View Full Version : Rotation matrix optimization

06-28-1996, 01:03 AM
Dear Subscriber,
This is a question for all Spoor and Veldpaus fans;

The method proposed by Spoor and Veldpaus ('Rigid body motion calculated
from spatial coordinates of markers', J. Biomechanics, 1980,Vol 13
pp391-393) allows the derivation of a rotation matrix, R, and a
translation vector, v, to provide a least squares approximation of the
motion of a body as described by the change in position of several markers (as
used for gait analysis etc.). My attempts to apply this method to the
motion of the thigh about the hip joint centre have resulted in the
following question:

If I consider the thigh movement to be only a
rotation, i.e. v=0, does the value of R calculated using the Spoor and
Veldpaus method still provide a least squares fit?

>From my analysis it would seem that the solution using R would provide the
best available by use of a rotation only. This could then be further
improved by a translation. (This would not hold for the reverse, i.e. the
calculated v would not provide the best least squares fit possible using
only a translation vector.)

In short can anybody confirm that Spoor and Veldpaus' R will provide a
least squares approximation or suggest another method (with associated
references) of finding the rotation matrix which provides this solution.

I will post a summary of any useful information gathered.

Thank you for your time,

Ben Stansfield

University of Strathclyde