Is there an oriented clustering algorithm?

Question

I'm looking for a clustering algorithm that will make cluster depending on a orientation. The DBSCAN algorithm cluster points based on a constant radius :

https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/DBSCAN-Illustration.svg/800px-DBSCAN-Illustration.svg.png

Is there a implementation of DBSCAN that is based on "ellipse instead of circle" ?

EDIT: MY SOLUTION

Ok so my solution was to work on my data set. I had a set of 2D points and I wanted to favor the definition of clusters depending of a given orientation.

My solution was to center my set of point on the origin of the coordinate system, rotate them by the orientation you want and apply this vector field on the set of point : X(x, y) = (x-x*a, y) , where a is the factor that determine if the orientation should matter a lot or not (a ∈ [0, 1]) .

Then apply the DBSCAN of this modified dataset.

I hope I was clear enough, don't hesitate to ask me if it's not the case.