Package us.ihmc.euclid.rotationConversion

Class QuaternionConversion

java.lang.Object

us.ihmc.euclid.rotationConversion.QuaternionConversion

public abstract class QuaternionConversion
extends java.lang.Object

This class gathers all the methods necessary to converts any type of rotation into a quaternion.

To convert an orientation into other data structure types see:

• for axis-angle: AxisAngleConversion,
• 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 an axis-angle represents a zero orientation.

Constructor Summary

Constructors

Constructor	Description
QuaternionConversion()

Method Summary

Modifier and Type	Method	Description
static void	computePitchQuaternion(double pitch, QuaternionBasics quaternionToPack)	Sets the given quaternion to represent a counter clockwise rotation around the y-axis of an angle pitch.
static void	computeRollQuaternion(double roll, QuaternionBasics quaternionToPack)	Sets the given quaternion to represent a counter clockwise rotation around the x-axis of an angle roll.
static void	computeYawQuaternion(double yaw, QuaternionBasics quaternionToPack)	Sets the given quaternion to represent a counter clockwise rotation around the z-axis of an angle yaw.
static void	convertAxisAngleToQuaternion(double ux, double uy, double uz, double angle, QuaternionBasics quaternionToPack)	Converts the given axis-angle into a quaternion.
static void	convertAxisAngleToQuaternion(AxisAngleReadOnly axisAngle, QuaternionBasics quaternionToPack)	Converts the given axis-angle into a quaternion.
static void	convertMatrixToQuaternion(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22, QuaternionBasics quaternionToPack)	Converts the given rotation matrix into a quaternion.
static void	convertMatrixToQuaternion(RotationMatrixReadOnly rotationMatrix, QuaternionBasics quaternionToPack)	Converts the given rotation matrix into a quaternion.
static void	convertMatrixToQuaternion(RotationScaleMatrixReadOnly rotationScaleMatrix, QuaternionBasics quaternionToPack)	Converts the given rotation part of the given rotation-scale matrix into a quaternion.
static void	convertRotationVectorToQuaternion(double rx, double ry, double rz, QuaternionBasics quaternionToPack)	Converts the rotation vector into a quaternion.
static void	convertRotationVectorToQuaternion(Vector3DReadOnly rotationVector, QuaternionBasics quaternionToPack)	Converts the rotation vector into a quaternion.
static void	convertYawPitchRollToQuaternion(double[] yawPitchRoll, QuaternionBasics quaternionToPack)	Converts the given yaw-pitch-roll angles into a quaternion.
static void	convertYawPitchRollToQuaternion(double yaw, double pitch, double roll, QuaternionBasics quaternionToPack)	Converts the given yaw-pitch-roll angles into a quaternion.

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 an axis-angle represents a zero orientation.

See Also:

Constant Field Values

Constructor Detail

QuaternionConversion

public QuaternionConversion()

Method Detail

computeYawQuaternion

public static final void computeYawQuaternion(double yaw,
                                              QuaternionBasics quaternionToPack)

Sets the given quaternion to represent a counter clockwise rotation around the z-axis of an angle yaw.

Parameters:

yaw - the angle to rotate about the z-axis.

quaternionToPack - the quaternion in which the result is stored.

computePitchQuaternion

public static final void computePitchQuaternion(double pitch,
                                                QuaternionBasics quaternionToPack)

Sets the given quaternion to represent a counter clockwise rotation around the y-axis of an angle pitch.

Parameters:

pitch - the angle to rotate about the y-axis.

quaternionToPack - the quaternion in which the result is stored.

computeRollQuaternion

public static final void computeRollQuaternion(double roll,
                                               QuaternionBasics quaternionToPack)

Sets the given quaternion to represent a counter clockwise rotation around the x-axis of an angle roll.

