org.biojava.nbio.structure.geometry

Class UnitQuaternions

java.lang.Object

org.biojava.nbio.structure.geometry.UnitQuaternions

public class UnitQuaternions
extends Object

UnitQuaternions is a static Class that contains methods for calculating and using unit quaternions. It assumes the use of Quat4d Class from vecmath to represent the unit quaternions, and it also implements some of the basic methods that the library is missing.

A Unit Quaternion is a four-dimensional vector used to describe a three-dimensional attitude representation (axis and angle of rotation). By definition, unit quaternions are always normalized, so their length is always 1.

Since:

5.0.0

Author:

Aleix Lafita

Method Summary

Modifier and Type	Method and Description
static double	dotProduct(javax.vecmath.Quat4d q1, javax.vecmath.Quat4d q2) Compute the dot (inner) product of two quaternions.
static javax.vecmath.Quat4d	orientation(javax.vecmath.Point3d[] points) The orientation represents the rotation of the principal axes with respect to the axes of the coordinate system (unit vectors [1,0,0], [0,1,0] and [0,0,1]).
static double	orientationMetric(javax.vecmath.Point3d[] a, javax.vecmath.Point3d[] b) The orientation metric is obtained by comparing the quaternion orientations of two sets of points in 3D.
static double	orientationMetric(javax.vecmath.Quat4d q1, javax.vecmath.Quat4d q2) The orientation metric is obtained by comparing two unit quaternion orientations.
static javax.vecmath.Quat4d	relativeOrientation(javax.vecmath.Point3d[] a, javax.vecmath.Point3d[] b) Calculate the relative quaternion orientation of two arrays of points.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

orientationMetric

public static double orientationMetric(javax.vecmath.Point3d[] a,
                                       javax.vecmath.Point3d[] b)

The orientation metric is obtained by comparing the quaternion orientations of two sets of points in 3D.

First, the quaternion orientation of each set of points is calculated using their principal axes with orientation(Point3d[]). Then, the two quaternions are compared using the method orientationMetric(Quat4d, Quat4d).

Parameters:

a - array of Point3d

b - array of Point3d

Returns:

the quaternion orientation metric

orientationMetric

public static double orientationMetric(javax.vecmath.Quat4d q1,
                                       javax.vecmath.Quat4d q2)

The orientation metric is obtained by comparing two unit quaternion orientations.

The two quaternions are compared using the formula: d(q1,q2) = arccos(|q1*q2|). The range of the metric is [0, Pi/2], where 0 means the same orientation and Pi/2 means the opposite orientation.

The formula is taken from: Huynh, D. Q. (2009). Metrics for 3D rotations: comparison and analysis. Journal of Mathematical Imaging and Vision, 35(2), 155–164. http://doi.org/10.1007/s10851-009-0161-2

Parameters:

q1 - quaternion as Quat4d object

q2 - quaternion as Quat4d object

Returns:

the quaternion orientation metric

orientation

public static javax.vecmath.Quat4d orientation(javax.vecmath.Point3d[] points)

The orientation represents the rotation of the principal axes with respect to the axes of the coordinate system (unit vectors [1,0,0], [0,1,0] and [0,0,1]).

The orientation can be expressed as a unit quaternion.

Parameters:

points - array of Point3d

Returns:

the orientation of the point cloud as a unit quaternion

relativeOrientation

public static javax.vecmath.Quat4d relativeOrientation(javax.vecmath.Point3d[] a,
                                                       javax.vecmath.Point3d[] b)

Calculate the relative quaternion orientation of two arrays of points.

Parameters:

a - point array

b - point array

Returns:

a unit quaternion representing the relative orientation

dotProduct

public static double dotProduct(javax.vecmath.Quat4d q1,
                                javax.vecmath.Quat4d q2)

Compute the dot (inner) product of two quaternions.

Parameters:

q1 - quaternion as Quat4d object

q2 - quaternion as Quat4d object

Returns:

the value of the quaternion dot product