Tor Lillqvist: A two-dimensional interval over integers

Guess what this means:

A two-dimensional interval over integers

This is most easily depicted as a set of integers, bounded by a lower and an upper value - but excluding the upper value. All inbetween values are included in the set. (see also http://en.wikipedia.org/wiki/Interval_%28mathematics%29)

Hmm, two-dimensional, but bounded by a lower and an upper value? And the Wikipedia article it refers to says that

 In mathematics, a (real) interval is a set of real numbers

while the above talks about integers. But oh well.

Got it yet? There's more:

The set is half-open, i.e. the lower bound is included, the upper bound not (if you're used to the notation - we're talking about [a,b) here, compared to closed [a,b] or fully open intervals (a,b)).

This again sounds a bit one-dimensional, but let's put that down as a case of copy/paste joy, and let's assume that the reader is able to extrapolate into two dimensions.

Does it sound familiar yet? Oh well, finally it says:

Alternatively, consider this a rectangle, where the rightmost pixel column and the bottommost pixel row are excluded

Oh. Sure, the concept of "rectangle" is so unfamiliar to programmers that it isn't worth mentioning except after some impressive-sounding mathematics jargon (that perhaps is not really useful in the case of finite, integer, ranges, but I digress). And yeah, let's mention pixels, too, all of a sudden. Of course, giving what apparently tries to be a strict mathematical definition, no need to mention whether the pixels here are centered on integer coordinates, or bounded by them. But I guess it's the former, as otherwise it would make little sense, or would it?

And what is right here, and especially, what is bottom? In mathematics, the y axis usually is depicted as pointing upwards, isn't it?

To make it even more fun, the data structure that this documents contains neither "range" or "rectangle" in its name, but "box"...