interpolation (continued)

[Simon Cox]

Another approach to interpolation which I forgot to mention is to
decompose the data into radial basis functions.  The most well known
of these is fourier analysis.  Of course in order to fit the inputs
exactly you need to expand the series up to the Nyquist frequency
(ie apply the sampling theorem).  This is equivalent to using a polynomial
of the same order as the number of inputs (+/- one or so) so includes
all the information that was present in the original data.  Other
basis functions can be used, and there have recently been some developments
using iterated function systems to produce models which have a
"fractal" behaviour (see Barnsley for details).  Some people like
this fractal interpolation since it can be shown that many natural
surfaces have scale dependent complexity, and the fractal interpolation
allows this complexity to be preserved as the observation scale is changed.
I have only seen this applied to gridded data, however, though my gut
feeling is that it might be very useful for irregularly distributed
data.

Simon Cox

----
__________________________________________________________________
				Dr Simon Cox
         __  L				
      ,~'  L_|\            	Department of Earth Sciences       
   ,-'         \         	Monash University    
   (            \		Clayton  Vic  3168  Australia
   \    ___     /	
    L,~'   "\_x/		Phone +61 3 565 5762
              u   		Fax   +61 3 565 5062
				simon at cerberus.earth.monash.edu.au
__________________________________________________________________