4-element vector that represents rotation in 3D. More...

#include <vnl_fwd.h>

Inheritance diagram for vnl_quaternion< T >:

Public Types
enum

typedef vnl_vector_fixed< T, n >	self

typedef size_t	size_type

typedef T	element_type
	Type defs for iterators. More...

typedef T *	iterator
	Type defs for iterators. More...

typedef T const *	const_iterator
	Const iterator type. More...

typedef vnl_c_vector< T >::abs_t	abs_t

Public Member Functions
	vnl_quaternion ()=default
	Constructor for null quaternion. More...

	vnl_quaternion (T x, T y, T z, T r)
	Construct quaternion from components x,y,z,r. More...

	vnl_quaternion (T theta_X, T theta_Y, T theta_Z)
	Construct quaternion from Euler Angles,. More...

	vnl_quaternion (vnl_vector_fixed< T, 3 > const &axis, double angle)
	Construct quaternion from axis and angle of rotation. More...

	vnl_quaternion (vnl_matrix_fixed< T, 3, 3 > const &transform)
	Construct quaternion from 3x3 row-major matrix. More...

	vnl_quaternion (vnl_vector_fixed< T, 3 > const &vec)
	Construct quaternion from a 3D vector. More...

	vnl_quaternion (vnl_vector_fixed< T, 4 > const &vec)
	Construct quaternion from a 4D vector. More...

	vnl_quaternion (vnl_quaternion< T > const &from)
	Copy constructor – Creates a copy of from quaternion. More...

	~vnl_quaternion ()=default
	Free internal array. More...

vnl_quaternion &	operator= (vnl_quaternion< T > const &rhs)
	Overloads assignment operator to copy rhs quaternion into lhs quaternion. More...

T &	x ()
	Imaginary component, parallel to axis of rotation. More...

T &	y ()
	Imaginary component, parallel to axis of rotation. More...

T &	z ()
	Imaginary component, parallel to axis of rotation. More...

T &	r ()
	Real component. More...

T	x () const
	Imaginary component, parallel to axis of rotation. More...

T	y () const
	Imaginary component, parallel to axis of rotation. More...

T	z () const
	Imaginary component, parallel to axis of rotation. More...

T	r () const
	Real component. More...

T	real () const
	Copies and returns the real part. More...

vnl_vector_fixed< T, 3 >	imaginary () const
	Copies and returns the imaginary part. More...

vnl_vector_fixed< T, 3 >	axis () const
	Axis of rotation. More...

double	angle () const
	Angle of rotation. More...

vnl_matrix_fixed< T, 3, 3 >	rotation_matrix_transpose () const
	3x3 rotation matrix. More...

vnl_matrix_fixed< T, 4, 4 >	rotation_matrix_transpose_4 () const
	4x4 rotation matrix. More...

vnl_quaternion< T >	conjugate () const
	Same real, opposite img part. More...

vnl_quaternion< T >	inverse () const
	Inverse for nonzero quat. More...

vnl_quaternion< T >	operator * (vnl_quaternion< T > const &) const
	Returns the product of two quaternions. More...

vnl_vector_fixed< T, 3 >	rotate (vnl_vector_fixed< T, 3 > const &) const
	Rotate 3D v. More...

vnl_vector_fixed< T, 3 >	rotation_euler_angles () const
	Rotation representation in Euler angles. More...

unsigned int	size () const
	Length of the vector. More...

void	put (unsigned int i, T const &v)
	Put value at given position in vector. More...

T	get (unsigned int i) const
	Get value at element i. More...

vnl_vector_fixed &	fill (T const &v)
	Set all values to v. More...

vnl_vector_fixed &	copy_in (T const *ptr)
	Sets elements to ptr[i]. More...

void	copy_out (T *ptr) const
	Copy elements to ptr[i]. More...

vnl_vector_fixed &	set (T const *ptr)
	Sets elements to ptr[i]. More...

T &	operator() (unsigned int i)
	Return reference to the element at specified index. More...

T const &	operator() (unsigned int i) const
	Return reference to the element at specified index. More...

T &	operator[] (const size_t i)
	Return the i-th element. More...

const T &	operator[] (const size_t i) const
	Return the i-th element. More...

T const *	data_block () const
	Access the contiguous block storing the elements in the vector. More...

T *	data_block ()
	Access the contiguous block storing the elements in the vector. More...

vnl_vector_ref< T >	as_ref ()
	Explicit conversion to a vnl_vector_ref. More...

const vnl_vector_ref< T >	as_ref () const
	Explicit conversion to a vnl_vector_ref. More...

	operator const vnl_vector_ref< T > () const
	Cheap conversion to vnl_vector_ref. More...

iterator	begin ()
	Iterator pointing to start of data. More...

const_iterator	begin () const
	Iterator pointing to start of data. More...

iterator	end ()
	Iterator pointing to element beyond end of data. More...

const_iterator	end () const
	Iterator pointing to element beyond end of data. More...

vnl_vector_fixed< T, n >	apply (T(*f)(T))
	Apply f to each element. More...

vnl_vector_fixed< T, n >	apply (T(*f)(const T &))
	Apply f to each element. More...

vnl_vector_fixed< T, n > &	operator+= (T s)

vnl_vector_fixed< T, n > &	operator+= (const vnl_vector_fixed< T, n > &v)

vnl_vector_fixed< T, n > &	operator+= (const vnl_vector< T > &v)

vnl_vector_fixed< T, n > &	operator-= (T s)

vnl_vector_fixed< T, n > &	operator-= (const vnl_vector_fixed< T, n > &v)

vnl_vector_fixed< T, n > &	operator-= (const vnl_vector< T > &v)

vnl_vector_fixed< T, n > &	operator *= (T s)

vnl_vector_fixed< T, n > &	operator/= (T s)

vnl_vector_fixed< T, n >	operator- () const

vnl_vector< T >	extract (unsigned int len, unsigned int start=0) const
	Returns a subvector specified by the start index and length. O(n). More...

vnl_vector< T >	as_vector () const
	Convert to a vnl_vector. More...

vnl_vector_fixed &	update (vnl_vector< T > const &, unsigned int start=0)
	Replaces elements with index beginning at start, by values of v. O(n). More...

abs_t	squared_magnitude () const
	Return sum of squares of elements. More...

abs_t	magnitude () const
	Return magnitude (length) of vector. More...

abs_t	one_norm () const
	Return sum of absolute values of the elements. More...

abs_t	two_norm () const
	Return sqrt of sum of squares of values of elements. More...

abs_t	inf_norm () const
	Return largest absolute element value. More...

vnl_vector_fixed< T, n > &	normalize ()
	Normalise by dividing through by the magnitude. More...

abs_t	rms () const
	Root Mean Squares of values. More...

T	min_value () const
	Smallest value. More...

T	max_value () const
	Largest value. More...

unsigned	arg_min () const
	Location of smallest value. More...

unsigned	arg_max () const
	Location of largest value. More...

T	mean () const
	Mean of values in vector. More...

T	sum () const
	Sum of values in a vector. More...

vnl_vector_fixed &	flip ()
	Reverse the order of the elements. More...

void	assert_size (unsigned sz) const
	Check that size()==sz if not, abort();. More...

void	assert_finite () const
	Check that this is finite if not, abort();. More...

bool	is_finite () const
	Return true if it's finite. More...

bool	is_zero () const
	Return true iff all the entries are zero. More...

bool	empty () const
	Return true iff the size is zero. More...

bool	operator_eq (vnl_vector_fixed< T, n > const &v) const
	Return true if *this == v. More...

bool	operator_eq (vnl_vector< T > const &v) const
	Return true if *this == v. More...

bool	read_ascii (std::istream &s)
	Read from text stream. More...

void	print (std::ostream &s) const
	Display the vector. More...

Static Public Member Functions
static void	add (const T a, const T b, T *r)

static void	add (const T a, T b, T r)

static void	sub (const T a, const T b, T *r)

static void	sub (const T a, T b, T r)

static void	sub (T a, const T b, T r)

static void	mul (const T a, const T b, T *r)

static void	mul (const T a, T b, T r)

static void	div (const T a, const T b, T *r)

static void	div (const T a, T b, T r)

Protected Attributes
T	data_ [n]

Private Types
typedef vnl_vector_fixed< T, 4 >	Base

Related Functions
(Note that these are not member functions.)
template<class T >
std::istream &	operator>> (std::istream &is, vnl_quaternion< T > &q)
	operator<<. More...

template<class T >
std::ostream &	operator<< (std::ostream &os, vnl_quaternion< T > const &q)
	operator<<. More...

template<class T >
void	x_write (std::ostream &os, vnl_quaternion< T > const &v, std::string name="vnl_quaternion")
	XML save vnl_quaternion to stream. More...

template<class T >
void	x_write_tree (std::ostream &os, vnl_quaternion< T > const &v, std::string name="vnl_quaternion")
	XML save vnl_quaternion as a 2-level tree to stream. More...

vnl_vector_fixed< T, n >	operator- (const vnl_vector_fixed< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator- (const T &s, const vnl_vector_fixed< T, n > &v)

vnl_vector_fixed< T, n >	operator- (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector< T >	operator- (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

vnl_vector< T >	operator- (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector_fixed< T, n >	operator- (const vnl_vector_fixed_ref_const< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator- (T s, const vnl_vector_fixed_ref_const< T, n > &v)

vnl_vector_fixed< T, n >	operator- (const vnl_vector_fixed_ref_const< T, n > &a, const vnl_vector_fixed_ref_const< T, n > &b)

void	vsl_b_write (vsl_b_ostream &os, const vnl_vector_fixed< T, n > &v)
	Binary save vnl_vector_fixed to stream. More...

void	vsl_b_read (vsl_b_istream &is, vnl_vector_fixed< T, n > &v)
	Binary load vnl_vector_fixed from stream. More...

void	vsl_print_summary (std::ostream &os, const vnl_vector_fixed< T, n > &b)
	Print human readable summary of object to a stream. More...

vnl_vector_fixed< std::complex< T >, n >	vnl_complexify (vnl_vector_fixed< T, n > const &R)
	Return complexified version of real fixed vector R. More...

vnl_vector_fixed< std::complex< T >, n >	vnl_complexify (vnl_vector_fixed< T, n > const &R, vnl_vector_fixed< T, n > const &I)
	Return complex fixed vector R+j*I from two real fixed vectors R and I. More...

T	vnl_cross_2d (const vnl_vector_fixed< T, 2 > &v1, const vnl_vector_fixed< T, 2 > &v2)
	Compute the 2-D cross product. More...

T	vnl_cross_2d (vnl_vector_fixed< T, 2 > const &v1, vnl_vector< T > const &v2)
	Compute the 2-D cross product. More...

T	vnl_cross_2d (vnl_vector< T > const &v1, vnl_vector_fixed< T, 2 > const &v2)
	Compute the 2-D cross product. More...

double	vnl_cross_2d (vnl_double_2 const &v1, vnl_double_2 const &v2)
	Cross product of two 2-vectors. More...

float	vnl_cross_2d (vnl_float_2 const &v1, vnl_float_2 const &v2)
	Cross product of two 2-vectors. More...

vnl_vector_fixed< T, 3 >	vnl_cross_3d (const vnl_vector_fixed< T, 3 > &v1, const vnl_vector_fixed< T, 3 > &v2)
	Compute the 3-D cross product. More...

vnl_vector_fixed< T, n >	vnl_cross_3d (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)
	Compute the 3-D cross product. More...

vnl_vector_fixed< T, n >	vnl_cross_3d (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)
	Compute the 3-D cross product. More...

vnl_double_3	vnl_cross_3d (vnl_double_3 const &v1, vnl_double_3 const &v2)
	Cross product of two 3-vectors. More...

vnl_float_3	vnl_cross_3d (vnl_float_3 const &v1, vnl_float_3 const &v2)
	Cross product of two 3-vectors. More...

vnl_vector_fixed< T, N >	operator * (vnl_diag_matrix_fixed< T, N > const &D, vnl_vector_fixed< T, N > const &A)
	Multiply a vnl_diag_matrix_fixed by a vnl_vector_fixed. n flops. More...

vnl_vector_fixed< T, N >	operator * (vnl_vector_fixed< T, N > const &A, vnl_diag_matrix_fixed< T, N > const &D)
	Multiply a vnl_vector_fixed by a vnl_diag_matrix_fixed. n flops. More...

vnl_vector_fixed< T, n >	operator * (const vnl_vector_fixed< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator * (const T &s, const vnl_vector_fixed< T, n > &v)

vnl_vector_fixed< T, n >	operator * (const vnl_vector_fixed_ref_const< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator * (T s, const vnl_vector_fixed_ref_const< T, n > &v)

vnl_vector_fixed< T, N >	vnl_imag (vnl_vector_fixed< std::complex< T >, N > const &C)
	Vector of imaginary parts of vnl_vector_fixed<std::complex<T>, N >. More...

vnl_double_3	operator+ (const vnl_double_3 &a, const vnl_double_3 &b)
	The binary addition operator. More...

vnl_vector_fixed< T, n >	operator+ (const vnl_vector_fixed< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator+ (const T &s, const vnl_vector_fixed< T, n > &v)

vnl_vector_fixed< T, n >	operator+ (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector< T >	operator+ (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

vnl_vector< T >	operator+ (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector_fixed< T, n >	operator+ (const vnl_vector_fixed_ref_const< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator+ (T s, const vnl_vector_fixed_ref_const< T, n > &v)

vnl_vector_fixed< T, n >	operator+ (const vnl_vector_fixed_ref_const< T, n > &a, const vnl_vector_fixed_ref_const< T, n > &b)

VNL_EXPORT std::ostream &	vnl_matlab_print (std::ostream &, vnl_vector_fixed< T, n > const &, char const *variable_name=nullptr, vnl_matlab_print_format=vnl_matlab_print_format_default)
	print a vnl_vector_fixed<T>. More...

