UDC 528.932(4)(084.3-16):681.335.2 
061.3(497.12-2) Radenci „1994":528 
DIGITAL TERRAIN MODEL 
OFEUROPE 
Slavko Pečnik 
Inštitut za geodezijo in fotogrametrijo FAGG, Ljubljana 
Received September 15, 1994 
Revised March 30, 1995 
Abstract 
A range of 8° x 12° (890 x 840 km of actual) size with basic 
grid 5' x 5' (9,3 x 6,7 km) has been chosen asa testing area 
for the outline scheme of The Digital Terrain Model of 
Europe. In the process of DTM generation the basic 5' x 5' 
grids were condense.d to a reasonable value. The goal of the 
project The Digital Terrain Model of Europe isto build a 
digital dala base f or the area that is covered with f our mode/s 
and to make a special application with the program system 
SCOP. 
Keywords: digital te1Tain model of Europe, Geodetic 
workshop, modified polyconic projection, Radenci, SCOP, 
1994 
INTRODUCTION 
A Digital Terrain Model (DTM) is a computer-supported representation of the 
~arth's surface, which is gaining importance in Slovenia. The applicability of 
DTMs knows almost no limits and to a great extent depends on the requirements 
and demands of users. Local DTMs were developed in the early phase of 
development of digital terrain models, which cover smaller, entirely local areas. A 
tendency to set up digital databases of regional DTMs has appeared lately, which 
include areas of large dimensions. Large-scale cartographic sources and with grids on 
the order of magnitude from 30 x 30 m (made in the USA) to 230 x 230 m (made for 
Northern Italy) were used. Two digital termin models were made for Slovenia with 
quadratic grids of 100 x 100 m and 500 x 500 m, which are compatible. The paper 
presents a cartographic source and the mathematical properties needed for the 
formation of a digital terrain model. A Modified Polyconic projection and the 
mathematical elements of a digital terrain model of a test area are also presented, as 
well as a method for the acquisition of input data used. The application 
"Axonometric Presentation of Models" enabled by the SCOP program system was 
chosen for the presentation of the set-up of the digital database. 
CARTOGRAPHIC SOURCE AND ITS MAT.HEMATICAL PROPERTIES 
A proposal by Austrian geographer and a professor at the University of Vienna, 
~rof. Albrecht Penck, for the preparation of an international map of the world 
(IMW) at 1:1 000 000 scale was accepted at the Vth lnternational Congress of 
Geodetski vestnik 39 (1995) 1 
Geographers in Bern in 1891. At subsequent conferences the following mathematical 
basis was determined for it: 
o Sheet size 
- Sheets will comprise an area of 4° of geographic latitude and 6° of 
longitude, possibility of joining sheets (London, 1909); 
o Cartographic grid 
- Meridians and parallels of latitude are presented for each degree 
(London, 1909); 
• Projection 
The map projection should fulfill the following requirements: 
- meridians will be presented as straight lines 
- parallels will be presented as parts of eccentric circles 
Deformation of the carrying material (paper) will prevent the 
preparation of a conforming or equivalent projection. 
The International Map of the World at a scale of 1:1 000 000 in a Modified 
Polyconic projection was chosen from among the available cartographic material for 
the preparation of an outline scheme. 
MODIFIED POLYCONIC PROJEC'fION 
The projection is derived from a modification of an American Polyconic projection with the following characteristics: 
• the border parallels in each sheet are arcs of eccentric circles with their 
centre on the extension of the central meridian. 
• the linear projection scale along the parallels equals n=l 
• all meridians are mirrored as straight lines 
• the central meridian is shortened by a value s=0,271 cos2 <p (in mm), while 
the two meridians at a distance of ±2° from the central meridian are 
mirrored without deformations, m=l. 
• the cartographic grid is calculated at 1 °. 
Com:trnction of the cartographic grid 
Construction of the grid of meridians and parallels on sheets is based on rectangular coordinates of characteristic cross-sections of a 1 ° grid, with 
characteristic symmetry with regard to the central meridian. 
Cooirdinate system 
The coordinate system was determined on the basis of known coordinates of characteristic cross-sections of a degree-grid and the known length of the central 
meridian, shortened by the appropriate value. The coordinate beginning of each 
sheet is in the intersection point of the central meridian and the southernmost 
parallel. 
MATHEMA'fICAL ELEMENTS OF THE MODEL AND CON'fENT 
compromise solution was adopted with regard to the available cartograph~c 
source and its mathematical properties, i.e. each sheet should represent ari 
Geodetski vestnik 39 (1995) 1 
l 
independent model, which is also the characteristic of the Modified Polyconic 
projection. Four independent models were thus formed which can be joined into one 
model in any randomly selected projection. The maps chosen for the preparation of 
an outline scheme comprise an area of size 8° x 12°, which in nature is an area of size 
approximately 890 x 840 km. 
Coorrdinate system of the model 
The rectangular coordinate system is designed as required by the Regulations on the Preparation of Maps, and with an additional "Z" component represents a 
relatively well-oriented model with accurately determined coordinates of 
cross-sections of a geographic grid. 
