-7- 
c) bicubic polynomials (third order splines) 
0 1 4 
* 8 NY + a oye +8 x, + a Y + a yx. + a xy^ 
8 9 10 11 12 13 
2 7 2 5 
*RQAí4Y X^ 8 BAgX y 
15 
X x 8 + ax +a + a,xy + a xc + a ? + a X + a,x 2 
= b + b,x + boy + boxy + b 
1 
2 2 2 2 
x +b + b,x + b,x 
3 4 57 QUY t 94Xy 
2 2 3 
+ b xy +b x y +b x + b y? * b yx + b xy, 
8 9 10 11 12 13 
2-3 2 5 
* bay x^ F bg y 
they have continous first and second derivatives. 
To determine the 16 coefficients the following values need to be known for the 4 corners of 
a spline ares 
AX! oAx! à ‘ax! 
i 
Ant > mas 
  
94: day! Ay! 
Ay! 
i ox dy ax dy 
  
A mesh of spline areas is easily adaptable to least squares fitting. 
3.5. Restitution by Polynomials Representing Flight Path and Attitude Variations 
Rather than using arbitrary polynomials of the types (8) to (11) Baker and Mikhail /7/ determine 
special polynomials for direct use or for splines which correspond to terms contained in the 
model for flight path and attitude varrations. The choice of the proper coefficients depends 
entrirely on the assumptions made for the time varying behaviour of the parameters. This, 
quite in general, presents a real problem area needing further practical investigations. 
The differential relations (1) may be written as: 
2 
== (1 + te 
Ji 
om ) dw + dy = 
z 
- -]— 1 
+ sd de, + (ay, z, de) 3 yi 
in terms of photo coordinates; 
or simpler as: 
dx; y,dK + (2i ad + dx ) 
y 
dy. + dz, + (dy, + zdw) + 
i 
3 Z 2 
Z 
in terms of ground coordinates. 
The variations of the orientation parameters may be assumed in form of polynomials 
(see /7/, /48/ ).