VNL_EXPORT vnl_matrix_fixed< T, m, n >	outer_product (vnl_vector_fixed< T, m > const &a, vnl_vector_fixed< T, n > const &b)

vnl_matrix< T >	outer_product (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

vnl_matrix< T >	outer_product (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

VNL_EXPORT bool	operator< (vnl_vector_fixed< T, n > const &lhs, vnl_vector_fixed< T, n > const &rhs)
	Define a complete ordering on vnl_vector_fixed. More...

vnl_vector_fixed< T, N >	vnl_real (vnl_vector_fixed< std::complex< T >, N > const &C)
	Vector of real parts of vnl_vector_fixed<std::complex<T>, N >. More...

vnl_vector_fixed< T, n >	operator/ (const vnl_vector_fixed< T, n > &v, T s)

vnl_vector_fixed< T, n >	operator/ (const vnl_vector_fixed_ref_const< T, n > &v, T s)

vnl_vector_fixed< T, n >	element_product (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector< T >	element_product (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

vnl_vector< T >	element_product (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector_fixed< T, n >	element_quotient (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

vnl_vector< T >	element_quotient (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

vnl_vector< T >	element_quotient (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

T	dot_product (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

T	dot_product (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

T	dot_product (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

T	angle (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

T	angle (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

T	angle (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

T	vnl_vector_ssd (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

T	vnl_vector_ssd (const vnl_vector_fixed< T, n > &a, const vnl_vector< T > &b)

T	vnl_vector_ssd (const vnl_vector< T > &a, const vnl_vector_fixed< T, n > &b)

bool	operator== (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

bool	operator== (vnl_vector_fixed< T, n > const &a, vnl_vector< T > const &b)

bool	operator== (vnl_vector< T > const &a, vnl_vector_fixed< T, n > const &b)

bool	operator!= (const vnl_vector_fixed< T, n > &a, const vnl_vector_fixed< T, n > &b)

bool	operator!= (vnl_vector_fixed< T, n > const &a, vnl_vector< T > const &b)

bool	operator!= (vnl_vector< T > const &a, vnl_vector_fixed< T, n > const &b)

std::ostream &	operator<< (std::ostream &ostr, const vnl_vector_fixed< T, n > &v)

std::ostream &	operator<< (std::ostream &o, const vnl_vector_fixed_ref_const< T, n > &v)

std::istream &	operator>> (std::istream &ostr, vnl_vector_fixed< T, n > &v)

std::istream &	operator>> (std::istream &i, const vnl_vector_fixed_ref< T, n > &v)

void	x_write (std::ostream &os, vnl_vector_fixed< T, n > const &v, std::string name="vnl_vector_fixed")
	XML save vnl_vector_fixed to stream. More...

void	x_write_tree (std::ostream &os, vnl_vector_fixed< T, n > const &v, std::string name="vnl_vector_fixed")
	XML save vnl_vector_fixed as a 2-level tree to stream. More...

Detailed Description

template<class T>
class vnl_quaternion< T >

4-element vector that represents rotation in 3D.

vnl_quaternion is a 4-element vector with 1 real and 3 imaginary components:

q = r + (i*x + j*y + k*z)
r = cos(theta/2)
(x, y, z) = sin(theta/2) (kx, ky, kz)

where theta and k are respectively the angle and axis of rotation.

3D vectors can be thought of as pure imaginary quaternions, and so a quaternion is represented as a vnl_vector_fixed<T,4> with the imaginary part before the real part for 1-1 alignment.

Unit quaternions (i.e., for which $x^2 + y^2 + z^2 + r^2 = 1$ ) provide a more efficient representation for rotation than the usual orthonormal matrix that has nine parameters and six orthonormal constraints. The unit quaternion has only one unit magnitude constraint. Composing rotations with quaternions results in fewer multiplications and less error. To insure valid rotation results, the nearest unit quaternion is computed, and this is much easier than finding the nearest orthonormal matrix. Transforming vectors with a quaternion requires more operations compared to multiplication with the equivalent orthonormal matrix.

See also: vnl_vector_fixed and vnl_matrix_fixed for basic operations on vectors and matrices.; Envelope for envelope-letter scheme that avoids deep copy on return by value in arithmetic expressions like: q1 * q2 * q3 *...

Definition at line 29 of file vnl_fwd.h.

Member Typedef Documentation

◆ abs_t

typedef vnl_c_vector<T>::abs_t vnl_vector_fixed< T, n >::abs_t

inherited

Definition at line 365 of file vnl_vector_fixed.h.

◆ Base

template<class T>

typedef vnl_vector_fixed<T,4> vnl_quaternion< T >::Base

private

Definition at line 66 of file vnl_quaternion.h.

◆ const_iterator

typedef T const* vnl_vector_fixed< T, n >::const_iterator

inherited

Const iterator type.

Definition at line 296 of file vnl_vector_fixed.h.

◆ element_type

typedef T vnl_vector_fixed< T, n >::element_type

inherited

Type defs for iterators.

Definition at line 286 of file vnl_vector_fixed.h.

◆ iterator

typedef T* vnl_vector_fixed< T, n >::iterator

inherited

Type defs for iterators.

Definition at line 288 of file vnl_vector_fixed.h.

◆ self

typedef vnl_vector_fixed<T,n> vnl_vector_fixed< T, n >::self

inherited

Definition at line 93 of file vnl_vector_fixed.h.

◆ size_type

typedef size_t vnl_vector_fixed< T, n >::size_type

inherited

Definition at line 94 of file vnl_vector_fixed.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

Definition at line 96 of file vnl_vector_fixed.h.

Constructor & Destructor Documentation

◆ vnl_quaternion() [1/8]

template<class T>

vnl_quaternion< T >::vnl_quaternion ( )

default

Constructor for null quaternion.

◆ vnl_quaternion() [2/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion	(	T	tx,
		T	ty,
		T	tz,
		T	rea
	)

Construct quaternion from components x,y,z,r.

Creates a quaternion from its ordered components.

x, y, z denote the imaginary part, which are the coordinates of the rotation axis multiplied by the sine of half the angle of rotation. r denotes the real part, or the cosine of half the angle of rotation. Default is to create a null quaternion, corresponding to a null rotation or an identity transform, which has undefined rotation axis.

Definition at line 55 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [3/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion	(	T	theta_X,
		T	theta_Y,
		T	theta_Z
	)

Construct quaternion from Euler Angles,.

Construct quaternion from Euler Angles.

That is a rotation about the X axis, followed by Y, followed by the Z axis, using a fixed reference frame.

Definition at line 157 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [4/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion	(	vnl_vector_fixed< T, 3 > const &	axis,
		double	angle
	)

Construct quaternion from axis and angle of rotation.

Creates a quaternion from the normalized axis direction and the angle of rotation in radians.

Note: If you specify an angle in [0, 2pi], then methods angle() and axis() will return the same values. However, if you specify an angle in [-2pi, 0], then methods angle() and axis() will return values with opposite signs.

See also: vnl_quaternion::angle(); vnl_quaternion::axis()

Definition at line 66 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [5/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion ( vnl_matrix_fixed< T, 3, 3 > const & rot )

explicit

Construct quaternion from 3x3 row-major matrix.

Creates a quaternion from a rotation matrix.

Its orthonormal basis vectors are the matrix rows.

Note: this matrix must have determinant +1; this is not verified!

Warning: Takes the transpose of the rotation matrix, i.e., the orthonormal vectors must be the rows of the matrix, not the columns.

Definition at line 105 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [6/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion ( vnl_vector_fixed< T, 3 > const & vec )

Construct quaternion from a 3D vector.

