We present a method for visualizing vasculature based on clinical computed tomography or magnetic resonance data. The vessel skeleton as well as the diameter information per voxel serve as input. Our method adheres to these data, while producing smooth transitions at branchings and closed, rounded ends by means of convolution surfaces. We examine the filter design with respect to irritating bulges, unwanted blending and the correct visualization of the vessel diameter. The method has been applied to a large variety of anatomic trees. We discuss the validation of the method by means of a comparison to other visualization methods. Surface distance measures are carried out to perform a quantitative validation. Furthermore, we present the evaluation of the method which has been accomplished on the basis of a survey by 11 radiologists and surgeons.