One of the query optimization scenarios I’ve seen a lot over the years is finding something within some distance from a point. For example, finding people within some distance of yourself, apartments in a radius from a postal code, and so on.
These queries usually use the great-circle formula. That might be because Google finds lots of pages claiming that this is the right way to do a radius search. “The earth is not flat!”, they all say. That’s true, but it doesn’t mean that the great-circle formula is a good approach. It’s usually a really bad approach, in fact. It’s needlessly precise for most things, not precise enough for others, and it’s an expensive query to execute; all the trig functions tend to eat a bunch of CPU, and make it impossible to use ordinary indexes. This is true for all of the databases I’ve used—MySQL, Postgres, and SQL Server.
The great-circle formula is needlessly precise for a few reasons:
- Within the radiuses I’ve usually seen, the earth is flat, or close enough that it doesn’t make a difference. Looking for an apartment within 25 miles of downtown? The error introduced by pretending that the earth is flat on such a small scale doesn’t matter. The Pythagorean theorem would work just as well.
- “Downtown” is not a point, it’s an area. Nobody is going to argue if you return search results that vary by a few miles, or even more.
- Nobody drives in a straight line from downtown to their apartment. People usually search within a physical radius as a proxy for “find me something conveniently close.” They don’t really expect the miles as-the-crow-flies to be a good proxy—it’s just one they’re used to. In reality, that apartment just across the river might be too far away from work, because you’d have to drive a long way to get to a bridge. (Unless you want to swim to the office every day, that is.)
In cases where you really do need precision, there’s a reasonable chance that the great-circle formula still isn’t right for you, because not only is the earth not flat, the earth isn’t a sphere either.
What’s the optimization I usually suggest? It’s usually perfectly acceptable to just return results within a square centered on the point of interest. In most cases, the results will be just as satisfactory to the users. The remainder are usually very special cases.