Creates a quaternion from a vector.

3D vector is converted into an imaginary quaternion with same (x, y, z) components.

Definition at line 80 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [7/8]

template<class T >

vnl_quaternion< T >::vnl_quaternion ( vnl_vector_fixed< T, 4 > const & vec )

Construct quaternion from a 4D vector.

Creates a quaternion from a vector.

4D vector is assumed to be a 4-element quaternion, to provide casting between vector and quaternion

Definition at line 92 of file vnl_quaternion.hxx.

◆ vnl_quaternion() [8/8]

template<class T>

vnl_quaternion< T >::vnl_quaternion ( vnl_quaternion< T > const & from )

inline

Copy constructor – Creates a copy of from quaternion.

Definition at line 97 of file vnl_quaternion.h.

◆ ~vnl_quaternion()

template<class T>

vnl_quaternion< T >::~vnl_quaternion ( )

inlinedefault

Free internal array.

Member Function Documentation

◆ add() [1/2]

static void vnl_vector_fixed< T, n >::add	(	const T *	a,
		const T *	b,
		T *	r
	)

inlinestaticinherited

Definition at line 466 of file vnl_vector_fixed.h.

◆ add() [2/2]

static void vnl_vector_fixed< T, n >::add	(	const T *	a,
		T	b,
		T *	r
	)

inlinestaticinherited

Definition at line 472 of file vnl_vector_fixed.h.

◆ angle()

template<class T >

double vnl_quaternion< T >::angle ( ) const

Angle of rotation.

Queries the rotation angle of the quaternion.

Note: Returned angle lies in [0, 2*pi]

Returned angle lies in [0, 2*pi]

Definition at line 196 of file vnl_quaternion.hxx.

◆ apply() [1/2]

vnl_vector_fixed< T, n > vnl_vector_fixed< T, n >::apply ( T(*)(T) f )

inherited

Apply f to each element.

Returns a new vector with the result.

Definition at line 60 of file vnl_vector_fixed.hxx.

◆ apply() [2/2]

vnl_vector_fixed< T, n > vnl_vector_fixed< T, n >::apply ( T(*)(const T &) f )

inherited

Apply f to each element.

Returns a new vector with the result.

Definition at line 70 of file vnl_vector_fixed.hxx.

◆ arg_max()

unsigned vnl_vector_fixed< T, n >::arg_max ( ) const

inlineinherited

Location of largest value.

Definition at line 401 of file vnl_vector_fixed.h.

◆ arg_min()

unsigned vnl_vector_fixed< T, n >::arg_min ( ) const

inlineinherited

Location of smallest value.

Definition at line 398 of file vnl_vector_fixed.h.

◆ as_ref() [1/2]

vnl_vector_ref<T> vnl_vector_fixed< T, n >::as_ref ( )

inlineinherited

Explicit conversion to a vnl_vector_ref.

This is a cheap conversion for those functions that have an interface for vnl_vector but not for vnl_vector_fixed. There is also a conversion operator that should work most of the time.

See also: vnl_vector_ref::non_const

Definition at line 268 of file vnl_vector_fixed.h.

◆ as_ref() [2/2]

const vnl_vector_ref<T> vnl_vector_fixed< T, n >::as_ref ( ) const

inlineinherited

Explicit conversion to a vnl_vector_ref.

This is a cheap conversion for those functions that have an interface for vnl_vector but not for vnl_vector_fixed. There is also a conversion operator that should work most of the time.

See also: vnl_vector_ref::non_const

Definition at line 275 of file vnl_vector_fixed.h.

◆ as_vector()

vnl_vector<T> vnl_vector_fixed< T, n >::as_vector ( ) const

inlineinherited

Convert to a vnl_vector.

Definition at line 359 of file vnl_vector_fixed.h.

◆ assert_finite()

void vnl_vector_fixed< T, n >::assert_finite ( ) const

inlineinherited

Check that this is finite if not, abort();.

This function does or tests nothing if NDEBUG is defined

Definition at line 419 of file vnl_vector_fixed.h.

◆ assert_size()

void vnl_vector_fixed< T, n >::assert_size ( unsigned sz ) const

inlineinherited

Check that size()==sz if not, abort();.

This function does or tests nothing if NDEBUG is defined

Definition at line 415 of file vnl_vector_fixed.h.

◆ axis()

template<class T >

vnl_vector_fixed< T, 3 > vnl_quaternion< T >::axis ( ) const

Axis of rotation.

Queries the direction of the rotation axis of the quaternion.

Note: Axis not well defined for theta==0. In such a case (or if provided axis==(0,0,0)), this function returns (0,0,1).

A null quaternion will return zero for angle and k direction for axis.

Definition at line 205 of file vnl_quaternion.hxx.

◆ begin() [1/2]

iterator vnl_vector_fixed< T, n >::begin ( )

inlineinherited

Iterator pointing to start of data.

Definition at line 290 of file vnl_vector_fixed.h.

◆ begin() [2/2]

const_iterator vnl_vector_fixed< T, n >::begin ( ) const

inlineinherited

Iterator pointing to start of data.

Definition at line 298 of file vnl_vector_fixed.h.

◆ conjugate()

template<class T >

vnl_quaternion< T > vnl_quaternion< T >::conjugate ( ) const

Same real, opposite img part.

Returns the conjugate of given quaternion, having same real and opposite imaginary parts.

Definition at line 255 of file vnl_quaternion.hxx.

◆ copy_in()

vnl_vector_fixed& vnl_vector_fixed< T, n >::copy_in ( T const * ptr )

inlineinherited

Sets elements to ptr[i].

Note: ptr[i] must be valid for i=0..size()-1

Definition at line 211 of file vnl_vector_fixed.h.

◆ copy_out()

void vnl_vector_fixed< T, n >::copy_out ( T * ptr ) const

inlineinherited

Copy elements to ptr[i].

Note: ptr[i] must be valid for i=0..size()-1

Definition at line 220 of file vnl_vector_fixed.h.

◆ data_block() [1/2]

T const * vnl_vector_fixed< T, n >::data_block ( ) const

inherited

Access the contiguous block storing the elements in the vector.

O(1). data_block()[0] is the first element of the vector

Definition at line 50 of file vnl_vector_fixed.hxx.

◆ data_block() [2/2]

T * vnl_vector_fixed< T, n >::data_block ( )

inherited

Access the contiguous block storing the elements in the vector.

O(1). data_block()[0] is the first element of the vector

Definition at line 55 of file vnl_vector_fixed.hxx.

◆ div() [1/2]

static void vnl_vector_fixed< T, n >::div	(	const T *	a,
		const T *	b,
		T *	r
	)

inlinestaticinherited

Definition at line 508 of file vnl_vector_fixed.h.

◆ div() [2/2]

static void vnl_vector_fixed< T, n >::div	(	const T *	a,
		T	b,
		T *	r
	)

inlinestaticinherited

Definition at line 514 of file vnl_vector_fixed.h.

◆ empty()

bool vnl_vector_fixed< T, n >::empty ( ) const

inlineinherited

Return true iff the size is zero.

Definition at line 433 of file vnl_vector_fixed.h.

◆ end() [1/2]

iterator vnl_vector_fixed< T, n >::end ( )

inlineinherited

Iterator pointing to element beyond end of data.

