Abstract: Accurate visualizations of complex vascular structures are essential for medical applications, such as diagnosis, therapy planning and medical education. Vascular trees are usually described using centerlines, since they capture both the topology and the geometry of the vasculature in an intuitive manner. State-of-the-art vessel segmentation algorithms deliver vascular outlines as free-form contours along the centerline, since this allows capturing anatomical pathologies. However, existing methods for generating surface representations from centerlines can only cope with circular outlines. We present a novel model-based technique that is capable of generating intersection-free surfaces from centerlines with complex outlines. Vascular segments are described by local signed distance functions and combined using Boolean operations. An octree-based surface generation strategy automatically computes watertight, scale-adaptive meshes with a controllable quality. In contrast to other approaches, our method generates a reliable representation that guarantees to capture all vessels regardless of their size.