ra 
vn 
re 
lic 
ng 
of 
ch 
es 
la 
ne 
nd 
nd 
James Olaleye 
  
  
  
Figure 2: Natural and Apparent Direction Axes of Vector Spaces: (a) the R-space 
(b) the C-space 
  
  
The apparent direction vectors constitute the row- and column spaces of a 3-D rotation matrix and are expressed 
analytically as (Olaleye 1992): 
R- Space direction vectors: 
cosf cosk 
R, = | sinw sin £ cosk + cosw sin k 
— cosw sin f cosk + sin w sin k 
— cosf sin k 
R, =| — sinw sin £ sin k + cosw cosk 
cosw sin f sin k + sinw cosk 
sin f 
R, = | — sinw cosw 
= 
s 
cosw COS£ 
C-space direction vectors 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
659