The ddx and ddy functions return the partial derivatives of a given value with respect to screen coordinates.
In other words: the slope of the function described by the value. Or in other words again: the rate at which a given value changes across the screen.
For example ddx( position ) will tell you how much the surface slopes either left or right. So normalize( cross( ddx(position), ddy(position) ) ) returns a normal to the surface.
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