Package org.robwork.sdurw

Class Quaterniond

java.lang.Object

org.robwork.sdurw.Rotation3DVectord

org.robwork.sdurw.Quaterniond

public class Quaterniond
extends Rotation3DVectord

A Quaternion \mathbf{q}\in \mathbb{R}^4 a complex
number used to describe rotations in 3-dimensional space.
q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z

Quaternions can be added and multiplied in a similar way as usual
algebraic numbers. Though there are differences. Quaternion
multiplication is not commutative which means
Q\cdot P \neq P\cdot Q

Constructor Summary

Constructors

Constructor	Description
Quaterniond()	constuct Quaterinion of {0,0,0,1}
Quaterniond(double qx, double qy, double qz, double qw)	Creates a Quaternion
Quaterniond(long cPtr, boolean cMemoryOwn)
Quaterniond(Quaterniond quat)	Creates a Quaternion from another Quaternion
Quaterniond(Rotation3Dd rot)	Extracts a Quaternion from Rotation matrix using setRotation(const rw::math::Rotation3D<R>& rot)

Method Summary

Modifier and Type	Method	Description
Quaterniond	add()	Unary plus.
void	delete()
EigenQuaterniond	e()	Convert to an Eigen Quaternion.
boolean	equals(Quaterniond r)	Comparison (equals) operator
double	get(long i)
static long	getCPtr(Quaterniond obj)
double	getLength()	get length of quaternion \sqrt{q_x^2+q_y^2+q_z^2+q_w^2}
double	getLengthSquared()	get squared length of quaternion q_x^2+q_y^2+q_z^2+q_w^2
double	getQw()	get method for the w component
double	getQx()	get method for the x component
double	getQy()	get method for the y component
double	getQz()	get method for the z component
Quaterniond	multiply(double s)	Scalar multiplication.
Quaterniond	negate()	Unary minus.
void	normalize()	normalizes this quaternion so that normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}}
void	set(long i, double d)
long	size()	The dimension of the quaternion (i.e.
Quaterniond	slerp(Quaterniond v, double t)	Calculates a slerp interpolation between this and v. The slerp interpolation ensures a constant velocity across the interpolation. For t=0 the result is this and for t=1 it is v. Note: Algorithm and implementation is thanks to euclideanspace.com
Rotation3Dd	toRotation3D()	Calculates the 3\times 3 Rotation matrix
java.lang.String	toString()

Methods inherited from class org.robwork.sdurw.Rotation3DVectord

getCPtr

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Quaterniond

public Quaterniond(long cPtr,
                   boolean cMemoryOwn)

Quaterniond

public Quaterniond()

constuct Quaterinion of {0,0,0,1}

Quaterniond

public Quaterniond(double qx,
                   double qy,
                   double qz,
                   double qw)

Creates a Quaternion

Parameters:

qx - [in] q_x

qy - [in] q_y

qz - [in] q_z

qw - [in] q_w

Quaterniond

public Quaterniond(Quaterniond quat)

Creates a Quaternion from another Quaternion

Parameters:

quat - [in] Quaternion

Quaterniond

public Quaterniond(Rotation3Dd rot)

Extracts a Quaternion from Rotation matrix using
setRotation(const rw::math::Rotation3D<R>& rot)

Parameters:

rot - [in] A 3x3 rotation matrix \mathbf{rot}

Method Detail

getCPtr

public static long getCPtr(Quaterniond obj)

delete

public void delete()

Overrides:

delete in class Rotation3DVectord

getQx

public double getQx()

get method for the x component

Returns:

the x component of the quaternion

getQy

public double getQy()

get method for the y component

Returns:

the y component of the quaternion

getQz

public double getQz()

get method for the z component

Returns:

the z component of the quaternion

getQw

public double getQw()

get method for the w component

Returns:

the w component of the quaternion

getLength

public double getLength()

get length of quaternion
\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}

Returns:

the length og this quaternion

getLengthSquared

public double getLengthSquared()

get squared length of quaternion
q_x^2+q_y^2+q_z^2+q_w^2

Returns:

the length og this quaternion

normalize

public void normalize()

normalizes this quaternion so that
normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}}

toRotation3D

public Rotation3Dd toRotation3D()

Calculates the 3\times 3 Rotation matrix

Overrides:

toRotation3D in class Rotation3DVectord

Returns:

A 3x3 rotation matrix \mathbf{rot}
\mathbf{rot} = \left[ \begin{array}{ccc} 1-2(q_y^2-q_z^2) 2(q_x\ q_y+q_z\ q_w) 2(q_x\ q_z-q_y\ q_w) \\ 2(q_x\ q_y-q_z\ q_w) 1-2(q_x^2-q_z^2) 2(q_y\ q_z+q_x\ q_w)\\ 2(q_x\ q_z+q_y\ q_w) 2(q_y\ q_z-q_x\ q_z) 1-2(q_x^2-q_y^2) \end{array} \right]

size

public long size()

The dimension of the quaternion (i.e. 4).
This method is provided to help support generic algorithms using
size() and operator[].

slerp

public Quaterniond slerp(Quaterniond v,
                         double t)

Calculates a slerp interpolation between this and v.

The slerp interpolation ensures a constant velocity across the interpolation.
For t=0 the result is this and for t=1 it is v.

Note: Algorithm and implementation is thanks to euclideanspace.com

multiply

public Quaterniond multiply(double s)

Scalar multiplication.

negate

public Quaterniond negate()

Unary minus.

add

public Quaterniond add()

Unary plus.

equals

public boolean equals(Quaterniond r)

Comparison (equals) operator

e

public EigenQuaterniond e()

Convert to an Eigen Quaternion.

Returns:

Eigen Quaternion representation.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

get

public double get(long i)

set

public void set(long i,
                double d)