Package pamMaths

Class PamQuaternion

java.lang.Object

pamMaths.PamQuaternion

All Implemented Interfaces:

Serializable, Cloneable

public class PamQuaternion
extends Object
implements Cloneable, Serializable

Basically a quaternion is a vector which can encode three dimensional orientation information (e.g. heading, pitch and roll). Means we can get rid of Euler angles if we want to. This particular qauternion class assumes that the heading rotates around the z-axis, pitch rotates around the x-axis and roll rotates around the y-axis.

Wikipedia Description 15/11/2013

Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to rotation matrices they are more numerically stable and may be more efficient. Quaternions have found their way into applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics,[1] and orbital mechanics of satellites

Code is heavily based on code from Prasanna Velagapudi. Copyright (c) 2008, Prasanna Velagapudi invalid input: '<'pkv@cs.cmu.edu>. Permission to use, modify and distribute. https://github.com/psigen/robotutils/blob/master/src/main/java/robotutils/Quaternion.java

Note this code is also available in the apache common 3+ library. PAMGUARD currently implements the Apache 2.2 library so have made unique class.

Author:

Prasanna Velagapudi. Modified by Jamie Macaulay to use Jama and support the PAMGUARD vector and orientation conventions.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final long	serialVersionUID	Determines if a de-serialized object is compatible with this class.
static final double	SINGULARITY_NORTH_POLE	This defines the north pole singularity cutoff when converting from quaternions to Euler angles.
static final double	SINGULARITY_SOUTH_POLE	This defines the south pole singularity cutoff when converting from quaternions to Euler angles.

Constructor Summary

Constructors

Constructor	Description
PamQuaternion(double[] q)	Wrap a quaternion in vector form.
PamQuaternion(double heading, double pitch, double roll)	Create a quartenion from euler angles.
PamQuaternion(double w, double x, double y, double z)	Construct a new quaternion.

Method Summary

Modifier and Type	Method	Description
PamQuaternion	clone()
static double[]	fromEulerAngles(double heading, double pitch, double roll)	Create a quaternion from euler angles.
static double[]	fromEulerAnglesb(double heading, double pitch, double roll)
static PamQuaternion	fromRotation(Jama.Matrix m)
static PamQuaternion	fromTransform(Jama.Matrix t)
double[]	getArray()	Access the components of the quaternion.
double	getW()	Access the w-component (scalar) of the quaternion.
double	getX()	Access the x-component ("i") of the quaternion.
double	getY()	Access the y-component ("j") of the quaternion.
double	getZ()	Access the z-component ("k") of the quaternion.
double[]	toEulerAngles()	Returns the components of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.
double	toHeading()	Returns the yaw component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.
double	toPitch()	Returns the roll component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.
double	toRoll()	Returns the pitch component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.
Jama.Matrix	toRotation()	Converts quaternion to (3x3) rotation matrix.
String	toString()
Jama.Matrix	toTransform()

Methods inherited from class java.lang.Object

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

Field Details

serialVersionUID

public static final long serialVersionUID

Determines if a de-serialized object is compatible with this class. Maintainers must change this value if and only if the new version of this class is not compatible with old versions. See Sun docs for invalid input: '<'a href=http://java.sun.com/products/jdk/1.1/docs/guide /serialization/spec/version.doc.html> details.

See Also:

• Constant Field Values

SINGULARITY_NORTH_POLE

public static final double SINGULARITY_NORTH_POLE

This defines the north pole singularity cutoff when converting from quaternions to Euler angles.

See Also:

• Constant Field Values

SINGULARITY_SOUTH_POLE

public static final double SINGULARITY_SOUTH_POLE

This defines the south pole singularity cutoff when converting from quaternions to Euler angles.

See Also:

• Constant Field Values

Constructor Details

PamQuaternion

public PamQuaternion(double w,
 double x,
 double y,
 double z)

Construct a new quaternion.

Parameters:

w - the w-coordinate of the object

x - the x-coordinate of the object

y - the y-coordinate of the object

z - the z-coordinate of the object

PamQuaternion

public PamQuaternion(double[] q)

Wrap a quaternion in vector form.

Parameters:

q - a quaternion vector in {w, x, y, z} form.

PamQuaternion

public PamQuaternion(double heading,
 double pitch,
 double roll)

Create a quartenion from euler angles.

Parameters:

heading - -0-360 degrees. Input in RADIANS

pitch - - 90->90 degrees. Input in RADIANS

roll - -0->180 and 0->-180. Input in RADIANS

Method Details

getW

public double getW()

Access the w-component (scalar) of the quaternion.

Returns:

the w-component of the quaternion.

getX

public double getX()

Access the x-component ("i") of the quaternion.

Returns:

the x-component of the quaternion.

getY

public double getY()

Access the y-component ("j") of the quaternion.

Returns:

the y-component of the quaternion.

getZ

public double getZ()

Access the z-component ("k") of the quaternion.

Returns:

the z-component of the quaternion.

getArray

public double[] getArray()

Access the components of the quaternion.

Returns:

the components of the quaternion in {w, x, y, z} form.

fromRotation

public static PamQuaternion fromRotation(Jama.Matrix m)

toRotation

public Jama.Matrix toRotation()

Converts quaternion to (3x3) rotation matrix.

Returns:

a 2D 3x3 rotation matrix representing the quaternion.

fromTransform

public static PamQuaternion fromTransform(Jama.Matrix t)

toTransform

public Jama.Matrix toTransform()

fromEulerAngles

public static double[] fromEulerAngles(double heading,
 double pitch,
 double roll)

Create a quaternion from euler angles.

Parameters:

heading - 0-360 degrees. Input in RADIANS

pitch - 90->90 degrees. Input in RADIANS

roll - 0->180 and 0->-180.

Returns:

fromEulerAnglesb

public static double[] fromEulerAnglesb(double heading,
 double pitch,
 double roll)

toPitch

public double toPitch()

Returns the roll component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.

Returns:

the roll (x-axis rotation) of the robot.

toRoll

public double toRoll()

Returns the pitch component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.

Returns:

the pitch (y-axis rotation) of the robot.

toHeading

public double toHeading()

Returns the yaw component of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.

Returns:

the yaw (z-axis rotation) in RADIANS

toEulerAngles

public double[] toEulerAngles()

Returns the components of the quaternion if it is represented as standard roll-pitch-yaw Euler angles.

Returns:

an array of the form {roll, pitch, yaw}.

clone

public PamQuaternion clone()

toString

public String toString()

Overrides:

toString in class Object