Exact values representing rigorous evaluation of the 
theoretical camera model are computed along the bounding edge of each 
differentially narrow framelet. These values form row entries for 
interpolation tables. Linear interpolation within the tables, according to 
the mean value theorem can always represent the values to any desired 
accuracy if the table interval is small enough. However, the relatively 
steady curvature of the functions involved would indicate that some simple 
scheme to model the curvature would increase the accuracy of the 
interpolation. Autometric has recently implemented a 3 point Lagrange 
Interpolating Polynomial approach, which indeed increases accuracy, while 
minimizing the size of the interpolation tables required. The 
interpolation uses the 3 points of the table which surround the 
interpolation point to compute a Lagrange Interpolating Polynomial, which 
is then used for the interpolation. The mathematics which are used are 
presented below. 
LAGRANGE INTERPOLATION 
The interpolation for all tables, both for static and time- 
dependent parameters, is handled using a Lagrange 3 point technique. This 
technique was adopted by Autometric to reduce the amount of data stored in 
the numerical tables. Figure 2 shows diagrammatically how the algorithm is 
used. By convention, the interpolation point is placed between the first 
and second nodes of the interpolation set by selecting the correct points 
from the table. 
Let the indices of the tables be as follows: 
n is the number of rows in the table 
tg is the coordinate of independent variable for the first 
row in the table of interest 
dt is the interval in the independent axis at which the 
tables were constructed 
i represents the ith row in the table which varies from l 
to n 
t(1) is the value of the independent variable for row i 
v(i) is the value of a dependent variable in row i of the 
table computed from the rigorous model 
Now let the point of interest be represented by: 
t is the value for the independent variable in question 
v(t) is the value for the dependent variable we are seeking 
The interpolation proceeds as follows: 
(1) Compute the row number of the first of the three rows 
required: 
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