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In reading the discussions on splines of various orders, I must note little
comment of weighted splines, splines under tension and other ideas for
generating smoothing splines rather than interpolating splines. Grace Wahbas
text: Spline Models for Observational Data, SIAM 1990 and Helmuth Spaths
text, whose title I can't remember, Utilitas Mathematicas, U. of Winnipeg,
197x? both deal with this topic.
The need seems to be to fit data for further data extraction, when
the fidelity of the raw data is suspect due to noise or other error source.
In that case the need to capture the existing data set exactly seems to be
of less importance than in allowing the extraction of 'believable' velocity
or acceleration values. Higher order splines giving inter point oscillations
would not seem desirable from this standpoint. Data smoothing via Bezier
curves is often discussed in texts on computer graphics, and offers an
alternative to cubic splines.
Tim Smith
Dept. of Mech Eng
UNB, F'ton, Canada
comment of weighted splines, splines under tension and other ideas for
generating smoothing splines rather than interpolating splines. Grace Wahbas
text: Spline Models for Observational Data, SIAM 1990 and Helmuth Spaths
text, whose title I can't remember, Utilitas Mathematicas, U. of Winnipeg,
197x? both deal with this topic.
The need seems to be to fit data for further data extraction, when
the fidelity of the raw data is suspect due to noise or other error source.
In that case the need to capture the existing data set exactly seems to be
of less importance than in allowing the extraction of 'believable' velocity
or acceleration values. Higher order splines giving inter point oscillations
would not seem desirable from this standpoint. Data smoothing via Bezier
curves is often discussed in texts on computer graphics, and offers an
alternative to cubic splines.
Tim Smith
Dept. of Mech Eng
UNB, F'ton, Canada