# Simple Partial Derivative?

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Genesiiis    122
Hi guys, I've been wanting to read through GPU gems for ages and finely have some time to do so. I was reading through chapter 1 of the first GPU gems online HERE. Now a little way down it gets on to discussing the normal to the wave surface, and defines two functions W(x,y,t) and H(x,y,t) (can find them as "Equation 1" and "Equation 2") where W is the hight of a wave given a point (x,y) across a plane at time t, and H is merely a sum of multiple W functions, should you want to make it that bit more wavy ;D. Now about a quarter of the way down, (find:"Equation 7") we find the partial derivative of H with respect to x, which basically is the PD of W wrt x. So a simplified form of W could take: So the PD of W should be: Now perhaps that is the same as what is written in GPU gems but they write the coefficient of the PD of W is: Now I couldn't understand this, is this representing the dot product of the vector D with the x component of the point? that doesn't make sense as they are of two different dimensions. Or looking at the equation for W the "dot" is vertically central which I feel is the normal practice for a dot product, and with the PD the coefficients dot is aligned to the bottom. Does that in fact mean that the coefficient is actually meaning the x component of the vector D (I have written is D_x), using some dot style class variable access! I think what makes it more iffy to understand is the use of the subscript 'i' in most of the equations in GPU gems, to signify the use a many different constant scalars and vectors summed to give more realistic effects. Perhaps someone could shed some light on that for me, it would be really appreciated, thanks a lot guys :D

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apatriarca    2365
The notation in that article is really confusing. I think it's just a way to represent the first component of the vector D.

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Genesiiis    122
Hey apatriarca :D, thanks so much for the reply, just as I suspected. Yeh I know exactly what you mean, a lot of the notation just seems rather non-standard or non-intuitive.

Oh well I just have to do the working to figure out what the author of any confusing articles mean, which in truth ill probably find quite fund ;D.

Thanks a lot apatriarca really appreciated :D