Parameters:

roll - the angle to rotate about the x-axis.

quaternionToPack - the quaternion in which the result is stored.

convertAxisAngleToQuaternion

public static final void convertAxisAngleToQuaternion(AxisAngleReadOnly axisAngle,
                                                      QuaternionBasics quaternionToPack)

Converts the given axis-angle into a quaternion.

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

Edge case:

• if either component of the axis-angle is Double.NaN, the quaternion is set to Double.NaN.
• if the length of the axis is below EPS, the rotation matrix is set to the neutral quaternion.

Parameters:

axisAngle - the axis-angle to use for the conversion. Not modified.

quaternionToPack - the quaternion in which the result is stored.

convertAxisAngleToQuaternion

public static final void convertAxisAngleToQuaternion(double ux,
                                                      double uy,
                                                      double uz,
                                                      double angle,
                                                      QuaternionBasics quaternionToPack)

Converts the given axis-angle into a quaternion.

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

Edge case:

• if either component of the axis-angle is Double.NaN, the quaternion is set to Double.NaN.
• if the length of the axis is below EPS, the rotation matrix is set to the neutral quaternion.

Parameters:

ux - the axis x-component of the axis-angle to use for the conversion.

uy - the axis y-component of the axis-angle to use for the conversion.

uz - the axis z-component of the axis-angle to use for the conversion.

angle - the angle of the axis-angle to use for the conversion.

quaternionToPack - the quaternion in which the result is stored.

convertMatrixToQuaternion

public static void convertMatrixToQuaternion(RotationScaleMatrixReadOnly rotationScaleMatrix,
                                             QuaternionBasics quaternionToPack)

Converts the given rotation part of the given rotation-scale matrix into a quaternion.

After calling this method, the rotation part of the rotation-scale matrix and the quaternion represent the same orientation.

Edge case:

• if the rotation matrix contains at least one Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.

convertMatrixToQuaternion

public static void convertMatrixToQuaternion(RotationMatrixReadOnly rotationMatrix,
                                             QuaternionBasics quaternionToPack)

Converts the given rotation matrix into a quaternion.

After calling this method, the rotation matrix and the quaternion represent the same orientation.

Edge case:

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

Parameters:

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

quaternionToPack - the quaternion in which the result is stored.

convertMatrixToQuaternion

public static void convertMatrixToQuaternion(double m00,
                                             double m01,
                                             double m02,
                                             double m10,
                                             double m11,
                                             double m12,
                                             double m20,
                                             double m21,
                                             double m22,
                                             QuaternionBasics quaternionToPack)

Converts the given rotation matrix into a quaternion.

After calling this method, the rotation matrix and the quaternion represent the same orientation.

Edge case:

• if the rotation matrix contains at least one Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.

convertRotationVectorToQuaternion

public static void convertRotationVectorToQuaternion(Vector3DReadOnly rotationVector,
                                                     QuaternionBasics quaternionToPack)

Converts the rotation vector into a quaternion.

After calling this method, the rotation vector and the quaternion represent the same orientation.

Edge case:

• if the rotation vector contains at least a Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.

convertRotationVectorToQuaternion

public static void convertRotationVectorToQuaternion(double rx,
                                                     double ry,
                                                     double rz,
                                                     QuaternionBasics quaternionToPack)

Converts the rotation vector into a quaternion.

After calling this method, the rotation vector and the quaternion represent the same orientation.

Edge case:

• if the rotation vector contains at least a Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.

convertYawPitchRollToQuaternion

public static void convertYawPitchRollToQuaternion(double[] yawPitchRoll,
                                                   QuaternionBasics quaternionToPack)

Converts the given yaw-pitch-roll angles into a quaternion.

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

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.

convertYawPitchRollToQuaternion

public static void convertYawPitchRollToQuaternion(double yaw,
                                                   double pitch,
                                                   double roll,
                                                   QuaternionBasics quaternionToPack)

Converts the given yaw-pitch-roll angles into a quaternion.

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

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the quaternion 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.

quaternionToPack - the quaternion in which the result is stored.