Page 334 - Programming Microcontrollers in C

Table Look-up 319

Table Look-Up

Often in the implementation of a practical problem it is necessary to
implement a conversion of data in a completely heuristic manner.
Observations are made and a curve of sorts is fit to the data. It is then
desired to put a few samples of this curve into a data table and then
calculate values between these samples with an accuracy that usually
requires interpolation between the points contained in the data table.
Such tables are usually sparse in that the number of measured points
across the range covered by the table are few. The curve in Figure
6-1 shows an example of such a conversion table, and the table itself
is shown as Table 6-3.

250

200

150

100

50

0
20 40 80 120 180
Figure 6-1: Data Conversion Curve

X Y

20 5
40 15
80 50
120 120
180 240
Table 6-3: Look-Up Table

The object of the program is to deliver to the program a number
like 67 and get the proper result back from the table look-up routine.
The x value of 67 lies between the 40 and the 80 entry in the table.
Therefore, the interpolation calculation needed in this case is