The spherical range and bearing computations described in this document's parent use the universally familiar sin and cos functions quite liberally. Many people see these pure mathematical functions as quite beautiful. They see them as a reflection of nature. Or even as part of the very fabric of the universe. This is probably because, when viewed against a fixed frame of reference in space and time, they trace out apparently smooth (and beautiful) periodic curves. The idea of replacing such things of beauty with something as crude and frumpy as a look-up table is pure anathema.
This beauty is however like all beauty: in the eye of the beholder. Nature does not set out to make sine curves. They are merely one consequence of one microscopic event following another ad infinitum. They are the global outcome of a myriad iterations of a single fractal processes. They become visible to us only when we take our observer's licence of freezing time and rigidifying space with our artificial systems of co-ordinates and units of measurement. They are nothing more than human aids to comprehension.
The lowly look-up table, on the other hand, makes no pretence of being the fabric of the universe. Nevertheless, it does define the same set of waypoints which the natural fractal process visits on its journey through time and space. And it finds them for you much more quickly than does the 'pure' mathematical function. The truth is that neither one is a fundamental component of the universe. Reality is relativistic and fractal. You cannot freeze time or rigidify space. Motion is key to existence.
The mathematician and the physicist with their beautiful functions therefore have no cause to look down upon the engineer and the programmer for using look-up tables.
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© 1997 Robert John Morton