…well, at least not in geometric terms.  Any origin you pick ought to do the job.

(It’s been a while since I wrote about research-y stuff.)

Briefly: if you’re working with geometry in a basis given by a set of linearly independent vectors, your points will themselves be vectors — giving the coefficients of each basis vector in a linear combination.  The “origin” is whatever point in space corresponds to the zero vector.

Put that way, it should be pretty obvious that there’s no fixed choice of origin — it can be anywhere.  In fact, it’s fairly easy to move your origin around — just translate everything else in the world.

Taken even further, it’s sometimes useful to deal with multiple origins for the same set of geometry.  After all, an origin is just a point in space, right?  It’s easy to go from one origin to another when needed, so why not pick the origin that’s most convenient for any given chunk of geometry?  (How useful this is depends on your application, of course.)

Had I kept in mind that there’s nothing special about any particular origin when I wrote code a year and a quarter ago, I might’ve saved myself a few weeks of debugging just now when my implicit assumption that there’s one global origin became shockingly obsolete.