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From |
Dan Weitzenfeld <dan.weitzenfeld@emsense.com> |

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. > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Smoothing/Spline and momentum***From:*Dan Weitzenfeld <dan.weitzenfeld@emsense.com>

**st: RE: Smoothing/Spline and momentum***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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