| polar interpolation [message #33528] |
Thu, 09 January 2003 19:20  |
Thomas Gutzler
Messages: 44
Registered: November 2002
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Member |
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Good morning,
I am looking for a function that can do a polar interpolation of a
[2,n]-array.
What I don't want is to convert polar koordinates to rect, interpolate,
and reconvert them to polar.
I'm not sure if the given IDL-functions can do this and unfortunatiely I
couldn't google anything that helps. Neither davids nor RSIs page could
help :(
Tom
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| Re: polar interpolation [message #33628 is a reply to message #33528] |
Mon, 13 January 2003 09:40  |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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Stein Vidar Hagfors Haugan wrote:
>
> James Kuyper <kuyper@saicmodis.com> writes:
>
>> Thomas Gutzler wrote:
>>>
>>> Good morning,
>>>
>>> I am looking for a function that can do a polar interpolation of a
>>> [2,n]-array.
>>> What I don't want is to convert polar koordinates to rect, interpolate,
>>> and reconvert them to polar.
>>
>> If you have data that comes close to the pole, that's precisely what you
>> should do. Otherwise, you're going to see some very bizarre results in
>> that vicinity. The pole is a singular point in that coordinate system,
>> and you can only approach it by using a coordinate system where it isn't
>> a singular point.
>>
>> If you don't come close to the pole, you should be able to use ordinary
>> interpolation routines, treating rho, theta as if they were x and y.
>> That won't produce exactly the right results, but anything that produces
>> exactly the right results is going to be mathematically equivalent to
>> converting back to rectangular coordinates.
>
> Wouldn't it be better to do the interpolation close to the pole in a
> rotated (i.e. translated) polar coordinate system? Tilt the polar axis
> by 90 degrees, interpolate, tilt back?
That would work, but it has no advantages over converting to rectangular
coordinates, and it has the disadvantage of treating near-polar data
differenently from other data. The conversion from polar coordinates
with one pole to polar coordinates with a different pole is no simpler
than the conversion to rectangular coordinates. In fact, the easiest way
to do the conversion is to use rectangular coordinates as an
intermediate step. Rotation around a polar axis is simple; moving the
polar axis is not.
--
James Kuyper
MODIS Level 1 Lead
Science Data Support Team
(301) 352-2150
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| Re: polar interpolation [message #33671 is a reply to message #33625] |
Sun, 19 January 2003 19:33 |
Thomas Gutzler
Messages: 44
Registered: November 2002
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Member |
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Hi,
Rick Towler wrote:
>
> Interpolate between points a and b:
>
> iFactor = (Ti - Ta) / (Tb - Ta)
> Ri = Ra + (iFactor * (Rb - Ra))
> Where Ti is the Theta value where you are interpolating your radius Ri.
I stole this from interpol.pro. The function is the same, just other
names for variables:
; ,----------------------------------------------------------- -----
; | Purpose:
; | linear, polar interpolation for irregular grids
; | T: The theta values (in degrees) for R (radius). This vector
; | must have same # of elements as R. The values MUST be
; | "monotonically ascending" or "descending" (see problem below).
; | U: The theta values for the result. The result will have
; | the same number of elements as U. U does not need to be
; | monotonic. If U is outside the range of T, then the
; | closest two endpoints of (T,R) are linearly extrapolated.
; `----------------------------------------------------------- ------
FUNCTION polar_interpol, R, T, U
m = N_elements(R) ; # of input pnts
s = VALUE_LOCATE(T, U) > 0L < (m-2) ; Subscript intervals.
p = ( U - T[s] ) * ( R[s+1] - R[s] ) / ( T[s+1] - T[s] ) + R[s]
RETURN, p
END
But what to do, if an array like this wants to be interpolated:
R: [1,2,3]
T: [340,350,20]
U: [355,5,15,25]
I can see 2 solutions at the moment:
1) - find the first index (i) after crossing the magic 0-line.
In this case: i_T = 2 and i_U = 1
- T[i_T:*] = T[i_T:*] + 360
- U[i_U:*] = U[i_U:*] + 360
- interpolate T: [340,350,380], U: [355,365,375,385]
- RESULT = [2.16667, 2.50000, 2.83333, 3.16667]
2) - split the vectors
R1: [1,2,2.33333] (last value must be interpolated)
T1: [340,350,360]
U1: [355]
R2: [2.33333,3]
T2: [0,20]
U2: [5,15,25]
- interpolate separately
RESULT1: [2.16667]
RESULT2: [2.50000, 2.83333, 3.16667]
- return [RESULT1, RESULT2]
Is there a trick to do this easier, using some strange functions
(VALUE_LOCATE was strange for me) ?
Keep in mind that the next step would be a quadratic interpolation.
thanks, Tom
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