… Istanbul 2004 
coordinates of 
f projects from 
| to X, Y and Z 
tor of equation 
rds to limitless, 
ive to the lines 
Pze relative to 
| be acquired in 
  
y^ 
b. 
Le, 
fre 
Cs 
parameters xy, 
, @ K can be 
limitless points 
lirectly used to 
1e parallel to y 
her the vertical 
ach point (u, y) 
quation (2) and 
iat value. The 
n 0 is 
: 0°, 0# 90° 
point p(x, y) of 
se p is fitting 
vhich project is 
(8) 
) and (2), then 
Y: yrc, (2-7. 
YJ)T64 7-2.) 
Ye -27;) 
Y Ze) 
ion (3) and (4): 
centre (Xp, Yo) 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
A S eR cos, Fi HR smut (9) 
Substitute equation (9) into co-linear equations (1) and (2), then 
tud a (X, + R-cost- Xo h(V, or Rsint-Y3060(7—7.) 
emn a,(X, +R cost — Xg) +b,(Y, + R-sint - Y.) (Z -Z;) 
{Xo + R-C08t~ XV +0), + R-sint ~Y ) +e (Z ~ 2, ) 
a (X, R-cost —X.)- b, E R-sint -Y9)*c(Z-2,) 
  
  
Mz Ma =f 
Because p, — Xo, pz ^ Yo, p; ^ R, so that among equation (3) 
and (4): 
b, 7 bi; bo; b;57 0, 
Cu = jp. C27 dj. €Cj5 7 ag; Sin t, 
€) 740), C270», C237 dz COSt 
2.2.3 Curve: Ground: If the tangent direction of a point p(x, y) 
in a curve is 9, similar as the case of straight line, when —45° < 
0 x 45° or 135° < @ < 225°, point p(x, y) is fitting equation (1) 
and (3), otherwise p is fitting equation (2) and (4). 
The tangent equation of the curve in point (Xj, ¥;) of plane Z = 
Zp is: 
X=X, +¢t-cos0, Y=Y, +1 sing, (10) 
Similar as the case of straight line, here p; =0; among equation 
(3) and (4): 
Cj 7 -E a5, sin 0; cy; =-t ay sin 0; 
By the principle mentioned above, it is easy to conclude the 
visual point, infinite point, straight line, circle, arc and curve in 
to an uniform mathematical model: co-linear equation, and 
perform unitive adjustment. 
3. APPLICATION OF GENERALIZED POINT 
PHOTOGRAMMETRY 
3.1 Computation of Image Parameter from Vanish Point 
and Modelling by Single Image 
Three interior parameters xo, yo, f and three exterior parameters 
9, €, k, can be calculated by equations (5), (6) and (7). The 
principle point (xe, yo) of image is the intersection of three 
perpendiculars in the triangle consisted of three vanishes. The 
focus can be calculated by formula: 
p = T = x. = 30) 7 (sc my Y E) 19 
The angle elements are 
  
tan @ = NT tx vy IT «xt o49 — (12) 
tan @ = Vi. + Yoo (13) 
tan x = x, Liv. (14) 
The computation of the coordinates of project center and 
building modeling is performed synchronously. Taking simplest 
building as an example (Figure 1), let point 2 as origin, X;— Y; 
=7,=0, 23g x-axis, and let its length be L, X,=L, Y;3= Z; = 0, 
then: 
    
  
  
  
  
  
  
  
  
  
  
  
  
  
x Xr =X + WV, — > )—a, ; r ? 
0-X; =(Z ZU Xo ) eO 273 af =(0- zs 
qe -x)te05-X-6/ a 
; b AT, + ” jy )- t ^ 
0- Y, =(7, -Z i» xo) by; Yo) A z(0—Z.) Va 
2 (X 7x,)te05 -y,)-6f iw, 
; x —x,)+a,(y,-y,)-a- EU 
1-25 0 moque 
C (s TX ) +C, Q5 =) w; 
; bx, x) *553-Y)-5f 2 V 
0-X, (Z; -Z5)- ! 208 yo) Af 2(0-27.3-: 
es -x,)e5-7X,)-6f W; 
5 4 
3 17 
IN | 7 08S 0 & 
2 3 
Figure 1 Stereo Building 
The coordinates of project center can be calculated: 
à RES OS My i gm 
UW, — IW, W, } W, 
The other two parameters width W and height H of the building 
can be computed by the coordinates of project center and co- 
linear equation with right angle condition. 
Based on the computed initial values, suppose 1(0, W, 0), 2(0, 0, 
0), 3(L, 0, 0), 4(L, W, H, 5(, W, H), 6(0, 0, H), 7(L, 0, H), 11 
parameters can be solved. Figure 2 is an example of 
computation of image parameters from vanish point and 
modelling by single image. 
  
b Stereo Model 
Figure 2 Computation of Image Parameter from Vanish 
Point and Modelling by Single Image 
a Original Image 
3.2 Determination of Image Parameter by Matching 
between Vector and Image 
The problem of data update is how to use exist data, be more 
exact, how to use exist information. AS well-known, if the new 
image would be applied to update the exist map, their 
superposition is the most important step. After determining the 
image parameter, rectifying the image to ortho-image consistent 
with the map, the image could be superposed on the map. 
Therefore, in data update, except selecting control point by 
traditional manual way, whether the large mount of line 
elements of objects on the map could be applied as control is 
very important for the realization of the automation for data