Package us.ihmc.euclid.tools

Class AxisAngleTools

java.lang.Object

us.ihmc.euclid.tools.AxisAngleTools

public abstract class AxisAngleTools
extends java.lang.Object

This class provides a collection of static tools to perform operations on axis-angles.

This class is mostly used to centralize operations on axis-angles, these operations are available in classes such as AxisAngle and the user should always using this classes instead of using tools classes. The API of these tools classes is more likely to change over time.

Author:

Sylvain Bertrand

Field Summary

Fields

Modifier and Type	Field	Description
static double	EPS	Tolerance used to identify edge cases, such as when the axis part of an axis-angle can not be normalized.

Constructor Summary

Constructors

Constructor	Description
AxisAngleTools()

Method Summary

Modifier and Type	Method	Description
static void	addTransform(AxisAngleReadOnly axisAngle, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Transforms the tuple tupleOriginal using axisAngle and adds the result to tupleTransformed.
static void	appendPitchRotation(AxisAngleReadOnly axisAngleOriginal, double pitch, AxisAngleBasics axisAngleToPack)	Append a rotation about the y-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static void	appendRollRotation(AxisAngleReadOnly axisAngleOriginal, double roll, AxisAngleBasics axisAngleToPack)	Append a rotation about the x-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static void	appendYawRotation(AxisAngleReadOnly axisAngleOriginal, double yaw, AxisAngleBasics axisAngleToPack)	Append a rotation about the z-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static double	distance(AxisAngleReadOnly aa1, AxisAngleReadOnly aa2)	Computes and returns the distance between the two axis-angles aa1 and aa2.
static void	inverseTransform(AxisAngleReadOnly axisAngle, Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)	Performs the inverse of the transform of the matrix matrixOriginal using axisAngle and stores the result in matrixTransformed.
static void	inverseTransform(AxisAngleReadOnly axisAngle, RotationMatrixReadOnly rotationMatrixOriginal, RotationMatrix rotationMatrixTransformed)	Performs the inverse of the transform of the rotation matrix rotationMatrixOriginal using axisAngle and stores the result in rotationMatrixTransformed.
static void	inverseTransform(AxisAngleReadOnly axisAngle, Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfTransformInXYPlane)	Performs the inverse of the transform of the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.
static void	inverseTransform(AxisAngleReadOnly axisAngle, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Performs the inverse of the transform of the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.
static void	inverseTransform(AxisAngleReadOnly axisAngle, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionTransformed)	Performs the inverse of the transform of the quaternion quaternionOriginal using axisAngle and stores the result in quaternionTransformed.
static void	inverseTransform(AxisAngleReadOnly axisAngle, Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)	Performs the inverse of the transform of the vector vectorOriginal using axisAngle and stores the result in vectorTransformed.
static void	multiply(AxisAngleReadOnly orientation1, boolean inverse1, Orientation3DReadOnly orientation2, boolean inverse2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.
static void	multiply(AxisAngleReadOnly aa1, AxisAngleReadOnly aa2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of aa1 and aa2 and stores the result in axisAngleToPack.
static void	multiply(Orientation3DReadOnly orientation1, boolean inverse1, AxisAngleReadOnly orientation2, boolean inverse2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.
static void	multiply(Orientation3DReadOnly orientation1, boolean inverse1, Orientation3DReadOnly orientation2, boolean inverse2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.
static void	multiplyInvertBoth(AxisAngleReadOnly aa1, AxisAngleReadOnly aa2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of the inverse of aa1 and the inverse of aa2 and stores the result in axisAngleToPack.
static void	multiplyInvertLeft(AxisAngleReadOnly aa1, AxisAngleReadOnly aa2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of the inverse of aa1 and aa2 and stores the result in axisAngleToPack.
static void	multiplyInvertRight(AxisAngleReadOnly aa1, AxisAngleReadOnly aa2, AxisAngleBasics axisAngleToPack)	Performs the multiplication of aa1 and the inverse of aa2 and stores the result in axisAngleToPack.
static void	prependPitchRotation(double pitch, AxisAngleReadOnly axisAngleOriginal, AxisAngleBasics axisAngleToPack)	Prepend a rotation about the y-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static void	prependRollRotation(double roll, AxisAngleReadOnly axisAngleOriginal, AxisAngleBasics axisAngleToPack)	Prepend a rotation about the x-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static void	prependYawRotation(double yaw, AxisAngleReadOnly axisAngleOriginal, AxisAngleBasics axisAngleToPack)	Prepend a rotation about the z-axis to axisAngleOriginal and stores the result in axisAngleToPack.
static void	transform(AxisAngleReadOnly axisAngle, Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)	Transforms the matrix matrixOriginal using axisAngle and stores the result in matrixTransformed.
static void	transform(AxisAngleReadOnly axisAngle, RotationMatrixReadOnly rotationMatrixOriginal, RotationMatrix rotationMatrixTransformed)	Transforms the rotation matrix rotationMatrixOriginal using axisAngle and stores the result in rotationMatrixTransformed.
static void	transform(AxisAngleReadOnly axisAngle, Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfTransformInXYPlane)	Transforms the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.
static void	transform(AxisAngleReadOnly axisAngle, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Transforms the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.
static void	transform(AxisAngleReadOnly axisAngle, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionTransformed)	Transforms the quaternion quaternionOriginal using axisAngle and stores the result in quaternionTransformed.
static void	transform(AxisAngleReadOnly axisAngle, Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)	Transforms the vector vectorOriginal using axisAngle and stores the result in vectorTransformed.

