Efficient calculation of solar position using rectangular coordinates

There have been many algorithms published for calculating the position of the Sun. Most of them are simplified in some way, offering either reduced accuracy or a limited range of valid times. A different approach to the problem is presented here, derived from the approach used by some large astronomical telescope control systems, in which rectangular coordinates are used to transform the celestial coordinates into a direction as seen from a site (or multiple sites) on the surface of the Earth. This reduces the computational complexity for the conversion to topocentric coordinates. For applications in which calculations are repeated at a high rate, such as for solar tracking, this approach also enables a simple interpolation to be used for the Sun's equatorial position vector, which brings a further dramatic reduction in the computational complexity of the most detailed published algorithms, with a smaller loss of accuracy compared with any of the simpler published algorithms.