| Re: Interpolation [message #59883 is a reply to message #2184] |
Sat, 12 April 2008 17:56   |
tarequeaziz
Messages: 20
Registered: November 2007
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Junior Member |
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On Apr 12, 6:26 pm, "ben.bighair" <ben.bigh...@gmail.com> wrote:
> 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
Hi Ben,
Thanks once again for your reply and also taking time to look into
this problem.
I am trying to attach a picture of my problem. well, looks like I cant
attach a picture here.
Anyways, I am going to give another shot at this. And,once again Boss,
thanks so much for your help.
Alright, lets start:
Think of a big circle. Close to the periphery, there is another little
circle inside of that big circle. Now, this little guy's positions are
the
bones of contentions. The coordinate system used are just rectangular
ones. We want them to be in polar.
At the same time I want the these positions in such a way that they
corresponds to a r-theta grid 'designed' by me.
That's why we are trying to interpolate.We want to get the
interpolated points based on our desired r-theta values.
In other words
Step one: Real data in a XY frame
Step two: 'Design a new xy frame, say X'Y' frame, whose values are
generated from a chosen r_vec and theta_vec.
Step 3: Now interpolate from XY to X'Y'.
Now how does it sound?
Once again, Thank you so much for your help.
Best,
Tareque
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