Now, equations (47), (48) and (49) are applicable to the fictitious photograph; that is, 
  
  
T = M! 
xv dyYx (74) 
\ ty! 
Xy Ag ¥y (75) 
t Le 
x, 0 (76) 
x! x, 
in which q! = -2 and q = — . 
X Xa Y Yo 
Obviously, from equation (73): 
' -— 
vo dE het Be Tuy 
iN T y "P TTloxX. T f.aY. = Pan! (77) 
a 12 a 22° à 32 © e 
T - 
Eesha Tl Tf 
iy 7 ow Fox +r,y -r.f (78) 
b 12% * foofp. 732 
Once dy and dy are known, the coordinates of the vanishing points in the fictitious photo- 
graph can be obtained using equations (54), (55), (47), (48) and (49); that is, 
yz = +f V- (ay dy + 1) (camera points upward) (54) 
= -f V- cas dy * 1) (camera points downward) 
-f2 
y! = y! = — (55) 
2 Y y. 
Ot tt 
XX x n 
t = (ot 
x Wy Cas) 
e e © 
x^ 0 (49) 
The locations of the vanishing points in the real photograph can now be obtained by applying 
the transformation represented by equation (56) to the vanishíng points in the fictitious 
photograph. The resulting coordinates are: 
  
  
  
' t 
: f IE sf 
x T ef Y..xt Lr tfr (79) 
Mx * F2. ‘33 : 
f oy 
: Eo T foy Tot 
ya = "f r VAT mir oF (29) 
315% T Tx. "33 
t * 
1 fp EQ = Tyaf 
x = -f FT fr f (81) 
Y fi f323Yy .T33 
r 1 +p gl = yp of 
Ye © =f 21 T T2 ~ 03 (82) 
1 
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