Rendering large numbers of dense line bundles in three dimensions is a common need for many visualization techniques, including streamlines and fiber tractography. Unfortunately, depiction of spatial relations inside these line bundles is often difficult but critical for understanding the represented structures. Many approaches evolved for solving this problem by providing special illumination models or tube-like renderings. Although these methods improve spatial perception of individual lines or related sets of lines, they do not solve the problem for complex spatial relations between dense bundles of lines. In this paper, we present a novel approach that improves spatial and structural perception of line renderings by providing a novel ambient occlusion approach suited for line rendering in real time.