secting vectors on the upper surface of the slab (in the x-y 
plane of the ''floating'' cartesian coordinate system mentioned 
above) was chosen. This conformal transformation, often used 
by structural engineers and apparently theoretically justifiable 
in structural mechanics (Lenschow and Sozen, 1966), is based 
on an arbitrary point ot be used as origin (Fig. 19), and two 
arbitrary vectors intersecting at this point. 
  
Fig. 19 - ‘Floating’ control for coordinate transformation 
In Fig. 19, the transformation system is defined by 
two vectors ( (1) and (2 ) intersecting in a point (A) and 
passing through two arbitrary points (B & C). Point P is a 
general point whose coordinates X Y 2 in one coordinate 
system is to be transformed in another coordinate system (X', 
Y', Z'). The X and X'-axes may be chosen along the vectors AB 
and A'B' respectively. 
Let the direction cosines of lines 1, 2, and 3 with respect 
to the first coordinate system be as given in Table ll.