2D C. Geometry: Redirecting edges (Linked half-edge list)

Given the case that i have an edge e which intersects with several other edges at the vertex V as shown here:
http://www.praxis-freising.de/eehalfedge.jpg
(everything in 2D)

I want to split and connect this edge e with the vertex V.
Splitting one of the half edges into the two parts e1 and e2 is quite simple.

But one needs to redirect the pointers of the half-edges.
When taking the above posted image as an example, the half-edge e1 must be redirected to the half-edge e3 to preserve the validity of the edge list. How to find this next half-edge?

The only option that came to my mind is calculating and comparing the angles of all the half-edges of the vertex and inserting the half-edge between the neighboring half-edges, but that doesn't really seem like a proper solution for the problem.

Thanks in advanceStart Free Trial