Used internally to implement angle operations. More...

#include <Quaternion.h>

Public Member Functions
constexpr	Quaternion ()
	Default constructor. More...

	Quaternion (const OrientationVector &rot)
	Constructor which converts a orientation vector into the corresponding quaternion representation. More...

	Quaternion (const PositionVector &loc)
	Constructor which converts a position vector into the corresponding quaternion representation; x, y, and z are copied over. More...

	Quaternion (double rx, double ry, double rz)
	Constructor which converts a orientation vector, specified in individual terms, into the corresponding quaternion representation. More...

constexpr	Quaternion (double x, double y, double z, double w)
	Primary constructor. More...

double	angle_to (const Quaternion &target) const
	Calculates the angle between the orientations represented by this, and the target Quaternion. More...

Quaternion &	conjugate ()
	Conjugate this quaternion in-place; may use in place of invert for unit quaternions for better performance. More...

double	dot_product (const Quaternion &rhs) const
	Calculates the Quaternion dot product between this, and the right-hand-side; this is the inner-product, over the product of the magnitude of both sides. More...

Quaternion	exp () const
	Calculate e to the power of this quaternion, return result as new quaternion. More...

void	exp_this ()
	Calculate e to the power of this quaternion, store result in this quaternion. More...

void	from_angular_vector (const OrientationVector &rot)

void	from_angular_vector (double rx, double ry, double rz)

void	from_linear_vector (const PositionVector &loc)

void	from_linear_vector (double x, double y, double z)

double	imag () const
	Returns the magnitude of imaginary part of this quaternion. More...

double	inner_product (const Quaternion &rhs) const
	Calculates the Quaternion inner-product between this, and the right-hand-side, which is the sum of the pair-wise multiplication of each corresponding term of the Quaternions. More...

void	invert ()
	Inverts this quaternion to its reciprical. More...

Quaternion	ln () const
	Calculate the natural log of this quaternion, return result in a new quaternion. More...

void	ln_this ()
	Calculate natural log of this quaternion, store result in this quaternion. More...

double	m11 () const
	Row 1 Column 1 of orientation matrix equivalent to this quaternion. More...

double	m12 () const
	Row 1 Column 2 of orientation matrix equivalent to this quaternion. More...

double	m13 () const
	Row 1 Column 3 of orientation matrix equivalent to this quaternion. More...

double	m21 () const
	Row 2 Column 1 of orientation matrix equivalent to this quaternion. More...

double	m22 () const
	Row 2 Column 2 of orientation matrix equivalent to this quaternion. More...

double	m23 () const
	Row 2 Column 3 of orientation matrix equivalent to this quaternion. More...

double	m31 () const
	Row 3 Column 1 of orientation matrix equivalent to this quaternion. More...

double	m32 () const
	Row 3 Column 2 of orientation matrix equivalent to this quaternion. More...

double	m33 () const
	Row 3 Column 3 of orientation matrix equivalent to this quaternion. More...

double	mag () const
	Returns the magnitude of this quaternion. More...

double	mag_squared () const
	Returns the magnitude of this quaternion, squared. More...

Quaternion &	negate ()
	Flip the sign of all parts of the quaternion; equivalent to (but potentially faster than) this->scale(-1);. More...

Quaternion	operator* (const Quaternion &rhs) const
	Calculate hamilton product, this * rhs, and return new Quaternion. More...

Quaternion &	operator*= (const Quaternion &rhs)
	Calculate hamilton product, this * rhs, and store into this. More...

constexpr Quaternion	operator- () const
	Copy and conjugate this quaternion. More...

void	orient_by (Quaternion rot)
	Treat this quaternion as a position quaternion (w should be zero), and orient it by the orientation represented by rot. More...

Quaternion	pow (const Quaternion &e) const
	Calculate this quaternion raised to a quaternion power, return result in a new quaternion. More...

Quaternion	pow (double e) const
	Calculate this quaternion raised to a scalar power, return result in a new quaternion. More...

void	pow_this (const Quaternion &e)
	Calculate this quaternion raised to a quaternion power, store result in this quaternion. More...

void	pow_this (double e)
	Calculate this quaternion raised to a scalar power, store result in this quaternion. More...

void	pre_multiply (const Quaternion &lhs)
	Calculate hamilton product, lhs * this, and store into this. More...

void	scale (double s)
	Multiply each part of this quaternion by s. More...

