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

#include <vnl_quaternion.h>

Inheritance diagram for vnl_quaternion< T >:

Public Types
enum
typedef vnl_vector_fixed< T, n >	self
typedef unsigned int	size_type
typedef T	element_type
	Type defs for iterators.
typedef T *	iterator
	Type defs for iterators.
typedef T const *	const_iterator
	Const iterator type.
typedef vnl_c_vector< T >::abs_t	abs_t
Public Member Functions
	vnl_quaternion ()
	Constructor for null quaternion.
	vnl_quaternion (T x, T y, T z, T r)
	Construct quaternion from components x,y,z,r.
	vnl_quaternion (T theta_X, T theta_Y, T theta_Z)
	Construct quaternion from Euler Angles,.
	vnl_quaternion (vnl_vector_fixed< T, 3 > const &axis, double angle)
	Construct quaternion from axis and angle of rotation.
	vnl_quaternion (vnl_matrix_fixed< T, 3, 3 > const &transform)
	Construct quaternion from 3x3 row-major matrix.
	vnl_quaternion (vnl_vector_fixed< T, 3 > const &vec)
	Construct quaternion from a 3D vector.
	vnl_quaternion (vnl_vector_fixed< T, 4 > const &vec)
	Construct quaternion from a 4D vector.
	vnl_quaternion (vnl_quaternion< T > const &from)
	Copy constructor -- Creates a copy of from quaternion.
	~vnl_quaternion ()
	Free internal array.
vnl_quaternion &	operator= (vnl_quaternion< T > const &rhs)
	Overloads assignment operator to copy rhs quaternion into lhs quaternion.
T &	x ()
	Imaginary component, parallel to axis of rotation.
T &	y ()
	Imaginary component, parallel to axis of rotation.
T &	z ()
	Imaginary component, parallel to axis of rotation.
T &	r ()
	Real component.
T	x () const
	Imaginary component, parallel to axis of rotation.
T	y () const
	Imaginary component, parallel to axis of rotation.
T	z () const
	Imaginary component, parallel to axis of rotation.
T	r () const
	Real component.
T	real () const
	Copies and returns the real part.
vnl_vector_fixed< T, 3 >	imaginary () const
	Copies and returns the imaginary part.
vnl_vector_fixed< T, 3 >	axis () const
	Axis of rotation.
double	angle () const
	Angle of rotation.
vnl_matrix_fixed< T, 3, 3 >	rotation_matrix_transpose () const
	3x3 rotation matrix.
vnl_matrix_fixed< T, 4, 4 >	rotation_matrix_transpose_4 () const
	4x4 rotation matrix.
vnl_quaternion< T >	conjugate () const
	Same real, opposite img part.
vnl_quaternion< T >	inverse () const
	Inverse for nonzero quat.
vnl_quaternion< T >	operator* (vnl_quaternion< T > const &) const
	Returns the product of two quaternions.
vnl_vector_fixed< T, 3 >	rotate (vnl_vector_fixed< T, 3 > const &) const
	Rotate 3D v.
vnl_vector_fixed< T, 3 >	rotation_euler_angles () const
	Rotation representation in Euler angles.
unsigned	size () const
	Length of the vector.
void	put (unsigned int i, T const &v)
	Put value at given position in vector.
T	get (unsigned int i) const
	Get value at element i.
vnl_vector_fixed &	fill (T const &v)
	Set all values to v.
vnl_vector_fixed &	copy_in (T const *ptr)
	Sets elements to ptr[i].
void	copy_out (T *ptr) const
	Copy elements to ptr[i].
vnl_vector_fixed &	set (T const *ptr)
	Sets elements to ptr[i].
T &	operator() (unsigned int i)
	Return reference to the element at specified index.
