Visualizing directed edges without crossing

Question

I am given a directed graph with set of nodes with fixed positions (Map of cities) and want to add connections to them, so that I have as few crossings as possible. For simplicity, let's consider only one source (compare to the attached image). For an undirected graph, straight lines would work perfectly fine. Now, for the directed version, I tried using quadratic bezier curves with a control point at x_1, y_2, which eliminates a lot, but not all crossings. I feel like there must be a general formula for a curve that can be applied without crossings, right?

Example for current approach

Answer 1

Alright, extending my research I found a paper offering a solution that may work for me using circle arcs based on the circle packing theorem instead of bezier curves. (Article, Circle Packing algorithm)