I would like to create my own Chaikin curve without modifier. Like Bezier curves I would like to have a control structure (mesh1) and my subdivided mesh (mesh 2). The mesh 2 must control the mesh 1. The mesh one must not be changed in edit mode.
I'm stuck on this problem for a while and I have not found anything in the docs related to it.

Do you have an idea to solve my problem? (structures, methods, sources codes NURBS / Bezier ...)

Thanks.