fr.cnes.sirius.patrius.math.geometry.euclidean.threed

Class EulerRotation

java.lang.Object

fr.cnes.sirius.patrius.math.geometry.euclidean.threed.Rotation

fr.cnes.sirius.patrius.math.geometry.euclidean.threed.EulerRotation

All Implemented Interfaces:

Serializable

public class EulerRotation
extends Rotation

Rotation focusing on Euler angles. This is a specific class extending Rotation. It does not contain algorithmic code but allow to store an Euler rotation order.

Since:

4.1

Version:

$Id$

Author:

Emmanuel Bignon

See Also:

Serialized Form

Field Summary

Fields inherited from class fr.cnes.sirius.patrius.math.geometry.euclidean.threed.Rotation

IDENTITY

Constructor Summary

Constructors

Constructor and Description
EulerRotation(RotationOrder order, double alpha1, double alpha2, double alpha3) Constructor.

Method Summary

Modifier and Type	Method and Description
double[]	getAngles() Get the Cardan or Euler angles corresponding to the instance in the initial rotation order.
double[]	getAngles(RotationOrder order) Get the Cardan or Euler angles corresponding to the instance.
RotationOrder	getRotationOrder() Getter for the order of rotations to use for (alpha1, alpha2, alpha3) composition.
String	toString() Get a string representation for the rotation.

Methods inherited from class fr.cnes.sirius.patrius.math.geometry.euclidean.threed.Rotation

applyInverseTo, applyInverseTo, applyInverseTo, applyTo, applyTo, applyTo, distance, getAngle, getAxis, getMatrix, getQi, getQuaternion, isEqualTo, isEqualTo, lerp, revert, slerp

Methods inherited from class java.lang.Object

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

Constructor Detail

EulerRotation

public EulerRotation(RotationOrder order,
                     double alpha1,
                     double alpha2,
                     double alpha3)

Constructor.

Parameters:

order - order of rotations to use

alpha1 - angle of the first elementary rotation

alpha2 - angle of the second elementary rotation

alpha3 - angle of the third elementary rotation

See Also:

Rotation.Rotation(RotationOrder, double, double, double)

Method Detail

getAngles

public double[] getAngles(RotationOrder order)

Get the Cardan or Euler angles corresponding to the instance.

The equations show that each rotation can be defined by two different values of the Cardan or Euler angles set. For example if Cardan angles are used, the rotation defined by the angles a₁, a₂ and a₃ is the same as the rotation defined by the angles π + a₁, π - a₂ and π + a₃. This method implements the following arbitrary choices:

• for Cardan angles, the chosen set is the one for which the second angle is between -π/2 and π/2 (i.e its cosine is positive),
• for Euler angles, the chosen set is the one for which the second angle is between 0 and π (i.e its sine is positive).

Cardan and Euler angle have a very disappointing drawback: all of them have singularities. For Cardan angles, this is often called gimbal lock. There is nothing to do to prevent this, it is an intrinsic problem with Cardan and Euler representation (but not a problem with the rotation itself, which is perfectly well defined). For Cardan angles, singularities occur when the second angle is close to -π/2 or +π/2, for Euler angle singularities occur when the second angle is close to 0 or π, this implies that the identity rotation is always singular for Euler angles!

Overrides:

getAngles in class Rotation

Parameters:

order - rotation order to use

Returns:

an array of three angles, in the order specified by the set

getAngles

public double[] getAngles()

Get the Cardan or Euler angles corresponding to the instance in the initial rotation order.

Returns:

an array of three angles, in the order specified by the set

See Also:

Rotation.getAngles(RotationOrder)

getRotationOrder

public RotationOrder getRotationOrder()

Getter for the order of rotations to use for (alpha1, alpha2, alpha3) composition.

Returns:

the order of rotations to use for (alpha1, alpha2, alpha3) composition

toString

public String toString()

Get a string representation for the rotation.

Overrides:

toString in class Rotation

Returns:

a string representation for this rotation