# Re: st: RE: Smoothing/Spline and momentum

 From Dan Weitzenfeld To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Smoothing/Spline and momentum Date Wed, 4 Feb 2009 15:14:02 -0800

```Thanks, Nick, that was a vast, vast improvement over the linear
interpolation I've been using.
You're right, I did have timestamps, so  I used -cipolate- on x(t) and y(t).
I'm going to play around with polar coordinates as well.

On Wed, Feb 4, 2009 at 9:47 AM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
>
> Mata has cubic spline interpolation.
>
> A cubic interpolation routine is available as -cipolate- on SSC.
>
> You say you have x, y; I wonder if you also have time or some
> equivalent, say t. My instinct is that it might be easier to interpolate
> in terms of x = x(t) and y = y(t) rather than y = y(x) or x = x(y), but
> I'm not sure where that instinct comes from. I'm probably guessing by
> analogy with smoothing directions on the circle where a direction can
> quite naturally flip smoothly from (in compass terms) just W of N to
> just E of N and a good smoothing method has to respect that. One good
> solution is to decouple the smoothing into smmothing of sine and cosine
> and then take the arctangent.
>
> That leads laterally into mentioning that working with polar coordinates
> may make just as much sense.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Dan Weitzenfeld
>
> I have data consisting of X,Y coordinates of a moving object, sampled
> at an unfortunately low sampling rate.  I'm therefore trying to
> approximate location in the intervals between sampling points using
> some combination of interpolation and smoothing or splining.
> I have tried a bunch of methods (see below), but I'm having difficulty
> meeting my two goals:
> 1) the interpolated trajectory should always go through the sampled
> points (they are sampled without error, so I feel like I should hit
> them)
> 2) the interpolated trajectory should look like a moving object with
> momentum
>     a.  the trajectory should be somewhat smooth, what I would call
> "sports car smooth"
>     b.  velocity when entering a curve is taken into account  - a
> faster entry means a later, deeper apex
>
> So far, I have tried:
> -spline-
> -rcspline-
> -lowess-
> -smooth-
>
> I am wondering if anyone has any tips or package recommendations for
> solving this fun problem.
>
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```