T const &	operator() (unsigned int i) const
	Return reference to the element at specified index.
T &	operator[] (unsigned int i)
	Return the i-th element.
const T &	operator[] (unsigned int i) const
	Return the i-th element.
T const *	data_block () const
	Access the contiguous block storing the elements in the vector.
T *	data_block ()
	Access the contiguous block storing the elements in the vector.
vnl_vector_ref< T >	as_ref ()
	Explicit conversion to a vnl_vector_ref.
const vnl_vector_ref< T >	as_ref () const
	Explicit conversion to a vnl_vector_ref.
	operator const vnl_vector_ref< T > () const
	Cheap conversion to vnl_vector_ref.
iterator	begin ()
	Iterator pointing to start of data.
const_iterator	begin () const
	Iterator pointing to start of data.
iterator	end ()
	Iterator pointing to element beyond end of data.
const_iterator	end () const
	Iterator pointing to element beyond end of data.
vnl_vector_fixed< T, n >	apply (T(*f)(T))
	Apply f to each element.
vnl_vector_fixed< T, n >	apply (T(*f)(const T &))
	Apply f to each element.
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).
vnl_vector< T >	as_vector () const
	Convert to a vnl_vector.
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).
abs_t	squared_magnitude () const
	Return sum of squares of elements.
abs_t	magnitude () const
	Return magnitude (length) of vector.
abs_t	one_norm () const
	Return sum of absolute values of the elements.
abs_t	two_norm () const
	Return sqrt of sum of squares of values of elements.
abs_t	inf_norm () const
	Return largest absolute element value.
vnl_vector_fixed< T, n > &	normalize ()
	Normalise by dividing through by the magnitude.
abs_t	rms () const
	Root Mean Squares of values.
T	min_value () const
	Smallest value.
T	max_value () const
	Largest value.
unsigned	arg_min () const
	Location of smallest value.
unsigned	arg_max () const
	Location of largest value.
T	mean () const
	Mean of values in vector.
T	sum () const
	Sum of values in a vector.
vnl_vector_fixed &	flip ()
	Reverse the order of the elements.
void	assert_size (unsigned sz) const
	Check that size()==sz if not, abort();.
void	assert_finite () const
	Check that this is finite if not, abort();.
bool	is_finite () const
	Return true if it's finite.
bool	is_zero () const
	Return true iff all the entries are zero.
bool	empty () const
	Return true iff the size is zero.
bool	operator_eq (vnl_vector_fixed< T, n > const &v) const
	Return true if *this == v.
bool	operator_eq (vnl_vector< T > const &v) const
	Return true if *this == v.
bool	read_ascii (vcl_istream &s)
	Read from text stream.
void	print (vcl_ostream &s) const
	Display the vector.
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 >
vcl_ostream &	operator<< (vcl_ostream &os, vnl_quaternion< T > const &q)
	operator<<.
template<class T >
void	x_write (vcl_ostream &os, vnl_quaternion< T > const &v, vcl_string name="vnl_quaternion")
	XML save vnl_quaternion to stream.
template<class T >
void	x_write_tree (vcl_ostream &os, vnl_quaternion< T > const &v, vcl_string name="vnl_quaternion")
	XML save vnl_quaternion as a 2-level tree to stream.

