We present a pipeline to generate high quality quad dominant meshes for vascular structures from a given volumetric image. As common for medical image segmentation we use a Level Set approach to separate the region of interest from the background. However in contrast to the standard method we control the topology of the deformable object – defined by the Level Set function – which allows us to extract a proper skeleton which represents the global topological information of the vascular structure. Instead of solving a complex global optimization problem to compute a quad mesh, we divide the problem and partition the complex model into junction and tube elements, employing the skeleton of the vascular structure. After computing quad meshes for the junctions using the Mixed Integer Quadrangulation approach, we re-mesh the tubes using an algorithm inspired by the well known Bresenham Algorithm for drawing lines which distributes irregular elements equally over the entire tube element.