3D Lines are a widespread rendering primitive for the visualization of data from research fields like fluid dynamics or fiber tractography. Global illumination effects and transparent rendering improve the perception of three-dimensional features and decrease occlusion within the data set, thus enabling better understanding of complex line data. We present an efficient approach for high quality GPU-based rendering of line data with ambient occlusion and transparency effects. Our approach builds on GPU-based raycasting of rounded cones, which are geometric primitives similar to truncated cones, but with spherical endcaps. Object space ambient occlusion is provided by an efficient voxel cone tracing approach. Our core contribution is a new fragment visibility sorting strategy that allows for interactive visualization of line data sets with millions of line segments. We improve performance further by exploiting hierarchical opacity maps.