#include <vnl_quaternion.h>
Inheritance diagram for vnl_quaternion< T >:
vnl_quaternion is a 4-element vector with 1 real and 3 imaginary components:
where theta and k are respectively the angle and axis of rotation. 3D vectors can be thought of as 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 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.
Envelope for envelope-letter scheme that avoids deep copy on return by value in arithmetic expressions like: q1 * q2 * q3 *...
Definition at line 60 of file vnl_quaternion.h.
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 Tconst * | 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, T angle) | |
| Construct quaternion from axis and angle of rotation. | |
| vnl_quaternion (vnl_matrix_fixed< T, 3, 3 > const &transform) | |
| Construct quaternion from 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. | |
| T | 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, Tconst &v) |
| Put value at given position in vector. | |
| T | get (unsigned int i) const |
| Get value at element i. | |
| void | fill (Tconst &v) |
| Set all values to v. | |
| void | copy_in (Tconst *ptr) |
| Sets elements to ptr[i]. | |
| void | copy_out (T *ptr) const |
| Copy elements to ptr[i]. | |
| void | set (Tconst *ptr) |
| Sets elements to ptr[i]. | |
| T & | operator() (unsigned int i) |
| Return reference to the element at specified index. | |
| Tconst & | 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. | |
| Tconst * | 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 () 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+= (Ts) |
| 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-= (Ts) |
| 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 *= (Ts) |
| vnl_vector_fixed< T, n > & | operator/= (Ts) |
| 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. | |
| T | mean () const |
| Mean of values in vector. | |
| T | sum () const |
| Sum of values in a vector. | |
| void | 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 its 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, Tb, T *r) |
| static void | sub (const T *a, const T *b, T *r) |
| static void | sub (const T *a, Tb, T *r) |
| static void | sub (Ta, const T *b, T *r) |
| static void | mul (const T *a, const T *b, T *r) |
| static void | mul (const T *a, Tb, T *r) |
| static void | div (const T *a, const T *b, T *r) |
| static void | div (const T *a, Tb, 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.) | |
| vcl_ostream & | operator<< (vcl_ostream &os, vnl_quaternion< T > const &q) |
| operator<<. | |
typedef vnl_vector_fixed<T,4> vnl_quaternion< T >::Base [private] |
Definition at line 62 of file vnl_quaternion.h.
typedef vnl_vector_fixed<T ,n> vnl_vector_fixed< T , n >::self [inherited] |
Definition at line 85 of file vnl_vector_fixed.h.
typedef unsigned int vnl_vector_fixed< T , n >::size_type [inherited] |
Definition at line 86 of file vnl_vector_fixed.h.
typedef T vnl_vector_fixed< T , n >::element_type [inherited] |
typedef T * vnl_vector_fixed< T , n >::iterator [inherited] |
typedef T const* vnl_vector_fixed< T , n >::const_iterator [inherited] |
typedef vnl_c_vector<T >::abs_t vnl_vector_fixed< T , n >::abs_t [inherited] |
Definition at line 345 of file vnl_vector_fixed.h.
anonymous enum [inherited] |
Definition at line 88 of file vnl_vector_fixed.h.
| vnl_quaternion< T >::vnl_quaternion | ( | ) | [inline] |
| vnl_quaternion< T >::vnl_quaternion | ( | T | x, | |
| T | y, | |||
| T | z, | |||
| T | r | |||
| ) |
Construct quaternion from components x,y,z,r.
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.
| vnl_quaternion< T >::vnl_quaternion | ( | T | theta_X, | |
| T | theta_Y, | |||
| T | theta_Z | |||
| ) |
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 145 of file vnl_quaternion.txx.
| vnl_quaternion< T >::vnl_quaternion | ( | vnl_vector_fixed< T, 3 > const & | axis, | |
| T | angle | |||
| ) |
Construct quaternion from axis and angle of rotation.
Definition at line 63 of file vnl_quaternion.txx.
| vnl_quaternion< T >::vnl_quaternion | ( | vnl_matrix_fixed< T, 3, 3 > const & | rot | ) | [explicit] |
Construct quaternion from from 3x3 row-major matrix.
Its orthonormal basis vectors are row-wise. WARNING: Takes the transpose of the rotation matrix...
Definition at line 100 of file vnl_quaternion.txx.
| vnl_quaternion< T >::vnl_quaternion | ( | vnl_vector_fixed< T, 3 > const & | vec | ) |
Construct quaternion from a 3D vector.
3D vector is converted into an imaginary quaternion with same (x, y, z) components.
Definition at line 77 of file vnl_quaternion.txx.
| vnl_quaternion< T >::vnl_quaternion | ( | vnl_vector_fixed< T, 4 > const & | vec | ) |
Construct quaternion from a 4D 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.
| vnl_quaternion< T >::vnl_quaternion | ( | vnl_quaternion< T > const & | from | ) | [inline] |
Copy constructor -- Creates a copy of from quaternion.
Definition at line 93 of file vnl_quaternion.h.
| vnl_quaternion< T >::~vnl_quaternion | ( | ) | [inline] |
| 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 99 of file vnl_quaternion.h.
| 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 103 of file vnl_quaternion.h.
| 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 106 of file vnl_quaternion.h.
| 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 109 of file vnl_quaternion.h.
| T& vnl_quaternion< T >::r | ( | ) | [inline] |
Real component.
Use this accessor to both get and set the component.
Definition at line 112 of file vnl_quaternion.h.
| T vnl_quaternion< T >::x | ( | ) | const [inline] |
Imaginary component, parallel to axis of rotation.
Use this accessor to get the component.
Definition at line 116 of file vnl_quaternion.h.
| T vnl_quaternion< T >::y | ( | ) | const [inline] |
Imaginary component, parallel to axis of rotation.
