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Spa8nky

What is the meaning of the following math symbol?

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Hi folks, I have been reading through graphics programming gems 2 which I borrowed from the library and have been working on the "Apply Decals to Arbitary Surfaces" gem. The problem I am facing is that I don't understand the meaning of the ' (N'R) symbol in Equation 4.8.3. Can anyone help? Also, what book would be recommended to help decipher mathematical symbols; a kind of symbol dictionary if you will? [Edited by - Spa8nky on September 10, 2009 9:39:01 AM]

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You mean Eq. 4.8.3 here?

In English,

Dot product of the vector N with the vector R
--------------------------------------------- - epsilon
Norm of vector R
----------------------------------------------------------
1 - epsilon

where "epsilon" is a small number.

Notice what happens when epsilon is zero. Then you just have,

dot(N, R/||R||)

which means, "the component of N in the direction of R." You can think of this formula as being,

f("the component of N in the direction of R")

where


1 e
f(x) = ----- x - ------
1 - e 1 - e


is just the linear function such that

f(e) = 0
f(1) = 1

where now I'm using 'e' instead of 'epsilon.'

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Aha its a dot product not a '.....some idiot has drawn on the book.

I'm going to get a copy from Amazon then, seems like the sensible thing to do.

Also, a hard back book of math symbols would be pretty sweet!

Thanks for your help.



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Quote:
a kind of symbol dictionary..

It appears you just stumbled across a bad markup.

However, if you happen across a CRC Handbook (Chemical Rubber Company) in a bookstall or yardsale, it's worth a dollar or two and has lots of handy symbols and formulae.

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Quote:
Original post by Spa8nky
Aha its a dot product not a '.....some idiot has drawn on the book.

Wow. That is the awesomest idea ever. I'm going to go check out Numerical Recipes from the library and change stuff.

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Quote:
Original post by Spa8nky
Aha its a dot product not a '.....some idiot has drawn on the book.


Statisticians have historically used ' (prime) to denote the transpose. If N and R are column vectors, then NT is a row vector and the dot product of N and R can be written as NTR. A statistician might instead use the prime notation and write N'R.


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Awesome nugget of knowledge there, thanks :) It would explain why someone hs scrawled that symbol over the dot symbol then!

Still, deciphering this mathematics is hard enough at the best of times without other people making life harder by writing over the equations with their own interpretations :(

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