TOLERANCES IN DIGITAL MAPPING 
Dr.eng. Constantin Nigu 
Eng. Cälin Daniel Nitu 
RSPRS,Bucharest, Romania 
The automated cartography involves digital map achievement. The paper deals with the 
problems of digital map resolution and accuracy and the usual tolerances in digital 
mapping : the map resolution tolerance or fuzzy tolerance, the tolerance ensuring 
digitizing accuracy or tic match tolerance (maximum allowable tic 
registration error), 
the join map tolerance, the weed tolerance etc. 
KEY WORDS : Digital mapping, Resolution, Accuracy, Tolerance 
1. DIGITAL MAP RESOLUTION 
The digital map resolution expresses the 
precision for the appearance of map object 
localization and form for a given scale. 
The resolution expressed in terrain mea- 
suring units decreases with the decreasing 
of map scale, because the details must be 
smooth and simplified or even not be re- 
presented. The minimum sizes of terrain 
objects that must be represented on maps 
are called sometimes "the minimum mapping 
gizes" and are given as census values in 
the map series construction directions. 
Digital map data may be raster or vectorial 
data. The resolution analysis for one of 
the data type may be extended to the 
other one. 
One can determine the minimum size of the 
elementary raster cell through two ways, 
using cartographic or stereophotogrammetric 
grounds. 
The cartographic ground supposes that a 
drawing of a separate cartographic image 
asks the resolution of 14 lines/mm,suppo- 
sing the minimum line width O.1 mm on the 
map. This reason leads to the resolution 
1.7 m in the ground for the base map 
1:25,000 scale. 
The stereophotogrammetric ground supposes 
the elementary cell size as the spot size 
required in digital stereophotogrammetry 
for contours representation interval, In 
the case of digital correlation techni- 
ques, the longitudinal parralax error 9, 
” 
X 
gy, «Kl (1) 
y" 
where k is & constant and expresses the 
degree at which can result a stereoscopic 
correlation with a spot size 1. Conside- 
ring theheight error Gas a function of 
longitudinal parralax, after some trans- 
formations, the size spot 1 will be 
1 =f 3G (2) 
For the confidence degree 0,10, the 
height tolerance will be 3,3(j . If the 
contour interval is 5 m, (y - 1.5 m (for 
the 1:25,000 scale map). 
For B/H = 0.6 and 0.4< kK< 1.0 results 
0,90 1< 2,25 m. 
2. DIGITAL MAP ACCURACY 
158 
The map accuraoy belongs to the map 
Jesolution, : 
here are many factors that influence 
accuracy of the details position among 
which the source dats quality, the map 
scale, the cartographic accuracy on 
source cartographic materisl, the mini- 
mum line width etc. We summarize here 
only the study of the digitizing accura- 
cy and the coordinates transformation 
accuracy. 
21.1. Digitizing accuracy 
The vectorial digitizers may be assirila- 
ted with the photogramme:ric monocompa- 
rators and the accuracy may be studied 
with the wellknown methods (Jeypalan, 
1972). The digitizing accuracy test 
implies the test for pointing accuracy, 
the test for repetability etc. We used a 
grid on plane glass with a very good 
practical accuracy. For the ARISTOGRID 
digitizer,using a grid with 2304 points, 
we obtained the values : the maximum 
differences between three measurements in 
each point were 0,04 mm for x and 0,03 mm 
for y, the standard repetability error 
0,02 rr, the maximur standard error in 
point 0.021 mm and the starCard error of 
211 the measurements 0,12 mm, 
The conclusion was that tre values indica 
ted by the manufacturer are very good 
and the digitizer may be used for multi- 
ple measuring purposes. 
2.2, Tho transformation Bcouracy 
Por the transformation of coordinates 
from the digitizer system to the map pro- 
jection coordinste system one can use the 
similarity (the linear-conformal transfor 
mation), the affine transfornation, the 
projective transformation or the polino- 
mial transformation in the general form 
X = x + Ag (3) 
where À is the transformation matrix,g is 
the vector of individual transformations 
parameters, x is the vector of measured 
tic coordinates and X is the vector of 
coordinates in the digital map projection 
system. The parameters g may be determi- 
nated using a least square adjustment 
because the redundant operations are app- 
lied to set the basic equation system.We 
used the coordinates transformation sub- 
rout 
rye 
mati 
topc 
  
Pare 
  
No,c 
The 
tole 
Maxi 
errc 
  
Fron 
that 
use 
tior 
choi 
in € 
tole 
ranc 
tol« 
tol« 
3.1 
in : 
C001 
gra] 
Cons 
bigi 
map. 
In 
lut: 
thre 
end- 
thi: 
in « 
3.2 
Top: 
len, 
dan, 
thi: 
The 
dis 
thi: 
oth 
dan, 
ce ] 
3.3 
The 
agi: 
fea 
arc 
car 
3.4 
Con