In the previous chapter the first illustrative problem was to derive a way of

interpolating values between a number of discrete points: specific head and

discharge readings from an orifice plate flow measurement device. Using the

methods covered so far there is a range of options for this, some of which are:

1. linearly interpolate between each pair of points, leading to four equations to

cover the range of values;

2. fit a quadratic between the first three points and a second over the last three

points (using the middle point twice, once for each curve);

3. fit a cubic over the first four points and then a linear interpolation over the

other interval;

4. fit a fourth-order polynomial over the five points.