Package us.ihmc.euclid.rotationConversion

Class RotationMatrixConversion

java.lang.Object

us.ihmc.euclid.rotationConversion.RotationMatrixConversion

public abstract class RotationMatrixConversion
extends java.lang.Object

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

To convert an orientation into other data structure types see:

• for quaternion: QuaternionConversion,
• for axis-angle: AxisAngleConversion,
• 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
RotationMatrixConversion()

Method Summary

Modifier and Type	Method	Description
static void	computePitchMatrix(double pitch, RotationMatrix matrixToPack)	Sets the given rotation matrix to represent a counter clockwise rotation around the y-axis of an angle pitch.
static void	computeRollMatrix(double roll, RotationMatrix matrixToPack)	Sets the given rotation matrix to represent a counter clockwise rotation around the x-axis of an angle roll.
static void	computeYawMatrix(double yaw, RotationMatrix matrixToPack)	Sets the given rotation matrix to represent a counter clockwise rotation around the z-axis of an angle yaw.
static void	convertAxisAngleToMatrix(double ux, double uy, double uz, double angle, RotationMatrix matrixToPack)	Converts the given axis-angle into a rotation matrix.
static void	convertAxisAngleToMatrix(AxisAngleReadOnly axisAngle, RotationMatrix matrixToPack)	Converts the given axis-angle into a rotation matrix.
static void	convertQuaternionToMatrix(double qx, double qy, double qz, double qs, RotationMatrix matrixToPack)	Converts the given quaternion into a rotation matrix.
static void	convertQuaternionToMatrix(QuaternionReadOnly quaternion, RotationMatrix matrixToPack)	Converts the given quaternion into a rotation matrix.
static void	convertRotationVectorToMatrix(double rx, double ry, double rz, RotationMatrix matrixToPack)	Converts the given rotation vector into a rotation matrix.
static void	convertRotationVectorToMatrix(Vector3DReadOnly rotationVector, RotationMatrix matrixToPack)	Converts the given rotation vector into a rotation matrix.
static void	convertYawPitchRollToMatrix(double[] yawPitchRoll, RotationMatrix matrixToPack)	Converts the given yaw-pitch-roll angles into a rotation matrix.
static void	convertYawPitchRollToMatrix(double yaw, double pitch, double roll, RotationMatrix matrixToPack)	Converts the given yaw-pitch-roll angles into a rotation matrix.

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

RotationMatrixConversion

public RotationMatrixConversion()

Method Detail

computeYawMatrix

public static void computeYawMatrix(double yaw,
                                    RotationMatrix matrixToPack)

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

        / cos(yaw) -sin(yaw) 0 \
 this = | sin(yaw)  cos(yaw) 0 |
        \    0         0     1 /
 

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

computePitchMatrix

public static void computePitchMatrix(double pitch,
                                      RotationMatrix matrixToPack)

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

        /  cos(pitch) 0 sin(pitch) \
 this = |      0      1     0      |
        \ -sin(pitch) 0 cos(pitch) /
 

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

computeRollMatrix

public static void computeRollMatrix(double roll,
                                     RotationMatrix matrixToPack)

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

        / 1     0          0     \
 this = | 0 cos(roll) -sin(roll) |
        \ 0 sin(roll)  cos(roll) /
 

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertAxisAngleToMatrix

public static void convertAxisAngleToMatrix(AxisAngleReadOnly axisAngle,
                                            RotationMatrix matrixToPack)

Converts the given axis-angle into a rotation matrix.

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

Edge case:

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

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertAxisAngleToMatrix

public static void convertAxisAngleToMatrix(double ux,
                                            double uy,
                                            double uz,
                                            double angle,
                                            RotationMatrix matrixToPack)

Converts the given axis-angle into a rotation matrix.

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

Edge case:

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

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.

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertQuaternionToMatrix

public static void convertQuaternionToMatrix(QuaternionReadOnly quaternion,
                                             RotationMatrix matrixToPack)

Converts the given quaternion into a rotation matrix.

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

Edge case:

• if either component of the quaternion is Double.NaN, the rotation matrix is set to Double.NaN.
• if the norm of the quaternion is below EPS, the rotation matrix is set to identity.

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertQuaternionToMatrix

public static void convertQuaternionToMatrix(double qx,
                                             double qy,
                                             double qz,
                                             double qs,
                                             RotationMatrix matrixToPack)

Converts the given quaternion into a rotation matrix.

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

Edge case:

• if either component of the quaternion is Double.NaN, the rotation matrix is set to Double.NaN.
• if the norm of the quaternion is below EPS, the rotation matrix is set to identity.

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.

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertYawPitchRollToMatrix

public static void convertYawPitchRollToMatrix(double[] yawPitchRoll,
                                               RotationMatrix matrixToPack)

Converts the given yaw-pitch-roll angles into a rotation matrix.

After calling this method, the yaw-pitch-roll angles and the rotation matrix represent the same orientation.

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the rotation matrix 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 = RZ(yaw) * RY(pitch) * RX(roll)
 

     / cos(yaw) -sin(yaw) 0 \   /  cos(pitch) 0 sin(pitch) \   / 1     0          0     \
 R = | sin(yaw)  cos(yaw) 0 | * |      0      1     0      | * | 0 cos(roll) -sin(roll) |
     \    0         0     1 /   \ -sin(pitch) 0 cos(pitch) /   \ 0 sin(roll)  cos(roll) /
 

Parameters:

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertYawPitchRollToMatrix

public static void convertYawPitchRollToMatrix(double yaw,
                                               double pitch,
                                               double roll,
                                               RotationMatrix matrixToPack)

Converts the given yaw-pitch-roll angles into a rotation matrix.

After calling this method, the yaw-pitch-roll angles and the rotation matrix represent the same orientation.

Edge case:

• if either of the yaw, pitch, or roll angle is Double.NaN, the rotation matrix 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 = RZ(yaw) * RY(pitch) * RX(roll)
 

     / cos(yaw) -sin(yaw) 0 \   /  cos(pitch) 0 sin(pitch) \   / 1     0          0     \
 R = | sin(yaw)  cos(yaw) 0 | * |      0      1     0      | * | 0 cos(roll) -sin(roll) |
     \    0         0     1 /   \ -sin(pitch) 0 cos(pitch) /   \ 0 sin(roll)  cos(roll) /
 

Parameters:

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

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

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

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertRotationVectorToMatrix

public static void convertRotationVectorToMatrix(Vector3DReadOnly rotationVector,
                                                 RotationMatrix matrixToPack)

Converts the given rotation vector into a rotation matrix.

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

Edge case:

• if either component of the rotation vector is Double.NaN, the rotation matrix 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.

matrixToPack - the rotation matrix in which the result is stored. Modified.

convertRotationVectorToMatrix

public static void convertRotationVectorToMatrix(double rx,
                                                 double ry,
                                                 double rz,
                                                 RotationMatrix matrixToPack)

Converts the given rotation vector into a rotation matrix.

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

Edge case:

• if either component of the rotation vector is Double.NaN, the rotation matrix 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.

matrixToPack - the rotation matrix in which the result is stored. Modified.