Detailed Description

3D rotation class.

Rotations are currently represented using quaternions and a cached copy of the rotation matrix. The quaternion allows for fast and stable composition and the cached rotation matrix means that rotations are performed quickly. See http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation for a comparison of different implementations of rotations.

Currently the rotation can be initialized from either:

XYZ Euler angles
Rotation Matrix
Quaternion
angle/axis representation

Note:: This class is a geometric primitive. Also, this class is not not initialized by its default constructor.

List of all members.

Public Member Functions
	Rotation3D (const VectorD< 4 > &v)
	Create a rotation from an unnormalized vector 4.
	Rotation3D ()
	Create an invalid rotation.
	Rotation3D (double a, double b, double c, double d)
	Create a rotation from a quaternion.
const Vector3D	get_derivative (const Vector3D &o, unsigned int i) const
	Return the derivative of the position x with respect to internal variable i.
Rotation3D	get_inverse () const
	Return the rotation which undoes this rotation.
const Vector4D &	get_quaternion () const
	return the quaterion so that it can be stored
Vector3D	get_rotated (const Vector3D &o) const
	Rotate a vector around the origin.
double	get_rotated_one_coordinate (const Vector3D &o, unsigned int coord) const
	Gets only the requested rotation coordinate of the vector.
Vector3D	get_rotation_matrix_row (int i) const
Vector3D	operator* (const Vector3D &v) const
	Rotate a vector around the origin.
Rotation3D	operator* (const Rotation3D &q) const
	multiply two rotations
Rotation3D	operator/ (const Rotation3D &r) const
	Compute the rotation which when composed with r gives this.
const Rotation3D &	operator/= (const Rotation3D &r)
void	show (std::ostream &out=std::cout) const

Euler Angles
There are many conventions for how to define Euler angles, based on choices of which of the x,y,z axis to use in what order and whether the rotation axis is in the body frame (and hence affected by previous rotations) or in in a fixed frame. See http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles for a general description. All Euler angles are specified in radians. The names are all `rotation_from_{fixed/body}_abc()` where abc is the ordering of x,y,z.
Rotation3D	get_rotation_from_fixed_zxz (double phi, double theta, double psi)
	Initialize a rotation from euler angles.

Friends
Rotation3D	compose (const Rotation3D &a, const Rotation3D &b)

Related Functions
(Note that these are not member functions.)
Rotation3D	compose (const Rotation3D &a, const Rotation3D &b)
std::pair< Vector3D, double >	get_axis_and_angle (const Rotation3D &rot)
	Decompose a Rotation3D object into a rotation around an axis.
double	get_distance (const Rotation3D &r0, const Rotation3D &r1)
	Return a distance between the two rotations.
Rotation3D	get_identity_rotation_3d ()
	Return a rotation that does not do anything.
Rotation3D	get_interpolated (const Rotation3D &a, const Rotation3D &b, double f)
	Interpolate between two rotations.
Rotation3D	get_random_rotation_3d ()
	Pick a rotation at random from all possible rotations.
Rotation3D	get_random_rotation_3d (const Rotation3D &center, double distance)
	Pick a rotation at random near the provided one.
Rotation3D	get_rotation_about_axis (const Vector3D &axis, double angle)
	Generate a Rotation3D object from a rotation around an axis.
Rotation3D	get_rotation_from_matrix (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
	Generate a Rotation3D object from a rotation matrix.
Rotation3D	get_rotation_from_vector4d (const VectorD< 4 > &v)
	Compute a rotatation from an unnormalized quaternion.
Rotation3D	get_rotation_taking_first_to_second (const Vector3D &v1, const Vector3D &v2)
	Create a rotation from the first vector to the second one.

Constructor & Destructor Documentation

IMP::algebra::Rotation3D::Rotation3D ( const VectorD< 4 > & v )

Create a rotation from an unnormalized vector 4.

IMP::algebra::Rotation3D::Rotation3D ( )

Create an invalid rotation.

