A 



E y' i+1 = JX JCY C CA i CS,+8)D - Y i+1 tt,+Zrt 2 d£ . (24) 



-A 



The transform generated arc length and weighting factors are deter- 

 mined relative to the results of the previous iteration by: 



W S = E S /E , (25) 



W S = E S /E , (26) 



y y 



W C = E°/E , (27) 



xx *■ J 



W C = E C /E , (28) 



y y ' 



where E is the average value of equations (21) through (24). The 

 arc length functions are given by: 



MCVM - Y S j [(|f) 2 * Cff) 2 ] 15 dS , (29) 



and 



+ ,B) = y c I rrl2L,2 M r ^y, 2 - 



A(5 ,0) = Y j [(||) 2 + ( |Z)2]* dc , (30 ) 



o 



1* s c 



for j< 5 <_ A and y an d Y a ^e prorating factors taken such 



that A(A,n) is exactly the known length of the given curve. Two 



levels of approximation are involved in the error function. The ith 



approximation of these quantities is involved in the interpolation of 



the given curves. This approximation is mandatory in deriving a 



deterministic form for these quantities relative to the i+1 level. 



The iterative procedure is initiated by setting all coefficients 

 to zero, all weighting factors to unity, and equations (29) and (30) 

 are given by y s ?* and y c ^ , respectively. The first 

 estimates of g , B and the Fourier-type coefficients 



