colvarmodule::quaternion Class Reference

1-dimensional vector of real numbers with four components and a quaternion algebra More...

#include <colvartypes.h>

Public Member Functions
	quaternion (cvm::real x, cvm::real y, cvm::real z)
	Constructor from a 3-d vector.
	quaternion (cvm::real const qv[4])
	Constructor component by component.
	quaternion (cvm::real q0i, cvm::real q1i, cvm::real q2i, cvm::real q3i)
	Constructor component by component.
	quaternion (cvm::vector1d< cvm::real > const &v)
void	set_from_euler_angles (cvm::real phi_in, cvm::real theta_in, cvm::real psi_in)
	quaternion ()
	Default constructor.
void	set (cvm::real value)
	Set all components to a scalar.
void	reset ()
	Set all components to zero (null quaternion)
void	reset_rotation ()
	Set the q0 component to 1 and the others to 0 (quaternion representing no rotation)
std::string	to_simple_string () const
int	from_simple_string (std::string const &s)
cvm::real &	operator[] (int i)
	Access the quaternion as a 4-d array (return a reference)
cvm::real	operator[] (int i) const
	Access the quaternion as a 4-d array (return a value)
cvm::vector1d< cvm::real > const	as_vector () const
cvm::real	norm2 () const
	Square norm of the quaternion.
cvm::real	norm () const
	Norm of the quaternion.
cvm::quaternion	conjugate () const
	Return the conjugate quaternion.
void	operator*= (cvm::real a)
void	operator/= (cvm::real a)
void	set_positive ()
void	operator+= (cvm::quaternion const &h)
void	operator-= (cvm::quaternion const &h)
cvm::rvector	get_vector () const
	Return the vector component.
cvm::rvector	rotate (cvm::rvector const &v) const
	Rotate v through this quaternion (put it in the rotated reference frame)
cvm::quaternion	rotate (cvm::quaternion const &Q2) const
	Rotate Q2 through this quaternion (put it in the rotated reference frame)
cvm::rmatrix	rotation_matrix () const
	Return the 3x3 matrix associated to this quaternion.
cvm::quaternion	position_derivative_inner (cvm::rvector const &pos, cvm::rvector const &vec) const
	Multiply the given vector by the derivative of the given (rotated) position with respect to the quaternion.
cvm::real	cosine (cvm::quaternion const &q) const
	Return the cosine between the orientation frame associated to this quaternion and another.
cvm::real	dist2 (cvm::quaternion const &Q2) const
	Square distance from another quaternion on the 4-dimensional unit sphere: returns the square of the angle along the shorter of the two geodesics.
cvm::quaternion	dist2_grad (cvm::quaternion const &Q2) const
void	match (cvm::quaternion &Q2) const
	Choose the closest between Q2 and -Q2 and save it back. Not required for dist2() and dist2_grad()
cvm::real	inner (cvm::quaternion const &Q2) const
	Inner product (as a 4-d vector) with Q2; requires match() if the largest overlap is looked for.

Static Public Member Functions
static size_t	output_width (size_t real_width)
	Tell the number of characters required to print a quaternion, given that of a real number.

Public Attributes
cvm::real	q0
cvm::real	q1
cvm::real	q2
cvm::real	q3

Friends
std::ostream &	operator<< (std::ostream &os, cvm::quaternion const &q)
	Formatted output operator.
std::istream &	operator>> (std::istream &is, cvm::quaternion &q)
	Formatted input operator.
cvm::quaternion	operator+ (cvm::quaternion const &h, cvm::quaternion const &q)
cvm::quaternion	operator- (cvm::quaternion const &h, cvm::quaternion const &q)
cvm::quaternion	operator* (cvm::quaternion const &h, cvm::quaternion const &q)
	Provides the quaternion product. NOTE: for the inner product use: h.inner (q);
cvm::quaternion	operator* (cvm::real c, cvm::quaternion const &q)
cvm::quaternion	operator* (cvm::quaternion const &q, cvm::real c)
cvm::quaternion	operator/ (cvm::quaternion const &q, cvm::real c)

Detailed Description

1-dimensional vector of real numbers with four components and a quaternion algebra

Member Function Documentation

dist2_grad()

cvm::quaternion colvarmodule::quaternion::dist2_grad ( cvm::quaternion const &  Q2 ) const

inline

Gradient of the square distance: returns a 4-vector equivalent to that provided by slerp

set_from_euler_angles()

void colvarmodule::quaternion::set_from_euler_angles ( cvm::real  phi_in, cvm::real  theta_in, cvm::real  psi_in  )

inline

"Constructor" after Euler angles (in radians)

http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles

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

• colvartypes.h
• colvartypes.cpp