I have a number of data sets that I have made non-dimensional across both the x and y axis, such that they range from 0 to 1.

I want to fit curves to each data set that are forced to intercept through both (0,0) and (1,1) so I can scale these fitted curves at a later data.

Fitting y=x^a does this, however, any other type of curve (sigmoid etc.) isn't always forced to do this... So I am wondering if there is a special case of (any) function or a program/spreadsheet/script/etc that will make a given curve pass through these points (0,0 and 1,1) without the use of piece wise functions...

any thoughts or advice?