| Re: Interpolation [message #59885 is a reply to message #2184] |
Sat, 12 April 2008 15:26   |
ben.bighair
Messages: 221
Registered: April 2007
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Senior Member |
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On Apr 12, 4:24 pm, tarequea...@gmail.com wrote:
> On Apr 12, 11:57 am, "ben.bighair" <ben.bigh...@gmail.com> wrote:
>
>
>
>> On Apr 11, 11:05 pm, tarequea...@gmail.com wrote:
>
>>> Hello All (IDL Gods),
>
>>> I am back with yet another problem.
>>> I know...I know...its friday night. I apologize for that. But I am
>>> really stuck here for a while.
>
>>> The problem:
>
>>> In a certain part of my code I need to do interpolation. The data that
>>> I am dealing with are from a XY grid. I need to convert them to polar
>>> coordinate. So, what I do is following:
>
>>> a. I generate a radius vector r_vec and a theta array containing
>>> values from zero to 2 pi.
>>> b. Now use the simple polar-to-rectangular coordinate transform i.e. x
>>> = r cos(theta) etc.
>>> c. Using these values I have a xy grid generated through a known r-
>>> theta values.
>>> d. Now think of superimposing the new xy grid(lets call it x'y' ) on
>>> to the old xy grid which contains the real data.
>>> e. This is the part where I need interpolation. I do interpolations to
>>> get the x'y' values from the xy points.
>
>>> So here's the question:
>
>>> ----- Is there any elegant way of doing this coordinate
>>> transformation ? (And in case you are thinking, "well you already have
>>> the xy data, so why not just convert to r-theta?", I have to say that
>>> the interpolation method actually gives me a way nicer dataset ).
>
>>> My 2nd trouble is, and this is probably the biggest and dumbest
>>> problem for me.
>
>>> ----- i was playing around with several interpolation routines from
>>> IDl. My boss's suggestion was to use 'bilinear'.
>>> but I thought to give others' a shot too. Problem is, when I am
>>> done with interpolation, result is nothing like what I was
>>> expecting. A run down version of the code is shown below:
>
>>> =======================start of code================================
>
>>> Nth= 10.
>>> dth= 1/Nth
>>> r_vec= findgen(Nth)/Nth
>>> theta_vec = findgen(Nth)/Nth * 2.*!Pi
>
>>> for i=0L,Nth - 1 do begin
>
>>> x[i]= r_vec[i]* cos(theta_vec)
>
>>> endfor
>
>>> for j=0L,Nth - 1 do begin
>
>>> y[j]= r_vec[j]* sin(theta_vec)
>
>>> endfor
>
>>> ;print,y
>
>>> ;plot,x,y
>
>>> ------------------------------------------------------------ -----------
>>> Now I create the 'main' dataset on which I am going to use
>>> interpolation scheme.
>
>>> rr = findgen(20.)/30.
>>> tht = findgen(20.)/30. *2*!Pi
>
>>> m = fltarr(20,20)
>
>>> for j=0,19 do begin
>>> for i=0,19 do begin
>
>>> m[i,j] = rr[i]*cos(tht[j]) + 5.*rr[i]*sin(tht[j])
>
>>> ;print,i
>>> endfor
>>> endfor
>
>>> m_p=bilinear(m,x,y)
>
>>> End
>>> =======================End of Code=================================
>
>>> The problem is, as I mentioned above, when I plot m and the
>>> interpolated m_p, they do not look like similar at all.
>
>>> Any help will be greatly appreciated.
>
>>> Thanks in advance.
>
>>> ~tareque
>
>> Hi,
>
>> Coordinate transforms are very easy with CV_COORD().
>
>> I don't understand where you want to go with the interpolation. The
>> input coordinates to BILINEAR are rectangular and formed as indexed
>> based (as in subscript indices in X and Y.) As near as I can
>> reconstruct, X ranges from -0.500000 to 0.728115 and Y ranges
>> from -0.760845 to 0.285317. My reconstruction of your code is
>> below.
