Math formula which are more than useful

There are a few formula which can be quite useful and this in many different usage, from a brush shape to a "gain" function.

Let's start with something called "Sigmoid". It's a "S" shape like function which has the advantage to flat in / out. The formula for it is 1/(1+POWER(EXP(1),-X)) and look likes:



The next one which I use pretty often too is a "Gaussian" curve which can also be called "bell" curve. The formula for it is 1/EXP(X*X)



You have of course the well known one like X*X

X*X*X


SIN(X)


SQRT(ABS(X))


You may wonder when I use formulas like that, well, for example to reproduce movements, to make a movement more life like or to create more interesting transitions. For a programmer not knowing even a bit of math is simply not acceptable as at a some point he/she will need it.