A nonstandard interpolation function was used to find the time when the data crossed a certain value and consists of two parts. The first step is to employ a function called crossings which identified the set of indices, X, where one data point was below the value and the next above, or vice versa. The parameter sgn is need to specify whether ascending or descending crossings are needed.
Linear interpolation was then used to estimate the time when the data would reach the given value.
This procedure was used to find the midday values of the azimuth and altitude of the Sun. It produces some small errors so a linear fit was used to find the times of the equinoxes and solstices.
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