I'm a bit amazed by this answer. It seems like you think that MySQL is a magic wand of some kind. The OP is quite unclear what kind of queries he wants to perform - and until he clears that up, I don't see how a relational database is going to help you here.

Let's adress your reasoning.

Databases have lots of functions you can use without having to code your own custom data structures. This saves lots of time.

Actually, relational databases have lots of functions that deal with tabular data. Polygons are not not tabular data - it's geometrical data.

Most databases are optimized in ways you could never do in your life time even if you wrote your program in straight assembler. The reason for this is there are a lot of very smart people who spend their time figuring out how to make things quicker and working on databases. For instance, I couldn't code MySQL if I had an entire lifetime.

Most databases are optimized, yes. But they are optimized to deal with transactions, and to perform queries in a relational structure. Things that don't have much to do with geometrical data.

Databases are very quick. I have a database with a hundred thousand records and I can get very specialized SELECTs done in a few hundreths of a second.

Actually, database aren't quick. Databases spend a lot of resources in being consistent, robust and atomic. They can find records reasonable quickly if they can make use of simple indices. I don't see what kind of indices you can use.

Databases cache information for you. So if you perform the same calculation twice you don't need to worry about it.

Yes, but it's not at all clear whether the OP's problem makes this relevant.

Perhaps I'm seeing this all wrong, and you have a brilliant set of tables, indices are relations in mind. In that case, I'd like to see the schema.

Abigail