RotationMatrix

java.lang.Object
- us.ihmc.euclid.matrix.RotationMatrix

All Implemented Interfaces:

Clearable, EpsilonComparable<RotationMatrix>, GeometricallyComparable<RotationMatrix>, GeometryObject<RotationMatrix>, Settable<RotationMatrix>, Transformable, Matrix3DBasics, Matrix3DReadOnly, RotationMatrixReadOnly, Orientation3DBasics, Orientation3DReadOnly
```
public class RotationMatrix
extends java.lang.Object
implements Matrix3DBasics, RotationMatrixReadOnly, Orientation3DBasics, GeometryObject<RotationMatrix>
```
A RotationMatrix is a 3-by-3 matrix used to represent 3d orientations.
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.

A best effort has been put in the interface of RotationMatrix to maximize the use of the inherent properties of a rotation matrix and to minimize manipulation errors resulting in an improper rotation matrix.
Author:

Sylvain Bertrand

Field Summary
- Fields inherited from interface us.ihmc.euclid.orientation.interfaces.Orientation3DReadOnly
  ORIENTATION_2D_EPSILON

Constructor Summary

Constructors
Constructor	Description
`RotationMatrix()`	Create a new rotation matrix initialized to identity.
`RotationMatrix(double[] rotationMatrixArray)`	Creates a new rotation matrix and initializes it from the given array.
`RotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Creates a new rotation matrix and initializes it from the given 9 coefficients.
`RotationMatrix(org.ejml.data.DenseMatrix64F rotationMatrix)`	Creates a new rotation matrix that is the same as `rotationMatrix`.
`RotationMatrix(Matrix3DReadOnly rotationMatrix)`	Creates a new rotation matrix that is the same as `rotationMatrix`.
`RotationMatrix(RotationMatrixReadOnly other)`	Creates a new rotation matrix that is the same as `other`.
`RotationMatrix(Orientation3DReadOnly orientation)`	Creates a new rotation matrix that represents the same orientation as the given one.
`RotationMatrix(Vector3DReadOnly rotationVector)`	Creates a new rotation matrix representing the same orientation as the given rotation vector `rotationVector`.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`void`	`append(Orientation3DReadOnly orientation)`	Appends the given orientation to this orientation.
`void`	`appendInvertOther(Orientation3DReadOnly orientation)`	Appends the inverse of the given orientation to this orientation.
`void`	`appendPitchRotation(double pitch)`	Append a rotation about the y-axis to this rotation matrix.
`void`	`appendRollRotation(double roll)`	Append a rotation about the x-axis to this rotation matrix.
`void`	`appendYawRotation(double yaw)`	Append a rotation about the z-axis to this rotation matrix.
`void`	`applyInverseTransform(Transform transform)`	Transform this using the inverse of the given `transform`.
`void`	`applyTransform(Transform transform)`	Transform this using the given `transform`.
`boolean`	`epsilonEquals(RotationMatrix other, double epsilon)`	Tests on a per coefficient basis if this matrix is equal to the given `other` to an `epsilon`.
`boolean`	`equals(java.lang.Object object)`	Tests if the given `object`'s class is the same as this, in which case the method returns `Matrix3DReadOnly.equals(Matrix3DReadOnly)`, it returns `false` otherwise or if the `object` is `null`.
`boolean`	`geometricallyEquals(RotationMatrix other, double epsilon)`	Tests if `this` and `other` represent the same orientation to an `epsilon`.
`double`	`getM00()`	Gets the 1st row 1st column coefficient of this matrix.
`double`	`getM01()`	Gets the 1st row 2nd column coefficient of this matrix.
`double`	`getM02()`	Gets the 1st row 3rd column coefficient of this matrix.
`double`	`getM10()`	Gets the 2nd row 1st column coefficient of this matrix.
`double`	`getM11()`	Gets the 2nd row 2nd column coefficient of this matrix.
`double`	`getM12()`	Gets the 2nd row 3rd column coefficient of this matrix.
`double`	`getM20()`	Gets the 3rd row 1st column coefficient of this matrix.
`double`	`getM21()`	Gets the 3rd row 2nd column coefficient of this matrix.
`double`	`getM22()`	Gets the 3rd row 3rd column coefficient of this matrix.
`int`	`hashCode()`	Calculates and returns a hash code value from the value of each component of this matrix.
`void`	`interpolate(RotationMatrixReadOnly rf, double alpha)`	Performs a linear interpolation in SO(3) from `this` to `rf` given the percentage `alpha`.
`void`	`interpolate(RotationMatrixReadOnly r0, RotationMatrixReadOnly rf, double alpha)`	Performs a linear interpolation in SO(3) from `r0` to `rf` given the percentage `alpha`.
`void`	`invert()`	Inverts this rotation matrix.