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 edge cases, such as when the axis part of an axis-angle can not be normalized.

See Also:

Constant Field Values

Constructor Detail

AxisAngleTools

public AxisAngleTools()

Method Detail

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             Tuple3DReadOnly tupleOriginal,
                             Tuple3DBasics tupleTransformed)

Transforms the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.

Both tuples can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple in which the result is stored. Modified.

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    Tuple3DReadOnly tupleOriginal,
                                    Tuple3DBasics tupleTransformed)

Performs the inverse of the transform of the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, Tuple3DReadOnly, Tuple3DBasics) with an axis-angle that has an angle of opposite value compared to the given one.

Both tuples can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple in which the result is stored. Modified.

addTransform

public static void addTransform(AxisAngleReadOnly axisAngle,
                                Tuple3DReadOnly tupleOriginal,
                                Tuple3DBasics tupleTransformed)

Transforms the tuple tupleOriginal using axisAngle and adds the result to tupleTransformed.

Both tuples can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple in which the result is stored. Modified.

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             Tuple2DReadOnly tupleOriginal,
                             Tuple2DBasics tupleTransformed,
                             boolean checkIfTransformInXYPlane)

Transforms the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.

Both tuples can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple in which the result is stored. Modified.

checkIfTransformInXYPlane - whether this method should assert that the axis-angle represents a transformation in the XY plane.

Throws:

NotAMatrix2DException - if checkIfTransformInXYPlane == true and the axis-angle does not represent a transformation in the XY plane.

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    Tuple2DReadOnly tupleOriginal,
                                    Tuple2DBasics tupleTransformed,
                                    boolean checkIfTransformInXYPlane)

Performs the inverse of the transform of the tuple tupleOriginal using axisAngle and stores the result in tupleTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, Tuple2DReadOnly, Tuple2DBasics, boolean) with an axis-angle that has an angle of opposite value compared to the given one.

Both tuples can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple in which the result is stored. Modified.

checkIfTransformInXYPlane - whether this method should assert that the axis-angle represents a transformation in the XY plane.

Throws:

NotAMatrix2DException - if checkIfTransformInXYPlane == true and the axis-angle does not represent a transformation in the XY plane.

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             Matrix3DReadOnly matrixOriginal,
                             Matrix3D matrixTransformed)

Transforms the matrix matrixOriginal using axisAngle and stores the result in matrixTransformed.

Both matrices can be the same object for performing in place transformation.

matrixTransformed = R(axisAngle) * matrixOriginal * R(axisAngle)^-1
where R(axisAngle) is the function to convert an axis-angle into a 3-by-3 rotation matrix.

Parameters:

axisAngle - the axis-angle used to transform the matrix. Not modified.

matrixOriginal - the matrix to transform. Not modified.

matrixTransformed - the matrix in which the result is stored. Modified.

