MR::Quaternion< T > Struct Template Reference

#include <MRQuaternion.h>

Public Member Functions
constexpr	Quaternion () noexcept=default
constexpr	Quaternion (T a, T b, T c, T d) noexcept
constexpr	Quaternion (const Vector3< T > &axis, T angle) noexcept
constexpr	Quaternion (T real, const Vector3< T > &im) noexcept
constexpr	Quaternion (const Matrix3< T > &m)
constexpr	Quaternion (const Vector3< T > &from, const Vector3< T > &to) noexcept
	finds shorter arc rotation quaternion from one vector to another
constexpr Vector3< T >	im () const noexcept
	returns imaginary part of the quaternion as a vector
constexpr T	angle () const noexcept
	returns angle of rotation encoded in this quaternion
constexpr Vector3< T >	axis () const noexcept
	returns axis of rotation encoded in this quaternion
constexpr T	normSq () const
constexpr T	norm () const
constexpr Quaternion	operator- () const
	returns quaternion representing the same rotation, using the opposite rotation direction and opposite angle
void	normalize ()
	scales this quaternion to make its norm unit
Quaternion	normalized () const
constexpr Quaternion	conjugate () const noexcept
	computes conjugate quaternion, which for unit quaternions encodes the opposite rotation
constexpr Quaternion	inverse () const noexcept
	computes reciprocal quaternion
constexpr Vector3< T >	operator() (const Vector3< T > &p) const noexcept
	operator Matrix3< T > () const
	converts this into 3x3 rotation matrix
Quaternion &	operator*= (T s)
Quaternion &	operator/= (T s)

Static Public Member Functions
static Quaternion	lerp (const Quaternion &q0, const Quaternion &q1, T t)
	given t in [0,1], interpolates linearly two quaternions giving in general not-unit quaternion
static Quaternion	slerp (Quaternion q0, Quaternion q1, T t)
	given t in [0,1] and two unit quaternions, interpolates them spherically and produces another unit quaternion
static Matrix3< T >	slerp (const Matrix3< T > &m0, const Matrix3< T > &m1, T t)
	given t in [0,1] and two rotation matrices, interpolates them spherically and produces another rotation matrix
static AffineXf3< T >	slerp (const AffineXf3< T > &xf0, const AffineXf3< T > &xf1, T t, const Vector3< T > &p={})

Public Attributes
T	a = 1
	real part of the quaternion
T	b = 0
T	c = 0
T	d = 0
	imaginary part: b*i + c*j + d*k

Related Symbols
(Note that these are not member symbols.)
template<typename T >
T	dot (const Quaternion< T > &a, const Quaternion< T > &b)
	dot product
template<typename T >
Quaternion< T >	operator* (const Quaternion< T > &q1, const Quaternion< T > &q2)
	Hamilton product.
template<typename T >
Quaternion< T >	getClosestCanonicalQuaternion (const Quaternion< T > &base) noexcept
	returns closest to base canonical quaternion
template<typename T >
Matrix3< T >	slerp (const Matrix3< T > &m0, const Matrix3< T > &m1, T t)
	given t in [0,1] and two rotation matrices, interpolates them spherically and produces another rotation matrix
template<typename T >
AffineXf3< T >	slerp (const AffineXf3< T > &xf0, const AffineXf3< T > &xf1, T t, const Vector3< T > &p={})
template<typename T >
Matrix3< T >	orthonormalized (const Matrix3< T > &m)
	given any matrix, returns a close rotation matrix
template<typename T >
AffineXf3< T >	orthonormalized (const AffineXf3< T > &xf, const Vector3< T > &center={})

Detailed Description

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

Represents a quaternion following the notations from https://en.wikipedia.org/wiki/Quaternion

Constructor & Destructor Documentation

Quaternion() [1/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( )

constexprdefaultnoexcept

Quaternion() [2/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( T a, T b, T c, T d )

inlineconstexprnoexcept

Quaternion() [3/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( const Vector3< T > & axis, T angle )

constexprnoexcept

Quaternion() [4/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( T real, const Vector3< T > & im )

inlineconstexprnoexcept

Quaternion() [5/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( const Matrix3< T > & m )

constexpr

Quaternion() [6/6]

template<typename T >

MR::Quaternion< T >::Quaternion ( const Vector3< T > & from, const Vector3< T > & to )

constexprnoexcept

finds shorter arc rotation quaternion from one vector to another

Member Function Documentation

angle()

template<typename T >

T MR::Quaternion< T >::angle ( ) const

inlinenodiscardconstexprnoexcept

returns angle of rotation encoded in this quaternion

axis()

template<typename T >

Vector3< T > MR::Quaternion< T >::axis ( ) const

inlinenodiscardconstexprnoexcept

returns axis of rotation encoded in this quaternion

conjugate()

template<typename T >

Quaternion MR::Quaternion< T >::conjugate ( ) const

inlinenodiscardconstexprnoexcept

computes conjugate quaternion, which for unit quaternions encodes the opposite rotation