`void`	`multiply(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`multiplyTransposeBoth(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`multiplyTransposeOther(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`multiplyTransposeThis(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`normalize()`	Orthonormalization of the rotation matrix using the Gram-Schmidt method.
`void`	`preMultiply(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`preMultiplyTransposeBoth(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`preMultiplyTransposeOther(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`preMultiplyTransposeThis(RotationMatrixReadOnly other)`	Performs a matrix multiplication on this.
`void`	`prepend(Orientation3DReadOnly orientation)`	Prepends the given orientation to this orientation.
`void`	`prependInvertOther(Orientation3DReadOnly orientation)`	Prepends the inverse of the given orientation to this orientation.
`void`	`prependPitchRotation(double pitch)`	Prepend a rotation about the y-axis to this rotation matrix.
`void`	`prependRollRotation(double roll)`	Append a rotation about the x-axis to this rotation matrix.
`void`	`prependYawRotation(double yaw)`	Prepend a rotation about the z-axis to this rotation matrix.
`void`	`set(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Sets the 9 coefficients of this matrix to the given ones.
`void`	`set(RotationMatrixReadOnly other)`	Sets this rotation matrix to equal the given one `other`.
`void`	`set(RotationMatrix other)`	Sets this rotation matrix to equal the given one `other`.
`void`	`set(Orientation3DReadOnly orientation3DReadOnly)`	Converts, if necessary, and sets this orientation to represents the same orientation as `orientation3DReadOnly`.
`void`	`setAndInvert(Matrix3DReadOnly matrix)`	Sets this rotation matrix to the invert of the given `matrix`.
`void`	`setAndInvert(RotationMatrixReadOnly other)`	Sets this rotation matrix to the invert of the given one `other`.
`void`	`setAndNormalize(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Sets the 9 coefficients of this rotation matrix and then normalizes `this`.
`void`	`setAndNormalize(Matrix3DReadOnly matrix)`	Sets this rotation matrix to equal the 3D matrix `matrix` and then normalizes `this`.
`void`	`setAndNormalize(RotationMatrixReadOnly other)`	Sets this rotation matrix to equal the given `other` and then normalizes `this`.
`void`	`setAndTranspose(Matrix3DReadOnly matrix)`	Sets this rotation matrix to the transpose of the given `matrix`.
`void`	`setAndTranspose(RotationMatrixReadOnly other)`	Sets this rotation matrix to the transpose of the given `other`.
`void`	`setAxisAngle(double x, double y, double z, double angle)`	Sets this orientation to represents the same orientation as an axis-angle given its 4 components.
`void`	`setColumns(Tuple3DReadOnly firstColumn, Tuple3DReadOnly secondColumn, Tuple3DReadOnly thirdColumn)`	Sets this rotation matrix from the given tuples each holding on the values of each column.
`void`	`setQuaternion(double x, double y, double z, double s)`	Sets this orientation to represents the same orientation as a quaternion given its 4 components.
`void`	`setRotationMatrix(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Sets this orientation to represents the same orientation as a rotation matrix given its 9 components.
`void`	`setRotationVector(double x, double y, double z)`	Sets this orientation to represents the same orientation as a rotation vector given its 3 components.
`void`	`setRows(Tuple3DReadOnly firstRow, Tuple3DReadOnly secondRow, Tuple3DReadOnly thirdRow)`	Sets this rotation matrix from the given tuples each holding on the values of each row.
`void`	`setToPitchMatrix(double pitch)`	Sets this rotation matrix to represent a counter clockwise rotation around the y-axis of an angle `pitch`.
`void`	`setToRollMatrix(double roll)`	Sets this rotation matrix to represent a counter clockwise rotation around the x-axis of an angle `roll`.
`void`	`setToYawMatrix(double yaw)`	Sets this rotation matrix to represent a counter clockwise rotation around the z-axis of an angle `yaw`.
`void`	`setToZero()`	Sets this rotation matrix to identity representing a 'zero' rotation.
`void`	`setUnsafe(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)`	Sets the 9 coefficients of this rotation matrix without performing any checks on the data provided.
`void`	`setYawPitchRoll(double yaw, double pitch, double roll)`	Sets this orientation to represents the same orientation as a yaw-pitch-roll representation.
`java.lang.String`	`toString()`	Provides a `String` representation of this matrix as follows: m00, m01, m02 m10, m11, m12 m20, m21, m22
`void`	`transpose()`	Transposes this matrix: m = m^T.

