Package us.ihmc.euclid.matrix.interfaces

Interface RotationMatrixReadOnly

All Superinterfaces:

Matrix3DReadOnly, Orientation3DReadOnly

All Known Implementing Classes:

RotationMatrix

public interface RotationMatrixReadOnly
extends Matrix3DReadOnly, Orientation3DReadOnly

Read interface used for 3-by-3 rotation matrices.

A rotation matrix is used to represent a 3D orientation through its 9 coefficients. A rotation matrix has to comply to several constraints:

• each column of the matrix represents a unitary vector,
• each row of the matrix represents a unitary vector,
• every pair of columns of the matrix represents two orthogonal vectors,
• every pair of rows of the matrix represents two orthogonal vectors,
• the matrix determinant is equal to 1.

A rotation matrix has the nice property R^T = R^-1.

Author:

Sylvain Bertrand

Field Summary

Fields inherited from interface us.ihmc.euclid.orientation.interfaces.Orientation3DReadOnly

ORIENTATION_2D_EPSILON

Method Summary

Modifier and Type	Method	Description
default void	addTransform(Tuple3DBasics tupleToTransform)	Transforms the given tuple by this matrix and add the result to the tuple.
default void	addTransform(Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Transforms the given tuple tupleOriginal by this matrix and add the result to tupleTransformed.
default double	distance(RotationMatrixReadOnly other)	Computes and returns the distance between this rotation matrix and the other.
default boolean	geometricallyEquals(RotationMatrixReadOnly other, double epsilon)	Tests if this and other represent the same orientation to an epsilon.
default void	get(AxisAngleBasics axisAngleToPack)	Converts, if necessary, and packs this orientation into an axis-angle.
default void	get(RotationMatrix rotationMatrixToPack)	Converts, if necessary, and packs this orientation into a 3-by-3 rotation matrix.
default void	get(Vector3DBasics rotationVectorToPack)	Deprecated. Use getRotationVector(Vector3DBasics) instead
default void	get(QuaternionBasics quaternionToPack)	Converts, if necessary, and packs this orientation in a quaternion.
default void	getEuler(Tuple3DBasics eulerAnglesToPack)	Computes and packs the orientation described by this orientation as the Euler angles.
default double	getPitch()	Computes and returns the pitch angle from the yaw-pitch-roll representation of this orientation.
default double	getRoll()	Computes and returns the roll angle from the yaw-pitch-roll representation of this orientation.
default void	getRotationVector(Vector3DBasics rotationVectorToPack)	Converts and packs this orientation in a 3D rotation vector.
default double	getYaw()	Computes and returns the yaw angle from the yaw-pitch-roll representation of this orientation.
default void	getYawPitchRoll(double[] yawPitchRollToPack)	Converts and packs this orientation in a yaw-pitch-roll representation.
default void	inverseTransform(Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)	Performs the inverse of the transforms to the given 3D matrix matrixOriginal by this matrix and stores the result in matrixTransformed.
default void	inverseTransform(Matrix3D matrixToTransform)	Performs the inverse of the transforms to the given 3D matrix matrixOriginal by this matrix.
default void	inverseTransform(Tuple2DBasics tupleToTransform)	Performs the inverse of the transform to the given tuple by this matrix.
default void	inverseTransform(Tuple2DBasics tupleToTransform, boolean checkIfOrientation2D)	Performs the inverse of the transform to the given tuple by this matrix.
default void	inverseTransform(Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed)	Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	inverseTransform(Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfOrientation2D)	Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	inverseTransform(Tuple3DBasics tupleToTransform)	Performs the inverse of the transform to the given tuple by this matrix.
default void	inverseTransform(Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	inverseTransform(Vector4DBasics vectorToTransform)	Performs the inverse of the transform to the vector part the given 4D vector by this matrix.
default void	inverseTransform(Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)	Performs the inverse of the transform to the vector part the given 4D vector vectorOriginal by this matrix and stores the result in vectorTransformed.
default boolean	isOrientation2D(double epsilon)	Tests if this orientation 3D actually represents a rotation strictly around the z-axis.
default void	transform(Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)	Transforms the given 3D matrix matrixOriginal by this matrix and stores the result in matrixTransformed.
default void	transform(Matrix3D matrixToTransform)	Transforms the given 3D matrix by this matrix.
default void	transform(Tuple2DBasics tupleToTransform)	Transforms the given tuple by this matrix.
default void	transform(Tuple2DBasics tupleToTransform, boolean checkIfOrientation2D)	Transforms the given tuple by this matrix.
default void	transform(Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed)	Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	transform(Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfOrientation2D)	Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	transform(Tuple3DBasics tupleToTransform)	Transforms the given tuple by this matrix.
default void	transform(Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)	Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.
default void	transform(Vector4DBasics vectorToTransform)	Transforms the vector part of the given 4D vector.
default void	transform(Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)	Transforms the vector part of the given 4D vector vectorOriginal and stores the result into vectorTransformed.