im()

template<typename T >

Vector3< T > MR::Quaternion< T >::im ( ) const

inlinenodiscardconstexprnoexcept

returns imaginary part of the quaternion as a vector

inverse()

template<typename T >

Quaternion MR::Quaternion< T >::inverse ( ) const

inlinenodiscardconstexprnoexcept

computes reciprocal quaternion

lerp()

template<typename T >

static Quaternion MR::Quaternion< T >::lerp ( const Quaternion< T > & q0, const Quaternion< T > & q1, T t )

inlinestaticnodiscard

given t in [0,1], interpolates linearly two quaternions giving in general not-unit quaternion

norm()

template<typename T >

T MR::Quaternion< T >::norm ( ) const

inlinenodiscardconstexpr

normalize()

template<typename T >

void MR::Quaternion< T >::normalize ( )

inline

scales this quaternion to make its norm unit

normalized()

template<typename T >

Quaternion MR::Quaternion< T >::normalized ( ) const

inlinenodiscard

normSq()

template<typename T >

T MR::Quaternion< T >::normSq ( ) const

inlinenodiscardconstexpr

operator Matrix3< T >()

template<typename T >

MR::Quaternion< T >::operator Matrix3< T > ( ) const

nodiscard

converts this into 3x3 rotation matrix

operator()()

template<typename T >

Vector3< T > MR::Quaternion< T >::operator() ( const Vector3< T > & p ) const

nodiscardconstexprnoexcept

for unit quaternion returns the rotation of point p, which is faster to compute for single point; for multiple points it is faster to create matrix representation and apply it to the points

operator*=()

template<typename T >

Quaternion & MR::Quaternion< T >::operator*= ( T s )

inline

operator-()

template<typename T >

Quaternion MR::Quaternion< T >::operator- ( ) const

inlinenodiscardconstexpr

returns quaternion representing the same rotation, using the opposite rotation direction and opposite angle

operator/=()

template<typename T >

Quaternion & MR::Quaternion< T >::operator/= ( T s )

inline

slerp() [1/3]

template<typename T >

static AffineXf3< T > MR::Quaternion< T >::slerp ( const AffineXf3< T > & xf0, const AffineXf3< T > & xf1, T t, const Vector3< T > & p = {} )

inlinestaticnodiscard

given t in [0,1] and rigid transformations, interpolates them spherically and produces another rigid transformation; p is the only point that will have straight line movement during interpolation

slerp() [2/3]

template<typename T >

static Matrix3< T > MR::Quaternion< T >::slerp ( const Matrix3< T > & m0, const Matrix3< T > & m1, T t )

inlinestaticnodiscard

given t in [0,1] and two rotation matrices, interpolates them spherically and produces another rotation matrix

slerp() [3/3]

template<typename T >

static Quaternion MR::Quaternion< T >::slerp ( Quaternion< T > q0, Quaternion< T > q1, T t )

staticnodiscard

given t in [0,1] and two unit quaternions, interpolates them spherically and produces another unit quaternion

Friends And Related Symbol Documentation

dot()

template<typename T >

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

related

dot product

getClosestCanonicalQuaternion()

template<typename T >

Quaternion< T > getClosestCanonicalQuaternion ( const Quaternion< T > & base )

related

returns closest to base canonical quaternion

operator*()

template<typename T >

Quaternion< T > operator* ( const Quaternion< T > & q1, const Quaternion< T > & q2 )

related

Hamilton product.

orthonormalized() [1/2]

template<typename T >

AffineXf3< T > orthonormalized ( const AffineXf3< T > & xf, const Vector3< T > & center = {} )

related

given any affine transformation, returns a close rigid transformation; center point will be transformed to same point by both input and output transformations

orthonormalized() [2/2]

template<typename T >

Matrix3< T > orthonormalized ( const Matrix3< T > & m )

related

given any matrix, returns a close rotation matrix

slerp() [1/2]

template<typename T >

AffineXf3< T > slerp ( const AffineXf3< T > & xf0, const AffineXf3< T > & xf1, T t, const Vector3< T > & p = {} )

related

given t in [0,1] and rigid transformations, interpolates them spherically and produces another rigid transformation; p is the only point that will have straight line movement during interpolation

slerp() [2/2]

template<typename T >

Matrix3< T > slerp ( const Matrix3< T > & m0, const Matrix3< T > & m1, T t )

related

given t in [0,1] and two rotation matrices, interpolates them spherically and produces another rotation matrix

Member Data Documentation

a

template<typename T >

T MR::Quaternion< T >::a = 1

real part of the quaternion

b

template<typename T >

T MR::Quaternion< T >::b = 0

c

template<typename T >

T MR::Quaternion< T >::c = 0

d

template<typename T >

T MR::Quaternion< T >::d = 0

imaginary part: b*i + c*j + d*k

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

• MRQuaternion.h