Definition at line 293 of file vnl_vector_fixed.h.

◆ end() [2/2]

const_iterator vnl_vector_fixed< T, n >::end ( ) const

inlineinherited

Iterator pointing to element beyond end of data.

Definition at line 300 of file vnl_vector_fixed.h.

◆ extract()

vnl_vector<T> vnl_vector_fixed< T, n >::extract	(	unsigned int	len,
		unsigned int	start = `0`
	)		const

inlineinherited

Returns a subvector specified by the start index and length. O(n).

Definition at line 352 of file vnl_vector_fixed.h.

◆ fill()

vnl_vector_fixed& vnl_vector_fixed< T, n >::fill ( T const & v )

inlineinherited

Set all values to v.

Definition at line 202 of file vnl_vector_fixed.h.

◆ flip()

vnl_vector_fixed< T, n > & vnl_vector_fixed< T, n >::flip ( )

inherited

Reverse the order of the elements.

Element i swaps with element size()-1-i

Definition at line 91 of file vnl_vector_fixed.hxx.

◆ get()

T vnl_vector_fixed< T, n >::get ( unsigned int i ) const

inherited

Get value at element i.

Definition at line 156 of file vnl_vector_fixed.hxx.

◆ imaginary()

template<class T>

vnl_vector_fixed<T,3> vnl_quaternion< T >::imaginary ( ) const

inline

Copies and returns the imaginary part.

Definition at line 135 of file vnl_quaternion.h.

◆ inf_norm()

abs_t vnl_vector_fixed< T, n >::inf_norm ( ) const

inlineinherited

Return largest absolute element value.

Definition at line 380 of file vnl_vector_fixed.h.

◆ inverse()

template<class T >

vnl_quaternion< T > vnl_quaternion< T >::inverse ( ) const

Inverse for nonzero quat.

Returns the inverse of given quaternion.

For unit quaternion representing rotation, the inverse is the same as the conjugate.

Definition at line 265 of file vnl_quaternion.hxx.

◆ is_finite()

bool vnl_vector_fixed< T, n >::is_finite ( ) const

inherited

Return true if it's finite.

Definition at line 100 of file vnl_vector_fixed.hxx.

◆ is_zero()

bool vnl_vector_fixed< T, n >::is_zero ( ) const

inherited

Return true iff all the entries are zero.

Definition at line 112 of file vnl_vector_fixed.hxx.

◆ magnitude()

abs_t vnl_vector_fixed< T, n >::magnitude ( ) const

inlineinherited

Return magnitude (length) of vector.

Definition at line 371 of file vnl_vector_fixed.h.

◆ max_value()

T vnl_vector_fixed< T, n >::max_value ( ) const

inlineinherited

Largest value.

Definition at line 395 of file vnl_vector_fixed.h.

◆ mean()

T vnl_vector_fixed< T, n >::mean ( ) const

inlineinherited

Mean of values in vector.

Definition at line 404 of file vnl_vector_fixed.h.

◆ min_value()

T vnl_vector_fixed< T, n >::min_value ( ) const

inlineinherited

Smallest value.

Definition at line 392 of file vnl_vector_fixed.h.

◆ mul() [1/2]

static void vnl_vector_fixed< T, n >::mul	(	const T *	a,
		const T *	b,
		T *	r
	)

inlinestaticinherited

Definition at line 496 of file vnl_vector_fixed.h.

◆ mul() [2/2]

static void vnl_vector_fixed< T, n >::mul	(	const T *	a,
		T	b,
		T *	r
	)

inlinestaticinherited

Definition at line 502 of file vnl_vector_fixed.h.

◆ normalize()

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::normalize ( )

inlineinherited

Normalise by dividing through by the magnitude.

Definition at line 383 of file vnl_vector_fixed.h.

◆ one_norm()

abs_t vnl_vector_fixed< T, n >::one_norm ( ) const

inlineinherited

Return sum of absolute values of the elements.

Definition at line 374 of file vnl_vector_fixed.h.

◆ operator *()

template<class T >

vnl_quaternion< T > vnl_quaternion< T >::operator * ( vnl_quaternion< T > const & rhs ) const

Returns the product of two quaternions.

Multiplication of two quaternions is not symmetric and has fewer operations than multiplication of orthonormal matrices. If object is rotated by r1, then by r2, then the composed rotation (r2 o r1) is represented by the quaternion (q2 * q1), or by the matrix (m1 * m2). Note that matrix composition is reversed because matrices and vectors are represented row-wise.

Definition at line 282 of file vnl_quaternion.hxx.

◆ operator *=()

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator *= ( T s )

inlineinherited

Definition at line 318 of file vnl_vector_fixed.h.

◆ operator const vnl_vector_ref< T >()

vnl_vector_fixed< T, n >::operator const vnl_vector_ref< T > ( ) const

inlineinherited

Cheap conversion to vnl_vector_ref.

Sometimes, such as with templated functions, the compiler cannot use this user-defined conversion. For those cases, use the explicit as_ref() method instead.

Definition at line 281 of file vnl_vector_fixed.h.

◆ operator()() [1/2]

T & vnl_vector_fixed< T, n >::operator() ( unsigned int i )

inherited

Return reference to the element at specified index.

There are assert style boundary checks - #define NDEBUG to turn them off.

Definition at line 20 of file vnl_vector_fixed.hxx.

◆ operator()() [2/2]

T const & vnl_vector_fixed< T, n >::operator() ( unsigned int i ) const

inherited

Return reference to the element at specified index.

There are assert style boundary checks - #define NDEBUG to turn them off.

Definition at line 30 of file vnl_vector_fixed.hxx.

◆ operator+=() [1/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator+= ( T s )

inlineinherited

Definition at line 312 of file vnl_vector_fixed.h.

◆ operator+=() [2/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator+= ( const vnl_vector_fixed< T, n > & v )

inlineinherited

Definition at line 324 of file vnl_vector_fixed.h.

◆ operator+=() [3/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator+= ( const vnl_vector< T > & v )

inlineinherited

Definition at line 330 of file vnl_vector_fixed.h.

◆ operator-()

vnl_vector_fixed<T,n> vnl_vector_fixed< T, n >::operator- ( ) const

inlineinherited

Definition at line 344 of file vnl_vector_fixed.h.

◆ operator-=() [1/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator-= ( T s )

inlineinherited

Definition at line 315 of file vnl_vector_fixed.h.

◆ operator-=() [2/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator-= ( const vnl_vector_fixed< T, n > & v )

inlineinherited

Definition at line 327 of file vnl_vector_fixed.h.

◆ operator-=() [3/3]

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator-= ( const vnl_vector< T > & v )

inlineinherited

Definition at line 337 of file vnl_vector_fixed.h.

◆ operator/=()

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator/= ( T s )

inlineinherited

Definition at line 321 of file vnl_vector_fixed.h.

◆ operator=()

template<class T>

vnl_quaternion& vnl_quaternion< T >::operator= ( vnl_quaternion< T > const & rhs )

inline

Overloads assignment operator to copy rhs quaternion into lhs quaternion.

Definition at line 103 of file vnl_quaternion.h.

