View Full Version : Re: cubic vs quintic spline

Jesus Dapena
07-28-1995, 07:29 AM
Gerry Gottlieb says:

> Just to take a different approach to this controversy, one
> message to apply in the future is to collect extra data at
> the beginning and end of your record so it is not necessary
> to worry about these kinds of things.

That is good advice, but unfortunately sometimes it is not enough.
Vaughan found in his dropping ball experiment that the bias at the ends of
the data set (forcing the 2nd derivative to zero) messed up not only the
ends of the data set, but also the middle of the trial (although not so
badly as the ends of the trial).

Also, in situations involving impacts it is not advisable to input
into the smoothing subroutine data corresponding to the period after the
impact. Consider for instance a baseball bat hitting a ball. If you input
coordinate data corresponding to the period before the impact and also to
the period after the impact, there is no way that any smoothing program will
be able to handle that properly. The program will assume that the very
sudden decrease in the velocity of the bat that occurs during impact cannot
have occurred in such a short period of time. Therefore, the smoothing
subroutine will yield a smaller value than the real one for the peak
deceleration, and it will also spread out that deceleration over a longer
period of time than the actual period of contact between the bat and the
ball. The researcher will consequently be led to believe that the bat
starts to slow down before the impact actually occurs. If you are computing
torques, you will find (falsely!) that the musculature reverses its activity
as it strives to slow down the bat before impact. In a case like that, it
is best to include in your input to the smoothing program only pre-impact
data. (Even doing this, you are likely to have problems with smoothing near
the impact, but you will definitely be better off than if you mix pre- and
post-impact data.)

Jesus Dapena
Jesus Dapena
Department of Kinesiology
Indiana University
Bloomington, IN 47405, USA
1-812-855-8407 (office phone)
dapena@valeri.hper.indiana.edu (email)