Methods inherited from interface us.ihmc.euclid.matrix.interfaces.Matrix3DReadOnly

checkIfMatrix2D, checkIfRotationMatrix, containsNaN, determinant, epsilonEquals, equals, get, get, get, get, getColumn, getColumn, getElement, getM00, getM01, getM02, getM10, getM11, getM12, getM20, getM21, getM22, getRow, getRow, isIdentity, isIdentity, isMatrix2D, isMatrix2D, isMatrixSkewSymmetric, isMatrixSkewSymmetric, isRotationMatrix, isRotationMatrix

Methods inherited from interface us.ihmc.euclid.orientation.interfaces.Orientation3DReadOnly

checkIfOrientation2D, checkIfOrientation2D, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, isOrientation2D, toStringAsYawPitchRoll, transform, transform, transform, transform, transform, transform

Method Detail

isOrientation2D

default boolean isOrientation2D(double epsilon)

Tests if this orientation 3D actually represents a rotation strictly around the z-axis.

This is commonly used to test if this orientation can be used to transform 2D geometry object.

The implementation of this test depends on the type of representation used for this orientation.

This rotation matrix is considered to be an orientation 2D if:

• the last diagonal coefficient m22 is equal to 1.0 +/- epsilon,
• the coefficients m20, m02, m21, and m12 are equal to 0.0 +/- epsilon.

Specified by:

isOrientation2D in interface Orientation3DReadOnly

Parameters:

epsilon - the tolerance to use.

Returns:

true if this orientation represents a 2D orientation in the XY-plane, false otherwise.

distance

default double distance(RotationMatrixReadOnly other)

Computes and returns the distance between this rotation matrix and the other.

Parameters:

other - the other rotation matrix to compute the distance. Not modified.

Returns:

the angle representing the distance between the two rotation matrices. It is contained in [0, pi].

get

@Deprecated
default void get(Vector3DBasics rotationVectorToPack)

Deprecated.

Use getRotationVector(Vector3DBasics) instead

Computes and packs the orientation described by this rotation matrix as a rotation vector.

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:

rotationVectorToPack - the rotation vector representing the same orientation as this. Modified.

get

default void get(RotationMatrix rotationMatrixToPack)

Converts, if necessary, and packs this orientation into a 3-by-3 rotation matrix.

Specified by:

get in interface Orientation3DReadOnly

Parameters:

rotationMatrixToPack - the rotation matrix into which this orientation is to be stored. Modified.

get

default void get(AxisAngleBasics axisAngleToPack)

Converts, if necessary, and packs this orientation into an axis-angle.

Specified by:

get in interface Orientation3DReadOnly

Parameters:

axisAngleToPack - the axis-angle into which this orientation is to be stored. Modified.

get

default void get(QuaternionBasics quaternionToPack)

Converts, if necessary, and packs this orientation in a quaternion.

Specified by:

get in interface Orientation3DReadOnly

Parameters:

quaternionToPack - the quaternion into which this orientation is to be stored. Modified.

getRotationVector

default void getRotationVector(Vector3DBasics rotationVectorToPack)

Converts and packs this orientation in a 3D rotation vector.

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.

Specified by:

getRotationVector in interface Orientation3DReadOnly

Parameters:

rotationVectorToPack - the rotation vector in which this orientation is to be stored. Modified.

getEuler

default void getEuler(Tuple3DBasics eulerAnglesToPack)

Computes and packs the orientation described by this orientation as the Euler angles.

WARNING: the Euler angles or yaw-pitch-roll representation is sensitive to gimbal lock and is sometimes undefined.

Specified by:

getEuler in interface Orientation3DReadOnly

Parameters:

eulerAnglesToPack - the tuple in which the Euler angles are stored. Modified.

getYawPitchRoll

default void getYawPitchRoll(double[] yawPitchRollToPack)

Converts and packs this orientation in a yaw-pitch-roll representation.

WARNING: the Euler angles or yaw-pitch-roll representation is sensitive to gimbal lock and is sometimes undefined.

