23 
U = c x +a jU+a 2 v+a 3 w+a 4 u 2 +a 5 v 2 +a 6 v; 2 +a ? uv+a 8 vw+a g wu+. . . 
V = Cy+bjU+b 2 v+b g w+b 4 u 2 +b 5 v 2 +b & w 2 +b ? uv+b 8 vw+b g wu+... .... 4.37 
W = c z + c L u+c 2 v+c 3 w+c 4 u 2 +c 5 v 2 +c 6 w 2 +c y uv+c 8 vw+c g wu+. . . 
Conditions are applied to equations 4,37 such that the transformation in 
question is simultaneously conformal in the three projection planes u-v, 
v-w, and w-u. These conditions are: 
au 
3u = 
av 
av = 
aw 
aw 
CO 
CO 
• 
¿t 
• 
• 
• 
• 
au 
av 
av = 
au 
av 
aw = 
aw 
av 
.... 4.39 
aw 
au 
au = 
aw 
Evaluating conditions 4.38 and 4.39 with respect to equations 4.37, 
one obtains the following relations: 
a i 
= 
b 2 » 
C 3 
s 
S 
3 2 
= 
~ b 1 
= 
C 
3 3 
= 
-°1 
= 
- b 
b 3 
r 
~ C 2 
= 
a 
.... 4.40 
23 ** 
- 
- 2a s - 
- 2a s = 
b 7 “ 
° 9 
“ 
2e 
3 7 
r 
2b 3 = 
" 2b 4 = 
- 2b 6 * 
C 8 
r 
2f 
a 9 
= 
b 8 = 
_2C 4 = 
II 
in 
o 
CM 
1 
2C 6 
= 
2g 
a e 
r 
b 9 = 
C 7 
= 
0 
Substituting the relations of 4.40 in equations 4.37, one gets: