International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
2 
(X KG) Fr 
x 
ye -x)-KE( xr o 
r- (x =X) tQ = voi. 
b. Computing the joint points 
Fig.5 shows the projection of a building in a photo. In principle, 
all the lines that respectively parallel X, Y and Z coordinate axis 
should join in three points 7, J and K. If we pick some points 
along /3 and get the coordinate sets ((x,.yj). (X5). ... (XY). 
then we can get the line 4x + By = / using the formula below. 
Tr Tw 
Ty yy Tutt 
Be EX Y sts 
yx av y y 
And by the same means, we can get the description of line 24, 
then compute the coordinate of point / using the following 
formula. 
  
(3) 
Us Nat B3 —VB*N AB 
CS 449 8° —S AR*S AR 
NB*YV 4^ V 4* Y 4B 
SAL*S B Y AB" Y dB 
/ 
  
Y= 
And the coordinates of point / and K can be computed using the 
formula 3and 4. To ensure the precision of results, in practice, 
we usually take redundant points and compute the average. 
  
Fig.5 The Joint Points in A Image 
c. Computing the angle elements 
After the determination of the three joint points, next we will 
compute the three exterior angle elements 4, aandk. Taking one 
side face A of the building showed in Fig.5 as an example, we 
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calculate the three elements. Fig.6 shows the detail. The angle a 
is photo obliquity, and the range is from 0°to 90°. 4 is attitude 
angle, and it also ranges from 0°to 90°. And K is the angle from 
x coordinate axis counter-clockwise to the u coordinate axis 
with the range from 0°to 360°. 
  
Fig.6 The Angle Elements in A Image 
From the geometric relation of special Points, Lines and Faces 
in photogrammetry, obviously So: o/K and ov! /K, so we can 
draw the conclusion that oaS, Isa, “SaK, loa and Koa 
are all right-angled triangles. Based on relations of the right- 
angle and the coordinate axis, we can deduce the following 
formula. 
A= £ISa 
a = LSao (5) 
K= Zxu= Zxu = io! + dou = 2xol + Zola 
And the anglekis determined by the quadrant of the point a 
which is the cross of /K and Sv. Using coordinates of the points 
I, J. K, o and f, we can compute the length of oa, Sa, Jo and SI, 
then we can calculate the three exterior angle elements 4, dandk 
by the formula 6. 
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A = arcsin(— 
C 
s, f. 
& = arcsın(— (6) 
yı'=) Joa 
Ku are ( + arcsin(—) 
X; 7X9 lo 
d. Computing the scale 
Based on the above parameters xy, yy, f, 4,Q and K, we can found 
the model of building in object space. But without any 
coordinate and length information of reality, we can't 
determinate the size of the model. There are a few kinds of 
means could be used to get the scale between thé model and 
reality. For that we have already possessed plenty of digital 
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