Package us.ihmc.euclid.rotationConversion

Class AxisAngleConversion

java.lang.Object

us.ihmc.euclid.rotationConversion.AxisAngleConversion

public class AxisAngleConversion
extends java.lang.Object

This class gathers all the methods necessary to converts any type of rotation into an axis-angle.

To convert an orientation into other data structure types see:

• for quaternion: QuaternionConversion,
• for rotation matrix: RotationMatrixConversion,
• for rotation vector: RotationVectorConversion,
• for yaw-pitch-roll: YawPitchRollConversion.

Author:

Sylvain Bertrand

Field Summary

Fields

Modifier and Type	Field	Description
static double	EPS	Tolerance used to identify various edge cases, such as to identify when a quaternion is a neutral quaternion.

Constructor Summary

Constructors

Constructor	Description
AxisAngleConversion()

Method Summary

Modifier and Type	Method	Description
static void	convertMatrixToAxisAngle(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, AxisAngleBasics axisAngleToPack)	Converts the given rotation matrix into an axis-angle.
static void	convertMatrixToAxisAngle(RotationMatrixReadOnly rotationMatrix, AxisAngleBasics axisAngleToPack)	Converts the given rotation matrix into an axis-angle.
static void	convertMatrixToAxisAngle(RotationScaleMatrixReadOnly rotationScaleMatrix, AxisAngleBasics axisAngleToPack)	Converts the rotation part of the given rotation-scale matrix into an axis-angle.
static void	convertQuaternionToAxisAngle(double qx, double qy, double qz, double qs, AxisAngleBasics axisAngleToPack)	Converts the given quaternion into an axis-angle.
static void	convertQuaternionToAxisAngle(QuaternionReadOnly quaternion, AxisAngleBasics axisAngleToPack)	Converts the given quaternion into an axis-angle.
static void	convertRotationVectorToAxisAngle(double rx, double ry, double rz, AxisAngleBasics axisAngleToPack)	Converts the rotation vector into an axis-angle.
static void	convertRotationVectorToAxisAngle(Vector3DReadOnly rotationVector, AxisAngleBasics axisAngleToPack)	Converts the rotation vector into an axis-angle.
static void	convertYawPitchRollToAxisAngle(double[] yawPitchRoll, AxisAngleBasics axisAngleToPack)	Converts the given yaw-pitch-roll angles into an axis-angle.
static void	convertYawPitchRollToAxisAngle(double yaw, double pitch, double roll, AxisAngleBasics axisAngleToPack)	Converts the given yaw-pitch-roll angles into an axis-angle.

Methods inherited from class java.lang.Object

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

Field Detail

EPS

public static final double EPS

Tolerance used to identify various edge cases, such as to identify when a quaternion is a neutral quaternion.

See Also:

Constant Field Values

Constructor Detail

AxisAngleConversion

public AxisAngleConversion()

Method Detail

convertMatrixToAxisAngle

public static void convertMatrixToAxisAngle(RotationScaleMatrixReadOnly rotationScaleMatrix,
                                            AxisAngleBasics axisAngleToPack)

Converts the rotation part of the given rotation-scale matrix into an axis-angle.

After calling this method, the orientation represented by the axis-angle is the same as the given rotation part of the rotation-scale matrix.

Edge case:

• if the rotation matrix contains at least one Double.NaN, the axis-angle is set to Double.NaN.

Parameters:

rotationScaleMatrix - a 3-by-3 matrix representing an orientation and a scale. Only the orientation part is used during the conversion. Not modified.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertMatrixToAxisAngle

public static void convertMatrixToAxisAngle(RotationMatrixReadOnly rotationMatrix,
                                            AxisAngleBasics axisAngleToPack)

Converts the given rotation matrix into an axis-angle.

After calling this method, the orientation represented by the axis-angle is the same as the given rotation matrix.

Edge case:

• if the rotation matrix contains at least one Double.NaN, the axis-angle is set to Double.NaN.

Parameters:

rotationMatrix - a 3-by-3 matrix representing an orientation. Not modified.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertMatrixToAxisAngle

public static void convertMatrixToAxisAngle(double m00,
                                            double m01,
                                            double m02,
                                            double m10,
                                            double m11,
                                            double m12,
                                            double m20,
                                            double m21,
                                            double m22,
                                            AxisAngleBasics axisAngleToPack)

Converts the given rotation matrix into an axis-angle.

After calling this method, the orientation represented by the axis-angle is the same as the given rotation matrix.

Edge case:

• if the rotation matrix contains at least one Double.NaN, the axis-angle is set to Double.NaN.

