Huh. I thought it was obvious: e.g., the top-left corner of the screen is (0, 0), the bottom-right corner is (640, 480), and pixels are 1x1 — we take the coordinate of their top-left corner to be their coordinate, so the top-left pixel has coordinates (0, 0), and the bottom-right one has (639, 479), and obviously the coordinates of their centres are (0.5, 0.5) and (639.5, 479.5).

But apparently some people treated pixels as geometrical points without size?

It's normal in signal processing to treat samples (whether audio or image) as points. A lot of things stop making sense if you replace them with line segments and rectangles.

I prefer 9. It makes no less sense than 1, but it is conveniently much closer to the + and - keys.

My 0 key is twice as big as the rest of the digits.

Why compromise? Just have a helpful variable like Perl's $[ to set the first element index.

Which is rounded down to 0 or up to 1 at random.