Haje Korth wrote:
>
> JD,
> could you give me the source for your solution. Are you aware of a good
> textbook on this matter?
I would be interested also. I want to do some 2-D (or is it 3-D?) interpolation
but using bicubic interpolation. My (feeble) initial attempts to figure out how
have led me to my NR book, but the method of deriving the coefficients to do the
interpolation is brazenly swept under the rug.
paulv
>
> Thanks,
> Haje
>
> "JD Smith" <jdsmith@as.arizona.edu> wrote in message
> news:pan.2003.07.21.18.27.19.886736.21942@as.arizona.edu...
>> On Mon, 21 Jul 2003 08:40:58 -0700, Ian Chapman wrote:
>>
>>> Hi,
>>>
>>> I have created a 5 dimensional data cube (pressure, temperature,
>>> relative humidity, frequency, transmission) with a radiative transfer
>>> model. I have a user that will need to get transmission data for given
>>> values of the rest of the parameters, so I am currently planning to
>>> interpolate the cube to the input values of the user.
>>>
>>> Does anyone know of any multi-dimensional interpolation routines
>>> (similar to spline) that would be able to perform this task?
>>>
>>
>>
>> You could roll your own using VALUE_LOCATE to locate the point
>> (p,t,h,f) within each of the 4 relevant axes (bracketed between
>> i,j,k,l and i+1,j+1,k+1,l+1), and then perform quad-linear
>> interpolation on the 16 nearby grid points bracketing the desired
>> value. E.g., let:
>>
>> a=(p-p[i])/(p[i+1]-p[i])
>> b=(t-t[i])/(t[j+1]-t[j])
>> c=(h-h[i])/(h[k+1]-h[k])
>> d=(f-f[i])/(f[l+1]-f[l])
>>
>> The quad-linear interpolant over you whole data cube "z" would look
>> like:
>>
>> (1-a)(1-b)(1-c)(1-d) z[i ,j ,k ,l ] +
>> (1-a)(1-b)(1-c) d z[i ,j ,k ,l+1] +
>> (1-a)(1-b) c (1-d) z[i ,j ,k+1,l ] +
>> (1-a)(1-b) c d z[i ,j ,k+1,l+1] +
>> (1-a) b (1-c)(1-d) z[i ,j+1,k ,l ] +
>> (1-a) b (1-c) d z[i ,j+1,k ,l+1] +
>> (1-a) b c (1-d) z[i ,j+1,k+1,l ] +
>> (1-a) b c d z[i ,j+1,k+1,l+1] +
>> a (1-b)(1-c)(1-d) z[i+1,j ,k ,l ] +
>> a (1-b)(1-c) d z[i+1,j ,k ,l+1] +
>> a (1-b) c (1-d) z[i+1,j ,k+1,l ] +
>> a (1-b) c d z[i+1,j ,k+1,l+1] +
>> a b (1-c)(1-d) z[i+1,j+1,k ,l ] +
>> a b (1-c) d z[i+1,j+1,k ,l+1] +
>> a b c (1-d) z[i+1,j+1,k+1,l ] +
>> a b c d) z[i+1,j+1,k+1,l+1]
>>
>> The regularity of this pattern lends one to believe a generic n-linear
>> interpolation code could be written. Fancier interpolation methods
>> (cubic, spline, sinc) get much harder in higher dimensions.
>>
>> JD
--
Paul van Delst
CIMSS @ NOAA/NCEP/EMC
Ph: (301)763-8000 x7748
Fax:(301)763-8545
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