The yaw-pitch-roll representation describes a 3D orientation as a succession of three rotations around three axes:

1. yaw: rotation around the z-axis,
2. pitch: rotation around the y-axis,
3. roll: rotation around the x-axis.

As an example, a rotation matrix can be computed from a yaw-pitch-roll representation as follows:

     / 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) /
 

Specified by:

getYawPitchRoll in interface Orientation3DReadOnly

Parameters:

yawPitchRollToPack - the array in which the yaw-pitch-roll angles are stored. Modified.

getYaw

default double getYaw()

Computes and returns the yaw angle from the yaw-pitch-roll representation of this orientation.

WARNING: the Euler angles or yaw-pitch-roll representation is sensitive to gimbal lock and is sometimes undefined.

Specified by:

getYaw in interface Orientation3DReadOnly

Returns:

the yaw angle around the z-axis.

getPitch

default double getPitch()

Computes and returns the pitch angle from the yaw-pitch-roll representation of this orientation.

WARNING: the Euler angles or yaw-pitch-roll representation is sensitive to gimbal lock and is sometimes undefined.

Specified by:

getPitch in interface Orientation3DReadOnly

Returns:

the pitch angle around the y-axis.

getRoll

default double getRoll()

Computes and returns the roll angle from the yaw-pitch-roll representation of this orientation.

WARNING: the Euler angles or yaw-pitch-roll representation is sensitive to gimbal lock and is sometimes undefined.

Specified by:

getRoll in interface Orientation3DReadOnly

Returns:

the roll angle around the x-axis.

addTransform

default void addTransform(Tuple3DBasics tupleToTransform)

Transforms the given tuple by this matrix and add the result to the tuple.

tupleToTransform = tupleToTransform + this * tupleToTransform

Specified by:

addTransform in interface Matrix3DReadOnly

Specified by:

addTransform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

addTransform

default void addTransform(Tuple3DReadOnly tupleOriginal,
                          Tuple3DBasics tupleTransformed)

Transforms the given tuple tupleOriginal by this matrix and add the result to tupleTransformed.

tupleTransformed = tupleTransformed + this * tupleOriginal

Specified by:

addTransform in interface Matrix3DReadOnly

Specified by:

addTransform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple to add the result to. Modified.

transform

default void transform(Tuple3DBasics tupleToTransform)

Transforms the given tuple by this matrix.

tupleToTransform = this * tupleToTransform

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

transform

default void transform(Tuple3DReadOnly tupleOriginal,
                       Tuple3DBasics tupleTransformed)

Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this * tupleOriginal

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple to store the result. Modified.

transform

default void transform(Tuple2DBasics tupleToTransform)

Transforms the given tuple by this matrix.

tupleToTransform = this * tupleToTransform

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

transform

default void transform(Tuple2DReadOnly tupleOriginal,
                       Tuple2DBasics tupleTransformed)

Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this * tupleOriginal

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple to store the result. Modified.

transform

default void transform(Tuple2DBasics tupleToTransform,
                       boolean checkIfOrientation2D)

Transforms the given tuple by this matrix.

tupleToTransform = this * tupleToTransform

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

checkIfOrientation2D - whether this method should assert that this matrix represents a transformation in the XY plane.

transform

default void transform(Tuple2DReadOnly tupleOriginal,
                       Tuple2DBasics tupleTransformed,
                       boolean checkIfOrientation2D)

Transforms the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this * tupleOriginal

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

tupleTransformed - the tuple to store the result. Modified.

checkIfOrientation2D - whether this method should assert that this matrix represents a transformation in the XY plane.

transform

default void transform(Vector4DBasics vectorToTransform)

Transforms the vector part of the given 4D vector.

vectorToTransform.s = vectorToTransform.s
vectorToTransform.xyz = this * vectorToTransform.xyz

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

vectorToTransform - the vector to transform. Modified.

transform

default void transform(Vector4DReadOnly vectorOriginal,
                       Vector4DBasics vectorTransformed)

Transforms the vector part of the given 4D vector vectorOriginal and stores the result into vectorTransformed.

vectorTransformed.s = vectorOriginal.s
vectorTransformed.xyz = this * vectorOriginal.xyz

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

vectorOriginal - the vector to transform. Not modified.

