Question about curvature and Binary Trees

Hello, I was wondering if it were possible to add curvature to some existing code of mine. What I have is a system of binary trees that I grow through algorithmic means.

What I do at the moment is grow new points off existing points, and store the connections in the binary tree via points and lines (which are rigid). What I would like to do, since curved connections is more relevant to my research and more relevant to what I'm actually modelling, is try to modify what I have somewhat to graph (nor produce via my algorithm) curved geometry.

I have read a bit about bezier curves, located here: http://www.mathworks.com/matlabcentral/fileexchange/32817-bezier-curve, and something like this looks very alike to what I want to do. The problem with my binary trees is I can make a curved geometry for one path of the tree (start point to end point, with all intermittent points), but each curve produced for the one inlet and many outlets would be different, which would break my binary tree.

Does anyone have advice on how to do this? I can produce some pictures of some of my end products. Here is the link:

http://imgur.com/vayiSLp,zy8qafl#0