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    Matrix3DReadOnly matrixOriginal,
                                    Matrix3D matrixTransformed)

Performs the inverse of the transform of the matrix matrixOriginal using axisAngle and stores the result in matrixTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, Matrix3DReadOnly, Matrix3D) with an axis-angle that has an angle of opposite value compared to the given one.

Both matrices can be the same object for performing in place transformation.

matrixTransformed = R(axisAngle)^-1 * matrixOriginal * R(axisAngle)
where R(axisAngle) is the function to convert an axis-angle into a 3-by-3 rotation matrix.

Parameters:

axisAngle - the axis-angle used to transform the matrix. Not modified.

matrixOriginal - the matrix to transform. Not modified.

matrixTransformed - the matrix in which the result is stored. Modified.

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             QuaternionReadOnly quaternionOriginal,
                             QuaternionBasics quaternionTransformed)

Transforms the quaternion quaternionOriginal using axisAngle and stores the result in quaternionTransformed.

Both quaternionOriginal and quaternionTransformed can be the same object for performing in place transformation.

Note that this transformation is equivalent to concatenating the orientations of axisAngle and quaternionOriginal.

Parameters:

axisAngle - the axis-angle used to transform the quaternion. Not modified.

quaternionOriginal - the quaternion to transform. Not modified.

quaternionTransformed - the quaternion in which the result is stored. Modified.

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    QuaternionReadOnly quaternionOriginal,
                                    QuaternionBasics quaternionTransformed)

Performs the inverse of the transform of the quaternion quaternionOriginal using axisAngle and stores the result in quaternionTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, QuaternionReadOnly, QuaternionBasics) with an axis-angle that has an angle of opposite value compared to the given one.

Both quaternionOriginal and quaternionTransformed can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the quaternion. Not modified.

quaternionOriginal - the quaternion to transform. Not modified.

quaternionTransformed - the quaternion in which the result is stored. Modified.

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             Vector4DReadOnly vectorOriginal,
                             Vector4DBasics vectorTransformed)

Transforms the vector vectorOriginal using axisAngle and stores the result in vectorTransformed.

Both vectors can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

vectorOriginal - the vector to transform. Not modified.

vectorTransformed - the vector in which the result is stored. Modified.

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    Vector4DReadOnly vectorOriginal,
                                    Vector4DBasics vectorTransformed)

Performs the inverse of the transform of the vector vectorOriginal using axisAngle and stores the result in vectorTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, Vector4DReadOnly, Vector4DBasics) with an axis-angle that has an angle of opposite value compared to the given one.

Both vectors can be the same object for performing in place transformation.

Parameters:

axisAngle - the axis-angle used to transform the tuple. Not modified.

vectorOriginal - the vector to transform. Not modified.

vectorTransformed - the vector in which the result is stored. Modified.

transform

public static void transform(AxisAngleReadOnly axisAngle,
                             RotationMatrixReadOnly rotationMatrixOriginal,
                             RotationMatrix rotationMatrixTransformed)

Transforms the rotation matrix rotationMatrixOriginal using axisAngle and stores the result in rotationMatrixTransformed.

Both rotation matrices can be the same object for performing in place transformation.

rotationMatrixTransformed = R(axisAngle) * rotationMatrixOriginal
where R(axisAngle) is the function to convert an axis-angle into a 3-by-3 rotation matrix.

Note that this transformation is equivalent to concatenating the orientations of axisAngle and rotationMatrixOriginal.

Parameters:

axisAngle - the axis-angle used to transform the rotation matrix. Not modified.

rotationMatrixOriginal - the rotation matrix to transform. Not modified.

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

inverseTransform

public static void inverseTransform(AxisAngleReadOnly axisAngle,
                                    RotationMatrixReadOnly rotationMatrixOriginal,
                                    RotationMatrix rotationMatrixTransformed)

Performs the inverse of the transform of the rotation matrix rotationMatrixOriginal using axisAngle and stores the result in rotationMatrixTransformed.

This is equivalent to calling transform(AxisAngleReadOnly, RotationMatrixReadOnly, RotationMatrix) with an axis-angle that has an angle of opposite value compared to the given one.

