bilinear/cubic convolution

[Darrell McCauley]

Chris W Skelly (gewcs at jcu.edu.au) writes on 4 Jan 94:
>> Hello all. I would like to use bilinear interpolation or cubic
>> convolution interpolation to do some cross validation when
>> interpolating site data to raster format. My site data are scattered

>I am not sure if I understand you, but if you are going from site
>to cell and you use something like idw or krig the absolute distance
>from the site position to the cell center is used in the

The interpolation knows nothing about the site in question.
See below.

>interpolation. The actual point ceases to exist at the end of the
>day so whether it lines up with a cell centre or not is irrelavent.
>If you want exact interpolation (ie you want that specific
>point value to exist in the cell layer) they you just weight it
>appropriately.
>
>Can you explain why scattered data is a problem, I think I am 
>missing something...

When doing cross validation, I REMOVE some of the original data before
doing the interpolation [using s.kcv].  Point c is of the set of
removed points.

Then, I interpolate to a particular resolution. That gives me my 
estimate (Point %). Here are two cells of my raster map with
the site overlayed.

           ____|_____________|_____________|___
               |             |             |
               |             |             |
               |             |             |
               |    c %      |      %      |
               |             |             |
               |             |             |
           ____|_____________|_____________|___
               |             |             |

To get an error estimate:
1. nearest cell says subtract 'c' from the value of the left cell.
2. bilinear interpolation uses four neighboring cell values (2x2)
   to do 3 linear interpolations and get an approximate value at 'c'
3. cubic convolution uses 16 (4x4) surrounding cells, does some
   convolutions, etc.

With an infinite amount of disk space and time, I could
interpolate to an infinitely small cell size and use method #1.

[The real problem is that I'm using some canned interpolation
 software for which I do not have source code. Therefore, I cannot
 get estimates at precise points :( ]

I hope this clears things up.
--Darrell