Scale and units of the model 
All cross-section coordinates (y, x) of points were calculated at an accuracy of 1/1 000 mm at map scale 1: 1 000 000. This is justified by the fact of the given 
accuracy of the input data for the projection which are stated in the tables. At the 
same tirne these values represent a unit of one metre in nature. The "Z" coordinate 
was estimated at an accuracy of one metre in nature. This serves to establish the 
relation of equal accuracy and equal measurement units for both the positional and 
height presentation of the acquired data. 
Cartographic grid 
he basic cartographic grid of the projection is a degree-grid which is condensed 
to a density of five are minutes (5'). The described density of the grid is the 
smallest distance between cross-sections which serve as the method of acquisition of 
input data. This distance in nature is on the order of magnitude of approximately 9 
kilometres, depending on <pand '"A. At the same tirne this is also the density of the 
digital terrain model in question, which can be additionally condensed with the 
SCOP program. The rectangular coordinates of cross-section of the cartographic grid 
(hereinafter "profile points") (y, x) were calculated on the basis of input data of the 
projection with the use oflinear interpolation. The height component "Z", however, 
is interpolated fromcartographic material using a previously made transparency with 
profile points. 
Content of acquisition 
The geographic content which is the basis of the map and is required for the setting up of the base of the acquired digital terrain model is divided into two groups: 
• the basic group of acquired data are the so-called point elements: 
- reference points 
- cross-sectional points 
- height points, given by height, 
• line elements represent an additional group, which in the case of a closed 
polygon represents a plane element: 
- the coastline of the mainland 
- lake outline 
- the coastline of islands. 
Geodetski vestnik 39 (1995) 1 
DATA ACQUISITION METHODS 
he basis idea for data acquisition comprises a separate calculation of position 
coordinates (y, x) of points along cross-sections of equal latitude on one hand 
and manual acquisition of the "Z" component of identical points on the other, which 
is a consequence of non-existence or unavailability of published originals which 
would enable other methods of data acquisition. This above all means scanning of 
the surface and later automatic or semi-automatic vectorization of raster image. This 
method is the simplest form of indirect data acquisition and with this, analog-digital 
transformation of data acquired from a cartographic source. The method of work, 
dependent on the available cartographic source, dictated the writing of a computer 
program which will solve the problem of data acquisition, i.e. the calculation of 
position coordinates of points along the cross-sections. 
APPLICATION AXONOrytETRIC PRESENTATION OF MODELS 
The calculated coordinates of reference points and the knowledge of the distribution of reference points serve for a statement of the limits for generating 
a DTM and an axonometric presentation. In the phase of test processing of data it 
was established that in comparison with length, the height component "Z" of the 
points comprising the analysis should be increased by a factor enabling a real 
presentation of the relief. A multiplication factor with a value of Z=5 was chosen for 
the preparation of an axonometric presentation, which means an increase in height 
by a five-fold value of the input data. The analyzed DTM grid was additionally 
condensed to a grid which in nature has the dirnensions of 2 500 x 2 500 m, while on 
the map, at a scale of 1:1 000 000, it is 2,5 mm. Such a grid and the selection of a 
bell-shaped curve as the basic function enabled a generation of a DTM for the entire 
area. The selection of the basic function smoothened the digital model of relief 
which in practice meant the rounding of all transitions. 
The SCOP.PERSPECT module enables the preparation of axonometric presentation with a randomly chosen perspective of the discussed model. A part 
of the results can be seen in the enclosure. Axonometric presentation is only one of 
the possibilities of using the digital database of the DTM which was set up in the 
process for the preparation of a graduate thesis entitled Digital Terrain Model of 
Europe. 
Literature: 
Dovedan, Z., Fortran 77. Ljubljana, 1988 
Jovanovic, V., Matematička kartografija. Beograd, VGI, 1983 
Novak, T., Primerjalna analiza uporabe programskega paketa SCOP s sorodnimi programskimi 
paketi. Diplomska naloga. FAGG OGG, Ljubljana, 1993 
Peterca, M. et al., Kartografija. Beograd, VGI, 1974 
Peterca, M., Čolovic, G., Geodetska služba JNA, Beograd, 1987, št. 21, poglavje 5 
Rihtaršič, M., Fras, Z., Digitalni model reliefa. l. del: Teoretične osnove in uporaba DMR. 
Ljubljana, 1991 
SCOP, Product Information. Dunaj, Technical University Vienna, Institute of Photogrammetry and 
Remote Sensing, 1992 
SCOP, To Create and Apply Digital Elevation Mode/s. User Manual. Dunaj and Stuttgart, 1992 
Geodetski vestnik 39 (1995) 1 
r 
1 
AXONOMETRIC PRESENTATION OF .MODEL No 305 ( NE) 
of the MOD305 Model 
nomenclature 
direction oj view 
area covered the model 
Review: Matjaž Ivačič 
Dr. Drago Perko 
L32 
SWtoNE 
lower left: SE part of France 
upper left: NE part of France 
upper middle: S part of Gennany 
upper right: W part of Austria 
middle: Switzerland and N Italy 
lower middle: the Bay of Genoa 
Geodetski vestnik 39 ( 1995) 1