Both rotation matrices can be the same object for performing in place transformation.

rotationMatrixTransformed = R(axisAngle)^-1 * rotationMatrixOriginal
where R(axisAngle) is the function to convert an axis-angle into a 3-by-3 rotation matrix.

Note that this transformation is equivalent to concatenating the orientations of axisAngle and rotationMatrixOriginal.

Parameters:

axisAngle - the axis-angle used to transform the rotation matrix. Not modified.

rotationMatrixOriginal - the rotation matrix to transform. Not modified.

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

multiply

public static void multiply(AxisAngleReadOnly aa1,
                            AxisAngleReadOnly aa2,
                            AxisAngleBasics axisAngleToPack)

Performs the multiplication of aa1 and aa2 and stores the result in axisAngleToPack.

All three arguments can be the same object for in place operations.

Parameters:

aa1 - the first axis-angle in the multiplication. Not modified.

aa2 - the second axis-angle in the multiplication. Not modified.

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

multiply

public static void multiply(Orientation3DReadOnly orientation1,
                            boolean inverse1,
                            Orientation3DReadOnly orientation2,
                            boolean inverse2,
                            AxisAngleBasics axisAngleToPack)

Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.

More precisely, orientation1 and orientation2 are first converted to axis-angles, then an axis-angle multiplication is performed using the two first arguments as entry.

All three arguments can be the same object for in place operations.

Parameters:

orientation1 - the first orientation in the multiplication. Not modified.

inverse1 - whether the first orientation should be inverted in the multiplication.

orientation2 - the second orientation in the multiplication. Not modified.

inverse2 - whether the second orientation should be inverted in the multiplication.

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

multiply

public static void multiply(Orientation3DReadOnly orientation1,
                            boolean inverse1,
                            AxisAngleReadOnly orientation2,
                            boolean inverse2,
                            AxisAngleBasics axisAngleToPack)

Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.

More precisely, orientation1 is first converted to an axis-angle, then an axis-angle multiplication is performed using the two first arguments as entry.

All three arguments can be the same object for in place operations.

Parameters:

orientation1 - the first orientation in the multiplication. Not modified.

inverse1 - whether the first orientation should be inverted in the multiplication.

orientation2 - the second orientation in the multiplication. Not modified.

inverse2 - whether the second orientation should be inverted in the multiplication.

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

multiply

public static void multiply(AxisAngleReadOnly orientation1,
                            boolean inverse1,
                            Orientation3DReadOnly orientation2,
                            boolean inverse2,
                            AxisAngleBasics axisAngleToPack)

Performs the multiplication of orientation1 and orientation2 and stores the result in axisAngleToPack.

More precisely, orientation2 is first converted to an axis-angle, then an axis-angle multiplication is performed using the two first arguments as entry.

All three arguments can be the same object for in place operations.

Parameters:

orientation1 - the first orientation in the multiplication. Not modified.

inverse1 - whether the first orientation should be inverted in the multiplication.

orientation2 - the second orientation in the multiplication. Not modified.

inverse2 - whether the second orientation should be inverted in the multiplication.

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

multiplyInvertLeft

public static void multiplyInvertLeft(AxisAngleReadOnly aa1,
                                      AxisAngleReadOnly aa2,
                                      AxisAngleBasics axisAngleToPack)

Performs the multiplication of the inverse of aa1 and aa2 and stores the result in axisAngleToPack.

All three arguments can be the same object for in place operations.

Parameters:

aa1 - the first axis-angle in the multiplication. Not modified.

aa2 - the second axis-angle in the multiplication. Not modified.

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

multiplyInvertRight

public static void multiplyInvertRight(AxisAngleReadOnly aa1,
                                       AxisAngleReadOnly aa2,
                                       AxisAngleBasics axisAngleToPack)

Performs the multiplication of aa1 and the inverse of aa2 and stores the result in axisAngleToPack.

All three arguments can be the same object for in place operations.

Parameters:

aa1 - the first axis-angle in the multiplication. Not modified.

aa2 - the second axis-angle in the multiplication. Not modified.

