Hi everybody,

I'm looking for a particular parametrical curve who could fit the following
scheme: Imagine a unity square defined by the two following points
(0,0)-(1,1). For a given value of the parameter (let's say zero), the curve
would be the diagonal of the square. When the parameter would augment, it
would slowly distord in order to map the upper half border of the square [
i.e. defined by (0,0)-(0,1)-(1,1) ]. Ideally, when the parameter is
inifinite, the curve would exactly map this contour.

Does such a curve exist ? I'm pretty sure it does but I don't know where I
should look for this information.

Many thanks for any hints,

Marc.