>
>> Cheers,
>> Ben
>
>> PRO tareque
>
>> Nth= 10L
>> dth= 1.0/Nth
>> r_vec= findgen(Nth)/Nth
>> theta_vec = findgen(Nth)/Nth * 2.*!Pi
>> x = fltarr(nth)
>> y = fltarr(nth)
>
>> for i=0L,Nth - 1 do begin
>
>> x[i]= r_vec[i]* cos(theta_vec[i])
>
>> endfor
>
>> for j=0L,Nth - 1 do begin
>
>> y[j]= r_vec[j]* sin(theta_vec[j])
>
>> endfor
>
>> ;print,y
>
>> ;plot,x,y
>
>> ;----------------------------------------------------------- ------------
>> ;Now I create the 'main' dataset on which I am going to use
>> ;interpolation scheme.
>
>> rr = findgen(20.)/30.
>> tht = findgen(20.)/30. *2*!Pi
>
>> m = fltarr(20,20)
>
>> for j=0,19 do begin
>> for i=0,19 do begin
>
>> m[i,j] = rr[i]*cos(tht[j]) + 5.*rr[i]*sin(tht[j])
>
>> ;print,i
>> endfor
>> endfor
>
>> m_p=bilinear(m,x,y)
>
>> STOP
>> End
>
> hi Ben,
>
> Thanks for getting back to me on this.
>
> I guess I could not clearly state my problem before. So, I am going to
> give it another try:
>
> The data I deal with comes from a ccd camera and this goes some
> tinkering and tweaking (to account for background noise and stuff).
> Then this 'processed' data is in need for interpolation. why? well the
> reason being this, that these processed data are actually in XY
> frame.
> We want them to be on a polar coordinate. The reason I cannot use
> 'cv_coord' is because in that case I will get the data in a r-theta
> plane which is
> directly correlated to the experimental XY grid. If we use
> interpolation, then we can be on a XY grid (yes, it is XY grid) which
> is carefully 'designed' according to
> our 'own' r-theta values. So in this way we have more leverage over
> data manipulation.
>
> Was it any clearer than before?
>
> And one more thing, I could not find much changes in your version
> except for an inclusion of 'STOP'. Did i miss something here??
>
> Thanks again for your time.
> Much appreciated !
>
> ~ Tareque
Hi Again,
The only thing I did other than STOP (which I forgot to remove) was
redefine X and Y, which in your example were missing. I thought it
would be helpful for others if the whole thing worked. I should have
been clearer.
Speaking of clearer... I think I am more confused now. You might
need the intervention from the IDL gods that you originally
petitioned. Regardless of the parts I don't understand, the thing I
do get is that BILINEAR is looking for you to provide interpolation
coords that fit within the dimensions of the input array to be
sampled.
Take a peek at the second example in the online help for BILINEAR...
(slightly modified here...)
P = FINDGEN(3,3)
IX = [[0.5, 1.9], [1.1, 2.2]] ;Define the X subscripts.
JY = [[0.1, 0.9], [1.2, 1.8]] ;Define the Y subscripts.
Z = BILINEAR(P, IX, JY, MISSING = !VALUES.F_NAN) ;Interpolate.
PRINT, P
PRINT,Z
P prints as...
0.00000 1.00000 2.00000
3.00000 4.00000 5.00000
6.00000 7.00000 8.00000
Z prints as ...
0.800000 4.60000
4.70000 NaN
Note that IX and JY are mostly falling within the 0-2 range of indices
for a 3x3 array. BILINEAR can extrapolate - just remove the MISSING
keyword - but it can only extrapolate a little ways. In your example
IX are sampled at
0.00000 0.0809017 0.0618034 -0.0927051 -0.323607
-0.500000 -0.485410 -0.216312 0.247214 0.728115
and JY are sampled at ...
0.00000
0.0587785
0.190211
0.285317
0.235114
-4.37114e-08
-0.352671
-0.665740
-0.760845
-0.529007
Which to my way of thinking your are interpolating all around either
side of the [0,0] location. Is that what you intended? It is
possible that in my redo of your example I corrupted the X and Y
values you intended. In which case I would be not helping very much
at all!
Cheers,
Ben
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