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

multiplyInvertBoth

public static void multiplyInvertBoth(AxisAngleReadOnly aa1,
                                      AxisAngleReadOnly aa2,
                                      AxisAngleBasics axisAngleToPack)

Performs the multiplication of the inverse of aa1 and the inverse of aa2 and stores the result in axisAngleToPack.

All three arguments can be the same object for in place operations.

Parameters:

aa1 - the first axis-angle in the multiplication. Not modified.

aa2 - the second axis-angle in the multiplication. Not modified.

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

prependYawRotation

public static void prependYawRotation(double yaw,
                                      AxisAngleReadOnly axisAngleOriginal,
                                      AxisAngleBasics axisAngleToPack)

Prepend a rotation about the z-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the quaternions can be the same object.

                   / ux    =  0  \
 axisAngleToPack = | uy    =  0  | * axisAngleOriginal
                   | uz    =  1  |
                   \ angle = yaw /
 

Parameters:

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

axisAngleOriginal - the axis-angle on which the yaw rotation is prepended. Not modified.

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

appendYawRotation

public static void appendYawRotation(AxisAngleReadOnly axisAngleOriginal,
                                     double yaw,
                                     AxisAngleBasics axisAngleToPack)

Append a rotation about the z-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the axis-angles can be the same object.

                                       / ux    =  0  \
 axisAngleToPack = axisAngleOriginal * | uy    =  0  |
                                       | uz    =  1  |
                                       \ angle = yaw /
 

Parameters:

axisAngleOriginal - the axis-angle on which the yaw rotation is appended. Not modified.

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

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

prependPitchRotation

public static void prependPitchRotation(double pitch,
                                        AxisAngleReadOnly axisAngleOriginal,
                                        AxisAngleBasics axisAngleToPack)

Prepend a rotation about the y-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the axis-angles can be the same object.

                   / ux    =  0    \
 axisAngleToPack = | uy    =  1    | * axisAngleOriginal
                   | uz    =  0    |
                   \ angle = pitch /
 

Parameters:

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

axisAngleOriginal - the axis-angle on which the yaw rotation is prepended. Not modified.

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

appendPitchRotation

public static void appendPitchRotation(AxisAngleReadOnly axisAngleOriginal,
                                       double pitch,
                                       AxisAngleBasics axisAngleToPack)

Append a rotation about the y-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the axis-angles can be the same object.

                                       / ux    =  0    \
 axisAngleToPack = axisAngleOriginal * | uy    =  1    |
                                       | uz    =  0    |
                                       \ angle = pitch /
 

Parameters:

axisAngleOriginal - the axis-angle on which the yaw rotation is appended. Not modified.

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

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

prependRollRotation

public static void prependRollRotation(double roll,
                                       AxisAngleReadOnly axisAngleOriginal,
                                       AxisAngleBasics axisAngleToPack)

Prepend a rotation about the x-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the axis-angles can be the same object.

                   / ux    =  1   \
 axisAngleToPack = | uy    =  0   | * axisAngleOriginal
                   | uz    =  0   |
                   \ angle = roll /
 

Parameters:

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

axisAngleOriginal - the axis-angle on which the yaw rotation is prepended. Not modified.

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

appendRollRotation

public static void appendRollRotation(AxisAngleReadOnly axisAngleOriginal,
                                      double roll,
                                      AxisAngleBasics axisAngleToPack)

Append a rotation about the x-axis to axisAngleOriginal and stores the result in axisAngleToPack.

All the axis-angles can be the same object.

                                       / ux    =  1   \
 axisAngleToPack = axisAngleOriginal * | uy    =  0   |
                                       | uz    =  0   |
                                       \ angle = roll /
 

Parameters:

axisAngleOriginal - the axis-angle on which the yaw rotation is appended. Not modified.

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

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

distance

public static double distance(AxisAngleReadOnly aa1,
                              AxisAngleReadOnly aa2)

Computes and returns the distance between the two axis-angles aa1 and aa2.

Parameters:

aa1 - the first axis-angle to measure the distance. Not modified.

aa2 - the second axis-angle to measure the distance. Not modified.

Returns:

the angle representing the distance between the two axis-angles. It is contained in [0, 2pi]