Methods inherited from interface us.ihmc.euclid.matrix.interfaces.Matrix3DBasics
containsNaN, set, set, set, set, set, setIdentity, setToNaN

Methods inherited from interface us.ihmc.euclid.matrix.interfaces.Matrix3DReadOnly
checkIfMatrix2D, checkIfRotationMatrix, determinant, epsilonEquals, equals, get, get, get, get, getColumn, getColumn, getElement, getRow, getRow, isIdentity, isIdentity, isMatrix2D, isMatrix2D, isMatrixSkewSymmetric, isMatrixSkewSymmetric, isRotationMatrix, isRotationMatrix

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface us.ihmc.euclid.orientation.interfaces.Orientation3DBasics
appendInvertBoth, appendInvertThis, prependInvertBoth, prependInvertThis, setAndInvert, setAndNormalize, setEuler, setEuler, setRotationVector, setYawPitchRoll

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

Methods inherited from interface us.ihmc.euclid.matrix.interfaces.RotationMatrixReadOnly
addTransform, addTransform, distance, geometricallyEquals, get, get, get, get, getEuler, getPitch, getRoll, getRotationVector, getYaw, getYawPitchRoll, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, inverseTransform, isOrientation2D, transform, transform, transform, transform, transform, transform, transform, transform, transform, transform

- Constructor Detail
  - RotationMatrix
```
public RotationMatrix()
```
    Create a new rotation matrix initialized to identity.
  - RotationMatrix
```
public RotationMatrix(double m00,
                      double m01,
                      double m02,
                      double m10,
                      double m11,
                      double m12,
                      double m20,
                      double m21,
                      double m22)
```
    Creates a new rotation matrix and initializes it from the given 9 coefficients.
    
    Parameters:
    
    m00 - the 1st row 1st column coefficient for this matrix.
    
    m01 - the 1st row 2nd column coefficient for this matrix.
    
    m02 - the 1st row 3rd column coefficient for this matrix.
    
    m10 - the 2nd row 1st column coefficient for this matrix.
    
    m11 - the 2nd row 2nd column coefficient for this matrix.
    
    m12 - the 2nd row 3rd column coefficient for this matrix.
    
    m20 - the 3rd row 1st column coefficient for this matrix.
    
    m21 - the 3rd row 2nd column coefficient for this matrix.
    
    m22 - the 3rd row 3rd column coefficient for this matrix.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - RotationMatrix
```
public RotationMatrix(double[] rotationMatrixArray)
```
    Creates a new rotation matrix and initializes it from the given array.
```
        / rotationMatrixArray[0]  rotationMatrixArray[1]  rotationMatrixArray[2] \
 this = | rotationMatrixArray[3]  rotationMatrixArray[4]  rotationMatrixArray[5] |
        \ rotationMatrixArray[6]  rotationMatrixArray[7]  rotationMatrixArray[8] /
 
```
    Parameters:
    
    rotationMatrixArray - the array containing the values for this matrix. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - RotationMatrix
```
public RotationMatrix(org.ejml.data.DenseMatrix64F rotationMatrix)
```
    Creates a new rotation matrix that is the same as rotationMatrix.
    
    Parameters:
    
    rotationMatrix - the other 3D matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - RotationMatrix
```
public RotationMatrix(Matrix3DReadOnly rotationMatrix)
```
    Creates a new rotation matrix that is the same as rotationMatrix.
    
    Parameters:
    
    rotationMatrix - the other 3D matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - RotationMatrix
```
public RotationMatrix(RotationMatrixReadOnly other)
```
    Creates a new rotation matrix that is the same as other.
    
    Parameters:
    
    other - the other 3D matrix to copy the values from. Not modified.
  - RotationMatrix
```
public RotationMatrix(Orientation3DReadOnly orientation)
```
    Creates a new rotation matrix that represents the same orientation as the given one.
    
    Parameters:
    
    orientation - the orientation used to initialize this rotation matrix. Not modified.
  - RotationMatrix
```
public RotationMatrix(Vector3DReadOnly rotationVector)
```
    Creates a new rotation matrix representing the same orientation as the given rotation vector rotationVector.
    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 used to initialize this rotation matrix. Not modified.
- Method Detail
  - setToZero
```
public void setToZero()
```
    Sets this rotation matrix to identity representing a 'zero' rotation.
    
    Specified by:
    
    setToZero in interface Clearable
  - normalize
```
public void normalize()
```
    Orthonormalization of the rotation matrix using the Gram-Schmidt method.
    
    Specified by:
    
    normalize in interface Orientation3DBasics
    
    Throws:
    
    NotARotationMatrixException - if the orthonormalization failed.
  - transpose
```
public void transpose()
```
    Transposes this matrix: m = m^T.
  - setUnsafe
```
public void setUnsafe(double m00,
                      double m01,
                      double m02,
                      double m10,
                      double m11,
                      double m12,
                      double m20,
                      double m21,
                      double m22)
```
    Sets the 9 coefficients of this rotation matrix without performing any checks on the data provided.
    This method is meant for internal usage. Prefer using set(double, double, double, double, double, double, double, double, double) or setAndNormalize(double, double, double, double, double, double, double, double, double).
    
