Curve with fixed length adjustable from being a straight line to a circle

Hi all,

since my last thread obviously contained too many issues at the same time, i will try and phrase a rather simple question that i am starting to despair of:

I need a curve with a fixed length to be adjustable from being straight (line from point to point) to becoming circle (alternatively a segment of a circle).

the problem with my definition is that the line can never become completely straight..

thanks for your help!!