A 062

All spells origin points are actually at grid intersections. A character casting a spell "centered on you" can pick any of the grid intersections their character touches, and this relative centering of the spell continues. For example, if they are Medium size and pick the "northeast" one of their 4 grid intersections, the spell continues to be centered on their "northeast" corner as they move. A Large creature (10'x10') would have 9 grid intersections to pick among.

Any area spell affects all the creatures in all squares it covers unless there's a specific exception. (See page 307 of Dungeon Master's Guide for the grid squares covered by various area effects of different sizes.) Antimagic Field does not list such an exception, so it affects the portion of the spellcaster within its 10 grid squares. For a Medium spellcaster that would prevent them from spellcasting. A Large creature could select a spell center that would cover them completely, or they could instead pick an offset spell center that would allow them to originate magic in the other direction.