(2) Each new cell, defined by the appropriate percentage overlap, 
is tested for accuracy of fit by computing the residuals at 
all points and the corresponding RMSE calculated. Table 3 is a 
summary of these results. 
The corresponding degrees of fit at different percentage overlaps 
is summarised in Table 4. In some cells, the terrain is so rugged 
that the available data were not sufficient to define a polynomial 
surface to the required specifications of accuracy of fit. 
These cells are shown with a dash (-) in Table 3. at the corresponding 
percentage overlap. 
A further analysis of the results is shown by Fig. 2. In this 
figure, the RMSEs in all cells at a corresponding percentage overlap 
are added together and the average value computed both for the 
check points and for the overall. Since the RMSEs apply to the same 
corresponding cells, these averages at different percentage overlaps 
do reflect the differences in accuracy of fit in the test area at 
the different overlaps. 
Judging from the accuracy of fit of a fixed cell, the optimum 
percentage overlap for this test site at the given specification 
(i.e. accuracy of fit) is 15%. Overall, the optimum percentage 
overlap is 25%. These figures, however, will have to be taken with 
caution since the graphs in Fig.2 do not show definite minima. 
DISCUSSION AND RECOMMENDATIONS 
The method of least squares polynomial surface fitting with overlapping 
data has been developed with an assumption that one is working with 
a fixed grid (i.e. cell) size pattern. Therefore an overlap will have the 
meaning of an expansion of the cell size by an appropriate percentage in 
cell size. The data within a new cell area will be used to define the 
corresponding mathematical surface. 
Differences in RMSE of fit across cell boundaries is an indication of a 
discontinuity of surfaces across those cell boundaries. These differences 
are not zero as shown in the tables above; but rather they are kept to 
a minimum within working accuracy. Where the terrain is broken and the 
observed data are not of high enough density, this method fails-as shown 
in Table 4. 
The main factors influencing the use of this method for surface fitting 
are: 
type of terrain: different cells of different terrain types 
give different percentage overlap for the same accuracy of fit. 
This aspect requires further investigation on the type of terrain 
and the corresponding percent of overlap. 
(1)