    Parameters:
    
    m00 - the new 1st row 1st column coefficient for this matrix.
    
    m01 - the new 1st row 2nd column coefficient for this matrix.
    
    m02 - the new 1st row 3rd column coefficient for this matrix.
    
    m10 - the new 2nd row 1st column coefficient for this matrix.
    
    m11 - the new 2nd row 2nd column coefficient for this matrix.
    
    m12 - the new 2nd row 3rd column coefficient for this matrix.
    
    m20 - the new 3rd row 1st column coefficient for this matrix.
    
    m21 - the new 3rd row 2nd column coefficient for this matrix.
    
    m22 - the new 3rd row 3rd column coefficient for this matrix.
  - set
```
public void set(double m00,
                double m01,
                double m02,
                double m10,
                double m11,
                double m12,
                double m20,
                double m21,
                double m22)
```
    Sets the 9 coefficients of this matrix to the given ones.
    
    Specified by:
    
    set in interface Matrix3DBasics
    
    Parameters:
    
    m00 - the new 1st row 1st column coefficient for this matrix.
    
    m01 - the new 1st row 2nd column coefficient for this matrix.
    
    m02 - the new 1st row 3rd column coefficient for this matrix.
    
    m10 - the new 2nd row 1st column coefficient for this matrix.
    
    m11 - the new 2nd row 2nd column coefficient for this matrix.
    
    m12 - the new 2nd row 3rd column coefficient for this matrix.
    
    m20 - the new 3rd row 1st column coefficient for this matrix.
    
    m21 - the new 3rd row 2nd column coefficient for this matrix.
    
    m22 - the new 3rd row 3rd column coefficient for this matrix.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - setRows
```
public void setRows(Tuple3DReadOnly firstRow,
                    Tuple3DReadOnly secondRow,
                    Tuple3DReadOnly thirdRow)
```
    Sets this rotation matrix from the given tuples each holding on the values of each row.
```
        /  firstRow.getX()  firstRow.getY()  firstRow.getZ() \
 this = | secondRow.getX() secondRow.getY() secondRow.getZ() |
        \  thirdRow.getX()  thirdRow.getY()  thirdRow.getZ() /
 
```
    Parameters:
    
    firstRow - the tuple holding onto the values of the first row. Not modified.
    
    secondRow - the tuple holding onto the values of the second row. Not modified.
    
    thirdRow - the tuple holding onto the values of the third row. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - setColumns
```
public void setColumns(Tuple3DReadOnly firstColumn,
                       Tuple3DReadOnly secondColumn,
                       Tuple3DReadOnly thirdColumn)
```
    Sets this rotation matrix from the given tuples each holding on the values of each column.
```
        / firstColumn.getX() secondColumn.getX() thirdColumn.getX() \
 this = | firstColumn.getY() secondColumn.getY() thirdColumn.getY() |
        \ firstColumn.getZ() secondColumn.getZ() thirdColumn.getZ() /
 
```
    Parameters:
    
    firstColumn - the tuple holding onto the values of the first column. Not modified.
    
    secondColumn - the tuple holding onto the values of the second column. Not modified.
    
    thirdColumn - the tuple holding onto the values of the third column. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the resulting matrix is not a rotation matrix.
  - setAndNormalize
```
public void setAndNormalize(double m00,
                            double m01,
                            double m02,
                            double m10,
                            double m11,
                            double m12,
                            double m20,
                            double m21,
                            double m22)
```
    Sets the 9 coefficients of this rotation matrix and then normalizes this.
    
    Parameters:
    
    m00 - the new 1st row 1st column coefficient for this matrix.
    
    m01 - the new 1st row 2nd column coefficient for this matrix.
    
    m02 - the new 1st row 3rd column coefficient for this matrix.
    
    m10 - the new 2nd row 1st column coefficient for this matrix.
    
    m11 - the new 2nd row 2nd column coefficient for this matrix.
    
    m12 - the new 2nd row 3rd column coefficient for this matrix.
    
    m20 - the new 3rd row 1st column coefficient for this matrix.
    
    m21 - the new 3rd row 2nd column coefficient for this matrix.
    
    m22 - the new 3rd row 3rd column coefficient for this matrix.
    
    Throws:
    
    NotARotationMatrixException - if the normalization failed.
  - set
```
public void set(RotationMatrix other)
```
    Sets this rotation matrix to equal the given one other.
    
    Specified by:
    
    set in interface Settable<RotationMatrix>
    
    Parameters:
    
    other - the other rotation matrix to copy the values from. Not modified.
  - set
```
public void set(RotationMatrixReadOnly other)
```
    Sets this rotation matrix to equal the given one other.
    
    Parameters:
    
    other - the other rotation matrix to copy the values from. Not modified.
  - set
```
public void set(Orientation3DReadOnly orientation3DReadOnly)
```
    Description copied from interface: Orientation3DBasics
    
    Converts, if necessary, and sets this orientation to represents the same orientation as orientation3DReadOnly.
    
