Manfred H. Günzl 
  
  
  
  
  
  
  
  
  
  
  
  
N. Gu - N. € 
TY 
CY 
Ay Ay 
Ny — 2 
(Ay — Ax) (Ay Ant 
* ML 1 T XL 1 
| sAyAz | 5 AyAz| 
a FI 
Az . x mM 
P5kd -305€-20 argus X. 
ns 1.30 P=h6; EF =40;: 0228: 17, 1.36 
PEC 
Figure 2: Squares approximated by grid cells with different slopes. 
If the number of grid cells within the rectangle Ax x Ay can not be divided by 2, the approximating polygon can not 
divide it into two equal areas. Therefore, the distinction of the two cases P, and P» is required. The parameter 7, Of a 
| x | square with the orientation w derives to 
2E? 4-16.—- C? 
Toc (wl) 39P 
] 
= sin(2w) + cos(2w) — 1 sin(w), (5) 
This result can be used to compare the measurement of compactness derived by = with the parameter 7; 
E PEC 
error of factor 2 could be reduced to v/2. The mean error of 7,,,. derives to 
[ p*5 \ 
Ly Tom (80, 00Y00 745 = 
PEC 
. The maximum 
~ 1.21. (6) 
PEC 
Bln. {w; 00) A 
0 
2.2 Rectangular Shapes 
For land use segmentation the square shape is not a common shape. To make working in the fields with machines easier 
most agricultural fields in central Europe have got a more or less rectangular shape with miscellaneous aspect ratios. If 
the boarders of a [, x Ij rectangle are parallel to the grid 7, follows from (P, F,C) = (lal, 2(la + le), 4). 
= 
x 
     
    
    
    
  
  
  
  
  
  
  
  
  
  
  
  
  
  
J Axa 
mn emm 
(ID) (II) am Y c [D^ 
Aya A AnB B 
ANB | B | 
| A | | 
(Axa -Ax6)1 ! 
^ LAU | A / 
| ~ A | 
| D | ~ A 
| | 
Ayp J NY D Y | 
b o. 
NK 
  
  
Figure 3: Rectangles approximated by grid cells. 
| - 1p)? 1 1y La 
(ath) HL for vU: - 
p ole 7 
os 4l, lb 4v lp m 
T 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 353