[ncl-talk] NCL spline question

[Jonathan Vigh]

Hi Dennis,
    Do you mean use ftcurv separately for lat and for lon as functions 
of time? Would fitting each separately interfere the 2d nature of this 
problem?
Jonathan


On 12/23/2015 04:54 PM, Dennis Shea wrote:
> Try:
>
> http://www.ncl.ucar.edu/Document/Functions/Built-in/ftcurv.shtml
> http://www.ncl.ucar.edu/Document/Functions/Built-in/ftcurvs.shtml
>
> Experiment with the tension.
>
>
> Merry Christmas
> D
>
> On Wed, Dec 23, 2015 at 4:15 PM, Jonathan Vigh <jvigh at ucar.edu> wrote:
>> As an update to my question, a colleague informed me that Matlab has a
>> function called pchip: Piecewise Cubic Hermite Interpolating Polynomial
>> (PCHIP). It is the same as a regular cubic spline but it does not permit
>> overshoot/undershoot, which can occur with regular cubic splines.
>> http://www.mathworks.com/help/matlab/ref/pchip.html?s_tid=gn_loc_drop
>>
>> I think something like this would be sufficient for my problem.
>>
>> Do any of NCL's functions offer this type of spline?
>>
>> Thanks,
>>      Jonathan
>>
>>
>>
>> On 12/23/2015 04:01 PM, Jonathan Vigh wrote:
>>> Greetings NCL-Talk,
>>>
>>> I'm trying to generate an interpolatory spline* for a lat/lon tropical
>>> cyclone trajectory from a set of lat/lon points at semi-regular time
>>> intervals. The input points are regularly spaced (for the most part)
>>> 6-hourly Best Track points, however there are occasional irregular
>>> time points in between, such as the exact time of landfall. The
>>> desired output is a semi-regular grid of hourly points, but with the
>>> same few irregular time points as the for the input times.
>>>
>>> (*An interpolatory spline is one in which the interpolated spline
>>> passes through the points that are being interpolated from, as opposed
>>> to an approximating spline which does not have to pass through the
>>> points.)
>>>
>>> It was suggested that NCL's ftkurv function (from the FitGrid library)
>>> might do what I'd like, since this does an interpolation for
>>> parametric curves. If I understand my problem correctly, lat and lon
>>> can be thought of as parameters of time.
>>>
>>> The example plot for ftkurv looks promising:
>>> http://www.ncarg.ucar.edu/ngmath/fitgrid/plot4.html
>>>
>>> ftkurv (
>>>                  xi [*] : numeric,
>>>                  yi [*] : numeric,
>>>                  t  [*] : numeric,
>>>                  xo [*] : float,    ; or double
>>>                  yo [*] : float     ; or double
>>>          )
>>>
>>> In the example given for this function, the parameter array passed in
>>> for 't' is a regularly-spaced normalized parameter array that ranges
>>> from 0 to 1. I don't understand where this function gets any
>>> information about the input time values however. I built a test case
>>> for a real hurricane track and validated the interpolated spline
>>> points at the input points. I get zero "error" at the end points of
>>> the track, with maximum error in the middle. The error increases and
>>> decreases smoothly, suggesting an offset issue (probably related to
>>> time drift).
>>>
>>> - Does anybody know if this function allow for irregular parameter
>>> values for 't'?
>>> - Is there a way to use ftkurv in a way that makes it aware of the
>>> times of the input lat/lon?
>>>
>>> I've created a fairly detailed stand-alone test code, which is
>>> attached. Feel free to run to see the error characteristics of the
>>> ftkurv spline.
>>>
>>> Ultimately, I'd like to be able to do piecewise cubic spline
>>> interpolation along the lines of what is done for gps tracks:
>>> http://topofusion.com/spline.php (piecewise interpolation, matching
>>> derivatives to ensure continuity of slope, Bessel interpolation used
>>> to compute the first derivative by fitting a 3-point parabola for each
>>> point). If someone has already implemented something like this in NCL,
>>> that would of course be awesome. But I can make do with something more
>>> basic provided it can handle the irregular input/output times.
>>>
>>> If anyone has experience with this type of spline problem, or has
>>> suggestions on other NCL routines to try, I'd appreciate any input you
>>> can provide.
>>>
>>> Jonathan
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