◆ operator[]() [1/2]

T & vnl_vector_fixed< T, n >::operator[] ( const size_t i )

inherited

Return the i-th element.

Definition at line 40 of file vnl_vector_fixed.hxx.

◆ operator[]() [2/2]

const T & vnl_vector_fixed< T, n >::operator[] ( const size_t i ) const

inherited

Return the i-th element.

Definition at line 45 of file vnl_vector_fixed.hxx.

◆ operator_eq() [1/2]

bool vnl_vector_fixed< T, n >::operator_eq ( vnl_vector_fixed< T, n > const & v ) const

inlineinherited

Return true if *this == v.

Definition at line 436 of file vnl_vector_fixed.h.

◆ operator_eq() [2/2]

bool vnl_vector_fixed< T, n >::operator_eq ( vnl_vector< T > const & v ) const

inlineinherited

Return true if *this == v.

Definition at line 445 of file vnl_vector_fixed.h.

◆ print()

void vnl_vector_fixed< T, n >::print ( std::ostream & s ) const

inherited

Display the vector.

Output each element separated by a single space.

Definition at line 146 of file vnl_vector_fixed.hxx.

◆ put()

void vnl_vector_fixed< T, n >::put	(	unsigned int	i,
		T const &	v
	)

inlineinherited

Put value at given position in vector.

Definition at line 189 of file vnl_vector_fixed.h.

◆ r() [1/2]

template<class T>

T& vnl_quaternion< T >::r ( )

inline

Real component.

Use this accessor to both get and set the component.

Definition at line 116 of file vnl_quaternion.h.

◆ r() [2/2]

template<class T>

T vnl_quaternion< T >::r ( ) const

inline

Real component.

Use this accessor to get the component.

Definition at line 129 of file vnl_quaternion.h.

◆ read_ascii()

bool vnl_vector_fixed< T, n >::read_ascii ( std::istream & s )

inherited

Read from text stream.

Definition at line 125 of file vnl_vector_fixed.hxx.

◆ real()

template<class T>

T vnl_quaternion< T >::real ( ) const

inline

Copies and returns the real part.

Definition at line 132 of file vnl_quaternion.h.

◆ rms()

abs_t vnl_vector_fixed< T, n >::rms ( ) const

inlineinherited

Root Mean Squares of values.

Definition at line 389 of file vnl_vector_fixed.h.

◆ rotate()

template<class T >

vnl_vector_fixed< T, 3 > vnl_quaternion< T >::rotate ( vnl_vector_fixed< T, 3 > const & v ) const

Rotate 3D v.

Rotates 3D vector v with source quaternion and stores the rotated vector back into v.

The quaternion must be normalised first.

For speed and greater accuracy, first convert quaternion into an orthonormal matrix, then use matrix multiplication to rotate many vectors.

Definition at line 299 of file vnl_quaternion.hxx.

◆ rotation_euler_angles()

template<class T >

vnl_vector_fixed< T, 3 > vnl_quaternion< T >::rotation_euler_angles ( ) const

Rotation representation in Euler angles.

The angles returned will be [theta_X,theta_Y,theta_Z] where the final rotation is found be first applying theta_X radians about the X axis, then theta_Y about the Y-axis, etc. The axes stay in a fixed reference frame. The quaternion mut be normalised first.

The angles returned will be [theta_X,theta_Y,theta_Z] where the final rotation is found be first applying theta_X radians about the X axis, then theta_Y about the Y-axis, etc. The axes stay in a fixed reference frame.

Definition at line 171 of file vnl_quaternion.hxx.

◆ rotation_matrix_transpose()

template<class T >

vnl_matrix_fixed< T, 3, 3 > vnl_quaternion< T >::rotation_matrix_transpose ( ) const

3x3 rotation matrix.

Converts a normalized quaternion into a square rotation matrix with dimension dim.

The orthonormal vectors are the rows of the matrix, not its columns

This is the reverse counterpart of constructing a quaternion from a transformation matrix. WARNING this is inconsistent with the quaternion docs and q.rotate()

Definition at line 224 of file vnl_quaternion.hxx.

◆ rotation_matrix_transpose_4()

template<class T >

vnl_matrix_fixed< T, 4, 4 > vnl_quaternion< T >::rotation_matrix_transpose_4 ( ) const

4x4 rotation matrix.

Definition at line 246 of file vnl_quaternion.hxx.

◆ set()

vnl_vector_fixed& vnl_vector_fixed< T, n >::set ( T const * ptr )

inlineinherited

Sets elements to ptr[i].

Note: ptr[i] must be valid for i=0..size()-1

Definition at line 228 of file vnl_vector_fixed.h.

◆ size()

unsigned int vnl_vector_fixed< T, n >::size ( ) const

inlineinherited

Length of the vector.

This is always n.

Definition at line 186 of file vnl_vector_fixed.h.

◆ squared_magnitude()

abs_t vnl_vector_fixed< T, n >::squared_magnitude ( ) const

inlineinherited

Return sum of squares of elements.

Definition at line 368 of file vnl_vector_fixed.h.

◆ sub() [1/3]

static void vnl_vector_fixed< T, n >::sub	(	const T *	a,
		const T *	b,
		T *	r
	)

inlinestaticinherited

Definition at line 478 of file vnl_vector_fixed.h.

◆ sub() [2/3]

static void vnl_vector_fixed< T, n >::sub	(	const T *	a,
		T	b,
		T *	r
	)

inlinestaticinherited

Definition at line 484 of file vnl_vector_fixed.h.

◆ sub() [3/3]

static void vnl_vector_fixed< T, n >::sub	(	T	a,
		const T *	b,
		T *	r
	)

inlinestaticinherited

Definition at line 490 of file vnl_vector_fixed.h.

◆ sum()

T vnl_vector_fixed< T, n >::sum ( ) const

inlineinherited

Sum of values in a vector.

Definition at line 407 of file vnl_vector_fixed.h.

◆ two_norm()

abs_t vnl_vector_fixed< T, n >::two_norm ( ) const

inlineinherited

Return sqrt of sum of squares of values of elements.

Definition at line 377 of file vnl_vector_fixed.h.

◆ update()

vnl_vector_fixed< T, n > & vnl_vector_fixed< T, n >::update	(	vnl_vector< T > const &	v,
		unsigned int	start = `0`
	)

inherited

Replaces elements with index beginning at start, by values of v. O(n).

Definition at line 80 of file vnl_vector_fixed.hxx.

◆ x() [1/2]

template<class T>

T& vnl_quaternion< T >::x ( )

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to both get and set the component.

Definition at line 107 of file vnl_quaternion.h.

◆ x() [2/2]

template<class T>

T vnl_quaternion< T >::x ( ) const

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to get the component.

Definition at line 120 of file vnl_quaternion.h.

◆ y() [1/2]

template<class T>

T& vnl_quaternion< T >::y ( )

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to both get and set the component.

Definition at line 110 of file vnl_quaternion.h.

◆ y() [2/2]

template<class T>

T vnl_quaternion< T >::y ( ) const

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to get the component.

Definition at line 123 of file vnl_quaternion.h.

◆ z() [1/2]

template<class T>

T& vnl_quaternion< T >::z ( )

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to both get and set the component.

Definition at line 113 of file vnl_quaternion.h.

