Tips and links about the use of functions in a graphics environment.
Among other things you will find here some useful software ot visualize functions, some explaination about how to control them to get the result you need and many examples very convenient in production.
 
 

(article still in development)

Useful software

 

Math

Function examples

 

Useful linear map functions

Various kinds of periodic functions

Various periodic functions

cf https://en.wikipedia.org/wiki/Square_wave

 

Periodic oscillatory motion:


y = scaleY * periodFunc( scaleX * x + offsetX ) + offsetY


With:

periodFunc:  periodic function        eg: sin, cos
offsetX:       horizontal offset of the curve
offsetY:       vertical offset of the curve
scaleX:        period length             The higher the period is, the slower the oscillatory motion will be.
scaleY:        amplitude

       

Several ways to transform X to a periodic signal


- Use an oscillatory function such as sine or cosine
- Use a modulo

               

Bell function (or Gaussian function)

https://en.wikipedia.org/wiki/Gaussian_function

Eg: e^(-x^2)

 

y = scaleY * e^(-x^2 / bellWidth)


If another integer pair value than 2 is used for -x^2 the bell will get a flatten top.