    Specified by:
    
    set in interface Orientation3DBasics
    
    Parameters:
    
    orientation3DReadOnly - the new orientation. Not modified.
  - setAndNormalize
```
public void setAndNormalize(Matrix3DReadOnly matrix)
```
    Sets this rotation matrix to equal the 3D matrix matrix and then normalizes this.
    
    Parameters:
    
    matrix - the matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the normalization failed.
  - setAndNormalize
```
public void setAndNormalize(RotationMatrixReadOnly other)
```
    Sets this rotation matrix to equal the given other and then normalizes this.
    
    Parameters:
    
    other - the rotation matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if the normalization failed.
  - setAndInvert
```
public void setAndInvert(Matrix3DReadOnly matrix)
```
    Sets this rotation matrix to the invert of the given matrix.
    This operation uses the property:
    R^-1 = R^T
    of a rotation matrix preventing to actually compute the inverse of the matrix.
    
    Parameters:
    
    matrix - the matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if matrix is not a rotation matrix.
  - setAndInvert
```
public void setAndInvert(RotationMatrixReadOnly other)
```
    Sets this rotation matrix to the invert of the given one other.
    This operation uses the property:
    R^-1 = R^T
    of a rotation matrix preventing to actually compute the inverse of the matrix.
    
    Parameters:
    
    other - the matrix to copy the values from. Not modified.
  - setAndTranspose
```
public void setAndTranspose(Matrix3DReadOnly matrix)
```
    Sets this rotation matrix to the transpose of the given matrix.
    
    Parameters:
    
    matrix - the matrix to copy the values from. Not modified.
    
    Throws:
    
    NotARotationMatrixException - if matrix is not a rotation matrix.
  - setAndTranspose
```
public void setAndTranspose(RotationMatrixReadOnly other)
```
    Sets this rotation matrix to the transpose of the given other.
    
    Parameters:
    
    other - the matrix to copy the values from. Not modified.
  - setAxisAngle
```
public void setAxisAngle(double x,
                         double y,
                         double z,
                         double angle)
```
    Description copied from interface: Orientation3DBasics
    
    Sets this orientation to represents the same orientation as an axis-angle given its 4 components.
    
    Specified by:
    
    setAxisAngle in interface Orientation3DBasics
    
    Parameters:
    
    x - x-component of the axis part of the axis-angle.
    
    y - y-component of the axis part of the axis-angle.
    
    z - z-component of the axis part of the axis-angle.
    
    angle - the angle part of the axis-angle.
  - setRotationVector
```
public void setRotationVector(double x,
                              double y,
                              double z)
```
    Description copied from interface: Orientation3DBasics
    
    Sets this orientation to represents the same orientation as a rotation vector given its 3 components.
    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:
    
    setRotationVector in interface Orientation3DBasics
    
    Parameters:
    
    x - the x-component of the rotation vector.
    
    y - the y-component of the rotation vector.
    
    z - the z-component of the rotation vector.
  - setQuaternion
```
public void setQuaternion(double x,
                          double y,
                          double z,
                          double s)
```
    Description copied from interface: Orientation3DBasics
    
    Sets this orientation to represents the same orientation as a quaternion given its 4 components.
    
    Specified by:
    
    setQuaternion in interface Orientation3DBasics
    
    Parameters:
    
    x - the x-component of the quaternion.
    
    y - the y-component of the quaternion.
    
    z - the z-component of the quaternion.
    
    s - the s-component of the quaternion.
  - setYawPitchRoll
```
public void setYawPitchRoll(double yaw,
                            double pitch,
                            double roll)
```
    Description copied from interface: Orientation3DBasics
    Sets this orientation to represents the same orientation as 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:
    
    setYawPitchRoll in interface Orientation3DBasics
    
    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.
  - setRotationMatrix
```
public void setRotationMatrix(double m00,
                              double m01,
                              double m02,
                              double m10,
                              double m11,
                              double m12,
                              double m20,
                              double m21,
                              double m22)
```
    Description copied from interface: Orientation3DBasics
    
    Sets this orientation to represents the same orientation as a rotation matrix given its 9 components.
    
    Specified by:
    
    setRotationMatrix in interface Orientation3DBasics
    
    Parameters:
    
    m00 - the new 1st row 1st column coefficient of the rotation matrix.
    
    m01 - the new 1st row 2nd column coefficient of the rotation matrix.
    
    m02 - the new 1st row 3rd column coefficient of the rotation matrix.
    
    m10 - the new 2nd row 1st column coefficient of the rotation matrix.
    
    m11 - the new 2nd row 2nd column coefficient of the rotation matrix.
    
    m12 - the new 2nd row 3rd column coefficient of the rotation matrix.
    
    m20 - the new 3rd row 1st column coefficient of the rotation matrix.
    
    m21 - the new 3rd row 2nd column coefficient of the rotation matrix.
    
    m22 - the new 3rd row 3rd column coefficient of the rotation matrix.
  - setToYawMatrix
```
public void setToYawMatrix(double yaw)
```
    Sets this 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.
  - setToPitchMatrix
```
public void setToPitchMatrix(double pitch)
```
    Sets this 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.
  - setToRollMatrix
```
public void setToRollMatrix(double roll)
```
    Sets this 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.
  - invert
```
public void invert()
```
    Inverts this rotation matrix.
    This operation uses the property:
    R^-1 = R^T
    of a rotation matrix preventing to actually compute the inverse of the matrix.
    
