Expressive and efficient visualizations of complex vascular structures are essential for medical applications, such as diagnosis and therapy planning. A variety of techniques has been developed which provide smooth high-quality visualizations of vascular structures based on rather simple model assumptions. For diagnostic applications, these model assumptions and the resulting deviations from the actual vessel surface are not acceptable. We present a model-free approach which employs the binary result of a prior vessel segmentation as input. Instead of directly converting the segmentation result into a surface, we compute a point cloud which is adaptively refined at thin structures, where aliasing effects are particularly obvious and artifacts may occur. The point cloud is transformed into a surface representation by means of MPU Implicits, which provide a smooth piecewise quadratic approximation. Our method has been applied to a variety of datasets including pathologic cases. The gene...