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 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
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package org.apache.commons.math3.geometry.euclidean.threed;

This class is a utility representing a rotation order specification for Cardan or Euler angles specification. This class cannot be instanciated by the user. He can only use one of the twelve predefined supported orders as an argument to either the Rotation(RotationOrder, double, double, double) constructor or the Rotation.getAngles method. 
Since:
1.2/**
 * This class is a utility representing a rotation order specification
 * for Cardan or Euler angles specification.
 *
 * This class cannot be instanciated by the user. He can only use one
 * of the twelve predefined supported orders as an argument to either
 * the {@link Rotation#Rotation(RotationOrder,double,double,double)}
 * constructor or the {@link Rotation#getAngles} method.
 *
 * @since 1.2
 */
public final class RotationOrder {

    
Set of Cardan angles.
this ordered set of rotations is around X, then around Y, then
around Z
/** Set of Cardan angles.
     * this ordered set of rotations is around X, then around Y, then
     * around Z
     */
    public static final RotationOrder XYZ =
      new RotationOrder("XYZ", Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_K);

    
Set of Cardan angles.
this ordered set of rotations is around X, then around Z, then
around Y
/** Set of Cardan angles.
     * this ordered set of rotations is around X, then around Z, then
     * around Y
     */
    public static final RotationOrder XZY =
      new RotationOrder("XZY", Vector3D.PLUS_I, Vector3D.PLUS_K, Vector3D.PLUS_J);

    
Set of Cardan angles.
this ordered set of rotations is around Y, then around X, then
around Z
/** Set of Cardan angles.
     * this ordered set of rotations is around Y, then around X, then
     * around Z
     */
    public static final RotationOrder YXZ =
      new RotationOrder("YXZ", Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_K);

    
Set of Cardan angles.
this ordered set of rotations is around Y, then around Z, then
around X
/** Set of Cardan angles.
     * this ordered set of rotations is around Y, then around Z, then
     * around X
     */
    public static final RotationOrder YZX =
      new RotationOrder("YZX", Vector3D.PLUS_J, Vector3D.PLUS_K, Vector3D.PLUS_I);

    
Set of Cardan angles.
this ordered set of rotations is around Z, then around X, then
around Y
/** Set of Cardan angles.
     * this ordered set of rotations is around Z, then around X, then
     * around Y
     */
    public static final RotationOrder ZXY =
      new RotationOrder("ZXY", Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_J);

    
Set of Cardan angles.
this ordered set of rotations is around Z, then around Y, then
around X
/** Set of Cardan angles.
     * this ordered set of rotations is around Z, then around Y, then
     * around X
     */
    public static final RotationOrder ZYX =
      new RotationOrder("ZYX", Vector3D.PLUS_K, Vector3D.PLUS_J, Vector3D.PLUS_I);

    
Set of Euler angles.
this ordered set of rotations is around X, then around Y, then
around X
/** Set of Euler angles.
     * this ordered set of rotations is around X, then around Y, then
     * around X
     */
    public static final RotationOrder XYX =
      new RotationOrder("XYX", Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_I);

    
Set of Euler angles.
this ordered set of rotations is around X, then around Z, then
around X
/** Set of Euler angles.
     * this ordered set of rotations is around X, then around Z, then
     * around X
     */
    public static final RotationOrder XZX =
      new RotationOrder("XZX", Vector3D.PLUS_I, Vector3D.PLUS_K, Vector3D.PLUS_I);

    
Set of Euler angles.
this ordered set of rotations is around Y, then around X, then
around Y
/** Set of Euler angles.
     * this ordered set of rotations is around Y, then around X, then
     * around Y
     */
    public static final RotationOrder YXY =
      new RotationOrder("YXY", Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_J);

    
Set of Euler angles.
this ordered set of rotations is around Y, then around Z, then
around Y
/** Set of Euler angles.
     * this ordered set of rotations is around Y, then around Z, then
     * around Y
     */
    public static final RotationOrder YZY =
      new RotationOrder("YZY", Vector3D.PLUS_J, Vector3D.PLUS_K, Vector3D.PLUS_J);

    
Set of Euler angles.
this ordered set of rotations is around Z, then around X, then
around Z
/** Set of Euler angles.
     * this ordered set of rotations is around Z, then around X, then
     * around Z
     */
    public static final RotationOrder ZXZ =
      new RotationOrder("ZXZ", Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_K);

    
Set of Euler angles.
this ordered set of rotations is around Z, then around Y, then
around Z
/** Set of Euler angles.
     * this ordered set of rotations is around Z, then around Y, then
     * around Z
     */
    public static final RotationOrder ZYZ =
      new RotationOrder("ZYZ", Vector3D.PLUS_K, Vector3D.PLUS_J, Vector3D.PLUS_K);

    
Name of the rotations order. /** Name of the rotations order. */
    private final String name;

    
Axis of the first rotation. /** Axis of the first rotation. */
    private final Vector3D a1;

    
Axis of the second rotation. /** Axis of the second rotation. */
    private final Vector3D a2;

    
Axis of the third rotation. /** Axis of the third rotation. */
    private final Vector3D a3;

    
Private constructor.
This is a utility class that cannot be instantiated by the user,
so its only constructor is private.
Params:
name – name of the rotation order
a1 – axis of the first rotation
a2 – axis of the second rotation
a3 – axis of the third rotation/** Private constructor.
     * This is a utility class that cannot be instantiated by the user,
     * so its only constructor is private.
     * @param name name of the rotation order
     * @param a1 axis of the first rotation
     * @param a2 axis of the second rotation
     * @param a3 axis of the third rotation
     */
    private RotationOrder(final String name,
                          final Vector3D a1, final Vector3D a2, final Vector3D a3) {
        this.name = name;
        this.a1   = a1;
        this.a2   = a2;
        this.a3   = a3;
    }

    
Get a string representation of the instance.
Returns:
a string representation of the instance (in fact, its name)/** Get a string representation of the instance.
     * @return a string representation of the instance (in fact, its name)
     */
    @Override
    public String toString() {
        return name;
    }

    
Get the axis of the first rotation.
Returns:
axis of the first rotation/** Get the axis of the first rotation.
     * @return axis of the first rotation
     */
    public Vector3D getA1() {
        return a1;
    }

    
Get the axis of the second rotation.
Returns:
axis of the second rotation/** Get the axis of the second rotation.
     * @return axis of the second rotation
     */
    public Vector3D getA2() {
        return a2;
    }

    
Get the axis of the second rotation.
Returns:
axis of the second rotation/** Get the axis of the second rotation.
     * @return axis of the second rotation
     */
    public Vector3D getA3() {
        return a3;
    }

}