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1.Influence on Coordinates 
Suppose the coordinates of a point 
measured on DCI are (x,y) and the 
coresponding rectangular coordinates are 
(X,, y) ‚The errors of coordinates can 
be got by using formula (5). 
AX=X—X; =X— (X+ycosa)= —ycosa 
{ Ay=y—-y,.=y—ysina=y (1 —sinæ) (20) 
For 0°<a =90° ,the signs of AX. AY vary 
with quadrants as what are showed in 
Tab.1.For 90° <a <180° ,the signs of AX. AY 
vary with quadrants as what are showed in 
Tab.2. 
  
  
  
  
  
  
  
Tab.1 
AX Ay 
quadrant I «0 »0 
quadrant II «0 »0 
quadrant III »0 «0 
quadrant IV »0 «0 
Tab.2 
AX ^Y 
quadrant I »0 «0 
quadrant II »0 «0 
quadrant III «0 »0 
quadrant IV «0 »0 
  
  
  
2.Influence on Distance 
As=, (x2—x1)2+ (y2—y1)? 
— J/KGOa —X1)? t Cya - y)? 2 (X2 — Xi (yo — y1 cosa 
=2 (X2—X1) (yz—y) cosa yi?c027/ (J(x2 —x1)2+ (y2—y1)2 
xz — X12 + (y2—y1)2+2 (X2—X1) (yz2—y1)C08 @) 
  
  
for DCI, a z 90° ‚So 
A X A ycosa 
As=- 
s (21) 
For 0^«e x90 ,if AX. AY have the same 
sign, Asx0;if AX. Ay have the contrary 
sign, As=0 .For 90°<a <180° ,if AX. Ay have 
the same sign,then as=0 sif AX. AY have 
the contrary sign, then 4ASs0 
3.Influence on area 
AS =S —Ssina=S (1 —sina) 
AS 
S 
  
For a € (0°, 180°), AS »0is always correct 
.This means that area measured by DCI is 
always larger than its true value. 
4.Influence on Azimuthal Angle 
X 
A R =arctg 5 —arctg 
AY 
AX ] +ctga (23) 
  
  
  
  
  
Ay sina 
For 0° <a <90° Jif 
cose AX _ cosa 
1 —sina Ay 1 +sina 
then AR=0 if 
AX cosa AX cosa 
= ; or — - 
AY 1 —sina AY 1 +sina 
then AR<O 
61 
  
  
  
For 90° <a <180° „LE 
Cosa AX cosa 
— - = = 7 
1 +sina AY 1 —sina 
then AR=0 ;if 
AX cosa AX cosa 
= : cor — : 
AY 1 +sina AY 1 —sina 
then AR<O 
In cadastre and photogrammetry, coordinate 
errors of x and y are required less than 
0.1mm on map,error of distance less than 
0.2mm on map and the relative error of 
area less than 1/1000.The maximum error 
allowance values of x,y,distance and area 
can be acquired by using fomulas (20), 
(21) and (22).The results are showed in 
Tab.3. 
  
  
Tab.3 
allowance |90° —@ | max 
x 0.1mm 41" 
y 0.1mm 1° 09'45* 
distance 0.2mm 4 58° 
area 1/1000 2° 43’ 45" 
  
  
  
As showed in Tab. 3 , x is the most 
sensitive  paremeter to the angle between 
x-axis and  y-axis.It requires that|90'—a 
<41".Area is the most insensitive one. 
Even if |90°—a | is up to 2 43 45” , the 
area measured is still less than the 
value of allowance . If all of the 
parameters are  considreed at the same 
time,it required that [90°—a | <41". This 
is nearly identical to the technical 
specification of 45". 
An Algorithm of Calculating A-angle 
The angle between x-axis and y-axis is 
one of the most important specifications 
of DCI.It is also very useful to know 
the value of in the process of measure 
with DCI. A algorithm of calculating «à 
is developed as fllows. 
Determine two points A and B( line AB 
is not parallel to either x-axis or 
y-axis) and measure their coordinates 
(x, ‚yı) and (x,,y,) on a piece of paper 
.See Fig.7(a).Then rotate the paper about 
90*.In this position,point A and B become 
A'and B' with coordinates of (x/,y,') and 
(x;,YX,),See Fig.7(b).Then for Fig.7(a), 
S 2= (x2—X1)2+(ÿ2—Y1)?+2 (X2 —X1) CY2 — Y1 )COSA 
for fig.7(b), 
S2= (xi - xy? -(yb -y)0? 9 2(6 — xD) (y2—yi)cosa 
so 
(x2—x1)2+ (y2—y1)2— (x3—x1)2—(y2—y1)? 
2( (X —XD Cy2— y) — (X2—xX1) (y2—Yy1)] 
(24) 
  
cosa — 
In fact, d -angle can be calculated by 
several groups of data in order to 
get a more accurate value.Tab.4 and Tab. 
5 gives an example to calculate d -angle. 
Conclusion 
It is showed in this paper that plane 
c -angle coordinate system is the