Smooth curve through all points of data?
Mateusz Papiernik
Is it possible in any way to draw a smooth curve (smooth as in
acsplines) that would go through EACH point of data given? I
experimented with point weights, but it doesn't seem to really solve the
problem. With many functions I was able to extrapolate the amount of
data by giving additional "fake points" on track, so the curve was much
more accurate, but now I'm not sure how to do that mathematically, and
acsplines with different weights goes near my points, but not through
them. The same goes for bezier, or even worse. The function looks like
logarithmic, but has some differences in behaviour after the steep
raising, so I can't find good function equation to fit a curve either.
Also, the amount of data isn't great enough to use with lines instead of
smooth. Am I missing something?
Thanks!
--
Mateusz Papiernik, Maticomp Webdesign
Projektowanie i realizacja witryn WWW
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Hans-Bernhard Bröker
> Is it possible in any way to draw a smooth curve (smooth as in
> acsplines) that would go through EACH point of data given?
In general, those are contradictory goals.
That said, I'm somewhat amazed you managed to find both "smooth
acsplines" and "smooth bezier", but not "smooth csplines", which does
exactly what you ask.
goo...@catking.net
wrote:
Be very careful with "smooth fits" . They can very easily bear no
resemblance to the reality of what your data represents.
You'd generally be better having some idea of a mathematical model ,
if that is possible, and then trying to fit a function using fit
command.
Since nearly all data has experimental errors and uncertainties,
forcing a line to go through all points is rarely a good idea. Also
splines, while nice and smooth are defined to fulfill certain
conditions. They may not be appropriate for your data.
csplines are a good case in point and can badly overshoot around rapid
changes in direction, or give the impression of oscillations that are
not in the data.
Use with caution and be aware that you are probably adding fictional
information to your data. Pretty much like adding your false points.
Don't think it is somehow more legit because it's done in a
mathematical way.
It easy to fall into the trap of thinking that if it's done by a
computer in a mathematical way it must be correct.
Mateusz Papiernik
> Be very careful with "smooth fits" . They can very easily bear no
> resemblance to the reality of what your data represents.
Thanks for your comprehensive answer. I finally managed to fit functions
instead of smoothing. Thanks again.