

Jun 27, 2012, 09:48 PM  

Quote:
FYI, I was looking for the simplest function that would look like the generic graphs we've all seen showing what "expo" does. Keeping in mind that this might be implemented on lowpowered hardware and math functions would likely have to be implemented from scratch, I decided to simplify exponential functions to only the lowest order terms, i.e. linear and cubic. As hardware (microcontrollers) continue to get more and more powerful, it is probably now practical to implement more sophisticated functions. In particular, I think the tanh() and sinh() functions are worth investigating. It looks to me as though the sinh function is what we want for "soft around the centre" exponential, and tanh looks like the way to get the opposite behaviour. It would be interesting to represent sinh and tanh as polynomials, keep only the first two or three terms, and see what comes out of that. Quote:
Most likely including the x^5 term in addition to the x and x^3 terms I used would do the trick. As a corollary, I think the reason why all the formulae you looked at agreed with each other is this: all of them are essentially cubic representations (i.e to order x^3) of exponential functions with the same boundary conditions. Flieslikeabeagle 

Jun 29, 2012, 11:11 AM  


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