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 62 of file vnl_quaternion.h.

Member Typedef Documentation

typedef vnl_c_vector<T>::abs_t vnl_vector_fixed< T, n >::abs_t [inherited]

Definition at line 348 of file vnl_vector_fixed.h.

template<class T>

typedef vnl_vector_fixed<T,4> vnl_quaternion< T >::Base [private]

Definition at line 64 of file vnl_quaternion.h.

typedef T const* vnl_vector_fixed< T, n >::const_iterator [inherited]

Const iterator type.

Definition at line 283 of file vnl_vector_fixed.h.

typedef T vnl_vector_fixed< T, n >::element_type [inherited]

Type defs for iterators.

Definition at line 273 of file vnl_vector_fixed.h.

typedef T* vnl_vector_fixed< T, n >::iterator [inherited]

Type defs for iterators.

Definition at line 275 of file vnl_vector_fixed.h.

typedef vnl_vector_fixed<T,n> vnl_vector_fixed< T, n >::self [inherited]

Definition at line 91 of file vnl_vector_fixed.h.

typedef unsigned int vnl_vector_fixed< T, n >::size_type [inherited]

Definition at line 92 of file vnl_vector_fixed.h.

Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 94 of file vnl_vector_fixed.h.

Constructor & Destructor Documentation

template<class T>

vnl_quaternion< T >::vnl_quaternion ( ) [inline]

Constructor for null quaternion.

Definition at line 68 of file vnl_quaternion.h.

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 52 of file vnl_quaternion.txx.

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 154 of file vnl_quaternion.txx.

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 63 of file vnl_quaternion.txx.

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 102 of file vnl_quaternion.txx.

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 77 of file vnl_quaternion.txx.

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 89 of file vnl_quaternion.txx.

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 95 of file vnl_quaternion.h.

template<class T>

vnl_quaternion< T >::~vnl_quaternion ( ) [inline]

Free internal array.

Definition at line 98 of file vnl_quaternion.h.

Member Function Documentation

static void vnl_vector_fixed< T, n >::add	(	const T *	a,
		const T *	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 449 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::add	(	const T *	a,
		T	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 455 of file vnl_vector_fixed.h.

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 193 of file vnl_quaternion.txx.

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.

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.

unsigned vnl_vector_fixed< T, n >::arg_max ( ) const [inline, inherited]

Location of largest value.

Definition at line 384 of file vnl_vector_fixed.h.

unsigned vnl_vector_fixed< T, n >::arg_min ( ) const [inline, inherited]

Location of smallest value.

Definition at line 381 of file vnl_vector_fixed.h.

vnl_vector_ref<T> vnl_vector_fixed< T, n >::as_ref ( ) [inline, inherited]

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 255 of file vnl_vector_fixed.h.

const vnl_vector_ref<T> vnl_vector_fixed< T, n >::as_ref ( ) const [inline, inherited]

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 262 of file vnl_vector_fixed.h.

vnl_vector<T> vnl_vector_fixed< T, n >::as_vector ( ) const [inline, inherited]

Convert to a vnl_vector.

Definition at line 342 of file vnl_vector_fixed.h.

void vnl_vector_fixed< T, n >::assert_finite ( ) const [inline, inherited]

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

This function does or tests nothing if NDEBUG is defined

Definition at line 402 of file vnl_vector_fixed.h.

void vnl_vector_fixed< T, n >::assert_size ( unsigned sz ) const [inline, inherited]

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

This function does or tests nothing if NDEBUG is defined

Definition at line 398 of file vnl_vector_fixed.h.

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 202 of file vnl_quaternion.txx.

iterator vnl_vector_fixed< T, n >::begin ( ) [inline, inherited]

Iterator pointing to start of data.

Definition at line 277 of file vnl_vector_fixed.h.

const_iterator vnl_vector_fixed< T, n >::begin ( ) const [inline, inherited]

Iterator pointing to start of data.

Definition at line 285 of file vnl_vector_fixed.h.

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 252 of file vnl_quaternion.txx.

vnl_vector_fixed& vnl_vector_fixed< T, n >::copy_in ( T const * ptr ) [inline, inherited]

Sets elements to ptr[i].

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

Definition at line 187 of file vnl_vector_fixed.h.

void vnl_vector_fixed< T, n >::copy_out ( T * ptr ) const [inline, inherited]

Copy elements to ptr[i].

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

Definition at line 196 of file vnl_vector_fixed.h.

T const* vnl_vector_fixed< T, n >::data_block ( ) const [inline, 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 235 of file vnl_vector_fixed.h.

T* vnl_vector_fixed< T, n >::data_block ( ) [inline, 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 240 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::div	(	const T *	a,
		const T *	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 491 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::div	(	const T *	a,
		T	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 497 of file vnl_vector_fixed.h.

bool vnl_vector_fixed< T, n >::empty ( ) const [inline, inherited]

Return true iff the size is zero.