    This is equivalent to this.transpose().
    
    Specified by:
    
    invert in interface Orientation3DBasics
  - multiply
```
public void multiply(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = this * other
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - append
```
public void append(Orientation3DReadOnly orientation)
```
    Description copied from interface: Orientation3DBasics
    Appends the given orientation to this orientation.
    Let's consider the following:
    - three coordinate systems A, B, and C.
    - this represents the orientation of B relative to A.
    - orientation represents the orientation of C relative to B.
    The result of calling this method will be that this, represents the orientation of C relative to A.
    
    Appending orientations is in some way similar to summing translations. However, while the addition for translation is commutative, the "append" operation on orientation is NOT commutative. Such that: this.append(orientation) ≠ orientation.append(this).
    Specified by:
    
    append in interface Orientation3DBasics
    
    Parameters:
    
    orientation - the orientation to append to this orientation. Not modified.
  - multiplyTransposeThis
```
public void multiplyTransposeThis(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = this^T * other
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - multiplyTransposeOther
```
public void multiplyTransposeOther(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = this * other^T
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - appendInvertOther
```
public void appendInvertOther(Orientation3DReadOnly orientation)
```
    Description copied from interface: Orientation3DBasics
    Appends the inverse of the given orientation to this orientation.
    Let's consider the following:
    - three coordinate systems A, B, and C.
    - this represents the orientation of B relative to A.
    - orientation represents the orientation of B relative to C.
    The result of calling this method will be that this, represents the orientation of C relative to A.
    
    This operation is in some way similar to subtracting translations, as in this operation can be seen as subtracting orientation to this.
    Specified by:
    
    appendInvertOther in interface Orientation3DBasics
    
    Parameters:
    
    orientation - the orientation which the inverse is to be appended to this orientation. Not modified.
  - multiplyTransposeBoth
```
public void multiplyTransposeBoth(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = this^T * other^T
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - appendYawRotation
```
public void appendYawRotation(double yaw)
```
    Append a rotation about the z-axis to this rotation matrix.
```
               / cos(yaw) -sin(yaw) 0 \
 this = this * | sin(yaw)  cos(yaw) 0 |
               \    0         0     1 /
 
```
    Specified by:
    
    appendYawRotation in interface Orientation3DBasics
    
    Parameters:
    
    yaw - the angle to rotate about the z-axis.
  - appendPitchRotation
```
public void appendPitchRotation(double pitch)
```
    Append a rotation about the y-axis to this rotation matrix.
```
               /  cos(pitch) 0 sin(pitch) \
 this = this * |      0      1     0      |
               \ -sin(pitch) 0 cos(pitch) /
 
```
    Specified by:
    
    appendPitchRotation in interface Orientation3DBasics
    
    Parameters:
    
    pitch - the angle to rotate about the y-axis.
  - appendRollRotation
```
public void appendRollRotation(double roll)
```
    Append a rotation about the x-axis to this rotation matrix.
```
               /  cos(pitch) 0 sin(pitch) \
 this = this * |      0      1     0      |
               \ -sin(pitch) 0 cos(pitch) /
 
```
    Specified by:
    
    appendRollRotation in interface Orientation3DBasics
    
    Parameters:
    
