maybe you'll get more helpful replies if you'll ask questions in one thread?

as about
[B(u) - A(u)] . [B(u) - A(u)]
,
in math, [] is usually the same as ()
. mean dot product. That is, [B(u) - A(u)] . [B(u) - A(u)] = (B(u) - A(u)) . (B(u) - A(u))= {B(u) - A(u)} . {B(u) - A(u)} = squared length of [B(u) - A(u)] = |B(u)-A(u)|2 and so-on. It is squared distance between circles.

line overhead: in this case it is sign of that writer tries to make his text be less readable. I guess, he mean (A-B).(A-B)

The line overhead may well be to indicate a complex conjugate - though that is just the first thing off the top of my head, there may be dozens more. Perhaps a little of the context might help find the meaning intended by the notation?

If you're in the logic world, the overscore is a logical inversion (not), which makes your second expression (in C):

!(A && B) || !(A && B)

Where two variable beside eachother is an AND, and the '.' is an OR.

Since A and B are the centres of circles, it's pretty likely that AB with a bar on top indicates the vector from A to B. If you're picky (and mathemathicians tend to be) a vector and a point is not the same thing so you indicate that you're talking about a vector by putting a bar on top of the symbol. OA with a bar on top would be the vector from the origin to A and what you normally mean when you say the "vector" A when it is in fact a point.

Sometimes bold face is used instead of the overbar which is far more readable IMO. I often use a bar on top of a variable to indicate it's a vector if I'm writing by hand on paper or a blackboard or something, but never in printed text.

Oh and I saw Dmytry made a small typo, AB with bar is (B-A) not the other way around. Just so you don't get confused. Although it doesn't matter in this case, but anyway...

Quote:Original post by GameCat
Since A and B are the centres of circles, it's pretty likely that AB with a bar on top indicates the vector from A to B. If you're picky (and mathemathicians tend to be) a vector and a point is not the same thing so you indicate that you're talking about a vector by putting a bar on top of the symbol. OA with a bar on top would be the vector from the origin to A and what you normally mean when you say the "vector" A when it is in fact a point.

Sometimes bold face is used instead of the overbar which is far more readable IMO. I often use a bar on top of a variable to indicate it's a vector if I'm writing by hand on paper or a blackboard or something, but never in printed text.

Oh and I saw Dmytry made a small typo, AB with bar is (B-A) not the other way around. Just so you don't get confused. Although it doesn't matter in this case, but anyway...

Yes, thanks for correction, probably it's meant to mean that.

But still, i think such notation is kind of mathy-looking jargon, kinda mix of geometry notation and algebraic notation. If A and B is points or vectors, (B-A) is obviously vector, and 1.) no bar over it needed , 2.) it is clear what direction vector does have. I think it is bad sign that new notations is "invented" for places where it is not needed. I really don't like papers that are very simple but are presented as something lot more complex. Unfortunately, many game math papers either don't explain things, or is like that.

Also, IIRC bar is drawn over points and vectors, but not drawn over scalars(aka "just numbers").
IIRC,
_
A
is valid notation even if A is point...

Well, I've never seen the overbar used to indicate a point, but I'm sure there are people that just use it to indicate vectors and don't differentiate between vectors and points! ;)

Anyway, I think the notation orginally was a small arrow on top of the variable (pointing right) which is slightly more intuitive, but then it morphed into a bar for typographical reasons. You can get the arrow in LaTex for example.

I agree that it's really annoying when notation isn't explained, it's just the writer being lazy. It's especially common if you're studying some standard formula from a field you're not familliar with and some of the variables have a certain meaning by convention in that field, so they're not commented on at all! Like s being travelled distance in the scattering medium in many scattering formulations for example. It's ok just using theta and phi for spherical coordinates, or x, y and z for cartesian ones, but anything beyond that really requires explanation.