Definition at line 416 of file vnl_vector_fixed.h.

iterator vnl_vector_fixed< T, n >::end ( ) [inline, inherited]

Iterator pointing to element beyond end of data.

Definition at line 280 of file vnl_vector_fixed.h.

const_iterator vnl_vector_fixed< T, n >::end ( ) const [inline, inherited]

Iterator pointing to element beyond end of data.

Definition at line 287 of file vnl_vector_fixed.h.

vnl_vector< T > vnl_vector< T >::extract	(	unsigned int	len,
		unsigned int	start = `0`
	)		const `[inherited]`

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

Definition at line 587 of file vnl_vector.txx.

vnl_vector_fixed& vnl_vector_fixed< T, n >::fill ( T const & v ) [inline, inherited]

Set all values to v.

Definition at line 178 of file vnl_vector_fixed.h.

vnl_vector_fixed& vnl_vector_fixed< T, n >::flip ( ) [inherited]

Reverse the order of the elements.

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

T vnl_vector_fixed< T, n >::get ( unsigned int i ) const [inline, inherited]

Get value at element i.

Definition at line 175 of file vnl_vector_fixed.h.

template<class T>

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

Copies and returns the imaginary part.

Definition at line 133 of file vnl_quaternion.h.

abs_t vnl_vector_fixed< T, n >::inf_norm ( ) const [inline, inherited]

Return largest absolute element value.

Definition at line 363 of file vnl_vector_fixed.h.

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 262 of file vnl_quaternion.txx.

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

Return true if it's finite.

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

Return true iff all the entries are zero.

abs_t vnl_vector_fixed< T, n >::magnitude ( ) const [inline, inherited]

Return magnitude (length) of vector.

Definition at line 354 of file vnl_vector_fixed.h.

T vnl_vector_fixed< T, n >::max_value ( ) const [inline, inherited]

Largest value.

Definition at line 378 of file vnl_vector_fixed.h.

T vnl_vector_fixed< T, n >::mean ( ) const [inline, inherited]

Mean of values in vector.

Definition at line 387 of file vnl_vector_fixed.h.

T vnl_vector_fixed< T, n >::min_value ( ) const [inline, inherited]

Smallest value.

Definition at line 375 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::mul	(	const T *	a,
		const T *	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 479 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::mul	(	const T *	a,
		T	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 485 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::normalize ( ) [inline, inherited]

Normalise by dividing through by the magnitude.

Definition at line 366 of file vnl_vector_fixed.h.

abs_t vnl_vector_fixed< T, n >::one_norm ( ) const [inline, inherited]

Return sum of absolute values of the elements.

Definition at line 357 of file vnl_vector_fixed.h.

vnl_vector_fixed< T, n >::operator const vnl_vector_ref< T > ( ) const [inline, inherited]

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 268 of file vnl_vector_fixed.h.

T& vnl_vector_fixed< T, n >::operator() ( unsigned int i ) [inline, inherited]

Return reference to the element at specified index.

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

Definition at line 208 of file vnl_vector_fixed.h.

T const& vnl_vector_fixed< T, n >::operator() ( unsigned int i ) const [inline, inherited]

Return reference to the element at specified index.

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

Definition at line 218 of file vnl_vector_fixed.h.

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 279 of file vnl_quaternion.txx.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator*= ( T s ) [inline, inherited]

Definition at line 305 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator+= ( T s ) [inline, inherited]

Definition at line 299 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator+= ( const vnl_vector_fixed< T, n > & v ) [inline, inherited]

Definition at line 311 of file vnl_vector_fixed.h.

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

Definition at line 317 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n> vnl_vector_fixed< T, n >::operator- ( ) const [inline, inherited]

Definition at line 331 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator-= ( T s ) [inline, inherited]

Definition at line 302 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator-= ( const vnl_vector_fixed< T, n > & v ) [inline, inherited]

Definition at line 314 of file vnl_vector_fixed.h.

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

Definition at line 324 of file vnl_vector_fixed.h.

vnl_vector_fixed<T,n>& vnl_vector_fixed< T, n >::operator/= ( T s ) [inline, inherited]

Definition at line 308 of file vnl_vector_fixed.h.