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

transform

default void transform(Matrix3D matrixToTransform)

Transforms the given 3D matrix by this matrix.

matrixToTransform = this * matrixToTransform * this^-1

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

matrixToTransform - the matrix to transform. Modified.

transform

default void transform(Matrix3DReadOnly matrixOriginal,
                       Matrix3D matrixTransformed)

Transforms the given 3D matrix matrixOriginal by this matrix and stores the result in matrixTransformed.

matrixTransformed = this * matrixOriginal * this^-1

Specified by:

transform in interface Matrix3DReadOnly

Specified by:

transform in interface Orientation3DReadOnly

Parameters:

matrixOriginal - the matrix to transform. Not modified.

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

inverseTransform

default void inverseTransform(Tuple3DBasics tupleToTransform)

Performs the inverse of the transform to the given tuple by this matrix.

tupleToTransform = this^-1 * tupleToTransform

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

inverseTransform

default void inverseTransform(Tuple3DReadOnly tupleOriginal,
                              Tuple3DBasics tupleTransformed)

Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this^-1 * tupleOriginal

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

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

inverseTransform

default void inverseTransform(Tuple2DBasics tupleToTransform)

Performs the inverse of the transform to the given tuple by this matrix.

tupleToTransform = this^-1 * tupleToTransform

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

inverseTransform

default void inverseTransform(Tuple2DReadOnly tupleOriginal,
                              Tuple2DBasics tupleTransformed)

Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this^-1 * tupleOriginal

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

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

inverseTransform

default void inverseTransform(Tuple2DBasics tupleToTransform,
                              boolean checkIfOrientation2D)

Performs the inverse of the transform to the given tuple by this matrix.

tupleToTransform = this^-1 * tupleToTransform

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleToTransform - the tuple to transform. Modified.

checkIfOrientation2D - whether this method should assert that this matrix represents a transformation in the XY plane.

inverseTransform

default void inverseTransform(Tuple2DReadOnly tupleOriginal,
                              Tuple2DBasics tupleTransformed,
                              boolean checkIfOrientation2D)

Performs the inverse of the transform to the given tuple tupleOriginal by this matrix and stores the result in tupleTransformed.

tupleTransformed = this^-1 * tupleOriginal

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

tupleOriginal - the tuple to transform. Not modified.

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

checkIfOrientation2D - whether this method should assert that this matrix represents a transformation in the XY plane.

inverseTransform

default void inverseTransform(Vector4DBasics vectorToTransform)

Performs the inverse of the transform to the vector part the given 4D vector by this matrix.

vectorToTransform.s = vectorToTransform.s
vectorToTransform.xyz = this^-1 * vectorToTransform.xyz

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

vectorToTransform - the vector to transform. Modified.

inverseTransform

default void inverseTransform(Vector4DReadOnly vectorOriginal,
                              Vector4DBasics vectorTransformed)

Performs the inverse of the transform to the vector part the given 4D vector vectorOriginal by this matrix and stores the result in vectorTransformed.

vectorTransformed.s = vectorOriginal.s
vectorTransformed.xyz = this^-1 * vectorOriginal.xyz

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

vectorOriginal - the vector to transform. Not modified.

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

inverseTransform

default void inverseTransform(Matrix3D matrixToTransform)

Performs the inverse of the transforms to the given 3D matrix matrixOriginal by this matrix.

matrixToTransform = this^-1 * matrixToTransform * this^-1

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

matrixToTransform - the matrix to transform. Not modified.

inverseTransform

default void inverseTransform(Matrix3DReadOnly matrixOriginal,
                              Matrix3D matrixTransformed)

Performs the inverse of the transforms to the given 3D matrix matrixOriginal by this matrix and stores the result in matrixTransformed.

matrixTransformed = this^-1 * matrixOriginal * this^-1

Specified by:

inverseTransform in interface Matrix3DReadOnly

Specified by:

inverseTransform in interface Orientation3DReadOnly

Parameters:

matrixOriginal - the matrix to transform. Not modified.

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

geometricallyEquals

default boolean geometricallyEquals(RotationMatrixReadOnly other,
                                    double epsilon)

Tests if this and other represent the same orientation to an epsilon.

Two rotation matrices are considered geometrically equal if the magnitude of their difference is less than or equal to epsilon.

Note that this.geometricallyEquals(other, epsilon) == true does not necessarily imply this.epsilonEquals(other, epsilon) and vice versa.

Parameters:

other - the other rotation matrix to compare against this. Not modified.

epsilon - the maximum angle between the two rotation matrices to be considered equal.

Returns:

true if the two rotation matrices represent the same geometry, false otherwise.