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Re: cubic vs quintic spline

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  • Re: cubic vs quintic spline

    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) (email)