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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Smoothing/Spline and momentum |

Date |
Wed, 4 Feb 2009 17:47:27 -0000 |

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/

**Follow-Ups**:**Re: st: RE: Smoothing/Spline and momentum***From:*Dan Weitzenfeld <dan.weitzenfeld@emsense.com>

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

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