The standard affect region function, based on a distance and the three affect region parameters (same as the editable mesh). This function is a cubic curve which returns 1 at distance 0, 0 if distance is greater than falloff, and other values for distance between 0 and falloff.
This is the function used inside the Affect_Region modifier. For the different editables, one of the data channels is the selection weight. If you wanted to, you could use this function to calculate the vertex selection weights on you own.
Affect_Region : Modifier