georegression.geometry

Class ConvertRotation3D_F64

java.lang.Object

georegression.geometry.ConvertRotation3D_F64

public class ConvertRotation3D_F64
extends java.lang.Object

Provides functions to convert between different parameterizations of 3D rotation matrices.

Constructor Summary

Constructors

Constructor and Description
ConvertRotation3D_F64()

Method Summary

Modifier and Type	Method and Description
static org.ejml.data.DenseMatrix64F	approximateRotationMatrix(org.ejml.data.DenseMatrix64F orig, org.ejml.data.DenseMatrix64F R) Finds a rotation matrix which is the optimal approximation to an arbitrary 3 by 3 matrix.
static org.ejml.data.DenseMatrix64F	eulerToMatrix(EulerType type, double rotA, double rotB, double rotC, org.ejml.data.DenseMatrix64F R) Converts an Euler coordinate into a rotation matrix.
static Quaternion_F64	eulerToQuaternion(EulerType type, double rotA, double rotB, double rotC, Quaternion_F64 q)
static double[]	matrixToEuler(org.ejml.data.DenseMatrix64F R, EulerType type, double[] euler) Converts a rotation matrix into an Euler angle of different types
static Quaternion_F64	matrixToQuaternion(org.ejml.data.DenseMatrix64F R, Quaternion_F64 quat) Extracts quaternions from the provided rotation matrix.
static Rodrigues_F64	matrixToRodrigues(org.ejml.data.DenseMatrix64F R, Rodrigues_F64 rodrigues) Converts a rotation matrix into Rodrigues_F64.
static double[]	quaternionToEuler(Quaternion_F64 q, EulerType type, double[] euler) Converts a quaternion into an euler rotation of different types
static org.ejml.data.DenseMatrix64F	quaternionToMatrix(Quaternion_F64 quat, org.ejml.data.DenseMatrix64F R) Converts a unit quaternion into a rotation matrix.
static Rodrigues_F64	quaternionToRodrigues(Quaternion_F64 quat, Rodrigues_F64 rodrigues) Converts a unit Quaternion_F64 into Rodrigues_F64.
static double[]	rodriguesToEuler(Rodrigues_F64 rodrigues, EulerType type, double[] euler) ConvertsRodrigues_F64 into an euler rotation of different types
static org.ejml.data.DenseMatrix64F	rodriguesToMatrix(Rodrigues_F64 rodrigues, org.ejml.data.DenseMatrix64F R) Converts Rodrigues_F64 into a rotation matrix.
static Quaternion_F64	rodriguesToQuaternion(Rodrigues_F64 rodrigues, Quaternion_F64 quat) Converts Rodrigues_F64 into a unit Quaternion_F64.
static org.ejml.data.DenseMatrix64F	rotX(double ang, org.ejml.data.DenseMatrix64F R) Creates a rotation matrix about the x-axis.
static org.ejml.data.DenseMatrix64F	rotY(double ang, org.ejml.data.DenseMatrix64F R) Creates a rotation matrix about the y-axis.
static org.ejml.data.DenseMatrix64F	rotZ(double ang, org.ejml.data.DenseMatrix64F R) Creates a rotation matrix about the z-axis.
static void	setRotX(double ang, org.ejml.data.DenseMatrix64F R) Sets the values in the specified matrix to a rotation matrix about the x-axis.
static void	setRotY(double ang, org.ejml.data.DenseMatrix64F r) Sets the values in the specified matrix to a rotation matrix about the y-axis.
static void	setRotZ(double ang, org.ejml.data.DenseMatrix64F r) Sets the values in the specified matrix to a rotation matrix about the z-axis.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ConvertRotation3D_F64

public ConvertRotation3D_F64()

Method Detail

rodriguesToMatrix

public static org.ejml.data.DenseMatrix64F rodriguesToMatrix(Rodrigues_F64 rodrigues,
                                                             org.ejml.data.DenseMatrix64F R)

Converts Rodrigues_F64 into a rotation matrix.

Parameters:

rodrigues - rotation defined using rotation axis angle notation.

R - where the results will be stored. If null a new matrix is declared/

Returns:

rotation matrix.

rodriguesToEuler

public static double[] rodriguesToEuler(Rodrigues_F64 rodrigues,
                                        EulerType type,
                                        double[] euler)

ConvertsRodrigues_F64 into an euler rotation of different types

Parameters:

rodrigues - rotation defined using rotation axis angle notation.

type - Type of Euler rotation

euler - (Output) Optional storage for Euler rotation

Returns:

The Euler rotation.

rodriguesToQuaternion

public static Quaternion_F64 rodriguesToQuaternion(Rodrigues_F64 rodrigues,
                                                   Quaternion_F64 quat)

Converts Rodrigues_F64 into a unit Quaternion_F64.

Parameters:

rodrigues - The angle of rotation around the rotation axis.

quat - Storage for quaternion coordinate. If null a new quaternion is created. Modified.

Returns:

unit quaternion coordinate.

quaternionToRodrigues

public static Rodrigues_F64 quaternionToRodrigues(Quaternion_F64 quat,
                                                  Rodrigues_F64 rodrigues)

Converts a unit Quaternion_F64 into Rodrigues_F64.

Parameters:

quat - (Input) Unit quaternion

rodrigues - (Optional) Storage for rodrigues coodinate. If null a new instance is created.

