Package georegression.geometry

Class ConvertRotation3D_F64

java.lang.Object
georegression.geometry.ConvertRotation3D_F64
public class ConvertRotation3D_F64 extends Object
Provides functions to convert between different parameterizations of 3D rotation matrices.

  • Constructor Details

    • ConvertRotation3D_F64

      public ConvertRotation3D_F64()

  • Method Details

    • rodriguesToMatrix

      public static DMatrixRMaj rodriguesToMatrix(Rodrigues_F64 rodrigues, @Nullable @Nullable DMatrixRMaj 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 internally.
      Returns:
      rotation matrix.

    • rodriguesToMatrix

      public static DMatrixRMaj rodriguesToMatrix(double x, double y, double z, @Nullable @Nullable DMatrixRMaj R)
      Converts axis angle (Rodrigues_F64) into a rotation matrix without needing to declare a storage variable.
      Parameters:
      x - x-component of rotation vector
      y - y-component of rotation vector
      z - z-component of rotation vector
      R - (Optional) storage for 3x3 rotation matrix. If null one will be declared internally.
      Returns:
      Rotation matrix.
      See Also:

    • rodriguesToMatrix

      public static DMatrixRMaj rodriguesToMatrix(double axisX, double axisY, double axisZ, double theta, @Nullable @Nullable DMatrixRMaj R)
      Converts axis angle (Rodrigues_F64) into a rotation matrix without needing to declare a storage variable.
      Parameters:
      axisX - x-component of normalized rotation vector
      axisY - y-component of normalized rotation vector
      axisZ - z-component of normalized rotation vector
      theta - magnitude of rotation in radians
      R - (Optional) storage for 3x3 rotation matrix. If null one will be declared internally.
      Returns:
      Rotation matrix.

    • rodriguesToEuler

      public static double[] rodriguesToEuler(Rodrigues_F64 rodrigues, EulerType type, @Nullable @org.jetbrains.annotations.Nullable 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(double rx, double ry, double rz, @Nullable @Nullable Quaternion_F64 quat)

      Converts 3-dof Rodrigues_F64 into a unit Quaternion_F64.

      Parameters:
      rx - x-axis in rotation vector
      ry - y-axis in rotation vector
      rz - z-axis in rotation vector
      quat - Storage for quaternion coordinate. If null a new quaternion is created. Modified.
      Returns:
      unit quaternion coordinate.

    • rodriguesToQuaternion

      public static Quaternion_F64 rodriguesToQuaternion(Rodrigues_F64 rodrigues, @Nullable @Nullable 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, @Nullable @Nullable 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, @Nullable @org.jetbrains.annotations.Nullable 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(DMatrixRMaj R, EulerType type, @Nullable @org.jetbrains.annotations.Nullable 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(DMatrixRMaj R, @Nullable @Nullable Quaternion_F64 quat)
      Extracts a unit quaternions from the provided rotation matrix.
      Parameters:
      R - (Input) rotation matrix
      quat - (Output) Optional storage for unit quaternion. If null a new class will be used.
      Returns:
      unit quaternion representation of the rotation matrix.

    • matrixToRodrigues

      public static Rodrigues_F64 matrixToRodrigues(DMatrixRMaj R, @Nullable @Nullable 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 DMatrixRMaj rotX(double ang, @Nullable @Nullable DMatrixRMaj 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, DMatrixRMaj 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 DMatrixRMaj rotY(double ang, @Nullable @Nullable DMatrixRMaj 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, DMatrixRMaj 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 DMatrixRMaj rotZ(double ang, @Nullable @Nullable DMatrixRMaj 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, DMatrixRMaj 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 DMatrixRMaj eulerToMatrix(EulerType type, double rotA, double rotB, double rotC, @Nullable @Nullable DMatrixRMaj 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, @Nullable @Nullable Quaternion_F64 q)

    • approximateRotationMatrix

      public static DMatrixRMaj approximateRotationMatrix(DMatrixRMaj orig, @Nullable @Nullable DMatrixRMaj 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||2F
      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 DMatrixRMaj quaternionToMatrix(Quaternion_F64 quat, @Nullable @Nullable DMatrixRMaj 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

    • quaternionToMatrix2

      public static DMatrixRMaj quaternionToMatrix2(Quaternion_F64 quat, @Nullable @Nullable DMatrixRMaj R)

      Converts a unit quaternion into a rotation matrix. Uses a more common but equivalent formulation. Can be used when you need the exact same solution as another implementation.

      Parameters:
      quat - Unit quaternion.
      R - Storage for rotation matrix. If null a new matrix is created. Modified.
      Returns:
      Rotation matrix

    • quaternionToMatrix2

      public static DMatrixRMaj quaternionToMatrix2(double w, double x, double y, double z, @Nullable @Nullable DMatrixRMaj R)
      Most common formulation. Explicitly takes advantage of norm=1

    • quaternionToMatrix

      public static DMatrixRMaj quaternionToMatrix(double w, double x, double y, double z, @Nullable @Nullable DMatrixRMaj R)
      Alternative formulation