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can be of different types depending on the intended use of the terrain 
(Collins, 1975). In this work, the stored elements of a surface 
are the coefficients of the surface polynomial (Segu, 1985). Now 
during any subsequent use of the surface, such as in interpolation, 
surface data analysis can be done directly on that surface by use of 
these surface elements. This is of great advantage. 
The elemens of a terrain surface stored in a computer are derived from 
field data by a process of surface fitting. Several techniques of 
surface fitting have been developed and tested both patchwise and 
globalwise. Jancaitis and Junkins (1973) describe some technique 
of surface fitting and its associated problems. 
Least Squares 
Least Squares technique is a very powerful tool for fitting experimental 
data to some mathematical model. Birge (1947)and Berztiss (1964) have 
covered this subject to great depths. The writer has adopted the 
principle of least squares in this work without prejudice. 
Chevbyshev Polynomials 
As pointed out earlier, there are many different techniques of carrying 
out surface fitting. The work carried out by the author has been 
based on Chebyshev polynomials (Segu, 1985). 
Surface fitting by Chebyshev Polynomials requires that the data be 
in profile mode. The profiles should be at regular intervals but the 
elevation data along these profiles need not necessarily be at regular 
intervals. 
PRINCIPLES OF OVERLAPPING 
DEM data for terrain surface fitting are acquired invariably in discrete 
mode either -pfptogrammetrically or by digitizing a contour map. The 
data can be in random, regular grid or profile form. 
If the captured data are fitted with least squares surface polynomials 
cellwise, the surfaces so derived will not, in general, be continuous 
across cell boundaries unless certain precautions are taken (Jancaitis 
and Junkins, 1973). The technique of overlapping the data across 
fixed cell boundaries as discussed in this paper is an attempt to solve 
this problem.