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I'm reading an article on how I can implement collision detection in my games.

It's a really good article. However, some of the maths is confusing me:

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What do the dots after N mean? I've seen posts on this site that say that it is a multiply function, however that would make no sense because he uses a star for multiplication as well. Some other posts say that it is like a cast (), however considering it is already in a cast, then I'd be really confused as to what is the case.

Also, what do the arrows mean? Some articles have said that it means "If and only if" - Does that mean that it only does the calculation on the second line if the one on the first line is true?

user2722083
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  • It is probably hard to do collision detection if you don't know any vector algebra. – GEdgar Feb 12 '15 at 13:06
  • @GEdgar Then i'll learn. And I just now learned one more thing by asking this question. I know that it'll be hard, but as a game programmer, I need to understand all this stuff. And unfortunately high school doesn't cover it. – user2722083 Feb 12 '15 at 13:13

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They are using the dot to denote the dot product of vectors. The $\implies$ means that the formula at the head of the arrow is a consequence of the formula at the tail. It is read as "implies".

Example

$$x+1=2\implies x=1$$

reads as "$x=1$ is a consequence of $x+1=2$". By that we mean (whether true or not) that in any universe, no matter what $x,+,=,1,2$ mean, as long as they satisfy the usual properties we assume them to have, then if $x+1=2$ occurs then necessarily $x=1$ occurs.

Tom
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    Good answer. Perhaps worth adding: the "if and only if" arrow would be $\iff$ – quid Feb 12 '15 at 12:17
  • Thank you. Could you please explain exactly what do you mean by "Consequence of the formula"? – user2722083 Feb 12 '15 at 12:17
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    @user2722083 It means that current expression follows from previous one, or (the same): "if previous is true then current is true as well (visa versa is not correct in general case)", or you just may read this arrow as "hence". – Andrei Rykhalski Feb 12 '15 at 12:30