Returns:

rodrigues

quaternionToEuler

public static double[] quaternionToEuler(Quaternion_F64 q,
                                         EulerType type,
                                         double[] euler)

Converts a quaternion into an euler rotation of different types

Parameters:

q - (Input) Normalized quaternion. Not modified.

type - Type of Euler rotation

euler - (Output) Optional storage for Euler rotation

Returns:

The Euler rotation.

matrixToEuler

public static double[] matrixToEuler(org.ejml.data.DenseMatrix64F R,
                                     EulerType type,
                                     double[] euler)

Converts a rotation matrix into an Euler angle of different types

Parameters:

R - (Input) Rotation matrix. Not modified.

type - Type of Euler rotation

euler - (Output) Optional storage for Euler rotation

Returns:

The Euler rotation.

matrixToQuaternion

public static Quaternion_F64 matrixToQuaternion(org.ejml.data.DenseMatrix64F R,
                                                Quaternion_F64 quat)

Extracts quaternions from the provided rotation matrix.

Parameters:

R - (Input) rotation matrix

quat - (Output) Optional storage for quaternion. If null a new class will be used.

Returns:

unit quaternion representation of the rotation matrix.

matrixToRodrigues

public static Rodrigues_F64 matrixToRodrigues(org.ejml.data.DenseMatrix64F R,
                                              Rodrigues_F64 rodrigues)

Converts a rotation matrix into Rodrigues_F64.

Parameters:

R - Rotation matrix.

rodrigues - Storage used for solution. If null a new instance is declared.

Returns:

The found axis and rotation angle.

rotX

public static org.ejml.data.DenseMatrix64F rotX(double ang,
                                                org.ejml.data.DenseMatrix64F R)

Creates a rotation matrix about the x-axis.

Parameters:

ang - the angle it rotates a point by in radians.

R - (Output) Optional storage for rotation matrix. Modified.

Returns:

The 3 by 3 rotation matrix.

setRotX

public static void setRotX(double ang,
                           org.ejml.data.DenseMatrix64F R)

Sets the values in the specified matrix to a rotation matrix about the x-axis.

Parameters:

ang - the angle it rotates a point by in radians.

R - (Output) Storage for rotation matrix. Modified.

rotY

public static org.ejml.data.DenseMatrix64F rotY(double ang,
                                                org.ejml.data.DenseMatrix64F R)

Creates a rotation matrix about the y-axis.

Parameters:

ang - the angle it rotates a point by in radians.

R - (Output) Optional storage for rotation matrix. Modified.

Returns:

The 3 by 3 rotation matrix.

setRotY

public static void setRotY(double ang,
                           org.ejml.data.DenseMatrix64F r)

Sets the values in the specified matrix to a rotation matrix about the y-axis.

Parameters:

ang - the angle it rotates a point by in radians.

r - A 3 by 3 matrix. Is modified.

rotZ

public static org.ejml.data.DenseMatrix64F rotZ(double ang,
                                                org.ejml.data.DenseMatrix64F R)

Creates a rotation matrix about the z-axis.

Parameters:

ang - the angle it rotates a point by in radians.

R - (Output) Optional storage for rotation matrix. Modified.

Returns:

The 3 by 3 rotation matrix.

setRotZ

public static void setRotZ(double ang,
                           org.ejml.data.DenseMatrix64F r)

Sets the values in the specified matrix to a rotation matrix about the z-axis.

Parameters:

ang - the angle it rotates a point by in radians.

r - A 3 by 3 matrix. Is modified.

eulerToMatrix

public static org.ejml.data.DenseMatrix64F eulerToMatrix(EulerType type,
                                                         double rotA,
                                                         double rotB,
                                                         double rotC,
                                                         org.ejml.data.DenseMatrix64F R)

Converts an Euler coordinate into a rotation matrix. Different type of Euler coordinates are accepted.

Parameters:

type - Which Euler coordinate is the input in

rotA - Angle of rotation around axis A. First rotation

rotB - Angle of rotation around axis B Second rotation

rotC - Angle of rotation around axis C Third rotation

R - (Output) Optional storage for output rotation matrix

Returns:

Rotation matrix

eulerToQuaternion

public static Quaternion_F64 eulerToQuaternion(EulerType type,
                                               double rotA,
                                               double rotB,
                                               double rotC,
                                               Quaternion_F64 q)

approximateRotationMatrix

public static org.ejml.data.DenseMatrix64F approximateRotationMatrix(org.ejml.data.DenseMatrix64F orig,
                                                                     org.ejml.data.DenseMatrix64F R)

Finds a rotation matrix which is the optimal approximation to an arbitrary 3 by 3 matrix. Optimality is specified by the equation below:

min ||R-Q||²_F
R
where R is the rotation matrix and Q is the matrix being approximated.

The technique used is based on SVD and is described in Appendix C of "A Flexible New Technique for Camera Calibration" Technical Report, updated 2002.

Both origin and R can be the same instance.

Parameters:

orig - Input approximate rotation matrix. Not modified.

R - (Optional) Storage for the approximated rotation matrix. Modified.

Returns:

Rotation matrix

quaternionToMatrix

public static org.ejml.data.DenseMatrix64F quaternionToMatrix(Quaternion_F64 quat,
                                                              org.ejml.data.DenseMatrix64F R)

Converts a unit quaternion into a rotation matrix.

Equations is taken from: Paul J. Besl and Neil D. McKay, "A Method for Registration of 3-D Shapes" IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 14, No. 2, Feb. 1992

Parameters:

quat - Unit quaternion.

R - Storage for rotation matrix. If null a new matrix is created. Modified.

Returns:

Rotation matrix