cog SC PT (29) 
o = 
ay Rz © y 
as w d i M di (30) 
o ya ya 7. Maz zz 
in which 
eg = By = Bo 
AX ZO En Bp 
AY 47 = Yx = Yoo 
Ay 7 = Yx m Yo) 
and 
BE Ya xD 
B, ^ YA. t NS 
In addition to equations (27) and (28), a third equation can be formed by 
subtracting equation (26) from (25): 
- = = - = 31 
x, x) (x, xy) + (y yo (vy yp 0 (31) 
Equation (31), also comprised of a dot product equated to zero, indicates that line 
nO is perpendicular to nen. This equation can also be used to locate the principal point. 
Figure 6 indicates that the principal point is the orthocenter of the triangle 
formed by the three vanishing points. It also indicates that any one vanishing point 
is the orthocenter of the triangle formed by the principal point and the other two vanish- 
ing points. Hence, equations (27), (28) and (31) can be used to locate the third 
vanishing point if the principal point and two of the vanishing points are known. 
The principal distance, f, can now be determined. The principal distance is 
implicit in equations (24), (25) and (26). Expressing f explicitly, we obtain: 
  
  
  
f-Y-G0x GuoA - Gu Guys (32) 
f= Velux) Grex) = (Gey ) xo (33) 
f= Volxx) (mx) = yy) Gy) (34) 
Any one of equations (32), (33) or (34) can be used to find the principal distance once 
the coordinates of the principal point in addition to the coordinates of the vanishing 
points, ns and n,, are known. 
N Z 
edi