1. Introduction 
During the past ten years, digital terrain models have found increasing 
use. They have been a subject of interest at the Congresses of the International 
Society for Photogrammetry in 1968 and 1972, in particular in Commissions IV and 
V [1], [2]. [5]. 
Of interest to Commission III, concerned with data processing, is 
especially the height interpolation in these models. A large number of publications 
on this subject, describing many different interpolation methods, has appeared and 
attempts to collect and compare at least some of them have already been made, as 
shown by references [1] to [11]. Because the published methods cover a wide range 
and the possibility of devising further and essentially different methods appears 
to be rather limited, the time appears to be opportune to compile as complete as 
possible a review and classification of the methods. 
Such a review is the subject of the present paper. The interpolation 
methods have here been arranged in six groups. Methods for the construction of 
profiles and of contour lines are reviewed also. These curves can be constructed 
by height interpolation in a digital terrain model alone, but often and with 
advantage curve interpolation methods are used. 
The accuracy which can be obtained from the interpolation depends, of 
course, both upon the density and distribution of the reference heights and upon 
the choice of method. Even the simplest interpolation method can be useful if the 
density of reference points is sufficiently great. From this point of view, even 
interpolation methods which produce artificial discontinuities in the surface 
representation of the terrain can be acceptable. However, because an abundant 
number of methods is available which do produce a continuous representation, and 
because a discontinuous representation can produce difficulties in profile and 
contour interpolation, the latter methods are dealt with only summarily. 
The bibliography attached to the present paper has been compiled by 
searching through most of the better known photogrammetric and some related 
journals, published in English, French, and German. Many publications on inter- 
polation can be found also in other journals. References to a number of them can 
be found in items [7], [25], [60], and [63] of the bibliography. A list of 
references which deal with the mathematical background of some of the interpolation 
methods concludes the bibliography. 
2. Interpolation methods and reference point patterns 
Reference points for digital terrain models must be chosen in such 
locations that they can serve for a satisfactory analytical representation of the 
terrain. They can be chosen in three different patterns: 
i. in more or less random positions; 
ii. on characteristic terrain features such as well-defined linear features, 
ridges, contour lines, fall lines (lines of greatest slope), highs and lows, or 
on parallel profiles; 
iii. at the nodes of a regular grid. 
In addition, in each case points will be chosen on such important features as 
breaklines in the terrain. 
The published methods of interpolation in a DTM can be arranged in six 
groups according to six essentially different ways in which the interpolation is 
performed. Each of these groups will be dealt with in one of the next six sections 
of this report.