Generating rectangular coordinates in polar coordinate order

This paper proposes a means by which 2D data represented using the rectangular coordinate system can be converted to its equivalent in the polar coordinate system. Taking note that the order in which data becomes available with a polar coordinate measuring device is most unnatural from the point of view of a rectangular coordinate system, this paper presents a simple yet elegant algorithm that generates the points of a rectangular coordinate system in the natural order in which they would be obtained in a polar coordinate system. The algorithm uses only integer arithmetic and a few simple tests. It can quickly identify the grid points between any two angles or the polar coordinate measurements needed to compute rectangular coordinate measurements by interpolation.