angle in radians

See also: #setFromAngleAxis(value_type, Vec3, Vec3)

Definition at line 822 of file quaternion.hpp.

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◆ setFromEuler() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setFromEuler ( const Vec3 & angradXYZ )

inlinenoexcept

Initializes this quaternion from the given Euler rotation array angradXYZ in radians.

The angradXYZ vector is laid out in natural order:

x - bank
y - heading
z - attitude

For details see setFromEuler(value_type, value_type, value_type).

Parameters

angradXYZ euler angle vector in radians holding x-bank, m_y-heading and m_z-attitude

Returns: this quaternion for chaining.

See also: setFromEuler(value_type, value_type, value_type)

Definition at line 853 of file quaternion.hpp.

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◆ setFromEuler() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Quaternion & jau::math::Quaternion< Value_type, >::setFromEuler	(	const value_type	bankX,
		const value_type	headingY,
		const value_type	attitudeZ
	)

inlinenoexcept

Initializes this quaternion from the given Euler rotation angles in radians.

The rotations are applied in the given order:

y - heading
z - attitude
x - bank

Implementation Details:

setIdentity() if all angles are is zero using epsilon
result is normalize()ed

Parameters

bankX	the Euler pitch angle in radians. (rotation about the X axis)
headingY	the Euler yaw angle in radians. (rotation about the Y axis)
attitudeZ	the Euler roll angle in radians. (rotation about the Z axis)

Returns: this quaternion for chaining.

See also: Matrix-FAQ Q60; Gems; euclideanspace.com-eulerToQuaternion; #toEuler(Vec3)

Definition at line 884 of file quaternion.hpp.

◆ toEuler()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr_cxx26 Vec3 jau::math::Quaternion< Value_type, >::toEuler ( )

inlinenoexcept

Transform this quaternion to Euler rotation angles in radians (pitchX, yawY and rollZ).

The result array is laid out in natural order:

x - bank
y - heading
z - attitude

Returns: new Vec3 euler angle result vector filled with x-bank, y-heading and m_z-attitude

See also: euclideanspace.com-quaternionToEuler; setFromEuler(value_type, value_type, value_type)

Definition at line 927 of file quaternion.hpp.

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◆ setFromMat() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::setFromMat	(	const value_type	m00,
		const value_type	m01,
		const value_type	m02,
		const value_type	m10,
		const value_type	m11,
		const value_type	m12,
		const value_type	m20,
		const value_type	m21,
		const value_type	m22
	)

inlineconstexprnoexcept

Compute the quaternion from a 3x3 column rotation matrix.

See Graphics Gems Code,
MatrixTrace.

Buggy Matrix-FAQ Q55

Returns: this quaternion for chaining.

See also: #setFromMatrix(Matrix4f)

Definition at line 963 of file quaternion.hpp.

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◆ setFromMat() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::setFromMat ( const Mat4f & m )

inlineconstexprnoexcept

Compute the quaternion from a 3x3 column rotation matrix from mat4f instance.

See Graphics Gems Code,
MatrixTrace.

Buggy Matrix-FAQ Q55

Returns: this quaternion for chaining.

See also: Matrix4f::getRotation(Quaternion); #setFromMatrix(value_type, value_type, value_type, value_type, value_type, value_type, value_type, value_type, value_type)

Definition at line 1014 of file quaternion.hpp.

◆ setFromAxes()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Quaternion & jau::math::Quaternion< Value_type, >::setFromAxes	(	const Vec3 &	xAxis,
		const Vec3 &	yAxis,
		const Vec3 &	zAxis
	)

inlineconstexprnoexcept

Initializes this quaternion to represent a rotation formed by the given three orthogonal axes.

No validation whether the axes are orthogonal is performed.

Parameters

xAxis	vector representing the orthogonal x-axis of the coordinate system.
yAxis	vector representing the orthogonal y-axis of the coordinate system.
zAxis	vector representing the orthogonal m_z-axis of the coordinate system.

Returns: this quaternion for chaining.

Definition at line 1029 of file quaternion.hpp.

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◆ toMatrix() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Mat4f jau::math::Quaternion< Value_type, >::toMatrix ( ) const

inlineconstexprnoexcept

Transform this quaternion to a normalized 4x4 column matrix representing the rotation.

Implementation Details:

makes identity matrix if magnitudeSquared() is is zero using epsilon

Returns: resulting normalized column matrix 4x4

See also: Matrix-FAQ Q54; #setFromMatrix(value_type, value_type, value_type, value_type, value_type, value_type, value_type, value_type, value_type); Matrix4f::setToRotation(Quaternion)

Definition at line 1049 of file quaternion.hpp.

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◆ toMatrix() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr Mat4f & jau::math::Quaternion< Value_type, >::toMatrix ( Mat4f & m ) const

inlineconstexprnoexcept

Transform this quaternion to a normalized 4x4 column matrix representing the rotation, see toMatrix().

Parameters

out	store for the resulting normalized column matrix 4x4

Returns: the given matrix store

Definition at line 1060 of file quaternion.hpp.