    roll - the angle to rotate about the x-axis.
  - preMultiply
```
public void preMultiply(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = other * this
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - prepend
```
public void prepend(Orientation3DReadOnly orientation)
```
    Description copied from interface: Orientation3DBasics
    Prepends the given orientation to this orientation.
    Let's consider the following:
    - three coordinate systems A, B, and C.
    - this represents the orientation of C relative to B.
    - orientation represents the orientation of B relative to A.
    The result of calling this method will be that this, represents the orientation of C relative to A.
    
    Prepending orientations is in some way similar to summing translations. However, while the addition for translation is commutative, the "prepend" operation on orientation is NOT commutative. Such that: this.prepend(orientation) ≠ orientation.prepend(this).
    Specified by:
    
    prepend in interface Orientation3DBasics
    
    Parameters:
    
    orientation - the orientation to prepend to this orientation. Not modified.
  - preMultiplyTransposeThis
```
public void preMultiplyTransposeThis(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = other * this^T
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - preMultiplyTransposeOther
```
public void preMultiplyTransposeOther(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = other^T * this
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - prependInvertOther
```
public void prependInvertOther(Orientation3DReadOnly orientation)
```
    Description copied from interface: Orientation3DBasics
    Prepends the inverse of the given orientation to this orientation.
    Let's consider the following:
    - three coordinate systems A, B, and C.
    - this represents the orientation of B relative to C.
    - orientation represents the orientation of B relative to A.
    The result of calling this method will be that this, represents the orientation of C relative to A.
    
    This operation is in some way similar to subtracting translations, as in this operation can be seen as subtracting orientation to this.
    Specified by:
    
    prependInvertOther in interface Orientation3DBasics
    
    Parameters:
    
    orientation - the orientation which the inverse is to be appended to this orientation. Not modified.
  - preMultiplyTransposeBoth
```
public void preMultiplyTransposeBoth(RotationMatrixReadOnly other)
```
    Performs a matrix multiplication on this.
    this = other^T * this^T
    
    Parameters:
    
    other - the other matrix to multiply this by. Not modified.
  - prependYawRotation
```
public void prependYawRotation(double yaw)
```
    Prepend a rotation about the z-axis to this rotation matrix.
```
        / cos(yaw) -sin(yaw) 0 \
 this = | sin(yaw)  cos(yaw) 0 | * this
        \    0         0     1 /
 
```
    Specified by:
    
    prependYawRotation in interface Orientation3DBasics
    
    Parameters:
    
    yaw - the angle to rotate about the z-axis.
  - prependPitchRotation
```
public void prependPitchRotation(double pitch)
```
    Prepend a rotation about the y-axis to this rotation matrix.
```
        /  cos(pitch) 0 sin(pitch) \
 this = |      0      1     0      | * this
        \ -sin(pitch) 0 cos(pitch) /
 
```
    Specified by:
    
    prependPitchRotation in interface Orientation3DBasics
    
    Parameters:
    
    pitch - the angle to rotate about the y-axis.
  - prependRollRotation
```
public void prependRollRotation(double roll)
```
    Append a rotation about the x-axis to this rotation matrix.
```
        /  cos(pitch) 0 sin(pitch) \
 this = |      0      1     0      | * this
        \ -sin(pitch) 0 cos(pitch) /
 
```
    Specified by:
    
    prependRollRotation in interface Orientation3DBasics
    
    Parameters:
    
    roll - the angle to rotate about the x-axis.
  - interpolate
```
public void interpolate(RotationMatrixReadOnly rf,
                        double alpha)
```
    Performs a linear interpolation in SO(3) from this to rf given the percentage alpha.
    This is equivalent to but much more computationally expensive than the Spherical Linear Interpolation performed with quaternions.
    
    Parameters:
    
    rf - the other rotation matrix used for the interpolation. Not modified.
    
    alpha - the percentage used for the interpolation. A value of 0 will result in not modifying this rotation matrix, while a value of 1 is equivalent to setting this rotation matrix to rf.
  - interpolate
```
public void interpolate(RotationMatrixReadOnly r0,
                        RotationMatrixReadOnly rf,
                        double alpha)
```
    Performs a linear interpolation in SO(3) from r0 to rf given the percentage alpha.
    This is equivalent to but much more computationally expensive than the Spherical Linear Interpolation performed with quaternions.
    
    Parameters:
    
    r0 - the first rotation matrix used in the interpolation. Not modified.
    
    rf - the second rotation matrix used in the interpolation. Not modified.
    
    alpha - the percentage to use for the interpolation. A value of 0 will result in setting this rotation matrix to r0, while a value of 1 is equivalent to setting this rotation matrix to rf.
  - applyTransform
```
public void applyTransform(Transform transform)
```
    Transform this using the given transform.
    this = R * this where 'R' is the 3-by-3 matrix representing the rotation part of the transform.
    
    Note: the transformation of a RotationMatrix strongly differs from the transformation of a Matrix3D.
    
    Specified by:
    
    applyTransform in interface Transformable
    
    Parameters:
    
    transform - the transform to use on this. Not modified.
  - applyInverseTransform
```
public void applyInverseTransform(Transform transform)
```
    Transform this using the inverse of the given transform.
    this = R^T * this where 'R' is the 3-by-3 matrix representing the rotation part of the transform.
    
    Note: the transformation of a RotationMatrix strongly differs from the transformation of a Matrix3D.
    
    Specified by:
    
    applyInverseTransform in interface Transformable
    
    Parameters:
    
    transform - the transform to use on this. Not modified.
  - getM00
```
public double getM00()
```
    Gets the 1st row 1st column coefficient of this matrix.
    
    Specified by:
    
    getM00 in interface Matrix3DReadOnly
    
    Returns:
    
    the 1st row 1st column coefficient.
  - getM01
```
public double getM01()
```
    Gets the 1st row 2nd column coefficient of this matrix.
    
    Specified by:
    
    getM01 in interface Matrix3DReadOnly
    
    Returns:
    
    the 1st row 2nd column coefficient.
  - getM02
```
public double getM02()
```
    Gets the 1st row 3rd column coefficient of this matrix.
    
    Specified by:
    
    getM02 in interface Matrix3DReadOnly
    
    Returns:
    
    the 1st row 3rd column coefficient.
  - getM10
```
public double getM10()
```
    Gets the 2nd row 1st column coefficient of this matrix.
    
    Specified by:
    
    getM10 in interface Matrix3DReadOnly
    
    Returns:
    
    the 2nd row 1st column coefficient.
  - getM11
```
public double getM11()
```
    Gets the 2nd row 2nd column coefficient of this matrix.
    
    Specified by:
    
    getM11 in interface Matrix3DReadOnly
    
    Returns:
    
    the 2nd row 2nd column coefficient.
  - getM12
```
public double getM12()
```
    Gets the 2nd row 3rd column coefficient of this matrix.
    
    Specified by:
    
    getM12 in interface Matrix3DReadOnly
    
    Returns:
    
    the 2nd row 3rd column coefficient.
  - getM20
```
public double getM20()
```
    Gets the 3rd row 1st column coefficient of this matrix.
    
    Specified by:
    
    getM20 in interface Matrix3DReadOnly
    
    Returns:
    
    the 3rd row 1st column coefficient.
  - getM21
```
public double getM21()
```
    Gets the 3rd row 2nd column coefficient of this matrix.
    
    Specified by:
    
    getM21 in interface Matrix3DReadOnly
    
    Returns:
    
    the 3rd row 2nd column coefficient.
  - getM22
```
public double getM22()
```
    Gets the 3rd row 3rd column coefficient of this matrix.
    
    Specified by:
    
    getM22 in interface Matrix3DReadOnly
    
    Returns:
    
    the 3rd row 3rd column coefficient.
  - equals
```
public boolean equals(java.lang.Object object)
```
    Tests if the given object's class is the same as this, in which case the method returns Matrix3DReadOnly.equals(Matrix3DReadOnly), it returns false otherwise or if the object is null.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    object - the object to compare against this. Not modified.
    
    Returns:
    
    true if object and this are exactly equal, false otherwise.
  - epsilonEquals
```
public boolean epsilonEquals(RotationMatrix other,
                             double epsilon)
```
    Tests on a per coefficient basis if this matrix is equal to the given other to an epsilon.
    
    Specified by:
    
    epsilonEquals in interface EpsilonComparable<RotationMatrix>
    
    Parameters:
    
    other - the other matrix to compare against this. Not modified.
    
    epsilon - the tolerance to use when comparing each component.
    
    Returns:
    
    true if the two matrices are equal, false otherwise.
  - geometricallyEquals
```
public boolean geometricallyEquals(RotationMatrix 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.
    
