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rtamstorf40
01-14-2003, 04:05 AM
Along these same lines you may want to take a look at a paper by Herda et
al. [1]. This paper is based on "swing-and-twist" but goes a step further
by using a quaternion field to obtain an easy-to-interpret representation
of the joint limits.

Sincerely,
Rasmus Tamstorf

[1]
@inproceedings{Herda02a,
author = "L. Herda and R. Urtasun and A. Hanson and P. Fua",
booktitle = "Automated Face and Gesture Recognition",
title = {{An Automatic Method For Determining Quaternion Field
Boundaries for Ball-and-Socket Joint Limits}},
address = "Washington, DC",
month = "May",
year = 2002
url = { http://cvlab.epfl.ch/~fua/papers/herda-et-al-fg02.pdf }
}

On Tue, 14 Jan 2003, Kjartan Halvorsen wrote:

> Dear Colleagues,
>
> In Biomechanics, Euler angles is the dominant representation of joint
> motion, as
> exemplified by the standardization proposal referred to by Dr. Veeger.
> (http://www.wbmt.tudelft.nl/mms/dsg/intersg/ISGproposal.pdf)
> The strength of the representation lies primarily in the close connection
> to anatomical nomenclature, which is valuable when interpreting 3D joint
> motion. The weakness of the representation is mathematical; see van den
> Bogert and Kwon's recent discussion. Herman Woltring fought for the
> acceptance of the "attitude vector" as the standard for representing 3D
> attitude (and rotations). See [1] and contemporary discussions on
> biomech-l.
>
> I would like to direct this forum's attention to a different representation
> of 3D rotation [2], proposed in the computer graphics literature as a
> convenient representation for ball-and-socket type of joints with large
> range of motion. The representation is sometimes called "swing-and-twist",
> and it has a straightforward interpretation and nice mathematical
> properties (no gimbal lock, singularity only for rotations ("swings") of
> 180 degrees from the reference orientation).
>
> A brief introduction to swing-and-twist: Consider the motion of the
> shoulder joint. The motion is decomposed in
> two rotations: a swing of the arm, which causes NO axial rotation of the
> humerus, followed by an axial rotation of the humerus (the
> twist part). The swing of the arm is represented by a rotation vector
> that is constrained to lie in the plane normal to the longitudinal axis of
> the humerus. The idea of a rotation vector may seem to imply that the
> swing-and-twist representation is as difficult to envision (interpret) as
> the attitude vector of Woltring. However, the swing axis lies in a fixed
> plane, and 2D geometry is a lot easier to visualize and understand than 3D
> (at least for most of us, it is).
>
> Take a look at Grassia's paper [2], online at
> http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf
> I think it offers a nice compromise between the ease of interpretation of
> Euler angles and the nice mathematical properties of the attitude vector.
>
> Yours sincerely,
>
> Kjartan Halvorsen
>
>
>
> [1]
> @article{biomech_woltring_94,
> author = {H.J. Woltring},
> title = {3-{D} attitude representation of human joints: A
> standardization proposal},
> journal = {Journal of Biomechanics},
> year = {1994},
> month = {},
> volume = {27},
> pages = {1399--1414},
> }
>
> [2]
> @article{biomech_grassia_98,
> author = {F.S. Grassia},
> title = {Practical parameterization of rotations using the exponential
> map},
> journal = {Journal of Graphics Tools},
> year = {1998},
> month = {},
> volume = {3},
> pages = {29--48},
> url = {http://www.cs.cmu.edu/~spiff/moedit99/expmap.pdf}
> }
>
>
> --
>
> The Department of Systems and Control
> Uppsala University
> http://www.syscon.uu.se/
> + 46 18 471 3150
>
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