I keep trying to explain to people that you keep subtracting something from itself as it goes along, and you get the difference table. Then if you add the differences back together, you get what you started with, except no starting position, which is the confounding fact. XD Poor mans calculus, useful when you have tabulated data but no equation - so its actually sometimes the only way to do it, even though its much easier to do than doing maths normally. youd almost call it completely childish. But noone understands out of my two partners here at my house, they just think im telling them lies, and going crazy, which is what happens when you talk to people that dont understand you, happens in every way every place, every time of your life. And I do it to other people too. Just doing calculus like a bum, gets you really far! Learning about functions! input and output, add and subtract, relative and absolute. Without doing a shred of true integration, derivation or algebra or factorization, just think about the simplicity of it, is a very useful thing, without reading a single maths book to the end or understanding a single professor there is!
Tabulating normal maps from the height map is cool. that is deriving. (subtract) And a normal map is the same thing as an emboss. making height maps from normal maps, is integration. (add) but like i said its imperfect because you lose information from just have the relative differences. But of course, the uses are endless, to the silly technique. as long as you can come up with it.
In this day and age of computers, redundant yes, useless no. Enormous amounts of money and effort were once put into using the difference methods to calculate mathematical tables. Before computers it was generally the only feasible method of table construction. HMSO (Her Majesty's Stationery Office) used to publish a manual of these techniques called "Interpolation and Allied Tables."
There is a perfectly good and practical example called "delta modulation" for transmitting audio signals in a digital channel. Instead of transmitting 16-bit data you can transmit 4-bit differences or even 1-bit differences. At the receiving end you simply integrate (i.e. sum) to recover the audio signal. The lack of a starting point or absolute value does not affect the quality or intelligibility of the audio signal, same as when passing the signal through a high pass filter, which is equivalent to differentiation. In other words, a low pass filter is integration, a high pass filter is differentiation.
I mean doing 'calculus' with data with an unknown equation, which is pretty much all the time with practical sensors. If you developed an equation, then you can go get the exact equation for the integration, I mean when you dont have it, the maths is simplified to + (adding up differences) and -. (getting the difference.) and you work tabulated. Thanks Mr chips for the support.