◆ toAxes() [1/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::toAxes	(	Vec3 &	xAxis,
		Vec3 &	yAxis,
		Vec3 &	zAxis,
		Matrix4< value_type > &	tmp
	)		const

inlineconstexprnoexcept

Extracts this quaternion's orthogonal rotation axes.

Parameters

xAxis	vector representing the orthogonal x-axis of the coordinate system.
yAxis	vector representing the orthogonal y-axis of the coordinate system.
zAxis	vector representing the orthogonal m_z-axis of the coordinate system.
tmp	temporary Matrix4 used for toMatrix()

Definition at line 1121 of file quaternion.hpp.

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◆ toAxes() [2/2]

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr void jau::math::Quaternion< Value_type, >::toAxes	(	Vec3 &	xAxis,
		Vec3 &	yAxis,
		Vec3 &	zAxis
	)		const

inlineconstexprnoexcept

Extracts this quaternion's orthogonal rotation axes.

Parameters

xAxis	vector representing the orthogonal x-axis of the coordinate system.
yAxis	vector representing the orthogonal y-axis of the coordinate system.
zAxis	vector representing the orthogonal m_z-axis of the coordinate system.

Definition at line 1135 of file quaternion.hpp.

◆ operator==()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr bool jau::math::Quaternion< Value_type, >::operator== ( const Quaternion< Value_type, > & o ) const

inlineconstexprnoexcept

Parameters

o	the object to compare for equality

Returns: true if this quaternion and the provided quaternion have roughly the same x, m_y, m_z and m_w values.

Definition at line 1148 of file quaternion.hpp.

◆ toString()

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

std::string jau::math::Quaternion< Value_type, >::toString ( ) const

inlinenoexcept

Definition at line 1158 of file quaternion.hpp.

Member Data Documentation

◆ zero

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr const value_type jau::math::Quaternion< Value_type, >::zero = value_type(0)

staticconstexpr

Definition at line 74 of file quaternion.hpp.

◆ one

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr const value_type jau::math::Quaternion< Value_type, >::one = value_type(1)

staticconstexpr

Definition at line 75 of file quaternion.hpp.

◆ two

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr const value_type jau::math::Quaternion< Value_type, >::two = value_type(2)

staticconstexpr

Definition at line 76 of file quaternion.hpp.

◆ half

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr const value_type jau::math::Quaternion< Value_type, >::half = one/two

staticconstexpr

Definition at line 77 of file quaternion.hpp.

◆ allowed_deviation

template<typename Value_type , std::enable_if_t< std::is_floating_point_v< Value_type >, bool > = true>

constexpr const value_type jau::math::Quaternion< Value_type, >::allowed_deviation = value_type(8.4) * std::numeric_limits<value_type>::epsilon()

staticconstexpr

Quaternion Epsilon, used with equals method to determine if two Quaternions are close enough to be considered equal.

Using {@value}, which is ~8.4 times std::numeric_limits<value_type>::epsilon().

Definition at line 85 of file quaternion.hpp.

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

jaulib/include/jau/math/mat4f.hpp
jaulib/include/jau/math/quaternion.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ value_type

◆ pointer

◆ const_pointer

◆ reference

◆ const_reference

◆ iterator

◆ const_iterator

◆ Vec3

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

◆ Quaternion() [2/4]

◆ Quaternion() [3/4]

◆ Quaternion() [4/4]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ magnitudeSquared()

◆ magnitude()

◆ w()

◆ setW()

◆ x()

◆ setX()

◆ y()

◆ setY()

◆ z()

◆ setZ()

◆ dot() [1/2]

◆ dot() [2/2]

◆ isIdentity()

◆ setIdentity()

◆ normalize()

◆ conjugate()

◆ invert()

◆ set()

◆ operator+=()

◆ operator-=()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ rotateByAngleNormalAxis() [1/2]

◆ rotateByAngleNormalAxis() [2/2]

◆ rotateByAngleX() [1/2]

◆ rotateByAngleX() [2/2]

◆ rotateByAngleY() [1/2]

◆ rotateByAngleY() [2/2]

◆ rotateByAngleZ() [1/2]

◆ rotateByAngleZ() [2/2]

◆ rotateByEuler() [1/2]

◆ rotateByEuler() [2/2]

◆ rotateVector() [1/2]

◆ rotateVector() [2/2]

◆ setSlerp()

◆ setLookAt()

◆ setFromVectors()

◆ setFromNormalVectors()

◆ setFromAngleAxis()

◆ setFromAngleNormalAxis()

◆ toAngleAxis()

◆ setFromEuler() [1/2]

◆ setFromEuler() [2/2]

◆ toEuler()

◆ setFromMat() [1/2]

◆ setFromMat() [2/2]

◆ setFromAxes()

◆ toMatrix() [1/2]

◆ toMatrix() [2/2]

◆ toAxes() [1/2]

◆ toAxes() [2/2]

◆ operator==()

◆ toString()

Member Data Documentation

◆ zero

◆ one

◆ two

◆ half

◆ allowed_deviation