In the different context of modern Japanese rules and if final-position, intersection, black-string, white-string, alive, dead, etc. are already defined, eye point can be defined as follows:
"In the final-position, a black-eye-string is an intersection that is empty and, recursively, any adjacent intersection that is empty or occupied by a stone of a dead white-string.
In the final-position, a white-eye-string is an intersection that is empty and, recursively, any adjacent intersection that is empty or occupied by a stone of a dead black-string.
In the final-position, an intersection of a black-eye-string is a black-eye-point if the black-eye-string is adjacent and only adjacent to intersections with stones of alive black-strings.
In the final-position, an intersection of a white-eye-string is a white-eye-point if the white-eye-string is adjacent and only adjacent to intersections with stones of alive white-strings.
An eye-point is either a black-eye-point or a white-eye-point."
-- RobertJasiek 2003-11-03.
The following treats eye point in its first meaning.
Bill: Well, maybe that's my problem. I don't know what you are talking about, or why it is important.
Richard Hunter: I'll second that. I don't understand what this page is trying to say. I would recommend beginners to ignore it.
Bildstein: By "creates or destroyes an eye", do you mean "creates an eye if played by Black to use your examples, but destroys the eye if played by White", or do you mean that it can be an eye point by having only one of these conditions? I can't understand how your fourth example is not an eye point, although I understand that it enlarges Black's eye space. Also, why is a in your last example not an eye point. It seems to comply with your definition.
Do eye points have something to do with vital points? I guess the vital point in the middle of an unsettled three would be an eye point, by your definition.
Soulpanda?: I think the last example is not an eye point because it connects the stones together into a string and this talks about stones aready part of a unit and not creating a unit. And the fourth example isn't one because an eye point is a single point eye. So we could say that a point played on a unit of stones that creates (or destroys I guess) a single point eye is an eye point.
See also the Eyes Collection.