where we have denoted as essentially direction cosines: 
Ay = -COs Q COS K 4 sin OQ sin o sin « 
Bj = -Cos w sin K 
Ci = sin OQ cos K -* cos Q sin o sin x 
À, 7 -cos @ sin K - sin Q sin Q cos Kk (13) 
B, = COS W COS K 
Cs = sin Q sin æ -cos @ sin w cos x 
D 2» gin Q cos o 
E = sin o 
F = cos Q cos w 
Each of the pair of formulas (11) and (12) represent the algebraic 
expression for the geometrical condition of co-linearity of the points O,r 
   
   
   
    
and R, solved explicitly for the coordinates of point R in the 1, J, k system 
^ ^ ^ 
and of point r in the 1, j, k system, respectively. The symmetrical arrangemen 
of the formulas is & direct consequence of the reversibility of any central 
perspective. (compare [1] page 8) 
In [2] the algebraic solution was continued by eliminating such X, , Y, 
and Z's from the solution which were not given as control data. This step led 
for relative control points, to an algebraic expression for the condition of 
Intersection, and correspondingly for partially given control points, to the 
condition of intersection at either one or two glven control coordinates. As a 
direct consequence of that approach, different types of conditional equations 
were obtained for the different types of control points. To complicate the 
sltuation further, the number of any particular set of such conditional equatioi 
depends on the number of camera stations involved in any specific triangulation 
problem. 
15