INTERNATIONAL SOCIETY OF PHOTOGRAMMETRY 
AND REMOTE SENSING 
LEAST SQUARES POLYNOMIAL SURFACE FITTING 
WITH OVERLAPPING DATA 
W.P. SEGU 
UNIVERSITY OF DAR ES SALAAM 
TANZANIA 
COMMISSION II 
ABSTRACT 
The author describes a method of least squares surface fitting, as 
a system for terrain elevation data processing, in which the elevation 
data are overlapped along common cell boundaries to avoid discontinuities 
of surfaces across the boundaries. The method has been tested using 
Chebyshev Polynomials and some test results are presented in this paper. 
INTRODUCTION 
Terrain elevation data can be presented in three main modes, namely 
discrete mode, graphical mode and functional mode. The functional mode 
of representing terrain elevation data gives rise to what can be described 
as Functional Digital Elevation Model (FDEM). 
FDEM is a mathematical expression representing terrain elevation, Z, of 
a point as a function of its plan coordinates (x,y). 
That is, 
Z = f (x, y) 
In expanded power series form, the expression can be written as:- 
2 2 
X = a + a. + a„y + a_x + a„xy + a,_y + 
o 1 2 3 4 5 
A computer hardware and software are required for storing and processing 
data in FDEM.