Script for curve inside a polygon?

 From:  Frenchy Pilou (PILOU)
4888.1 
For example here I can draw the internal curve tangent to the middles of the red plolygon by some conic curves

Does it possible to make a script for the entiere polygon?
With conic?
With another curves ? (nurbs :)


Rho is 0.65
This will valuable for any point on the yellow curve between 2 following segments inside any polygon!
Magic's geometry ;)