◆ z() [2/2]

template<class T>

T vnl_quaternion< T >::z ( ) const

inline

Imaginary component, parallel to axis of rotation.

Use this accessor to get the component.

Definition at line 126 of file vnl_quaternion.h.

Friends And Related Function Documentation

◆ angle() [1/3]

T angle	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ angle() [2/3]

T angle	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ angle() [3/3]

T angle	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ dot_product() [1/3]

T dot_product	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ dot_product() [2/3]

T dot_product	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ dot_product() [3/3]

T dot_product	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ element_product() [1/3]

vnl_vector_fixed< T, n > element_product	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ element_product() [2/3]

vnl_vector< T > element_product	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ element_product() [3/3]

vnl_vector< T > element_product	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ element_quotient() [1/3]

vnl_vector_fixed< T, n > element_quotient	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ element_quotient() [2/3]

vnl_vector< T > element_quotient	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ element_quotient() [3/3]

vnl_vector< T > element_quotient	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator *() [1/6]

vnl_vector_fixed< T, N > operator *	(	vnl_diag_matrix_fixed< T, N > const &	D,
		vnl_vector_fixed< T, N > const &	A
	)

Definition at line 337 of file vnl_diag_matrix_fixed.h.

◆ operator *() [2/6]

vnl_vector_fixed< T, N > operator *	(	vnl_vector_fixed< T, N > const &	A,
		vnl_diag_matrix_fixed< T, N > const &	D
	)

Definition at line 346 of file vnl_diag_matrix_fixed.h.

◆ operator *() [3/6]

vnl_vector_fixed< T, n > operator *	(	const vnl_vector_fixed_ref_const< T, n > &	v,
		T	s
	)

◆ operator *() [4/6]

vnl_vector_fixed< T, n > operator *	(	T	s,
		const vnl_vector_fixed_ref_const< T, n > &	v
	)

◆ operator *() [5/6]

vnl_vector_fixed< T, n > operator *	(	const vnl_vector_fixed< T, n > &	v,
		T	s
	)

◆ operator *() [6/6]

vnl_vector_fixed< T, n > operator *	(	const T &	s,
		const vnl_vector_fixed< T, n > &	v
	)

◆ operator!=() [1/3]

bool operator!=	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator!=() [2/3]

bool operator!=	(	vnl_vector_fixed< T, n > const &	a,
		vnl_vector< T > const &	b
	)

◆ operator!=() [3/3]

bool operator!=	(	vnl_vector< T > const &	a,
		vnl_vector_fixed< T, n > const &	b
	)

◆ operator+() [1/9]

vnl_double_3 operator+	(	const vnl_double_3 &	a,
		const vnl_double_3 &	b
	)

Definition at line 37 of file vnl_linear_operators_3.h.

◆ operator+() [2/9]

vnl_vector_fixed< T, n > operator+	(	const vnl_vector_fixed_ref_const< T, n > &	v,
		T	s
	)

◆ operator+() [3/9]

vnl_vector_fixed< T, n > operator+	(	T	s,
		const vnl_vector_fixed_ref_const< T, n > &	v
	)

◆ operator+() [4/9]

vnl_vector_fixed< T, n > operator+	(	const vnl_vector_fixed_ref_const< T, n > &	a,
		const vnl_vector_fixed_ref_const< T, n > &	b
	)

◆ operator+() [5/9]

vnl_vector_fixed< T, n > operator+	(	const vnl_vector_fixed< T, n > &	v,
		T	s
	)

◆ operator+() [6/9]

vnl_vector_fixed< T, n > operator+	(	const T &	s,
		const vnl_vector_fixed< T, n > &	v
	)

◆ operator+() [7/9]

vnl_vector_fixed< T, n > operator+	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator+() [8/9]

vnl_vector< T > operator+	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ operator+() [9/9]

vnl_vector< T > operator+	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator-() [1/8]

vnl_vector_fixed< T, n > operator-	(	const vnl_vector_fixed_ref_const< T, n > &	v,
		T	s
	)

◆ operator-() [2/8]

vnl_vector_fixed< T, n > operator-	(	T	s,
		const vnl_vector_fixed_ref_const< T, n > &	v
	)

◆ operator-() [3/8]

vnl_vector_fixed< T, n > operator-	(	const vnl_vector_fixed_ref_const< T, n > &	a,
		const vnl_vector_fixed_ref_const< T, n > &	b
	)

◆ operator-() [4/8]

vnl_vector_fixed< T, n > operator-	(	const vnl_vector_fixed< T, n > &	v,
		T	s
	)

◆ operator-() [5/8]

vnl_vector_fixed< T, n > operator-	(	const T &	s,
		const vnl_vector_fixed< T, n > &	v
	)

◆ operator-() [6/8]

vnl_vector_fixed< T, n > operator-	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator-() [7/8]

vnl_vector< T > operator-	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ operator-() [8/8]

vnl_vector< T > operator-	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator/() [1/2]

vnl_vector_fixed< T, n > operator/	(	const vnl_vector_fixed_ref_const< T, n > &	v,
		T	s
	)

◆ operator/() [2/2]

vnl_vector_fixed< T, n > operator/	(	const vnl_vector_fixed< T, n > &	v,
		T	s
	)

◆ operator<()

VNL_EXPORT bool operator<	(	vnl_vector_fixed< T, n > const &	lhs,
		vnl_vector_fixed< T, n > const &	rhs
	)

This is useful to create a set, or map of vectors.

Definition at line 71 of file vnl_operators.h.

◆ operator<<() [1/3]

template<class T >

std::ostream & operator<<	(	std::ostream &	os,
		vnl_quaternion< T > const &	q
	)

Definition at line 188 of file vnl_quaternion.h.

◆ operator<<() [2/3]

std::ostream & operator<<	(	std::ostream &	o,
		const vnl_vector_fixed_ref_const< T, n > &	v
	)

◆ operator<<() [3/3]

std::ostream & operator<<	(	std::ostream &	ostr,
		const vnl_vector_fixed< T, n > &	v
	)

◆ operator==() [1/3]

bool operator==	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ operator==() [2/3]

bool operator==	(	vnl_vector_fixed< T, n > const &	a,
		vnl_vector< T > const &	b
	)

◆ operator==() [3/3]

bool operator==	(	vnl_vector< T > const &	a,
		vnl_vector_fixed< T, n > const &	b
	)

◆ operator>>() [1/3]

template<class T >

std::istream & operator>>	(	std::istream &	is,
		vnl_quaternion< T > &	q
	)

Definition at line 176 of file vnl_quaternion.h.

◆ operator>>() [2/3]

std::istream & operator>>	(	std::istream &	i,
		const vnl_vector_fixed_ref< T, n > &	v
	)

◆ operator>>() [3/3]

std::istream & operator>>	(	std::istream &	ostr,
		vnl_vector_fixed< T, n > &	v
	)

◆ outer_product() [1/3]

vnl_matrix< T > outer_product	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ outer_product() [2/3]

vnl_matrix< T > outer_product	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ outer_product() [3/3]

VNL_EXPORT vnl_matrix_fixed< T, m, n > outer_product	(	vnl_vector_fixed< T, m > const &	a,
		vnl_vector_fixed< T, n > const &	b
	)

vnl_vector_fixed< std::complex< T >, n > vnl_complexify ( vnl_vector_fixed< T, n > const & R )

Definition at line 60 of file vnl_complexify.h.