Quaternion	slerp (const Quaternion &o, double t)
	If *this and o are unit quaternions, interpolate a quaternion that is partially between them, and return it as a new quaternion. More...

void	slerp_this (const Quaternion &o, double t)
	If this and o are unit quaternions, interpolate a quaternion that is partially between them, and store it in this. More...

void	to_angular_vector (double &rx, double &ry, double &rz) const

void	to_angular_vector (OrientationVector &rot) const

void	to_linear_vector (double &x, double &y, double &z) const

void	to_linear_vector (PositionVector &loc) const

constexpr double	w () const
	getter of w (or real scalar) part of quaternion More...

double	w (double new_w)
	setter of w (or real scalar) part of quaternion More...

constexpr double	x () const
	getter of x (or i) part of quaternion More...

double	x (double new_x)
	getter of x (or i) part of quaternion More...

constexpr double	y () const
	getter of y (or j) part of quaternion More...

double	y (double new_y)
	getter of y (or j) part of quaternion More...

constexpr double	z () const
	getter of z (or k) part of quaternion More...

double	z (double new_z)
	getter of z (or k) part of quaternion More...

Static Public Member Functions
static void	hamilton_product (Quaternion &into, const Quaternion &lhs, const Quaternion &rhs)
	Calculates the hamilton product of two quaternions, into a third. More...

Private Attributes
double	w_

double	x_

double	y_

double	z_

Detailed Description

Used internally to implement angle operations.

Not reference-frame aware.

Definition at line 74 of file Quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

constexpr gams::pose::Quaternion::Quaternion ( )

inlineconstexpr

Default constructor.

Initializes x, y, z, and w to zero.

Definition at line 80 of file Quaternion.h.

◆ Quaternion() [2/5]

constexpr gams::pose::Quaternion::Quaternion	(	double	x,
		double	y,
		double	z,
		double	w
	)

constexpr

Primary constructor.

Specifies each term explicitly

◆ Quaternion() [3/5]

gams::pose::Quaternion::Quaternion	(	double	rx,
		double	ry,
		double	rz
	)

Constructor which converts a orientation vector, specified in individual terms, into the corresponding quaternion representation.

See OrientationVector for details of the orientation vector representation.

◆ Quaternion() [4/5]

gams::pose::Quaternion::Quaternion ( const OrientationVector & rot )

explicit

Constructor which converts a orientation vector into the corresponding quaternion representation.

See OrientationVector for details of the orientation vector representation.

◆ Quaternion() [5/5]

gams::pose::Quaternion::Quaternion ( const PositionVector & loc )

explicit

Constructor which converts a position vector into the corresponding quaternion representation; x, y, and z are copied over.

The w term is 0

Member Function Documentation

◆ angle_to()

double gams::pose::Quaternion::angle_to ( const Quaternion & target ) const

Calculates the angle between the orientations represented by this, and the target Quaternion.

This is the smallest angle this can be orientd to arrive at target.

Parameters

target the target Quaternion

Returns: the angle in radians between this and the target

◆ conjugate()

Quaternion& gams::pose::Quaternion::conjugate ( )

Conjugate this quaternion in-place; may use in place of invert for unit quaternions for better performance.

Returns: *this, after conjugation

◆ dot_product()

double gams::pose::Quaternion::dot_product ( const Quaternion & rhs ) const

Calculates the Quaternion dot product between this, and the right-hand-side; this is the inner-product, over the product of the magnitude of both sides.

Parameters

rhs	the Quaternion to dot-multiply with

Returns: the scalar result.

◆ exp()

Quaternion gams::pose::Quaternion::exp ( ) const

Calculate e to the power of this quaternion, return result as new quaternion.

Returns: result

◆ exp_this()

void gams::pose::Quaternion::exp_this ( )

Calculate e to the power of this quaternion, store result in this quaternion.

◆ from_angular_vector() [1/2]

void gams::pose::Quaternion::from_angular_vector ( const OrientationVector & rot )

◆ from_angular_vector() [2/2]

void gams::pose::Quaternion::from_angular_vector	(	double	rx,
		double	ry,
		double	rz
	)

◆ from_linear_vector() [1/2]

void gams::pose::Quaternion::from_linear_vector ( const PositionVector & loc )

◆ from_linear_vector() [2/2]

void gams::pose::Quaternion::from_linear_vector	(	double	x,
		double	y,
		double	z
	)

◆ hamilton_product()

static void gams::pose::Quaternion::hamilton_product	(	Quaternion &	into,
		const Quaternion &	lhs,
		const Quaternion &	rhs
	)

static

Calculates the hamilton product of two quaternions, into a third.

The resulting quaternion represents the composed orientation of the args. The target quaternion can be one of the two source quaternion. The two source quaternions can be the same (for squaring)

Parameters

into	destination quaternion; will be overwritten
lhs	left-hand-side source quaternion (non-commutative)
rhs	right-hand-side source quaternion (non-commutative)

◆ imag()

double gams::pose::Quaternion::imag ( ) const

Returns the magnitude of imaginary part of this quaternion.

