Endovascular interventions can benefit from interactive simulation in their training phase but also during pre-operative and intra-operative phases if simulation scenarios are based on patient data. A key feature in this context is the ability to extract, from patient images, models of blood vessels that impede neither the realism nor the performance of simulation. This paper addresses both the segmentation and reconstruction of the vasculature from 3D Rotational Angiography data, and adapted to simulation: An original tracking algorithm is proposed to segment the vessel tree while filtering points extracted at the vessel surface in the vicinity of each point on the centerline; then an automatic procedure is described to reconstruct each local unstructured point set as a skeleton-based implicit surface (blobby model). The output of successively applying both algorithms is a new model of vasculature as a tree of local implicit models. The segmentation algorithm is compared with Multiple Hypothesis Testing (MHT) algorithm (Friman et al, 2010) on patient data, showing its greater ability to track blood vessels. The reconstruction algorithm is evaluated on both synthetic and patient data and demonstrates its ability to fit points with a subvoxel precision. Various tests are also reported where our model is used to simulate catheter navigation in interventional neuroradiology. An excellent realism, and much lower computational costs are reported when compared to triangular mesh surface models.