    Specified by:
    
    geometricallyEquals in interface GeometricallyComparable<RotationMatrix>
    
    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.
  - toString
```
public java.lang.String toString()
```
    Provides a String representation of this matrix as follows:
    m00, m01, m02
    m10, m11, m12
    m20, m21, m22
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    the String representing this matrix.
  - hashCode
```
public int hashCode()
```
    Calculates and returns a hash code value from the value of each component of this matrix.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hash code value for this matrix.

Class RotationMatrix

Field Summary

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

Constructor Summary

Method Summary

Methods inherited from interface us.ihmc.euclid.matrix.interfaces.Matrix3DBasics

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

Methods inherited from class java.lang.Object

Methods inherited from interface us.ihmc.euclid.orientation.interfaces.Orientation3DBasics

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

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

Constructor Detail

RotationMatrix

RotationMatrix

RotationMatrix

RotationMatrix

RotationMatrix

RotationMatrix

RotationMatrix

RotationMatrix

Method Detail

setToZero

normalize

transpose

setUnsafe

set

setRows

setColumns

setAndNormalize

set

set

set

setAndNormalize

setAndNormalize

setAndInvert

setAndInvert

setAndTranspose

setAndTranspose

setAxisAngle

setRotationVector

setQuaternion

setYawPitchRoll

setRotationMatrix

setToYawMatrix

setToPitchMatrix

setToRollMatrix

invert

multiply

append

multiplyTransposeThis

multiplyTransposeOther

appendInvertOther

multiplyTransposeBoth

appendYawRotation

appendPitchRotation

appendRollRotation

preMultiply

prepend

preMultiplyTransposeThis

preMultiplyTransposeOther

prependInvertOther

preMultiplyTransposeBoth

prependYawRotation

prependPitchRotation

prependRollRotation

interpolate

interpolate

applyTransform

applyInverseTransform

getM00

getM01

getM02

getM10

getM11

getM12

getM20

getM21

getM22

equals

epsilonEquals