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 101 of file vnl_quaternion.h.

T& vnl_vector_fixed< T, n >::operator[] ( unsigned int i ) [inline, inherited]

Return the i-th element.

Definition at line 227 of file vnl_vector_fixed.h.

const T& vnl_vector_fixed< T, n >::operator[] ( unsigned int i ) const [inline, inherited]

Return the i-th element.

Definition at line 230 of file vnl_vector_fixed.h.

bool vnl_vector_fixed< T, n >::operator_eq ( vnl_vector_fixed< T, n > const & v ) const [inline, inherited]

Return true if *this == v.

Definition at line 419 of file vnl_vector_fixed.h.

bool vnl_vector_fixed< T, n >::operator_eq ( vnl_vector< T > const & v ) const [inline, inherited]

Return true if *this == v.

Definition at line 428 of file vnl_vector_fixed.h.

void vnl_vector_fixed< T, n >::print ( vcl_ostream & s ) const [inherited]

Display the vector.

Output each element separated by a single space.

void vnl_vector_fixed< T, n >::put	(	unsigned int	i,
		T const &	v
	)		`[inline, inherited]`

Put value at given position in vector.

Definition at line 172 of file vnl_vector_fixed.h.

template<class T>

T& vnl_quaternion< T >::r ( ) [inline]

Real component.

Use this accessor to both get and set the component.

Definition at line 114 of file vnl_quaternion.h.

template<class T>

T vnl_quaternion< T >::r ( ) const [inline]

Real component.

Use this accessor to get the component.

Definition at line 127 of file vnl_quaternion.h.

bool vnl_vector_fixed< T, n >::read_ascii ( vcl_istream & s ) [inherited]

Read from text stream.

template<class T>

T vnl_quaternion< T >::real ( ) const [inline]

Copies and returns the real part.

Definition at line 130 of file vnl_quaternion.h.

abs_t vnl_vector_fixed< T, n >::rms ( ) const [inline, inherited]

Root Mean Squares of values.

Definition at line 372 of file vnl_vector_fixed.h.

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 296 of file vnl_quaternion.txx.

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 168 of file vnl_quaternion.txx.

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 221 of file vnl_quaternion.txx.

template<class T >

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

4x4 rotation matrix.

Definition at line 243 of file vnl_quaternion.txx.

vnl_vector_fixed& vnl_vector_fixed< T, n >::set ( T const * ptr ) [inline, inherited]

Sets elements to ptr[i].

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

Definition at line 204 of file vnl_vector_fixed.h.

unsigned vnl_vector_fixed< T, n >::size ( ) const [inline, inherited]

Length of the vector.

This is always n.

Definition at line 169 of file vnl_vector_fixed.h.

abs_t vnl_vector_fixed< T, n >::squared_magnitude ( ) const [inline, inherited]

Return sum of squares of elements.

Definition at line 351 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::sub	(	const T *	a,
		const T *	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 461 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::sub	(	const T *	a,
		T	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 467 of file vnl_vector_fixed.h.

static void vnl_vector_fixed< T, n >::sub	(	T	a,
		const T *	b,
		T *	r
	)		`[inline, static, inherited]`

Definition at line 473 of file vnl_vector_fixed.h.

T vnl_vector_fixed< T, n >::sum ( ) const [inline, inherited]

Sum of values in a vector.

Definition at line 390 of file vnl_vector_fixed.h.

abs_t vnl_vector_fixed< T, n >::two_norm ( ) const [inline, inherited]

Return sqrt of sum of squares of values of elements.

Definition at line 360 of file vnl_vector_fixed.h.

vnl_vector< T > & vnl_vector< T >::update	(	vnl_vector< T > const &	,
		unsigned int	start = `0`
	)		`[inherited]`

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

Definition at line 571 of file vnl_vector.txx.

template<class T>

T& vnl_quaternion< T >::x ( ) [inline]