Use this accessor to get the component.
Definition at line 119 of file vnl_quaternion.h.
| T vnl_quaternion< T >::z | ( | ) | const [inline] |
Imaginary component, parallel to axis of rotation.
Use this accessor to get the component.
Definition at line 122 of file vnl_quaternion.h.
| T vnl_quaternion< T >::r | ( | ) | const [inline] |
Real component.
Use this accessor to get the component.
Definition at line 125 of file vnl_quaternion.h.
| T vnl_quaternion< T >::real | ( | ) | const [inline] |
| vnl_vector_fixed<T,3> vnl_quaternion< T >::imaginary | ( | ) | const [inline] |
| vnl_vector_fixed< T, 3 > vnl_quaternion< T >::axis | ( | ) | const |
Axis of rotation.
Definition at line 193 of file vnl_quaternion.txx.
| T vnl_quaternion< T >::angle | ( | ) | const |
Angle of rotation.
Definition at line 184 of file vnl_quaternion.txx.
| vnl_matrix_fixed< T, 3, 3 > vnl_quaternion< T >::rotation_matrix_transpose | ( | ) | const |
3x3 rotation matrix.
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 212 of file vnl_quaternion.txx.
| vnl_matrix_fixed< T, 4, 4 > vnl_quaternion< T >::rotation_matrix_transpose_4 | ( | ) | const |
| vnl_quaternion< T > vnl_quaternion< T >::conjugate | ( | ) | const |
| vnl_quaternion< T > vnl_quaternion< T >::inverse | ( | ) | const |
Inverse for nonzero quat.
For unit quaternion representing rotation, the inverse is the same as the conjugate.
Definition at line 255 of file vnl_quaternion.txx.
| 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 272 of file vnl_quaternion.txx.
| vnl_vector_fixed< T, 3 > vnl_quaternion< T >::rotate | ( | vnl_vector_fixed< T, 3 > const & | ) | const |
Rotate 3D v.
The quaternion must be normalised first.
Definition at line 289 of file vnl_quaternion.txx.
| vnl_vector_fixed< T, 3 > vnl_quaternion< T >::rotation_euler_angles | ( | ) | const |
Rotation representation in Euler angles.
The angles raturned 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.
Definition at line 159 of file vnl_quaternion.txx.
| unsigned vnl_vector_fixed< T , n >::size | ( | ) | const [inline, inherited] |
| void vnl_vector_fixed< T , n >::put | ( | unsigned int | i, | |
| T const & | v | |||
| ) | [inline, inherited] |
| T vnl_vector_fixed< T , n >::get | ( | unsigned int | i | ) | const [inline, inherited] |
| void vnl_vector_fixed< T , n >::fill | ( | T const & | v | ) | [inline, inherited] |
| void 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 184 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 192 of file vnl_vector_fixed.h.
| void 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 200 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 205 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 215 of file vnl_vector_fixed.h.
| T & vnl_vector_fixed< T , n >::operator[] | ( | unsigned int | i | ) | [inline, inherited] |
| const T & vnl_vector_fixed< T , n >::operator[] | ( | unsigned int | i | ) | const [inline, inherited] |
| 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 232 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 237 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.
Definition at line 252 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.
Definition at line 259 of file vnl_vector_fixed.h.
| vnl_vector_fixed< T , n >::operator const vnl_vector_ref | ( | ) | 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 265 of file vnl_vector_fixed.h.
| iterator vnl_vector_fixed< T , n >::begin | ( | ) | [inline, inherited] |
| const_iterator vnl_vector_fixed< T , n >::begin | ( | ) | const [inline, inherited] |
| iterator vnl_vector_fixed< T , n >::end | ( | ) | [inline, inherited] |
| const_iterator vnl_vector_fixed< T , n >::end | ( | ) | const [inline, inherited] |
| 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.
| vnl_vector_fixed<T ,n>& vnl_vector_fixed< T , n >::operator+= | ( | T | s | ) | [inline, inherited] |
Definition at line 296 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 308 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 314 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 321 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/= | ( | 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- | ( | ) | const [inline, inherited] |
Definition at line 328 of file vnl_vector_fixed.h.
| vnl_vector<T > vnl_vector_fixed< T , n >::extract | ( | unsigned int | len, | |
| unsigned int | start = 0 | |||
| ) | const [inherited] |
Returns a subvector specified by the start index and length. O(n).
| vnl_vector<T > vnl_vector_fixed< T , n >::as_vector | ( | ) | const [inline, inherited] |
| vnl_vector_fixed& vnl_vector_fixed< T , n >::update | ( | vnl_vector< T > const & | , | |
| unsigned int | start = 0 | |||
| ) | [inherited] |
Replaces elements with index beginning at start, by values of v. O(n).
| abs_t vnl_vector_fixed< T , n >::squared_magnitude | ( | ) | const [inline, inherited] |
| abs_t vnl_vector_fixed< T , n >::magnitude | ( | ) | const [inline, inherited] |
| abs_t vnl_vector_fixed< T , n >::one_norm | ( | ) | const [inline, inherited] |
| 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 357 of file vnl_vector_fixed.h.
| abs_t vnl_vector_fixed< T , n >::inf_norm | ( | ) | const [inline, inherited] |
| vnl_vector_fixed<T ,n>& vnl_vector_fixed< T , n >::normalize | ( | ) | [inline, inherited] |
| abs_t vnl_vector_fixed< T , n >::rms | ( | ) | const [inline, inherited] |
| T vnl_vector_fixed< T , n >::min_value | ( | ) | const [inline, inherited] |
| T vnl_vector_fixed< T , n >::max_value | ( | ) | const [inline, inherited] |