I must prefix this by saying I am not entirely sure whether Mathematics is the best place for this, but as I am curious about the mathematical process behind this, I chose to post this here.
In waveshaping, a transfer function is applied to an input function. But, in most cases, we do not know the equation for the transfer function if it is one that has been hand drawn in i. e. the graph of the transfer function is drawn into the waveshaper.
Anyway, my question would be: mathematically, how do computers perform processing that necessitates knowledge of the equation of such functions?