| Re: polar interpolation [message #33519] |
Fri, 10 January 2003 08:05  |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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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.
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| Re: polar interpolation [message #33630 is a reply to message #33519] |
Mon, 13 January 2003 09:12  |
Stein Vidar Hagfors H[2]
Messages: 28
Registered: October 2002
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Junior Member |
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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?
--
------------------------------------------------------------ --------------
Stein Vidar Hagfors Haugan
ESA SOHO SOC/European Space Agency Science Operations Coordinator for SOHO
NASA Goddard Space Flight Center, Tel.: 1-301-286-9028
Mail Code 682.3, Bld. 26, Room G-1, Cell: 1-240-354-6066
Greenbelt, Maryland 20771, USA. Fax: 1-301-286-0264
------------------------------------------------------------ --------------
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| Re: polar interpolation [message #33641 is a reply to message #33519] |
Sun, 12 January 2003 18:33 |
Thomas Gutzler
Messages: 44
Registered: November 2002
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Member |
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James Kuyper wrote:
> 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.
define 'close' :)
I think the smallest distance to the pole will be 1/10 of the maximum
distance which is between 300 and 1000.
I should write both functions, compare, and then decide again if I want
to use the conversion-method. Just wanted to know _if_ there is another
way to do it.
Tom
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