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={})

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>
const Quaternion< T > *	getCanonicalQuaternions () noexcept
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

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

Public Member Functions