artisynth.core.mechmodels

Class DualQuaternionDeriv

java.lang.Object

artisynth.core.mechmodels.DualQuaternionDeriv

public class DualQuaternionDeriv
extends java.lang.Object

Utility methods for computing derivatives assocaited with dual quaternions.

Constructor Summary

Constructors

Constructor and Description
DualQuaternionDeriv()

Method Summary

Modifier and Type	Method and Description
static void	computeDerivs(Matrix4x3 DQrDr, Matrix4x3 DQtDr, DualQuaternion dqr, RigidTransform3d TW0) Compute the angular displacement derivatives of the rotational and translational parts of the dual quaternion dq representing the relative motion of a frame described with respect to a base frame.
static void	computeDQrDr(Matrix4x3 D, Quaternion qr) Compute derivative of the rotational part of a dual quaternion with respect to angular velocity.
static void	computeDQtDr(Matrix4x3 D, Quaternion qt, Quaternion qr) Compute derivative of the translation part of a dual quaternion with respect to angular velocity.
static void	computeJrJtt(Matrix3x4 Jr, Matrix3x4 Jtt, DualQuaternion dq, double m0, double me, Point3d r) Computes the Jr and Jtt matrices for a normalized dual quaternion, its original real and dual magnitudes m0 and me, and an original point position r.
static Matrix4x3	computeNumericDQrDr(RigidTransform3d TW, RigidTransform3d TW0)
static Matrix4x3	computeNumericDQtDr(RigidTransform3d TW, RigidTransform3d TW0)
static void	postmulDeriv(Matrix4x3 DR, Matrix4x3 D1, Quaternion q) Post-multiplies in place the columns of a 4x3 quaternion derivative matrix by a quaternon q.

Methods inherited from class java.lang.Object

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

Constructor Detail

DualQuaternionDeriv

public DualQuaternionDeriv()

Method Detail

computeDerivs

public static void computeDerivs(Matrix4x3 DQrDr,
                                 Matrix4x3 DQtDr,
                                 DualQuaternion dqr,
                                 RigidTransform3d TW0)

Compute the angular displacement derivatives of the rotational and translational parts of the dual quaternion dq representing the relative motion of a frame described with respect to a base frame. The angular displacement is defined with respect to the frame's current position (in world coordinates). If the current frame position id TW and the base frame is TWO, then the relative motion is described by

 TR = TW * inv(TW0)
 

Parameters:

DQrDr - returns the derivative of the rotational component

DQtDr - returns the derivative of the translational component

dqr - dual quaternion describing the relative motion

TW0 - base frame

computeDQrDr

public static void computeDQrDr(Matrix4x3 D,
                                Quaternion qr)

Compute derivative of the rotational part of a dual quaternion with respect to angular velocity.

Parameters:

D - returns the 4x3 derivative

qr - rotational part of the dual quaternuon

postmulDeriv

public static void postmulDeriv(Matrix4x3 DR,
                                Matrix4x3 D1,
                                Quaternion q)

Post-multiplies in place the columns of a 4x3 quaternion derivative matrix by a quaternon q.

computeDQtDr

public static void computeDQtDr(Matrix4x3 D,
                                Quaternion qt,
                                Quaternion qr)

Compute derivative of the translation part of a dual quaternion with respect to angular velocity.

Parameters:

D - returns the 4x3 derivative

qt - translational part of the dual quaternuon

qr - rotational part of the dual quaternuon

computeNumericDQtDr

public static Matrix4x3 computeNumericDQtDr(RigidTransform3d TW,
                                            RigidTransform3d TW0)

computeNumericDQrDr

public static Matrix4x3 computeNumericDQrDr(RigidTransform3d TW,
                                            RigidTransform3d TW0)

computeJrJtt

public static void computeJrJtt(Matrix3x4 Jr,
                                Matrix3x4 Jtt,
                                DualQuaternion dq,
                                double m0,
                                double me,
                                Point3d r)

Computes the Jr and Jtt matrices for a normalized dual quaternion, its original real and dual magnitudes m0 and me, and an original point position r.

Parameters:

Jr - returns the Jr matrix

Jtt - returns the Jtt matrix

dq - normalized dual quaternion

m0 - real magnitude of original non-normalized dual quaternion

me - dual magnitude of original non-normalized dual quaternion

r - original point position