IMP::algebra::Rotation3D::Rotation3D	(	double	a,
		double	b,
		double	c,
		double	d
	)

Create a rotation from a quaternion.

Exceptions:

base::ValueException if the rotation is not a unit vector.

Member Function Documentation

const Vector3D IMP::algebra::Rotation3D::get_derivative	(	const Vector3D &	o,
		unsigned int	i
	)		const

Return the derivative of the position x with respect to internal variable i.

Rotation3D IMP::algebra::Rotation3D::get_inverse ( ) const

Return the rotation which undoes this rotation.

const Vector4D& IMP::algebra::Rotation3D::get_quaternion ( ) const

return the quaterion so that it can be stored

Note that there is no guarantee on which of the two equivalent quaternions is returned.

Vector3D IMP::algebra::Rotation3D::get_rotated ( const Vector3D & o ) const

Rotate a vector around the origin.

double IMP::algebra::Rotation3D::get_rotated_one_coordinate	(	const Vector3D &	o,
		unsigned int	coord
	)		const

Gets only the requested rotation coordinate of the vector.

Vector3D IMP::algebra::Rotation3D::operator* ( const Vector3D & v ) const

Rotate a vector around the origin.

Rotation3D IMP::algebra::Rotation3D::operator* ( const Rotation3D & q ) const

multiply two rotations

Rotation3D IMP::algebra::Rotation3D::operator/ ( const Rotation3D & r ) const

Compute the rotation which when composed with r gives this.

Friends And Related Function Documentation

std::pair< Vector3D, double > get_axis_and_angle ( const Rotation3D & rot )

Note:: http://en.wikipedia.org/wiki/Rotation_matrix; www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm

double get_distance	(	const Rotation3D &	r0,
		const Rotation3D &	r1
	)

The distance runs between 0 and 1. More precisely, the distance returned is distance between the two quaternion vectors properly normalized, divided by sqrt(2).

A vector with distance d from the unit vector represents a rotation of

$\theta= \cos^{-1}\left(1-\sqrt{2}d\right)$

Rotation3D get_identity_rotation_3d ( )

Rotation3D get_interpolated	(	const Rotation3D &	a,
		const Rotation3D &	b,
		double	f
	)

It f ==0, return b, if f==1 return a.

Rotation3D get_random_rotation_3d ( )

Rotation3D get_random_rotation_3d	(	const Rotation3D &	center,
		double	distance
	)

This method generates a rotation that is within the provided distance of center.

Parameters:

[in]	center	The center of the rotational volume
[in]	distance	See get_distance(const Rotation3D&,const Rotation3D&) for a full definition.

Note:: The cost of this operation increases as distance goes to 0.

Rotation3D get_rotation_about_axis	(	const Vector3D &	axis,
		double	angle
	)

Parameters:

[in]	axis	the rotation axis passes through (0,0,0)
[in]	angle	the rotation angle in radians in the clockwise direction

Note:: http://en.wikipedia.org/wiki/Rotation_matrix; www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm

Rotation3D get_rotation_from_fixed_zxz	(	double	phi,
		double	theta,
		double	psi
	)

Parameters:

[in]	phi	Rotation around the Z axis in radians
[in]	theta	Rotation around the X axis in radians
[in]	psi	Rotation around the Z axis in radians

Note:: The first rotation is by an angle phi about the z-axis. The second rotation is by an angle theta in [0,pi] about the former x-axis , and the third rotation is by an angle psi about the former z-axis.

Rotation3D get_rotation_from_matrix	(	double	m00,
		double	m01,
		double	m02,
		double	m10,
		double	m11,
		double	m12,
		double	m20,
		double	m21,
		double	m22
	)

Rotation3D get_rotation_from_vector4d ( const VectorD< 4 > & v )

Rotation3D get_rotation_taking_first_to_second	(	const Vector3D &	v1,
		const Vector3D &	v2
	)

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

Rotation3D.h

Detailed Description

Public Member Functions

Euler Angles

Friends

Related Functions

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation