Ebrahjm, Mostafa Abdel-Bary 
For the analytical comparison and the geometric comparison the average errors = sum(abs(diff))/n and the standard 
deviation — sqr(sum(diff*diff)/(n-1)) (where diff is the difference in co-ordinate values and n is the number of points) 
have been computed. These methods lead to significant values for the accuracy of the evaluated methods. 
The position of the dome axis has been calculated from the center of each level (Xo, Yo) and the standard deviation of 
the position of the axis (oXo, oYo) is obtained . Also the radius of each level (R) has been calculated from different 
points co-ordinates and the standard deviation of the radius (cR) has been obtained for the various radiuses and 
tabulated as in table (1). 
    
  
  
1 3.205 oR 
2 on 0.018 
3 8213 0.018 
1 #* 3.217 a 
| 8. 3.216 on 
° 2215 0.018 
7 3.217 C 
| 8 — x 3.214 D 
29 3.216 Fils 
|" 30. — 3.220 oe 
ài —o 3.225 9o 
| qn — —— 3.223 Co 
13 — 3.225 0.035 
| d 3.220 0.037 
ss 3.222 Mod 
16 : 3.228 0.932 
  
  
  
  
RARES 
Al values are in meter 
Table (1) The dome axis’ position and the radius according to each level 
From table (1), the average co-ordinates of the dome axis position are : Xo = 3.218 m and Yo = 3.258 m and the 
standard deviations of the dome axis position are : oXo — 0.0056 m and oYo — 0.0033 m 
A curve fitting according to the Least Squares Error has been applied to find out the best formula for the profile of the 
vertical cross section of the dome by using the radius at each level as X and the levels as Y. The results of the curve 
fitting shows that the parabolic formula is the best formula for the profile. The formula that fits the results is : 
Y — 0.08785 x? 0.3078 X - 1.3732 
The circles radius at each level according to the values that calculated from the formula have been compared and 
tabulated in Table (2). Also Figure (4) shows the curve fitting results. 
  
  
  
  
  
Level No. X : : y  gQ Oo. Calculated Y 
1 2.546 | 0000 -0.020 
2.423 - 20.086 . -0.111 
3 2.306 . 0168 — -0.196 
4 2.249 0205 —— -0.236 
5 2.068 0319 -0.361 
6 1.961 = 0398 -0.412 
7 1.879 | 0445 -0.484 
8 1.781 0504 -0.546 
9 1.561 | 70.641 : -0.679 
10 1.416 0719 2 -0.761 
11 1.328 -0.775 -0.809 
12 1.090 0.915 -0.933 
13 0.893 -1.038 -1.028 
14 0.682 : -1.156 -1.122 
15 0.568 -1.210 -1.170 
16 0.314 -1.302 -1.268 
  
  
  
All values are in meter 
Table (2) The curve fitting accuracy 
The average error of the curve fitting = 0.032 m and the standard deviation of the curve fitting = 0.034 m 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 199