◆ inner_product()

double gams::pose::Quaternion::inner_product ( const Quaternion & rhs ) const

Calculates the Quaternion inner-product between this, and the right-hand-side, which is the sum of the pair-wise multiplication of each corresponding term of the Quaternions.

Note that unlike hamilton_product, this is commutative.

Parameters

rhs	the Quaternion to multiply with

Returns: the scalar result.

◆ invert()

void gams::pose::Quaternion::invert ( )

Inverts this quaternion to its reciprical.

Equivalent to (but slower than) conjugate if you know this quaternion is a unit quaternion.

◆ ln()

Quaternion gams::pose::Quaternion::ln ( ) const

Calculate the natural log of this quaternion, return result in a new quaternion.

Returns: result

◆ ln_this()

void gams::pose::Quaternion::ln_this ( )

Calculate natural log of this quaternion, store result in this quaternion.

◆ m11()

double gams::pose::Quaternion::m11 ( ) const

Row 1 Column 1 of orientation matrix equivalent to this quaternion.

◆ m12()

double gams::pose::Quaternion::m12 ( ) const

Row 1 Column 2 of orientation matrix equivalent to this quaternion.

◆ m13()

double gams::pose::Quaternion::m13 ( ) const

Row 1 Column 3 of orientation matrix equivalent to this quaternion.

◆ m21()

double gams::pose::Quaternion::m21 ( ) const

Row 2 Column 1 of orientation matrix equivalent to this quaternion.

◆ m22()

double gams::pose::Quaternion::m22 ( ) const

Row 2 Column 2 of orientation matrix equivalent to this quaternion.

◆ m23()

double gams::pose::Quaternion::m23 ( ) const

Row 2 Column 3 of orientation matrix equivalent to this quaternion.

◆ m31()

double gams::pose::Quaternion::m31 ( ) const

Row 3 Column 1 of orientation matrix equivalent to this quaternion.

◆ m32()

double gams::pose::Quaternion::m32 ( ) const

Row 3 Column 2 of orientation matrix equivalent to this quaternion.

◆ m33()

double gams::pose::Quaternion::m33 ( ) const

Row 3 Column 3 of orientation matrix equivalent to this quaternion.

◆ mag()

double gams::pose::Quaternion::mag ( ) const

Returns the magnitude of this quaternion.

◆ mag_squared()

double gams::pose::Quaternion::mag_squared ( ) const

Returns the magnitude of this quaternion, squared.

Faster than squaring the return value of mag()

◆ negate()

Quaternion& gams::pose::Quaternion::negate ( )

Flip the sign of all parts of the quaternion; equivalent to (but potentially faster than) this->scale(-1);.

Returns: *this, after negation

◆ operator*()

Quaternion gams::pose::Quaternion::operator* ( const Quaternion & rhs ) const

Calculate hamilton product, this * rhs, and return new Quaternion.

Parameters

rhs	right-hand-side to multiply with

Returns: a new Quaternion object holding the result

◆ operator*=()

Quaternion& gams::pose::Quaternion::operator*= ( const Quaternion & rhs )

Calculate hamilton product, this * rhs, and store into this.

Equivalent to hamilton_product(*this, *this, rhs)

Parameters

rhs	right-hand-side to multiply with

Returns: *this, the result

◆ operator-()

constexpr Quaternion gams::pose::Quaternion::operator- ( ) const

constexpr

Copy and conjugate this quaternion.

Returns: a new Quaternion, holding the conjugation of this

◆ orient_by()

void gams::pose::Quaternion::orient_by ( Quaternion rot )

Treat this quaternion as a position quaternion (w should be zero), and orient it by the orientation represented by rot.

Parameters

rot	the Quaternion angle to orient by

◆ pow() [1/2]

Quaternion gams::pose::Quaternion::pow ( const Quaternion & e ) const

Calculate this quaternion raised to a quaternion power, return result in a new quaternion.

Returns: result.

◆ pow() [2/2]

Quaternion gams::pose::Quaternion::pow ( double e ) const

Calculate this quaternion raised to a scalar power, return result in a new quaternion.

Returns: result.

◆ pow_this() [1/2]

void gams::pose::Quaternion::pow_this ( const Quaternion & e )

Calculate this quaternion raised to a quaternion power, store result in this quaternion.

◆ pow_this() [2/2]

void gams::pose::Quaternion::pow_this ( double e )

Calculate this quaternion raised to a scalar power, store result in this quaternion.

◆ pre_multiply()

void gams::pose::Quaternion::pre_multiply ( const Quaternion & lhs )

inline

Calculate hamilton product, lhs * this, and store into this.

Equivalent to hamilton_product(*this, lhs, *this)

Parameters

lhs	left-hand-side to multiply with

Definition at line 159 of file Quaternion.h.