◆ vnl_complexify() [2/2]

vnl_vector_fixed< std::complex< T >, n > vnl_complexify	(	vnl_vector_fixed< T, n > const &	R,
		vnl_vector_fixed< T, n > const &	I
	)

Definition at line 132 of file vnl_complexify.h.

◆ vnl_cross_2d() [1/5]

double vnl_cross_2d	(	vnl_double_2 const &	v1,
		vnl_double_2 const &	v2
	)

Definition at line 25 of file vnl_double_2.h.

◆ vnl_cross_2d() [2/5]

float vnl_cross_2d	(	vnl_float_2 const &	v1,
		vnl_float_2 const &	v2
	)

Definition at line 25 of file vnl_float_2.h.

◆ vnl_cross_2d() [3/5]

T vnl_cross_2d	(	const vnl_vector_fixed< T, 2 > &	v1,
		const vnl_vector_fixed< T, 2 > &	v2
	)

Definition at line 34 of file vnl_cross.h.

◆ vnl_cross_2d() [4/5]

T vnl_cross_2d	(	vnl_vector_fixed< T, 2 > const &	v1,
		vnl_vector< T > const &	v2
	)

Definition at line 44 of file vnl_cross.h.

◆ vnl_cross_2d() [5/5]

T vnl_cross_2d	(	vnl_vector< T > const &	v1,
		vnl_vector_fixed< T, 2 > const &	v2
	)

Definition at line 55 of file vnl_cross.h.

◆ vnl_cross_3d() [1/5]

vnl_double_3 vnl_cross_3d	(	vnl_double_3 const &	v1,
		vnl_double_3 const &	v2
	)

Definition at line 25 of file vnl_double_3.h.

◆ vnl_cross_3d() [2/5]

vnl_float_3 vnl_cross_3d	(	vnl_float_3 const &	v1,
		vnl_float_3 const &	v2
	)

Definition at line 25 of file vnl_float_3.h.

◆ vnl_cross_3d() [3/5]

vnl_vector_fixed< T, 3 > vnl_cross_3d	(	const vnl_vector_fixed< T, 3 > &	v1,
		const vnl_vector_fixed< T, 3 > &	v2
	)

Definition at line 79 of file vnl_cross.h.

◆ vnl_cross_3d() [4/5]

vnl_vector_fixed< T, n > vnl_cross_3d	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

Definition at line 93 of file vnl_cross.h.

◆ vnl_cross_3d() [5/5]

vnl_vector_fixed< T, n > vnl_cross_3d	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

Definition at line 103 of file vnl_cross.h.

◆ vnl_imag()

vnl_vector_fixed< T, N > vnl_imag ( vnl_vector_fixed< std::complex< T >, N > const & C )

Definition at line 49 of file vnl_imag.h.

◆ vnl_matlab_print()

VNL_EXPORT std::ostream & vnl_matlab_print	(	std::ostream &	,
		vnl_vector_fixed< T, n > const &	,
		char const *	variable_name = `nullptr`,
		vnl_matlab_print_format	= `vnl_matlab_print_format_default`
	)

◆ vnl_real()

vnl_vector_fixed< T, N > vnl_real ( vnl_vector_fixed< std::complex< T >, N > const & C )

Definition at line 49 of file vnl_real.h.

◆ vnl_vector_ssd() [1/3]

T vnl_vector_ssd	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ vnl_vector_ssd() [2/3]

T vnl_vector_ssd	(	const vnl_vector_fixed< T, n > &	a,
		const vnl_vector< T > &	b
	)

◆ vnl_vector_ssd() [3/3]

T vnl_vector_ssd	(	const vnl_vector< T > &	a,
		const vnl_vector_fixed< T, n > &	b
	)

◆ vsl_b_read()

void vsl_b_read	(	vsl_b_istream &	is,
		vnl_vector_fixed< T, n > &	v
	)

◆ vsl_b_write()

void vsl_b_write	(	vsl_b_ostream &	os,
		const vnl_vector_fixed< T, n > &	v
	)

◆ vsl_print_summary()

void vsl_print_summary	(	std::ostream &	os,
		const vnl_vector_fixed< T, n > &	b
	)

◆ x_write() [1/2]

template<class T >

void x_write	(	std::ostream &	os,
		vnl_quaternion< T > const &	v,
		std::string	name = `"vnl_quaternion< T >"`
	)

◆ x_write() [2/2]

void x_write	(	std::ostream &	os,
		vnl_vector_fixed< T, n > const &	v,
		std::string	name = `"vnl_vector_fixed< T, 4 >"`
	)

◆ x_write_tree() [1/2]

template<class T >

void x_write_tree	(	std::ostream &	os,
		vnl_quaternion< T > const &	v,
		std::string	name = `"vnl_quaternion< T >"`
	)

◆ x_write_tree() [2/2]

void x_write_tree	(	std::ostream &	os,
		vnl_vector_fixed< T, n > const &	v,
		std::string	name = `"vnl_vector_fixed< T, 4 >"`
	)

Member Data Documentation

◆ data_

T vnl_vector_fixed< T, n >::data_[n]

protectedinherited

Definition at line 90 of file vnl_vector_fixed.h.

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

core/vnl/vnl_fwd.h
core/vnl/vnl_quaternion.h
core/vnl/vnl_quaternion.hxx
core/vnl/xio/vnl_xio_quaternion.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Types

Related Functions

Detailed Description

template<class T> class vnl_quaternion< T >

Member Typedef Documentation

◆ abs_t

◆ Base

◆ const_iterator

◆ element_type

◆ iterator

◆ self

◆ size_type

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ vnl_quaternion() [1/8]

◆ vnl_quaternion() [2/8]

◆ vnl_quaternion() [3/8]

◆ vnl_quaternion() [4/8]

◆ vnl_quaternion() [5/8]

◆ vnl_quaternion() [6/8]

◆ vnl_quaternion() [7/8]

◆ vnl_quaternion() [8/8]

◆ ~vnl_quaternion()

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ angle()

◆ apply() [1/2]

◆ apply() [2/2]

◆ arg_max()

◆ arg_min()

◆ as_ref() [1/2]

◆ as_ref() [2/2]

◆ as_vector()

◆ assert_finite()

◆ assert_size()

◆ axis()

◆ begin() [1/2]

◆ begin() [2/2]

◆ conjugate()

◆ copy_in()

◆ copy_out()

◆ data_block() [1/2]

◆ data_block() [2/2]

◆ div() [1/2]

◆ div() [2/2]

◆ empty()

◆ end() [1/2]

◆ end() [2/2]

◆ extract()

◆ fill()

◆ flip()

◆ get()

◆ imaginary()

◆ inf_norm()

◆ inverse()

◆ is_finite()

◆ is_zero()

◆ magnitude()

◆ max_value()

◆ mean()

◆ min_value()

◆ mul() [1/2]

◆ mul() [2/2]

◆ normalize()

◆ one_norm()

◆ operator *()

◆ operator *=()

◆ operator const vnl_vector_ref< T >()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-()

template<class T>
class vnl_quaternion< T >