Very interesting stuff. Our project has been required to work with the ESRI ArcObjects stuff for the past 4 years and I've been dying to get inside of their algorithms. Thanks for resparking my curiosity.
if (random()) { crash(); }
else return UndefinedError;
Tongue in cheek, of course, and they've gotten noticeably better since 4 years ago. (I've been working with ArcObjects since their 8.3 release... shudder.)
If you're interested in how they implement vector operations:
As far as raster operations go, I think that GRASS does all they do, plus more. All of the above are nice open-source implementations so you can go as deep as you'd like. ;)
p.s. Most of the algorithms ESRI (and similar) use might not be spelled out in blog posts, but they certainly are in textbooks. ;)
p.p.s. Out of curiosity, what have you been working on? ESRI tech is about as anti-startup as one can imagine. It's like using Oracle for your startup's database.