◆ scale()

void gams::pose::Quaternion::scale ( double s )

Multiply each part of this quaternion by s.

◆ slerp()

Quaternion gams::pose::Quaternion::slerp	(	const Quaternion &	o,
		double	t
	)

If *this and o are unit quaternions, interpolate a quaternion that is partially between them, and return it as a new quaternion.

If either quaternion is not a unit quaternion, the calculation will not produce an error, but will be meaningless.

Parameters

o	the other unit quaternion
t	how "close" to this quaternion the result should be, in a range from 0 to 1, inclusive, where 0 is *this, 1 is o, and 0.5 is halfway inbetween.

Returns: the resulting interpolated quaternion

◆ slerp_this()

void gams::pose::Quaternion::slerp_this	(	const Quaternion &	o,
		double	t
	)

If *this and o are unit quaternions, interpolate a quaternion that is partially between them, and store it in *this.

If either quaternion is not a unit quaternion, the calculation will not produce an error, but will be meaningless.

Parameters

o	the other unit quaternion
t	how "close" to this quaternion the result should be, in a range from 0 to 1, inclusive, where 0 is *this, 1 is o, and 0.5 is halfway inbetween.

◆ to_angular_vector() [1/2]

void gams::pose::Quaternion::to_angular_vector	(	double &	rx,
		double &	ry,
		double &	rz
	)		const

◆ to_angular_vector() [2/2]

void gams::pose::Quaternion::to_angular_vector ( OrientationVector & rot ) const

◆ to_linear_vector() [1/2]

void gams::pose::Quaternion::to_linear_vector	(	double &	x,
		double &	y,
		double &	z
	)		const

◆ to_linear_vector() [2/2]

void gams::pose::Quaternion::to_linear_vector ( PositionVector & loc ) const

◆ w() [1/2]

constexpr double gams::pose::Quaternion::w ( ) const

constexpr

getter of w (or real scalar) part of quaternion

◆ w() [2/2]

double gams::pose::Quaternion::w ( double new_w )

setter of w (or real scalar) part of quaternion

◆ x() [1/2]

constexpr double gams::pose::Quaternion::x ( ) const

constexpr

getter of x (or i) part of quaternion

◆ x() [2/2]

double gams::pose::Quaternion::x ( double new_x )

getter of x (or i) part of quaternion

◆ y() [1/2]

constexpr double gams::pose::Quaternion::y ( ) const

constexpr

getter of y (or j) part of quaternion

◆ y() [2/2]

double gams::pose::Quaternion::y ( double new_y )

getter of y (or j) part of quaternion

◆ z() [1/2]

constexpr double gams::pose::Quaternion::z ( ) const

constexpr

getter of z (or k) part of quaternion

◆ z() [2/2]

double gams::pose::Quaternion::z ( double new_z )

getter of z (or k) part of quaternion

Member Data Documentation

◆ w_

double gams::pose::Quaternion::w_

private

Definition at line 394 of file Quaternion.h.

◆ x_

double gams::pose::Quaternion::x_

private

Definition at line 394 of file Quaternion.h.

◆ y_

double gams::pose::Quaternion::y_

private

Definition at line 394 of file Quaternion.h.

◆ z_

double gams::pose::Quaternion::z_

private

Definition at line 394 of file Quaternion.h.

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

src/gams/pose/Quaternion.h

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

◆ Quaternion() [2/5]

◆ Quaternion() [3/5]

◆ Quaternion() [4/5]

◆ Quaternion() [5/5]

Member Function Documentation

◆ angle_to()

◆ conjugate()

◆ dot_product()

◆ exp()

◆ exp_this()

◆ from_angular_vector() [1/2]

◆ from_angular_vector() [2/2]

◆ from_linear_vector() [1/2]

◆ from_linear_vector() [2/2]

◆ hamilton_product()

◆ imag()

◆ inner_product()

◆ invert()

◆ ln()

◆ ln_this()

◆ m11()

◆ m12()

◆ m13()

◆ m21()

◆ m22()

◆ m23()

◆ m31()

◆ m32()

◆ m33()

◆ mag()

◆ mag_squared()

◆ negate()

◆ operator*()

◆ operator*=()

◆ operator-()

◆ orient_by()

◆ pow() [1/2]

◆ pow() [2/2]

◆ pow_this() [1/2]

◆ pow_this() [2/2]

◆ pre_multiply()

◆ scale()

◆ slerp()

◆ slerp_this()

◆ to_angular_vector() [1/2]

◆ to_angular_vector() [2/2]

◆ to_linear_vector() [1/2]

◆ to_linear_vector() [2/2]

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]

Member Data Documentation

◆ w_

◆ x_

◆ y_

◆ z_