Parameters:

m00 - the 1st row 1st column coefficient of the rotation matrix.

m01 - the 1st row 2nd column coefficient of the rotation matrix.

m02 - the 1st row 3rd column coefficient of the rotation matrix.

m10 - the 2nd row 1st column coefficient of the rotation matrix.

m11 - the 2nd row 2nd column coefficient of the rotation matrix.

m12 - the 2nd row 3rd column coefficient of the rotation matrix.

m20 - the 3rd row 1st column coefficient of the rotation matrix.

m21 - the 3rd row 2nd column coefficient of the rotation matrix.

m22 - the 3rd row 3rd column coefficient of the rotation matrix.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertQuaternionToAxisAngle

public static void convertQuaternionToAxisAngle(QuaternionReadOnly quaternion,
                                                AxisAngleBasics axisAngleToPack)

Converts the given quaternion into an axis-angle.

After calling this method, the quaternion and the axis-angle represent the same orientation.

Edge case:

• if the quaternion contains at least one Double.NaN, the axis-angle is set to Double.NaN.
• if the norm of the vector part of the quaternion is less than 1.0E-12, the axis-angle is set to zero via AxisAngleBasics.setToZero().

Parameters:

quaternion - the unit quaternion to use for the conversion. Not modified.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertQuaternionToAxisAngle

public static void convertQuaternionToAxisAngle(double qx,
                                                double qy,
                                                double qz,
                                                double qs,
                                                AxisAngleBasics axisAngleToPack)

Converts the given quaternion into an axis-angle.

After calling this method, the quaternion and the axis-angle represent the same orientation.

Edge case:

• if the quaternion contains at least one Double.NaN, the axis-angle is set to Double.NaN.
• if the norm of the vector part of the quaternion is less than 1.0E-12, the axis-angle is set to zero via AxisAngleBasics.setToZero().

Parameters:

qx - the x-component of the quaternion.

qy - the y-component of the quaternion.

qz - the z-component of the quaternion.

qs - the s-component of the quaternion.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertRotationVectorToAxisAngle

public static void convertRotationVectorToAxisAngle(Vector3DReadOnly rotationVector,
                                                    AxisAngleBasics axisAngleToPack)

Converts the rotation vector into an axis-angle.

After calling this method, the rotation vector and the axis-angle represent the same orientation.

Edge case:

• if the rotation vector contains at least a Double.NaN, the axis-angle is set to Double.NaN.

WARNING: a rotation vector is different from a yaw-pitch-roll or Euler angles representation. A rotation vector is equivalent to the axis of an axis-angle that is multiplied by the angle of the same axis-angle.

Parameters:

rotationVector - the rotation vector to use in the conversion. Not modified.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertRotationVectorToAxisAngle

public static void convertRotationVectorToAxisAngle(double rx,
                                                    double ry,
                                                    double rz,
                                                    AxisAngleBasics axisAngleToPack)

Converts the rotation vector into an axis-angle.

After calling this method, the rotation vector and the axis-angle represent the same orientation.

Edge case:

• if the rotation vector contains at least a Double.NaN, the axis-angle is set to Double.NaN.

WARNING: a rotation vector is different from a yaw-pitch-roll or Euler angles representation. A rotation vector is equivalent to the axis of an axis-angle that is multiplied by the angle of the same axis-angle.

Parameters:

rx - the x-component of the rotation vector to use in the conversion.

ry - the y-component of the rotation vector to use in the conversion.

rz - the z-component of the rotation vector to use in the conversion.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertYawPitchRollToAxisAngle

public static void convertYawPitchRollToAxisAngle(double[] yawPitchRoll,
                                                  AxisAngleBasics axisAngleToPack)

Converts the given yaw-pitch-roll angles into an axis-angle.

After calling this method, the yaw-pitch-roll and the axis-angle represent the same orientation.

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the axis-angle is set to Double.NaN.

Note: the yaw-pitch-roll representation, also called Euler angles, corresponds to the representation of an orientation by decomposing it by three successive rotations around the three axes: Z (yaw), Y (pitch), and X (roll). The equivalent rotation matrix of such representation is:
R = R_Z(yaw) * R_Y(pitch) * R_X(roll)

Parameters:

yawPitchRoll - the yaw-pitch-roll angles to use in the conversion. Not modified.

axisAngleToPack - the axis-angle in which the result is stored. Modified.

convertYawPitchRollToAxisAngle

public static void convertYawPitchRollToAxisAngle(double yaw,
                                                  double pitch,
                                                  double roll,
                                                  AxisAngleBasics axisAngleToPack)

Converts the given yaw-pitch-roll angles into an axis-angle.

After calling this method, the yaw-pitch-roll and the axis-angle represent the same orientation.

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the axis-angle is set to Double.NaN.

Note: the yaw-pitch-roll representation, also called Euler angles, corresponds to the representation of an orientation by decomposing it by three successive rotations around the three axes: Z (yaw), Y (pitch), and X (roll). The equivalent rotation matrix of such representation is:
R = R_Z(yaw) * R_Y(pitch) * R_X(roll)

Parameters:

yaw - the yaw angle to use in the conversion.

pitch - the pitch angle to use in the conversion.

roll - the roll angle to use in the conversion.

axisAngleToPack - the axis-angle in which the result is stored. Modified.